Primary 5 Mathematics Ace The Exams with My 24/7 Personal Tutor Detailed Explanation of ALL Questions by Tutor in Virtual Classroom Consulting Editor: Dr Zhang Yong
Primary 5 Mathematics
Ace The Exams with My 24/7 Personal Tutor
Detailed Explanation of ALL Questions
by Tutor in Virtual Classroom
Consulting Editor: Dr Zhang Yong
ii
© Outreach Edusys Pte Ltd ALL RIGHTS RESERVED. No part of this book and the accompanying CDROM may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, CD duplication, replication, or by any information storage and retrieval system, without permission in writing from the Publisher. First Published 2010 ISBN: 978-981-4275-16-3 Published by: Outreach Edusys Pte Ltd (CRN: 200006571H) Distributed by: Outreach System Pte Ltd 20 Shaw Road, #07-03 Singapore 367956 Tel: +65 91162024 Fax: +65 35107345 Email: [email protected] Website: http://www.orlesson.org Please check URL regularly for new releases and promotions. Sample chapter and lesson for each title can be downloaded from above URL. Purchase online or call/SMS 9116-2024 today. FREE home delivery (one location within Singapore) for purchases above S$60/=.
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Preface
This book is written to assist pupils in preparing for the Primary 5 Math examinations. There are a total of 10 specially crafted examination style papers. The main features of the papers are as follows.
1. Questions are modeled after examination papers set by top well known Singapore schools.
2. Questions are crafted to highlight common misconceptions in each of
the topics. This book comes with a multimedia CDROM. The CDROM contains detailed explanation of each question in each paper by our teacher. These lessons ensure pupils understand the methods behind solving each question. Outreach Book Alive series brings the “tuition teacher” to you at zero cost. You may also want to try our online programme. These are interactive “diagnostic” modules consisting of multiple choice questions. The incorrect options to each question are carefully crafted using specific mis-conception in learners. If your child submit a wrong answer, our system will dynamically diagnose your child’s problem and bring him/her an explanation on why he/she is wrong, and what is the correct way to the solutions of such questions. Visit http://www.orlesson.org today.
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Contents Semestral Assessment 1 Mock Paper 1 Paper 1
Paper 2 1 8
Semestral Assessment 1 Mock Paper 2 Paper 1 Paper 2
15 23
Semestral Assessment 1 Mock Paper 3 Paper 1 Paper 2
30 38
Semestral Assessment 1 Mock Paper 4 Paper 1 Paper 2
45 53
Semestral Assessment 1 Mock Paper 5 Paper 1 Paper 2
60 67
Semestral Assessment 2 Mock Paper 1 Paper 1 Paper 2
74 80
Semestral Assessment 2 Mock Paper 2 Paper 1 Paper 2
88 94
Semestral Assessment 2 Mock Paper 3 Paper 1 Paper 2
101 108
Semestral Assessment 2 Mock Paper 4 Paper 1 Paper 2
115 122
Semestral Assessment 2 Mock Paper 5
Paper 1 Paper 2
129 137
Suggested Answers 144 Free Past Year School Exam Papers (from 2004 onwards) for download and print. Visit http://www.orlesson.org for links and download instructions. Subscribe to Outreach Lesson Online Access for hundreds of hours of lessons, and thousands of questions. Less than 70 cents a days for unlimited access to ALL subjects. For details, visit http://www.orlesson.org.
1
Semestral Assessment 1: Mock Paper 1 Paper 1 (Duration: 50 mins)
Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided.
1. Fill in the blank with an appropriate number that matches the pattern ______, 900 000, 800 000, 700 000
(1) 10 000 (2) 100 000 (3) 1 000 000 (4) 10 000 000 ( )
2. How many quarters are there in 321 ?
(1) 3 (2) 5 (3) 10 (4) 14 ( )3. In order to have
53 of the set below shaded, how many more squares must be
shaded?
(1) 9 (2) 8 (3) 7 (4) 6 ( ) 4. Find the value of 24 + 48 ÷6 – 6 (1) 6 (2) 22 (3) 26 (4) 36 ( ) 5. What is the correct numeral for the following statement?
Six hundred and six thousand, six hundred and sixty six
(1) 606 606 (2) 606 666 (3) 666 606 (4) 660 660 ( )
2
6. How many lines of symmetry are there in this letter?
I (1) 4 (2) 3 (3) 2 (4) 1 ( ) 7. If the product of 124 and 19 is calculated and rounded off to the nearest hundred,
what will be the final value? (1) 2000 (2) 2300 (3) 2400 (4) 2360 ( ) 8. A car can travel 9 230m with 1l of fuel. 300l of fuel was consumed in a month. How
many kilometers did the car travel in that month? (1) 2 769 (2) 27 690 (3) 276 900 (4) 2 769 000 ( ) 9. Mary’s weight is 27kg. She is 3
5as heavy as David. How much does David weigh?
(1) 15 kg (2) 45 kg (3) 54 kg (4) 84 kg ( ) 10. Two numbers have a difference of 72 and a sum of 166. Find the bigger number. (1) 138 (2) 119 (3) 94 (4) 49 ( ) 11. Sarimah bought 13
2kg of flour. She then used 51
8kg to bake cakes. After that, her
mother gave her another 114
kg of flour. How much flour did she have eventually?
(1) 738
kg (2) 138
kg
(3) 124
kg (4) 718
kg ( )
12. Caroline has 6 times as many stickers as Denise, but only half as many as Rachel
has. If Denise has 154 stickers less than Rachel, how many stickers does Caroline have?
(1) 14 (2) 77 (3) 84 (4) 160 ( )
3
13. Examine the pattern below carefully. How many sticks are there in the 18th pattern?
(1) 37 (2) 47 (3) 57 (4) 67 ( ) 14. Find the smallest value among the following expressions
(1) 0.80 (2) 1720
(3) 34
(4) 0.69
( ) 15. In the figure below, ∠ AOB = 93o. What is ∠BOC? Note that AOC is a straight line
and the figure is not to scale.
(1) 3o (2) 87o
(3) 90o (4) 273o
( ) Questions 16 to 25 carry 1mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 16. Write 9 080 011 in words.
17. Arrange these numbers in descending order. 8 883 008, 880 300, 8 880 003, 88 380
Ans: __________, __________, __________, __________
93oA
O
B
C
Pattern 1 Pattern 2 Pattern 3 Pattern 4 Pattern 18
?
4
18. What is the correct value of A?
Ans: _____________________ 19. Find the total of the first 6 multiples of 7
Ans: _____________________ 20. Express
949 as a mixed number
Ans: _____________________ 21. Calculate
95 x108
Ans: _____________________
7 503 906
7 000 000
A
3 906
3 000
900
6
5
22. Calculate 352 +2
21 and simplify your answer.
Ans: _____________________23. What is the proportion of the shaded area compared to the whole square? Write the
answer in fraction.
Ans: _____________________24. Find the largest possible odd number between 5 000 000 and 6 000 000 using all the
digits given.
9 0 1 7 2 6 5
Ans: _____________________25. Write the following statement as a numeral
Three million one hundred and forty-seven thousand six hundred and eighty-two
Ans: _____________________
6
Questions 26 to 30 carry 2 marks each. Show your working clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 26.
Mr. Ben chose a sofa set that cost $5 250. He paid the exact amount in 90 pieces of $100 and $50 notes. How many $50 notes did the cashier receive from Mr. Ben?
Ans: _____________________ 27. 10 tables and 20 chairs cost $650.
20 tables and 10 chairs cost $850. What is the cost of one table and one chair?
Ans: _____________________ 28. Mr. Tan, a worker, had 850 long nails, 620 short nails and 930 medium nails in a
container. He gave 41 of these nails to his colleague and used
121 of these nails to
make tables. How many nails did he have left?
Ans: _____________________
7
29. An oil producer is filling two empty barrels with oil. The first barrel fills at a rate of 90l per minute. After 1 minute, he starts filling the second barrel at a rate of 105l per minute. How many minutes will it take for the second barrel to contain the same amount of oil as the first barrel?
Ans: _____________________30. Mary and John were given the same amount of money by their mother. After
spending some of their money, Mary only has one-seventh as much money as John had. If John spent $1 572 and Mary spent $2 892, how much did each of them have at first?
Ans: _____________________
8
Semestral Assessment 1: Mock Paper 1 Paper 2 (Duration: 1 hr 40 mins)
Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. In a donation drive, team A and team B collected a total of $12 795. Team C and
team D collected a total of $17 245. Team A and team C collected the same amount of money. Team D collected 6 times as much money as team B. How much money did team D collect?
Ans: _____________________ 2. A shop is selling gloves for Christmas.
83 of the pairs are red,
41 of the pairs are
white and the remaining 114 pairs are dark blue. How many pairs of gloves does the shop have in total?
Ans: _____________________ 3. 1 kg of pork cost $2 more than 1 kg of chicken. 1 kg of beef cost $3 more than 1kg
of pork. Aunt Linda spent a sum of $99.60 on 6 kg of each type of meat. How much did she spend on the chicken and the beef?
Ans: _____________________
9
4. Cheese cakes are sold at $6.90 for 3. Curry puffs are sold at $5.20 for 4. (a) If Timmy could only spend $25 on each type of food, how many more curry puffs than cheese cakes could he buy? (b) Bobby paid $129.60 for an equal number of cheese cakes and curry puffs. How many cheese cakes and curry puffs did he buy altogether?
Ans: _____________________5. Peter wants to send a parcel to his friend in Indonesia. At the post office, he finds the
following table which shows the postage rates:
Mass not over Postage
First 30g $1.00
Next 50g $1.70
Per additional step of 25g $0.35 How much does Peter have to pay if his parcel weighs 197g?
Ans: _____________________
10
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. Given that AB is a line of symmetry in the figure below. Shade the squares to
complete the symmetric figure
Ans: _____________________[4] 7. The average number of Peter’s stickers and Jordan’s stickers is 924. Peter has 232
more stickers than Jordan. Albert has 172 stickers more than Peter. What fraction of Albert’s stickers are Jordan’s stickers? Write your answer in its simplest form
Ans: _____________________[4]
11
8. Three years from now Dan’s father’s age will be thrice Dan’s age. How old is Dan’s father now if he was 34 years old when Dan was born?
Ans: _____________________[4]9. The houses along a road are numbered from 1 to 150. The house number signs are
made of steel digits. How many digits are needed altogether to number the entire road?
Ans: _____________________[4]10. Find the perimeter of the figure below.
Ans: _____________________[4]
5 cm
8 cm
13 cm
36 cm
9 cm
7 cm
4 cm
A B
5 cm
12
11. A shop sells carpets at $15 per square meter. Uncle Tay wants to buy a carpet for his living room, which is 10m by 7m. How much does he have to pay?
Ans: _____________________[4] 12. When 60 packs of cookies are placed in a box, the total mass is 6 790g. When the
same box contains 25 packs of cookies, the mass is 4 655g. Find the mass of the box in kg.
Ans: _____________________[4] 13. Each tourist has to pay $1 215 for a 5-day tour to Vietnam. If there were 116 tourists
who chose that tour last month, how much did the travel agency receive?
Ans: _____________________[3]
13
14. Create a tessellation in the space provided by drawing 4 more unit shapes.
Ans: _____________________[4]15. Alex, Ben and Carl collected a total of 2 151 stamps. Alex collected 224 stamps
fewer Carl. Ben’s collection was 3 times as many as Carl’s. How many stickers did Carl have?
Ans: _____________________[4]16. How many lines of symmetry are there in the figure below, given that all line
segments are equal
Ans: _____________________[3]
14
17. A water tank 90 cm long, 40 cm wide and 15 cm high needed to be filled by two taps A and B. Tap A, which had a flow rate of 12l per minute, was turned on first. After
211 minutes, tap B, which can flow only
31 as fast as tap A, was turned on and both
tap continued to fill the tank. Since both taps were turned on, how long did it take to fill the tank completely? Express your answer in minutes and seconds.
Ans: _____________________[4] 18. A number of trees were planted around the perimeter of a rectangular parcel of land
that was 49m long and 35m wide. There was a tree in each corner. On each side of the land trees were planted 7m apart. How many trees were there in total?
Ans: _____________________[4]
15
Semestral Assessment 1: Mock Paper 2 Paper 1 (Duration: 50 mins)
Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided. 1. 76 x 50 can also be expressed as (1) 70 x 6 x 5 (2) 7 x 6 x 5 x 10 (3) 76 x 5 x 10 (4) 70 x 6 x 5 x 10 ( ) 2. Calculating 196 x 68 and rounding off to the nearest thousand, the result will be (1) 13 000 (2) 13 300 (3) 13 400 (4) 14 000 ( ) 3. What is the best estimate of 635 ÷ 80? (1) 6.35 (2) 63.5 (3) 8 (4) 7.5 ( ) 4. What is the value of 183 – 24 ÷ 3 x 4 + 12 (1) 139 (2) 163 (3) 224 (4) 712 ( ) 5. What value should be filled in the box to make the expression correct?
6.5 x 6 + x 3 = 78
(1) 13 (2) 14 (3) 39 (4) 41 6. Replace “?” with a correct number that fits the pattern below
0.7, 1.4, 0.8, 1.3, ___?___, 1.2 (1) 0.6 (2) 0.9 (3) 1.7 (4) 2.1 ( )
Marks
16
7. MNPQ is a trapezium. Which of the following shows a parallel pair of lines?
(1) MQ and XY (2) WZ and XY (3) WZ and YT (4) MQ and WZ ( ) 8. Aunt Sophie bought
52 kg of meat. Aunt Irene bought
74 kg of meat more than aunt
Sophie. How many kg of meat did both of them buy?
(1) 358 (2)
3522
(3) 3534 (4)
35131
( ) 9. Find one of the letters below that does not have any line of symmetry
(1) T (2) H
(3) A
(4) Z
( ) 10. Muthu had 25 kg of sugar. He packed them equally into 7 bags. There was 2kg of
sugar left over. How much sugar was there in each bag? (1) 3.28 kg (2) 3.29 kg (3) 3.57 kg (4) 3.58 kg ( )
Y Z
M W T X N
P Q
17
11. The graph below shows the number of customers visiting a shopping centre over a
period of 5 months. How many customers visited the shopping centre from January to March?
0
500
1000
1500
2000
2500
3000
3500
4000
January February March April May
(1) 7 200 (2) 7 300 (3) 7 400 (4) 7 500 ( ) 12. A tank measures 45 cm by 30 cm by 10 cm is filled with 4.5l of water. What fraction
of the tank is not filled?
(1) 31 (2)
32
(3) 139 (4)
134
( ) 13. In 147 683, which digit is in the ten thousands place? (1) 1 (2) 4 (3) 6 (4) 3 ( ) 14. 4 ten thousands + 4 thousands + 4 hundreds + 4 ones =? (1) 40 400 (2) 40 004 (3) 44 404 (4) 44 440 ( )
18
15. Find the correct numeral for the following expression
Three hundred and three thousands, three hundred and three (1) 303 303 (2) 330 330 (3) 330 303 (4) 333 000 Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 16. Given that MN is the line of symmetry of the figure below, shade two more squares
to complete the figure.
17. A child ticket to enter the zoo costs
52 that of an adult ticket. Mrs. Lim and her
daughter paid $49 for their tickets. How much does a child ticket cost?
Ans: _____________________ 18. The price of a car is $180 000 when rounded off to the nearest $1 000. What could
the lowest price of the car be? Provide your answer correct to the nearest dollar.
Ans: _____________________
19
19. Form the biggest even number using all the digits given
3, 6, 9, 5, 1, 2
Ans: _____________________20. Tony spent
41 of his money on a shirt and
53 of the remaining money on a pair of
jeans. What fraction of his money did he spend? (Use the simplest form for your answer).
Ans: _____________________21. At a concert,
51 of the audience were children and the rest were adults. There were
144 more adults than children. How many people were there in the audience?
Ans: _____________________22. What is the area of the triangle below?
Ans: _____________________
20
23. Mrs. Chan gave 97 of a cake to her 3 children to share. Each child had the same
portion. What fraction of the cake did each child get?
Ans: _____________________ 24.
Express the value of 1000
325
108
10014
+++ in decimal form.
Ans: _____________________ 25. Fann has
532 times the number of stamps that Alex has. What is the ratio of the
number of Alex’s stamps to Fann’s stamps?
Ans: _____________________ Questions 26 to 30 carry 2 marks each Show your working clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated. (20 marks) 26.
In the space provided, construct a line PQ that is perpendicular to line MN
M N
21
27. There are 4 teams in the Federation Cup tournament. Every team has to play one match with each of the other teams. How many matches are there in the tournament?
Ans: _____________________28. Selina started doing her homework at 7:45 PM. It took her 3
125 hours to complete all
the homework. At what time did she finish the task?
Ans: _____________________
22
29. The table below shows the parking rates at a shopping mall. Vanessa parked her car from 3.40 PM to 5.25 PM. How much money did she pay more the parking?
Parking rates 1st hour $2.50 Every additional hour or part there of $1.90
Ans: _____________________ 30. In the figure below, ABCD is a rectangle, ST is a straight line.
Calculate the difference between ∠x and ∠y
Ans: _____________________
A
B
C
D
S
T 41o
58o
80o
33o
x
y
23
Semestral Assessment 1: Mock Paper 2 Paper 2 (Duration: 1 hr 40 mins)
Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. A survey at a concert showed that
251 of the audience came by car,
41 came by bus
and the rest came by train. If there were 180 people who came by car, how many people came by train?
Ans: _____________________2. Mrs. Ng had a rectangular parcel of land that is 9m wide. The area of the parcel is
108m2. She wanted to repaint the fence around the land. a) Find the perimeter of the land. b) The fence surrounds the whole perimeter of the land. She paid $126 for the painting cost. How much did she have to pay to paint 1 meter of the fence?
Ans: _____________________3. Harry cycles to a basketball court every day. He can take either route 1 or route 2. He
chooses route 1 from Monday to Friday and route 2 from Saturday to Sunday. If he takes route 1, he has to cycle 4 km 300m. The total length of route 1 and route 2 together is 8 km 200 m. What is the total distance that Harry travels to the basketball court in a week? Give your answer in km.
Ans: _____________________
24
4. In a training field there is a starting position and several finish lines. The first finish line is 30m away from the starting point. Each of the finish line from the second one is twice as far from the starting point as the previous finishing line. Peter ran straight from the starting point to the first finish line and returned straight back to the starting point. He then ran straight to the second finish line and returned to the starting point again. He kept running, every time to the next finish line and returning to the starting line. If the last finish line is 240m away, how far did he run in total when he reached the starting point for the last time?
Ans: _____________________ 5. The graph below shows the number of visitors who visited Science Centre in the
period from July to December. a) What is the fraction of the number of visitors in the least visited month to the number of visitors in the most visited month?
b) If 32 of the visitors in July were children and there were twice as many boys
as girls, how many girls were there?
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Jul Aug Sep Oct Nov Dec
Ans: _____________________
25
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. Study the figures below. The figure on the left shows a rectangular strip of paper.
The figure on the right shows that strip when folded along the dotted line. It consists of 2 squares and 1 trapezium. a) Find the length of the paper strip. b) Find the area of the paper strip
Ans: _____________________[4]7. Jeffery spent
53 of his money on 18 cakes and 21 toy robots.
The cost of a toy robot is 2 times that of a cake. How many more toy robots could he buy with the remaining money?
Ans: _____________________[3]
3 cm
7 cm
26
8. Some girls bought a packet of strawberries to share among themselves. If each girl took 7 strawberries, there would be 4 extra strawberries. If each girl took 8 strawberries, there would be 4 strawberries short. a) How many strawberries did they buy? b) How many girls were there?
Ans: _____________________[4] 9. Freddie, Jason and Malik each had some toy cars. Jason and Malik had
1411 of what
Freddie had, and Malik had 157 of what Jason had.
a) If Freddie had 56 toy cars, how many toy cars did Jason have? b) How many toy cars did they have altogether?
Ans: _____________________[4] 10. Mary bought 7 similar notepads and 9 similar pens. Each notepad is $1.1 more
expensive than a pen. If the total money Mary spent was $33.3, how much did she pay for the pens?
Ans: _____________________[3]
27
11. Ross paid $85 for 10 notebooks and 4 files. Each notebook cost as much as 3 files. What is the price of a notebook?
Ans: _____________________[4]12. Study the figure below. Note that it is not drawn to scale. Answer the following
questions: a) What is the area of the unshaded part? b) What fraction of the whole figure is shaded?
Ans: _____________________[4]
30 cm
18cm
10 c
m
28
13. 72 of the fruits in a basket are pears. There are 30 more apples than pears. The rest of
the fruits are 90 oranges. How many more apple than oranges were there?
Ans: _____________________[4] 14. At a museum, the body of the whale skeleton on display is as long as the total length
of its head and tail. The head of the whale skeleton is 8m long. The length of the tail
is equal to that of the head plus 31 that of the body. How long is the whale skeleton?
Ans: _____________________[4] 15. A train departed from Clementi station.
115 of the passengers were adults.
43 of the
children were boys. The number of adult men is 41 that of women. There were 114
less girls than boys. At the next station, Dover, 9 women and 5 boys boarded the train. a) How many passengers were there altogether when the train left Clementi Station? b) How many male passengers were there on the train when it departed from Dover station?
Ans: _____________________[4]
29
16. Mrs. Liu bought 5 packets of sugar, A, B, C, D, and E. The mass of sugar in each packet is 500g, 600g, 800g, 900g and 1kg, respectively. Mrs. Liu kept one packet for herself and sold the other packets to Mrs. Chan and Mrs. Lim. Mrs. Lim bought twice the amount of sugar that Mrs. Chan bought. Which packet did Mrs. Liu keep for herself if she kept more than 500g?
Ans: _____________________[4]17. Alex, Benny, Carol and Dean stand in a straight row. Alex is not standing next to
Dean and Benny does not stand at the first position, how many possible ways are there to arrange the four pupils?
Ans: _____________________[4]18. Seven years ago Mrs. Goh’s age was
316 her son’s age. Now her age is three times
her son’s age. What is Mrs. Goh’s age now?
Ans: _____________________[4]
30
Semestral Assessment 1: Mock Paper 3 Paper 1 (Duration: 50 mins)
Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided.
1. What is the result of 95 x 63
(1) 14 (2) 28 (3) 35 (4) 42 ( ) 2.
53 of the people at a cartoon movie show are children.
94 of the children are girls.
What is the fraction of the number of girls to the number of people at the show?
(1) 31 (2)
157
(3) 21 (4)
154
( )
3. The ratio of the number of boys to the number of girls in a class is 3:5. If there are 32 pupils in the class, how many boys are there?
(1) 12 (2) 20 (3) 28 (4) 36 ( ) 4. In the figure below, which line is the base of triangle XZT if XT is its height?
(1) XY (2) ZT (3) YZ (4) YT ( )
X
Y
Z
T
31
5. In the following figure, the area of the shaded shape is 13 cm2. What is the area of the unshaded part of the triangle?
(1) 23 cm2 (2) 30 cm2
(3) 41 cm2 (4) 60 cm2
( ) 6. The Physics textbook of a university student weighs 3.9 kg. His Math textbook is
0.532 kg lighter than his Physics textbook. What is the total mass of the two books? (1) 3.368 kg (2) 4.432 kg (3) 7.268 kg (4) 8.332 kg ( ) 7. Find the value of 60 ÷ (14 – 4) x 3 (1) 2 (2) 18 (3) 25 (4) 30 ( ) 8. Patrick and Albert have 72 pokemon cards. Patrick has thrice as many as Albert.
How many cards does Patrick have? (1) 18 (2) 24 (3) 54 (4) 63 ( ) 9. Irene’s weight is
43 of David’s weight. David’s weight is
98 Peter’s weight. Express
Peter’s weight as a fraction of Irene’s weight.
(1) 1311 (2)
3659
(3) 23 (4)
32
( )
12 cm
9 cm
32
10. What is the area of the shaded triangle?
(1) 312 cm2 (2) 224 cm2 (3) 210 cm2 (4) 88 cm2 ( ) 11. Which of the following is greater than
32 ?
(1) 54 (2)
74
(3) 94 (4)
114
( ) 12. What is ∠r in the figure below? XOY is a straight line.
(1) 151o (2) 119o
(3) 61o (4) 29o
( ) 13. Which of the following is the best estimate for 605 x 48? (1) 600 x 40 (2) 600 x 50 (3) 700 x 40 (4) 700 x 50 ( )
29or
X O Y
28 cm 11 cm
16 c
m
33
14. In a running competition, the total time taken by the 2 boys was 350 seconds while the total time taken by the 3 girls was 555 seconds. Find the average time that a child took to complete the race.
(1) 102 seconds (2) 175 seconds (3) 181 seconds (4) 270 seconds ( ) 15. In 3 852 176, how many times is the value of digit 8 to the value of digit 1? (1) 8 (2) 80 (3) 800 (4) 8 000 ( ) Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 16. Kelvin bought a pair of skates with
75 of his money. He bought a calculator with
51
of his remainder. If he had $112 left, how much was the calculator?
Ans: _____________________17. The figure below is made up of 8 identical squares. The total area is 32m2. Each
corner of a square at a lower row is at the midpoint of the side of the square of the row above. What is the perimeter of the figure?
Ans: _____________________
34
18. While reading a book, Jerry noted that the product of the two facing pages that he was reading is 600. What are the page numbers of the two facing pages that Jerry was reading?
Ans: _____________________ 19. Kathy bought a badminton racket for $199. She also bought 5 similar boxes of
shuttlecocks. She gave the cashier $300 and was given a change of $41. How much was each box of shuttlecocks?
Ans: _____________________ 20. Kelvin and Elizabeth shared some sweets. The ratio of Kelvin’s sweets to Elizabeth’s
is 8:5. If they have 65 sweets in total, how many sweets did Elizabeth have?
Ans: _____________________ 21. Find digits X and Y from 0 to 9 so that
Ans: _____________________
X Y
Y
Y X
+
35
22. Jonathan had 32 as many crayons as Ali. After Ali received 4 new crayons and
Jonathan received 10 new crayons, they have the same number of crayons. How many crayons did both of them have altogether before they received new ones?
Ans: _____________________23. Miss Lisa divided 300 paper clips to her pupils. Each pupil received 15 paper clips.
The next day she divided some toy bricks to her pupils. Each pupil got 10 toy bricks. How many toy bricks did Miss Lisa gave the class?
Ans: _____________________24. Gupta and Davis had a total of $300. If Davis gave Gupta $18, he would have twice
as much money as Gupta. How much money did Gupta have at first?
Ans: _____________________25. Mrs. Tan made 225 lollipops and packed them equally into some boxes, each have
15 lollipops. Each box was sold at $12.30. After selling all the boxes, how much did she earn?
Ans: _____________________
36
Questions 26 to 30 carry 2 marks each Show your working clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 26.
Find the area of the figure below, which consists of a square, a rectangle, and 3 identical triangles.
Ans: _____________________ 27. Ali counted his savings and noted that all of his money was in $2, $5 and $10 notes.
31 of the notes are $2,
61 are $5 and the rest are $10. He had saved $1 794 in total.
What is the total value of $5 notes had he saved?
Ans: _____________________
3 cm
4 cm
7 cm
37
28. Darren needed to run 10km for training. He had run 914 km. How many more
kilometres did he have to run to complete the training? Express your answer correct to 2 decimal places.
Ans: _____________________29. Jimmy can make 30 paper birds every hour. Philip can make 50 paper birds every
hour. After Jimmy had started making paper birds for 2 hours, Philip also started. How many hours would Philip take to make the same number of paper birds as Jimmy?
Ans: _____________________30. The ratio of 2 whole numbers is 2:15. The bigger number is greater than 98 but
smaller than 108. Find the smaller number.
Ans: _____________________
38
Semestral Assessment 1: Mock Paper 3 Paper 2 (Duration: 1 hr 40 mins)
Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. Helen cycles
327 km to school. Jack cycles
85 of that distance to school. What is the
difference in distance they have to cycle to school? Express your answer as a fraction in its simplest form.
Ans: __________________km 2. Find the area of the shaded part in the figure bellow, given that ABCD is a rectangle
and CN is 3 times as long as ND.
Ans: _____________________
96 m
24 m
A B
D C
M
N
39
3. The ratio of the amount of petrol Mr. Quek used in January to the amount of petrol he used in February was 4:7. He used 60l of petrol in January. How much did he have to pay for petrol in total if the price of petrol was $2.50 per litre during those two months?
Ans: _____________________4. Nurbaya wanted to make 24l of strawberry drink from a 1.5l bottle of strawberry
syrup. She mixed the syrup with plain water in the ratio of 1:5. a) How much strawberry syrup is she short of? b) After buying more syrup and made the desired drink, she added another 2l of syrup to make the drink sweeter. Find the new ratio of syrup to water in the new drink.
Ans: _____________________5. A salesman earned $10 for each unit of product A and $4 for each unit of product B
that he sold. In a month, he earned a total of $11 400. The ratio of the number of product B units to product A units that he sold was 3:14. a) How many units of product A did he sell? b) What is the difference between the amount of money he collected from selling product A and the amount of money he collected from selling product B?
Ans: _____________________
40
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. Nancy had some stickers.
31 of them were used to make a scrapbook. She then
divided 32 of the remaining equally to her three friends. After making the scrapbook
and sharing stickers to her friends she had 42 stickers less than what she had at the beginning. How many stickers did each of her friends receive?
Ans: _____________________[4] 7. Suriyana and Fahan each had saved some 20-cent and 50-cent coins. Suriyana had a
total of 192 coins. The number of 20-cent coins that Suriyana had was 53 the number
of 50-cent coins that she had. The ratio of the number of 20-cent coins to the number
of 50-cent coins that Fahan had was 1:2. Fahan’s total number of coins is only 41
that of Suriyana. a) What is the ratio of the number of 20-cent coins Suriyana had to the number of 50-cent coins that Fahan had? b) What is the ratio of the amount of money that Suriyana had to the amount of money that Fahan had?
Ans: _____________________[4]
41
8. Find a number that gives a quotient of 189 and a remainder of 17 when divided by 55.
Ans: _____________________[3]9. Mr. Ong spent
125 of his working hours working with his computer. He worked for
31 of the day. How many minutes did he work with his computer?
Ans: _____________________[3]10. Tom and Jerry have some money. If Tom gives Jerry $5, he will have half what Jerry
has. If Jerry gives Tom $5, they will have the same amount. a) How much money does Tom have? b) How much money does Jerry have?
Ans: _____________________[4]
42
11. A box of 16 Pelican pens (box A) is sold at $14.70. A box of 24 Pelican pens (box B) is sold at $22.50. Is box A or box B the cheaper buy?
Ans: _____________________[4] 12. All the people at a party shake hands with one another. How many handshakes are
there if there are a) 3 people? b) 5 people? c) 10 people?
Ans: _____________________[4] 13. The ratio among 3 sides of a triangle is 4 : 2 : 5. The longest side is 300 cm. What is
the perimeter of the triangle?
Ans: _____________________[4]
43
14. Study the following pattern:
...51
41
541
41
31
431
31
21
321
−=×
−=×
−=×
Use the above pattern to calculate
20191...
541
431
321
×++
×+
×+
×
Give your answer in the simplest form.
Ans: _____________________[4]15. Mr. Green needed to go from A to B. He had travelled
83 of the distance and still
needed to travel another 480km. What is the distance from A to B?
Ans: _____________________[4]16. A rectangle water tank can contain a maximum of 105m3 of water. Its base is 5m
wide and 7m long. What is the depth of the tank?
Ans: _____________________[4]
44
17. What is the area of the right-angled trapezium ABCD as shown below?
Ans: _____________________[4] 18. 36 chickens and dogs have a total of 100 legs. How many chickens are there?
Ans: _____________________[4]
A B
C D
14 cm
26 cm 11
cm
45
Semestral Assessment 1: Mock Paper 4 Paper 1 (Duration: 50 mins)
Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided. 1. What is the area of triangle PQR?
(1) 66 cm2 (2) 175 cm2
(3) 225 cm2 (4) 297 cm2
( ) 2. Find the value of 84 ÷ (5 + 2) – 2 x 5 (1) 2 (2) 50 (3) 60 (4) 72 ( ) 3. COD is a straight line. Find ∠x if ∠x is 180 less than ∠y. (The figure is not drawn to
scale).
(1) 99o (2) 81o
(3) 36o (4) 9o
( )
x y
25 c
m
14 cm
R
P
Q
P S
46
4. What is the value of ∠a, given that AB and CD are straight lines?
(1) 32o (2) 48o
(3) 60o (4) 122o
( ) 5. Nelson, Jordan and Joe had a number of cookies. Nelson had 2 times the number of
cookies that Jordan had. Joe had the same number of cookies as Nelson. What is the ratio of the number of cookies that Nelson had to the total number of cookies of all three friend?
(1) 1:5 (2) 2:5 (3) 3:5 (4) 4:5 ( ) 6. A triangle of height 8cm and base 6cm is cut from each corner of a square. The
perimeter of the square is 80cm. Find the area of the remaining figure? (1) 208 cm2 (2) 250 cm2
(3) 304 cm2 (4) 352 cm2
( ) 7. How many thousands are there in one and a half million? (1) 15 (2) 150 (3) 1 500 (4) 15 000 ( ) 8. The difference between 430 000 and 550 000 is divided by 400. What is the final
value? (1) 30 (2) 300 (3) 3 000 (4) 30 000 ( ) 9. Round off 205 621 to the nearest thousand (1) 205 000 (2) 205 600 (3) 206 000 (4) 206 621 ( )
A B
C
D
138o
a
47
10. How many sixths are there in213 ?
(1) 0 (2) 5 (3) 15 (4) 21 ( ) 11. Mr. Koh’s garden is 25m long and 12m wide. The cost of mowing 1m2 of garden is
$15. How much must he pay to mow his whole garden? (1) $20 (2) $555 (3) $1 110 (4) $4 500 ( ) 12. Sally spent
32 of a Sunday practicing the piano.
How many hours did she spend on that Sunday practicing the piano? (1) 8 hours (2) 16 hours (3) 20 hours (4) 36 hours ( ) 13. Which of the following is not a symmetric figure?
(1) (2)
(3)
(4)
( ) 14. Find the area of the shaded figure.
(1) 112 cm2 (2) 266 cm2 (3) 308 cm2 (4) 420 cm2
( )
28 cm
19 c
m
8 cm
48
15. The graph below shows Mrs. Ong’s grocery expenses for her family from January to May. What is Mrs. Ong’s average grocery expense for the five months?
$0
$20
$40
$60
$80
$100
$120
$140
$160
$180
$200
Jan Feb Mar Apr May
(1) $100 (2) $125 (3) $150 (4) $175 ( ) Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 16. At a fruit stall, the ratio of apples to oranges is 2:3 and the ratio of apples to banana
is 4:9. Find the ratio of oranges to bananas.
Ans: _____________________ 17. Sylvia, Alan and Ronald are making paper stars together. Ronald and Alan made 221
paper stars altogether. Alan and Sylvia made 121 paper stars altogether. If Ronald made 5 times as many paper stars as Sylvia, how many paper stars did Alan make?
Ans: _____________________
49
18. Half of the pens at a stationary shop are blue. 81 of the remaining pens are red, while
the remaining pens are black. If there are 210 more black pens than red pens, how many pens are there altogether?
Ans: _____________________19. A drink stall had some cans of coke and soda water in the ratio 3:7. After selling 48
cans of soda and buying another 48 cans of coke, the shop had the same number of cans for each drink. How many cans of coke were there at first?
Ans: _____________________20. In triangle XYZ below, XZ = YZ = 9cm.
Calculate the area of the shaded area.
Ans: _____________________
4.5c
m
2 cmZ
X
Y
50
21. Danny and Fahan had $54 in total. If each boy was given another $8, the ratio of the amount that Danny had to the amount that Fahan had became 3:4. How much money did Fahan had at first?
Ans: _____________________ 22. Arrange the following fractions in ascending orders
57,
75,
54,
45
23. How many two thirds are there in 18?
Ans: _____________________ 24. Betsy had an average of 56 slices of fruit a month.
How many slices of fruit did she have in 432 months?
Ans: _____________________ 25. Fill in the box with an appropriate number
2
128=
Ans: _____________________
51
Questions 26 to 30 carry 2 marks each Show your workings clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 26.
The number of chocolate candies in a box is between 60 and 100. If 4 or 7 children share the box, each of them can have the same amount of candies. How many chocolate candies are there in the box?
Ans: _____________________27. Mr. Lee had a number of boxes. He packed them into 8 layers in a container. Each
layer has 7 rows. Each row has 6 boxes. How many boxes did Mr. Lee have?
Ans: _____________________28. Find A if
1252
415 =×A
Ans: _____________________
52
29. If a bus can carry 25 passengers, what is the minimum number of buses to carry 7 groups of passengers, each of which have 32 passengers?
Ans: _____________________ 30. Two pumps are used to fill a swimming pool. Pump A can fill the pool completely in
3 hours. Pump B can fill the pool completely in 2 hours. How long will it take to fill the pool completely if both taps are turned on at the same time?
Ans: __________________hours
53
Semestral Assessment 1: Mock Paper 4 Paper 2 (Duration: 1 hr 40 mins)
Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. Wu Wei was given a number of questions as homework. He answered
21 of the
number of questions on the first day. On the second day he answered 101 of the
number of questions. If he continued to answer 101 of the number of questions every
day from the third day, on what day will he finish all the questions?
Ans: _____________________2. For every 5 hour of work, Daniel was paid $80. How many hours had he worked if
he was paid $1440?
Ans: _____________________
54
3. What is the area of the shaded part in the figure below if each square has sides of 3 cm?
Ans: _____________________ 4. A piece of cloth is cut into two pieces. The area of the bigger piece is
127 that of the
original piece. If the area of the bigger piece is 138 cm2 more than that of the smaller piece, what is the area of the bigger piece?
Ans: _____________________ 5. Complete the figure below so that the dotted line is the line of symmetry
Ans: _____________________
55
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. In the figure below, what is the area of the square if the averaged perimeter of the
square and the triangle is 59 cm?
Ans: _____________________[4]7. The volume of petrol in barrel A is
41 the volume of petrol in barrel B. 24l of petrol
is moved from barrel B to barrel A. The volume of petrol in barrel A is now 21 the
volume of petrol in barrel B. How much petrol is there in barrel B in the end?
Ans: _____________________[4]
28 cm
12 c
m
56
8. Examine the pattern of the following figure. Find the missing number.
Ans: _____________________[4] 9. A shop is selling toy robots at $20 and dolls at $50. There are 23 more dolls than toy
robots. After selling some dolls for $900, the shop has 1.5 times as many dolls as toy robots. How many dolls did the shop have at first?
Ans: _____________________[3]
89 115
1020
5
117 258
4500
12
205
397
4816
?
57
10. Joey, Zhong Ren and Suriya had a total of $1 326. After Joey spent 52 of his money,
Zhong Ren spent 71 of his money, and Suriya spent
31 of her money, all of them had
the same amount of money. How much did they spend altogether?
Ans: _____________________[4]11. Fred, George and Harry shared some pokemon cards. The number of cards Fred had
is 114 the total of cards that George and Harry had. George had twice the number of
cards Fred had. a) If George had 104 cards, how many did Harry have? b) What was the number of cards three of them had altogether?
Ans: _____________________[4]12. Jane had
41 of his brother’s money. The product of their money is $400. How much
money did Jane have?
Ans: _____________________[3]
58
13. A pair of shoes is 9 times as expensive as a pair of socks. If 3 pairs of shoes and 5 pairs of socks cost $192, how much is a pair of shoes?
Ans: _____________________[4] 14. What is the area of the shaded part, if each small square is 4 cm x 4 cm?
Ans: _____________________[4] 15. A bag of rice is 2
21 times as heavy as a bag of powder. The average mass of the two
bags is 33.25 kg. What is the mass of the bag of powder?
Ans: _____________________[4]
59
16. The ratio of the number of pencils to the number of pens in a stationary shop was 3: 7. The stall owner then sold 36 pens and the number of pens became equal to the number of pencils. How many pens were there in the shop at first?
Ans: _____________________[4]17. The figure below is not drawn to scale. Find the area of the shaded part.
Ans: _____________________[4]18. Alice had 9 notepads and Ronald had 6 notepads. Alice then bought some more
notepads. After that the ratio of the number of notepads that she had to the number of notepads Ronald had is 7: 3. How many more notepads did Alice buy?
Ans: _____________________[4]
19 cm
15 c
m
15 c
m 7
cm
60
Semestral Assessment 1: Mock Paper 5 Paper 1 (Duration: 50 mins)
Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided.
1. Five pupils shared a 9l jug of orange juice. How many litres of orange juice did each pupil get?
(1) l135 (2) l
138
(3) l95 (4) l
541
( ) 2. Write 8.56 in fraction form
(1) 2514 (2)
12598
(3) 25148 (4)
2588
( ) 3. Which of the following ratio is not equivalent to 5 : 13 (1) 15 : 39 (2) 30 : 78 (3) 35 : 91 (4) 40 : 84 ( ) 4. In the diagram below, ABCD is a rectangle, AB = 7cm, AD = 5cm, BO = 4 cm, AO
= 9.5 cm. What is the base and height of the shaded triangle?
(1) 4 cm and 9.5 cm (2) 4 cm and 7 cm (3) 5 cm and 9.5 cm (4) 5 cm and 7 cm ( )
A B
C D
O
Marks
Marks
61
5. Each worker in a factory was given 300 short nails, 700 medium nails and 600 long nails. Find the ratio of the number of long nails to the total number of nails
(1) 3 : 13 (2) 7 : 16 (3) 3 : 8 (4) 3 : 16 ( ) 6. There were 45 strawberries in basket A. Basket B had 25 more strawberries than
basket A. What was the ratio of the number of strawberries in basket B to basket A? (1) 14 : 9 (2) 9 : 14 (3) 4 : 9 (4) 9 : 4 ( ) 7. What is the value of
98
413
× ?
(1) 926 (2)
1321
(3) 9
104 (4) 32
117
( ) 8. What is the value of 66 + 18 ÷ 3 + 4 x 5 (1) 48 (2) 92 (3) 116 (4) 160 ( ) 9. A tin contains
53 kg of candies. Mrs. Chua packed all the candies in the tin into 9
bags, each weighs the same. What was the mass of each candy bag?
(1) kg527 (2) kg
54
(3) kg151 (4) kg
512
( ) 10. A rectangle
43 m wide has an area of 9m2. What is its perimeter?
(1) 217 m (2) 12m
(3) 4312 m (4)
2125 m
( )
62
11. Ding Mei’s water bottle was full and had l23 of water. She drank l
103 and poured
away l41 of water. What was the fraction of the amount of water left in Ding Mei’s
bottle to the full bottle?
(1) 3019 (2)
2019
(3) 2011 (4)
201
( ) 12. Miss Sally needed to use 85cm of ribbon to tie a present. If she had to make 25
similar presents to her pupils, how many meters of ribbon were used? (1) 1.1 (2) 2.125 (3) 3.4 (4) 21.25 ( ) 13. Calculate the sum of 72.35 and 52.87. Round off your answer to 1 decimal place. (1) 124.2 (2) 125.2 (3) 126.2 (4) 127.2 ( ) 14. Joey, Lucy, Michael and Sam attended a physics test. There scores are shown in the
table below: Who had the score that is closest to the average score of all 4 pupils?
Pupil’s name Test score Joey 95 Lucy 83
Michael 77 Sam 71
(1) Joey (2) Lucy (3) Michael (4) Sam ( ) 15. Fatimah needed to walk 1.8 km to school. She had walked 216m. What percentage of
the journey did she still have to walk? (1) 12% (2) 13.64% (3) 75% (4) 88% ( )
63
Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 16. Write 8 006 500 in words.
17. What is the remainder when dividing 5603 by 7?
Ans: _____________________18. What fraction of 5km is 1300 m? Provide the simplest form for your answer.
Ans: _____________________19. Express
523 km in metres.
Ans: _____________________20. In the diagram shown below, MNPQ is a rectangle; K and H are midpoints of MN
and PQ respectively. What fraction of the figure is shaded?
Ans: _____________________
KM N
P Q H
64
21. Mei Mei, Jing Jing and Hui Hui were given the same homework. Mei Mei had done
41 of the homework. Hui Hui had done
21 of the homework. Jing Jing’s completed
portion of the homework is exactly midway between Mei Mei’s and Hui Hui’s. What fraction of the homework had Jing Jing done?
Ans: _____________________ 22. 1 carpenter can make 8 tables in a week. How many carpenters are required to make
40 tables in a week?
Ans: _____________________ 23. A = 1 + 2 + 3 + … + 99 + 100.
Find the value of A.
Ans: _____________________ 24. A carpenter completed a chair at 4.40 pm. It took him 2 hours 45 minutes to
complete his work. What time did he start?
Ans: _____________________
65
25. At first, Davis, Feng Xue and Ann had 181 stamps in total. Davis had 37 stamps. Feng Xue and Ann had the same amount of stamps. A few weeks later, Ann collected another 29 stamps. How many stamps did Ann have in the end?
Ans: _____________________ Questions 26 to 30 carry 2 marks each. Show your working clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 26.
Two numbers have a sum of 148.5 and a difference of 43.5. What are the two numbers?
Ans: ______________27. In the figure below, ABCD is a square of side 30 cm and DH =
37 HC. Find the area
of the shaded triangle.
Ans: _____________________
A B
CD H
66
28. There were 592 apples and pears in a fruit shop. After 94 of the apples and
72 of the
pears were sold, the number of pears and the number of apples left are the same. How many pears were sold?
Ans: _____________________ 29. At first, of a tank was filled with water. The total mass was 81.74 kg. Water was
then taken out of the tank until it was half filled. The total mass was 59.8 kg. What was the mass of the tank? Round off your answer to 1 decimal place.
Ans: _____________________ 30. Of all the adults at a concert, were women. There were 114 more children than
women. The ratio of the number of adults to the number of children was 3: 7. How many children were there at the concert?
Ans: _____________________
67
Semestral Assessment 1: Mock Paper 5 Paper 2 (Duration: 1 hr 40 mins)
Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. Grapes were sold at $0.65 per 250g in a market. Mr. Khoo bought 3.25 kg of grapes.
How much did he have to pay?
Ans: _____________________2. Find the area of triangle ACD in the figure below.
Ans: _____________________
A
B C
D
22 cm8 cm
16 c
m
7 cm
68
3. Three packets of candies had an average mass of 903.6g. The packet of apple candies weighed twice as much as the packet of strawberry candies. The packet of mango
candies is 54 the mass of the packet of strawberry candies. What is the mass of the
packet of apple candies? Express your answer up to 2 decimal places.
Ans: ___________________kg 4. 2 boxes of candies and 3 boxes of cookies have an average mass of 3.84 kg. 3 boxes
of candies and 2 boxes of cookies have an average mass of 3.7 kg. The candy boxes are identical and the cookies boxes are also identical. What is the total mass of 2 boxes of candies and 1 box of cookies?
Ans: _____________________ 5. There are two water taps, A and B. Tap A is used to fill in tank X and tap B is used
to fill in tank Y. In every minute, tap A can fill 8l more than tap B. However, 56.5l of water is drawn from each tank in every minute. When tank X has 54l, tank Y has 22l. a) How much water does tank Y receive per minute? b) How much water is there in tank Y after 1 hour?
Ans: _____________________
69
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. When Tom received his salary, he gave his mother
41 his salary. He then used
71 of
the remaining amount plus $54 to pay his bills. After that, he spent half of the remainder plus $27 to buy a computer. Finally, he saved the remaining $846. How much was his salary?
Ans: _______________[4]7. In the tables and chairs section of a warehouse, the ratio of the number of chairs to
that of tables is 5: 3. There are 64 wooden pieces of furniture and the rest are made of plastic. The number of plastic pieces is twice the number of wooden pieces. If there are 32 wooden chairs, what is the ratio of the number of plastic chairs to that of wooden tables?
Ans: _______________[4]
70
8. Betsy is 121 m tall. Her brother is
61 m taller than she is. What is the average height
of the two children? Round off your answer to 2 decimal places.
Ans: _______________[4] 9. Nicole read
51 of a magazine on Friday and
41 of the remaining on Saturday. On
Sunday she read twice as many pages as on Friday. What fraction of the magazine was not read?
Ans: _______________[4] 10. The ratio of the cost of an LCD monitor to that of a computer is
94 . The computer
costs $900. What is the average cost of the two devices?
Ans: _______________[3]
71
11. Ken bought 3 pairs of jeans and 2 shirts for $90. A pair of jeans was $5 more expensive than a shirt. How much did a pair of jeans cost?
Ans: _______________[4]12. The ratio of the number of Indian pupils to the number of Chinese pupils is 2: 7. The
ratio of the number of Malay pupils to the ratio of Chinese pupils is 3: 4. What is the ratio of the number of Indian pupils to the number of Malay pupils to the number of Chinese pupils?
Ans: _______________[4]13. A bank paid a fixed 0.68% saving interest per year. Bill opened an account and
deposited $172 000. How much interest would he earn after a year?
Ans: __$____________[4]
72
14. The total amount of money that Soo Hui and Margaret had is $630. If Margaret gave Soo Hui $52.70, Soo Hui would have eight times the amount that Margaret had. Initially, what was the difference in the amounts that they had at first?
Ans: _______________[4] 15. The total volume of water in tanks A, B and C is 400l. If half of the water in tank A
is taken away and the water in tank B is doubled, and 30l is added to tank C, the ratio of the volume of water in tank A to B to C will be 3: 2: 1. Find the amount of water in tank B initially.
Ans: _______________[4]
73
16. A set of furniture costs $3290. Mr. Tay bought the set with 20% discount. However, he had to pay 7% GST on the discounted price. How much did he have to pay for the set of furniture?
Ans: _______________[4]17. Use the following digits, each digit only once, to make the smallest even number that
is greater than 250 000.
0, 3, 7, 2, 9, 6
Ans: _______________[3]18. In a laboratory, the mass of some bacteria doubles every 12 minutes. If the mass is
128 mg at 5 p.m, what time was it when the mass was 0.5 mg?
Ans: _______________[4]
74
Semestral Assessment 2: Mock Paper 1 Paper 1 (Duration: 50 mins)
Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided. 1. The digit 9 in 5 298 637 is the _________________________ place (1) hundreds (2) thousands (3) ten thousands (4) hundred thousands ( ) 2. Which of the following numbers will result in 555 000 when being rounded off to the
nearest thousand? (1) 554 494 (2) 555 494 (3) 555 501 (4) 555 513 ( ) 3. 45 x 100 = ____________________- (1) 45 x 20 x 5 (2) 40 + 5 x 100 (3) 45 x 10 + 90 (4) (45 x 20) + (45 x 5) ( ) 4. Frank studied for 4
103 hours. For how many minutes did he study?
(1) 258 minutes (2) 300 minutes (3) 342 minutes (4) 400 minutes ( ) 5. Find the value of 650 – (27 + 123) ÷ 4 (1) 36.25 (2) 125 (3) 250 (4) 612.5 ( ) 6. Harry bought a pair of jeans with
32 of his money and used
41 of his remaining
money to buy some toys. What is the fraction of money left?
(1) 41 (2)
43
(3) 121 (4)
125
( )
75
7. Find the area of the figure below (not drawn to scale)
(1) 30 cm2 (2) 36 cm2 (3) 42 cm2 (4) 49 cm2 ( )8. What is the volume of a cube of side 4 cm? (1) 16 cm3 (2) 32 cm3 (3) 64 cm3 (4) 128 cm3 ( )9. What is the maximum number of 2-cm cubes that can be fitted into a rectangular box
measuring 9 cm by 6 cm by 4 cm? (1) 9 (2) 24 (3) 27 (4) 54 ( ) 10. Annie was sitting in a concert. The chairs were arranged in rows in a rectangular
manner. There were 6 chairs on Annie’s left and 8 chairs on her right. There were 10 rows in front of her and 11 rows behind her. How many chairs were there?
(1) 294 (2) 308 (3) 315 (4) 330 ( ) 11. Mei Mei jogged for the same distance every night. After a week, the total distance
covered was 1721 km. What was the distance that she jogged each day?
(1) 221 km (2) 3km
(3) 5km (4) 1021 km ( )
12. In a survey among pupils in a school,
53 of the participants are boys and
65 of these
boys likes basketball. The survey also shows that 31 of the girls like basketball too.
What fraction of the pupils like basketball?
(1) 3019 (2)
3011
(3) 1514 (4)
67 ( )
9
8 cm
76
13. Express 21 km 3 m in km. (1) 21. 003 km (2) 21. 03 km (3) 21.3 km (4) 210.3 km ( ) 14. What is the product of 56.31 and 60? (1) 3.3786 (2) 33.786 (3) 333.86 (4) 3 378.6 ( ) 15. The average mass of two packets of rice is 4 kg. Which of the following are the
likely mass of the two packets of rice? (1) 2.5 kg and 2.5 kg (2) 2.5 kg and 3.5 kg (3) 2.5 kg and 4.5 kg (4) 2.5 kg and 5.5 kg ( ) Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 16. What is the remainder when 3256 is divided by 19?
Ans: _____________________ 17. Write six hundred and eighty thousand, seven hundred and ninety-five as a numeral.
Ans: _____________________ 18. What is the difference between and ?
Ans: _____________________ 19. Calculate
290 – 36 ÷ 4 x (27 + 5) ÷ 2 + 115
Ans: _____________________
77
20. How many cubic centimetres are there in 1l 25 ml?
Ans: _____________________21. Pei Xin had
65 l of milk in her bottle. She drank
31 of the milk in the bottle. How
many liters of milk did she have left?
Ans: _____________________22. Find x if =×
32
4X 5
Ans: _____________________23. Express 63.08l in terms of milliliters.
Ans: _____________________24. The table below shows the prices of different fruits at a market.
Fruit Price (per kg) Apple $3.65
Strawberry $4.89 Kiwi $5.99
Watermelon $4.20 Uncle Tiong bought 2 kg of apple and 3 kg of kiwi. How much did he spend?
Ans: _____________________
78
25. Find X and Y if X : 5 : 9 = 7 : Y : 63
Ans: _____________________ Questions 26 to 30 carry 2 marks each Show your workings clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 26.
Mrs. Lim wants to give some pens to her pupils. If each pupil gets 7 pens, there will be 3 pens extra. If each pupil gets 8 pens, there will be 4 pens short. a) How many pupils are there? b) How many pens does Mrs. Lim have?
Ans: _____________________ 27. 75% of the candies in a box are chocolate flavored. 40% of the remainder is mango
flavored and the rest is strawberry flavored. a) Express the number of strawberry flavored candies as a fraction of the total
number of candies in the box. b) How many more chocolate flavored candies than strawberry flavored candies
are there if there are 20 mango flavored candies?
Ans: _____________________
79
28. The breadth of a rectangular floor is 15% of its perimeter. The length of the floor is 760 cm longer than its breadth. a) What is the area of the floor in m2? b) The floor is used to store identical cartons each has a base measuring 30 cm
by 30 cm. What is the maximum number of cartons that can be stored?
Ans: _____________________29. The table below shows the water tariffs (charges) for monthly water consumption
Volume consumed Charges per unit (dollars) First 40 units 1.17
Above 40 units 1.40 Mr. Choo’s family used 56 units in January. In February he paid $135 for his bill. a) How much water did Mr. Choo’s family use in February? b) On average, how many units of water were consumed by his family in a
month over this period? c) On average, how much does Mr. Choo have to pay for water bill in a month?
Ans: _____________________30. Peter has a number of books. Lixiang has
32 as many books as Peter has. Fahan has
half as many books as Peter has. If Lixiang has 32 books, how many books do they have altogether?
Ans: _____________________
80
Semestral Assessment 2: Mock Paper 1 Paper 2 (Duration: 1 hr 40 mins)
Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. The maximum score for a physics test is 50 marks. What is the highest possible
average score for 5 pupils who took the test, if it is known that one of them scored 15 marks?
Ans: _____________________ 2. Fred and George folded a number of paper birds. Fred folded 35% of the birds.
George folded 90 birds more than Fred. How many birds did George fold?
Ans: _____________________ 3. Mary, Andy and Bob donated some money to a charity fund. Mary donated 40%
what Andy donated and 50% less than what Bob donated. If they donated $660 altogether, how much did Andy donate?
Ans: _____________________
81
4. In the figure below, ABCD is a rhombus. What is ∠ABE? The figure is not drawn to scale.
Ans: _____________________5. Kin Eu had collected some stamps. After collecting another 12 stamps, the number
of stamps in his collection increased by 30%. How many stamps did he have at first?
Ans: _____________________
116o
A
B
C
D E
82
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. The table below shows the number of days pupils exercised in a week. What is the
fraction of the number of pupils that exercise 2 days or more to the total number of pupils? Express your answer correct to 2 decimal places. No. of exercised days 0 1 2 3 4 No. of pupils 5 9 7 16 5
Ans: _____________________[3] 7. In a festival that has 2500 participants, there are 1100 females. How many percent
more males than females are there? Round off your answer to 2 decimal places.
Ans: ____________________%[3] 8. The number of exercise questions that 3 pupils have completed is in the ratio of 2: 4:
5. If the pupil who had done the least completed 6 questions, what is the total number of questions that they have completed?
Ans: _____________________[4]
83
9. There are approximately 3300 adults and 1700 children in a stadium. If both above figures are corrected to the nearest hundred, what is the largest possible difference between these 2 figures?
Ans: _____________________[4]10. The area of the shaded part in the figure below is 54 cm2. SH =
41 PK.
What is the area of triangle PQR?
Ans: _____________________[4]
P
Q R
S
H K
84
11. The area of rectangle A is 3 times the area of square B. The unshaded area of rectangle A is 5 times the unshaded area of square B. If the shaded area is 27 cm2, what is the area of the square? The figure is not to scale.
Ans: _____________________[4] 12. Miss Chua brought some lollipops to share equally among 36 pupils at the end of a
camp. However, 9 pupils had to leave the camp early. Therefore, each of the remaining pupils received 3 more lollipops. How many lollipops did Miss Chua bring?
Ans: _____________________[4]
A
B
85
13. In the figure below, ABC is a right angled triangle at C. Its height is 9 cm and its base is 12 cm. 4 such identical triangles are used to form the square MNPQ. Find the side of the square MNPQ.
Ans: _____________________[4]14. In the figure below, a rectangle is divided into 4 smaller triangles A, B, C and D. The
area of triangle A is 31 the area of triangle B. The ratio of area of triangle A to that of
triangle D is 3: 5. The width of the rectangle is 6 cm. The area of triangle D is 30 cm2. Find the perimeter of the rectangle.
Ans: _____________________[4]
A
B C
D
Q
A
B C
M N
P
86
15. In a second-hand bookshop, story books are sold at $12 each and comic books are sold at $8 each. At first, there were 50% more story books than comic books. After
some time, 32 of the story books and all the comic books were sold. The shop
received $6400. When all the books were sold, how much would the shop receive?
Ans: _____________________[4] 16. Lucy had
31 the money that Aaron had. After that Aaron spent $45 and Lucy’s
mother gave her $6. Aaron still had $3 more than Lucy. How much money did Lucy have at first?
Ans: _____________________[4]
87
17. 53 of Joey’s marbles is equal to
72 the number of marbles that Thomas has. Ben has
twice the difference between Thomas and Joey’s marbles. Joey has 48 marbles less than Ben. How many marbles do they have altogether?
Ans: _____________________[4]18. Tank A measures 4 m by 6 m at the base and is 1 m high. Tank B has the base
dimensions of 5 m x 3 m and is twice as high as tank A. Both of them contain the same amount of water. The height of water level in tank A is half of its height. Find the height of water level in tank B.
Ans: _____________________[4]
88
Semestral Assessment 2: Mock Paper 2 Paper 1 (Duration: 50 mins)
Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided. 1. The square below is divided into three parts, A, B and C. The ratio between the areas
A and C is 8: 3. What is the ratio of the area of B to that of C?
(1) 3 : 8 (2) 5 : 3 (3) 8 : 5 (4) 8 : 11 ( ) 2. The average weight of 3 pupils is 38 kg. Andy weighs 33.5 kg. John is 3.5 kg heavier
than Bob. How heavy is John? (1) 42 kg (2) 38 kg (3) 33 kg (4) 30 kg ( )
3. Maria and Lily shared some money. Maria had of the total sum. Lily had $180 more than Maria. How much money did both of them have in total?
(1) 72 (2) 90 (3) 360 (4) 420 ( ) 4. Adil had 36 more stickers than Xiao Mei. Each of them then bought another 10
stickers. After that, Adil had 4 times as many stickers as Xiao Mei had. How many stickers did Adil have initially?
(1) 38 (2) 40 (3) 58 (4) 108 ( ) 5. Celine bought 2
52 kg of sugar and Sarah bought 1
65 kg of sugar. They used 2
101 kg
to bake some cakes. How many kilograms of sugar did both of them have eventually?
(1) 103 (2)
157
(3) 2152 (4) 4
307 ( )
89
6. Ivy bought 47 kg of charcoal for a BBQ but only used
53 of them. How many
kilograms of charcoal were left over?
(1) 107 (2) 1
201
(3) 1203 (4) 1
207
( ) 7. There are 32 students in a class. There are 24 students wearing spectacles. What is
the ratio of the number of students who wear spectacles to the number of students who do not?
(1) 1 : 3 (2) 3 : 1 (3) 3 : 4 (4) 4 : 3 ( ) 8. Ali is living in Singapore and he has collected stamps from Singapore, China and
India. The ratio of the number of Singapore stamps to the number of China stamps to the number of India stamps that he collected is 1: 1: 2. Ali collected 108 foreign stamps in total. How many local stamps were there?
(1) 27 (2) 36 (3) 81 (4) 144 ( ) 9. A container having a capacity of 33.5l is filled with lime juice drink. This container
is dispersed into 100 similar glasses for guests. How many liters of juice drink is there in each glass?
(1) 0.0335 l (2) 0.335 l (3) 3.35l (4) 3 350 l ( ) 10. Find the difference between 125.22 and 38.19. Express your answer as correct up to
1 decimal place. (1) 87.0 (2) 87.1 (3) 87.9 (4) 88.0 ( ) 11. A box containing 24 identical cans weighs 8.36 kg. What is the mass of the box (in
kg) if each can weighs 340g? (1) 0.2 kg (2) 0.418 kg (3) 0.5 kg (4) 2 kg ( ) 12. The distance from Hassan’s house in Serangoon to Patrick’s house in Paya Lebar is 5
515 m. Write that distance rounded off to the nearest kilometer. (1) 5 km (2) 6 km (3) 5 500 km (4) 60 km ( )
90
13. What is the value of digit 3 in 238 962 (1) 30 (2) 300 (3) 3 000 (4) 30 000 ( ) 14. Last month, a shop collected $65 098 from selling goods.
Express this amount to the nearest hundred (1) 65 000 (2) 65 100 (3) 66 000 (4) 66 100 ( ) 15. Express 3
41 as a percentage
(1) 0.325% (2) 3.25% (3) 32.5% (4) 325% ( ) Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 16. In an orchard there are apple trees and pear trees. The ratio of the number of apple
trees to the number of pear trees is 5: 9. What is the ratio of the number of pear trees to the total number of trees in the orchard?
Ans: _____________________ 17. A caterer mixed 2070 ml of orange syrup to 12.42 l of water to make orange juice
drink. What is the volume of juice drink made? Express your answer in liters.
Ans: _____________________
91
18. How many percent of the figure below is shaded?
Ans: _____________________19. Express
1258 in decimal form.
Ans: _____________________20.
65 Kg of flour is divided equally into 10 bags. What is the mass of flour in each bag?
Give your answer in its simplest fraction form.
Ans: _____________________21. 3 years ago, Mohammed’s age is
32 that of his brother. He is 15 years old now. How
old is his brother now?
Ans: _____________________
92
22. What percentage of the number of days in 2009 is the number of days in September?
Ans: _____________________ 23. Arrange these number in an ascending order
1000105 , 0.051, 0.501,
10051
Ans: _____________________ 24. 56 x 28 = 29 x 28 + 1 x 28 + ______ x 28
Ans: _____________________ 25. Write 64% as a simplest fraction.
Ans: _____________________ Questions 26 to 30 carry 2 marks each Show your working clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 26.
The price before tax of a plasma TV is $2100. A GST of 7% is charged on the price. How much does a buyer have to pay for the TV?
Ans: _____________________
93
27. The first carton has 1.25 l of lime juice. The second carton has 281 l of lime juice.
The third carton had 786 ml of lime juice. How many liters of lime juice are there in total? Round off your answer to 2 decimal places.
Ans: _____________________28. Kavitha saved
85 as much as Joshua saved. The two pupils saved $1053. How much
is Kavitha’s savings?
Ans: _____________________29. A small swimming pool of dimension 20 m x 10 m x 1.5 m is half filled with water.
4 pumps, each is running at a rate of 375 l per minute, is used to pump the pool. How long will it take to fill the pool completely?
Ans: _________________mins30. A movie ticket for an adult is $8.50 and that for a child is $5. During a certain
period, 126 more adults than children visited the cinema. The cinema collected $2907. How many adults visited the cinema in that period?
Ans: _____________________
94
Semestral Assessment 2: Mock Paper 2 Paper 2 (Duration: 1 hr 40 mins)
Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. Two boys and eight girls have saved an average of $604. The two boys have saved
an average of $592. What is the average of the savings of the girls?
Ans: _____________________ 2. There are 1200 pupils in a school. 20% of them are Indian. 65% of the remaining
pupils are Chinese and the rest are Malay. a) How many Chinese pupils are there? b) What percentage of pupils is Malay?
Ans: _____________________ 3. Mr. Chan sold a number of balloons in a 3-day carnival. On the first day he sold
51 of the balloons. The number of balloons he sold on the second day is
32 of what he
sold on the last day. 92 more balloons were sold on the last day than on the second day. Balloons are sold at $1.20 each. How much did Mr. Chan earn?
Ans: _____________________
95
4. Mr. Feng had 225 more tulips than roses in his garden to sell. After selling 53 of the
tulips and 31 of the roses, he had 858 flowers remaining. How many flowers did he
have at first?
Ans: _____________________5. The following figure is not drawn to scale. ABCD is a square. AEDF is a rhombus.
Triangle DFG is isosceles. C, G, D are on the same line. F is the midpoint of AG. Find a) ∠ AFD b) ∠ EDC c) ∠ DAE
Ans: _____________________
A B
C D
E F
G
40o
96
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. What is the total mass of a bag that weighs
83 of 4500g and a box that weighs 48%
of 18 kg? Express your answer in kg correct to 2 decimal places.
Ans: ___________________kg[3] 7. There are 15 trees planted in a line. The distance between any two adjacent trees is
the same. The seventh tree is 7920 cm away from the third tree. How far from the first tree is the last tree? Express your answer in meters.
Ans: _____________________[4] 8. When dropping a tennis ball from a height of 15m to the ground, Johannes realized
that the ball went up to 54 of the previous height for every bounce. Find the total
distance that the ball had travelled when it hit the ground the second time.
Ans: _____________________[4]
97
9. Mr. Lee has 4 children. His age is 3 times that of his youngest child. Each child was born 3 years before the next one. The total age of the 4 children and the father is 193 years. Find the age of Mr. Lee’s first child.
Ans: _____________________[4]10. Each small truck has 10 wheels. Each large truck has 14 wheels. A truck
manufacturer ordered 408 wheels for their 32 trucks. How many large trucks are there?
Ans: _____________________[4]11. Francis gave half of his salary plus $100 to his mother. He spent 25% of the
remaining plus $49 on furniture. He bought some books for $61. He gave 53 of his
remaining sum plus $53 to his sister. He saved the final $443. How much is Francis’s salary?
Ans: _____________________[4]
98
12. An elephant is 5.5 times as heavy as a zebra. The total mass of 2 elephants and 3 zebras is 1260 kg. What is the mass of 1 elephant and 4 zebras?
Ans: _____________________[4] 13. From January to August, Phoebe earned an average of $2340 per month. From
September to December, she earned some more money and the average earning over the entire year is $3290. What was the average amount of money that Phoebe earned a month in the period from September to December?
Ans: _____________________[4] 14. In a charity event, 3 scouts Benny, Ray and Kathy raised $1459 altogether. Ray
raised $296 less than Benny while Katy raised an amount 41 as much as Benny. How
much money did Kathy raise?
Ans: _____________________[4]
99
15. The ratio of the number of roses to the number of lilies to the number of tulips is
3:5:9. If there are 954 more tulips than roses, how many more lilies than roses are there?
Ans: _____________________[3]16. There are 20 more pages in a mathematics book than in a physics book. There are 70
more pages in a chemistry book than in a mathematics book. The total number of pages in 20 books of each type is 10 000. How many pages are there in a physics book?
Ans: _____________________[4]
100
17. In the figure below, the rectangle on the left is made by bending a wire. Another wire with the same length is bent to make the two identical isosceles triangles on the right. What is the area of one isosceles triangle?
Ans: _____________________[4] 18. The ratio of the amount of money Josh had to that Derek had was 3: 5. Derek spent
25% of his money on toys and 51 on stationeries. He also bought two pairs of shoes
for $150. He saved the remaining $246. How much money did Josh have?
Ans: _____________________[4]
33 c
m
75 cm
36 c
m
101
Semestral Assessment 2: Mock Paper 3 Paper 1 (Duration: 50 mins)
Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided.
1. What is the ratio of 31 hours to 56 minutes?
(1) 5 : 14 (2) 14 : 5 (3) 3 : 5 (4) 5 : 3 ( ) 2. What percentage of 4 m is 25 cm? (1) 6.25% (2) 62.5% (3) 0.16% (4) 16% ( )
3. In a factory, soya drink is poured from a 5.2l tank to fill some identical cans, each of which has a capacity of 330ml. What is the maximum number of cans that can be filled using one tank?
(1) 14 (2) 15 (3) 16 (4) 17 ( ) 4. Jane spent an average amount of $127 a month over 5 months. Find the total amount
that Jane spent over 5 months. (1) $600 (2) $635 (3) $660 (4) $700 ( ) 5. John had some money. He used 25% of his money to buy furniture and used of the
remainder to buy clothes. If the spent $300 on clothes, how much did he spend on furniture?
(1) $240 (2) $500 (3) $1200 (4) $1500 ( ) 6. Jane bought some pieces of clothes for an average cost of $24. After that, she bought
another piece that costs $96 and the average cost became $36. How many pieces of clothes did Jane buy altogether?
(1) 5 (2) 6 (3) 8 (4) 4 ( )
102
7. In the figure below, 1, 2, 3 and 4 together make a square. 2 and 3 are also squares
and they contribute 50% of the area of the figure. Which of the following pair will
form 85 of the figure?
1
2
3
(1) 1 and 2 (2) 3 and 4 (3) 1 and 4 (4) 2 and 3 ( ) 8. Harry and Jack each had some Pokémon cards.
52 of what Harry had is equal to
43
of what Jack had. What fraction of the total number of cards are Jack’s cards?
(1) 238 (2)
2315
(3) 823 (4)
1523
( ) 9. Find the value of 7 x (2 + 16 ÷ 2) – 1 (1) 14 (2) 21 (3) 62 (4) 69 ( ) 10. Find the largest fraction of the following
(1) 97 (2)
107
(3) 117 (4)
127
( ) 11. The distance from A to B is eight times the distance from B to C. What is the ratio of
the distance from A to B to the total distance? (1) 1 : 8 (2) 1 : 9 (3) 8 : 9 (4) 9 : 8 ( )
4
103
12. The volume of a tank is 56l when rounded off to the nearest litre. Which of the following is likely to be the actual volume of the tank in liter?
(1) 55.05 (2) 55.49 (3) 56.45 (4) 56.51 ( ) 13. David had $32 left after spending $48. What percentage of his money did he spend? (1) 40% (2) 60% (3) 67% (4) 80% ( ) 14. What is the ratio of the shaded part to the whole figure below?
(1) 1 : 4 (2) 4 : 5 (3) 4 : 9 (4) 5 : 9 ( ) 15. What is ∠ h in the figure below? FG is a straight line. The figure is not to scale.
(1) 35o (2) 45o
(3) 55o (4) 65o
( )
F G 35oh
104
Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 16. Write
2512 in percentage form.
Ans: _____________________ 17. A card board is 30 cm in length and 16 cm in breadth. What is the area of the card
board?
Ans: _____________________ 18. Four cans of iced tea costs $6. How much is two dozen cans?
Ans: _____________________ 19. Find ∠x given that ∠x = ∠y
Ans: _____________________
x
y
162o
105
20. In the figure below, ABCD is a rectangle, AI = ID, BJ = JC. What percentage of the whole area is the shaded area?
Ans: _____________________21. A pencil case can contain 12 pencils. If there are 390 pencils, how many pencil cases
are needed?
Ans: _____________________22. Angela has some short sleeved and long sleeved shirts.
157 of the shirts are long
sleeved. What is the ratio of the short sleeved shirts to the long sleeved shirts?
Ans: _____________________23. Brian has 50% more $2 notes than $5 notes. He has 45 notes in total. How much
money does he have?
Ans: _____________________
A B
C D
I J
106
24. What are the common factors of 18 and 45?
Ans: _____________________ 25. Kiara walked 55m in every minute. It took her 18 minutes to walk from home to
school. How far is her school from her home?
Ans: _____________________ Questions 26 to 30 carry 2 marks each Show your workings clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 26.
In 2009, Raphael is 9 years old. His father is 38 years older than he is. In how many years will his father’s age become three times his age?
Ans: _____________________ 27. Find the volume of a bottle if 36% of it can fill a 72ml cup completely.
Ans: _____________________
107
28. Find the maximum number of 40 cm cubic boxes that can be stored in a storeroom that is 5m wide, 6m long and 3m high.
Ans: _____________________29. Yvonne weighs 42.5 kg. Her bag weighs 4750g. If Yvonne wears her bag and stands
on an electronic scale, what value will the scale indicate? The scale expresses mass in kg.
Ans: _____________________30. Antoine needed to walk 1
52 km. He had walked some distance and still had to walk
for another 43 km. How far had he walked? Give your answer in meters.
Ans: _____________________
108
Semestral Assessment 2: Mock Paper 3 Paper 2 (Duration: 1 hr 40 mins)
Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. A water tank has dimensions 60 cm x 25 cm x 30 cm. Uncle Tiong is using a 3l pail
to fill the tank. How many times does he use the pail?
Ans: _____________________ 2. Study the figure below carefully.
ABCD is a square piece of paper. If I fold the piece along the line IK and then cut away along the lines IJ and JK, what is the area of the remaining piece?
Ans: _____________________
A B
C D
I
K
J A I
J
K
C D25 cm
18 cm
2 cm
109
3. Mrs. Ong bought 2 kg of grapes at a price of $3.20 per 100g. Mrs. Choo bought the same kind of grapes with a discount of $0.70 per 100g. She paid the same amount of money as Mrs. Ong did. How many more kilograms of grapes did Mrs. Choo buy compared to Mrs. Ong?
Ans: _____________________4. Fill in the blank with an appropriate number to complete the pattern.
1 , 4 , 9 , ________ , 25
Ans: _____________________5. The average distance that Mei Mei jumped over 5 attempts is 145 cm. The average
distance of the first 3 attempts is 155 cm. What is the average distance of the last 2 attempts?
Ans: _____________________
110
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. The figure below is not drawn to scale. ∠MNQ is 29o. MNPQ is a rhombus.
a) Find ∠ NMQ. b) If MN = NO, find ∠ NOP.
Ans: _____________________[4] 7. Guo Qi drank
51 of the carton of milk on the first day. Over the next two days he
drank 75% of the remaining milk. There was still 750ml of milk left. What is the volume of the carton of milk? Express your answer in liters.
Ans: _____________________[4]
M
N
P
Q O
111
8. An apple drink is made by mixing apple syrup and plain water in the ratio 2: 5. How many milliliters of apple syrup is needed to make 1.4 l of apple drink?
Ans: _____________________[3]9. Study the pattern below. The shapes are made by using toothpicks.
a) How many toothpicks are needed to make 5 shapes? b) How many shapes can be made using 258 toothpicks?
Ans: _____________________[4]10. The number of stickers that Pamela had is 40% of the number of stickers that Zoe
had. If the two children had 952 stickers altogether, how many stickers did Zoe have?
Ans: _____________________[3]
1 shape 2 shapes 3 shapes
112
11. Bala’s weight is 65 that of Chek Khoon and Chek Khoon is 4kg more than Darren. If
the average mass of the three boys is 44 kg, what is the mass of Chek Khoon?
Ans: _____________________[4] 12. A restaurant had sold 3 times more honey roasted chicken than black pepper chicken.
If 90 less honey roasted chicken had been sold, the number of black pepper chicken would have been twice the number of honey roasted chicken. a) How many honey roasted chickens were sold? b) How many black pepper chickens were sold?
Ans: _____________________[4] 13. If Andy buys 3 story books and 5 comic books, he will have $24 left. If he buys 5
story books and 3 comic books, he will need $16 more. Given that a comic book is sold at $18, how much does Andy have?
Ans: _____________________[4]
113
14. In the figure below, 1, 2, 3, 4 and 5 are all squares. What is the ratio of the total area of 1 and 2 to the total area of all the squares?
Ans: _____________________[4]15. Plastic tables were sold at $75 each and wooden tables were sold at $80 each. There
were 150 plastic tables in a shop at first. After selling all the tables, the shop received $12850. How many wooden tables were sold?
Ans: _____________________[4]16. In a class,
31 of the pupils like basketball,
41 of the remainder like chess, the rest like
swimming. There are 10 pupils who like chess. Each pupil only likes one sport. What is the number of pupils who like either chess or basketball?
Ans: _____________________[4]
1
3 2 4 5
114
17. Mr. Wong hired a transport company to deliver some glass products for him. For every safely transported product, the company charges $16.5. For every product that was broken on the way, the company compensates $66. Mr. Wong was charged $15,015 for the delivery. 90% of the products were delivered safely. How many products were broken on the way?
Ans: _____________________[4] 18. Mindy and Ryan had an equal amount of cookies. Each day, Mindy ate 23 cookies
and Ryan ate 8 more cookies than Mindy. a) How many days had passed when Mindy had 149 cookies left and Ryan had 53
cookies left? b) How many cookies did each of them have at first?
Ans: _____________________[4]
115
Semestral Assessment 2: Mock Paper 4 Paper 1 (Duration: 50 mins)
Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided. 1. An equilateral triangle and a right-angled triangle are placed next to each other as in
the figure below (not to scale). HAE is a straight line. Find ∠ EHB
(1) 30o (2) 60o
(3) 120o (4) 150o ( ) 2. Which of the following has the largest value?
(1) 25% (2) 51
(3) 0.26 (4) 1000
24 ( )
3. The average mass of a bag of rice and 3 bags of flour is 14 kg. If the bag of rice weighs 17 kg, what is the average mass of the three bags of flour?
(1) 6 kg (2) 8 kg (3) 10 kg (4) 13 kg ( ) 4. Amanda had 6 m of ribbon. She used 60% of the ribbon on the first day and of the
remainder on the second day. How many centimeters of ribbon did she have left? (1) 60 cm (2) 90 cm (3) 180 cm (4) 240 cm ( )5. Sarimah bought two similar pizzas. She saved
32 of a pizza for her mother and
shared the rest among herself and 5 friends. What fraction of a pizza did each child get?
(1) 31 (2)
92
(3) 154 (4)
152 ( )
A
B
C
H E
116
6. The table below shows the number of maximum marked papers scored by pupils in a class from August to November
Month Number of maximum marked papers August 33
September 49 October ?
November 52 The class scored an average of 46 maximum marked papers a month. How many maximum marked papers were there in October?
(1) 48 (2) 50 (3) 134 (4) 184 ( ) 7. Knowing that 483 x 7 = 3381, find the value of 483 x 0.07 (1) 3381 (2) 338.1 (3) 33.81 (4) 3.381 ( ) 8. Sally bought an LCD with a 30% discount and 7% GST for $749. What is the
original price of the LCD? (1) $700 (2) $1000 (3) $1042 (4) $1200 ( ) 9. Below is the parking charges at the car park of a shopping centre
First 2 hours $2.50 Subsequent 30 minutes or part thereof $1.50
Kelvin entered the car park at 3.45 pm. He paid $9.50 for parking charges when leaving the car park. What is the latest time possible that he left the car park?
(1) 7.15 pm (2) 7.45 pm (3) 6.15 pm (4) 6.45 pm ( ) 10. Josh wrote down two numbers on a piece of paper. 40% of the larger number is 84.
The difference between the two numbers is 78. What is the smaller number? (1) 288 (2) 34 (3) 132 (4) 210 ( ) 11. How many eighths are there in ?
(1) 13 (2) 16 (3) 24 (4) 26 ( )
117
12. ABCD is a parallelogram. ∠ABD = 47o. ∠ BCD = 105o. What is ∠ BDA?
(1) 28o (2) 38 o (3) 152 o (4) 208 o ( ) 13. 3 sticks have a total length of 192 cm. What is the average length? (1) 32 cm (2) 64 cm (3) 96 cm (4) 576 cm ( ) 14. There are 184 red, white and green marbles altogether. The number of green and
white marbles is 54. There are 150 red and white marbles altogether. What fraction of the total number of marbles is the number of white marbles?
(1) 365 (2)
465
(3) 515 (4)
975
( )15. Mrs. Liu made 4.82 l of lemon tea in a container. She poured them into 8 cups, each
of which had a capacity of 352 ml. What was the volume of lemon tea remaining in the container?
(1) 2.004l (2) 2.04l (3) 2.24l (4) 2.4l ( ) Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 16. In an aquarium, the ratio of the number of goldfish to that of clownfish is 2: 7. The
ratio of the number of clownfish to that of angelfish is 5: 2. What is the ratio of the number of goldfish to that of angelfish?
Ans: _____________________
A B
C D
118
17. Calculate 343
917
× . Remember to simplify your answer.
Ans: _____________________ 18. Uncle Tan kept some milk in the fridge. After his children drank 1
21 l of milk, there
was 165 l left. How much milk was there in the fridge at first?
Ans: _____________________ 19. If a pen costs $1.20 and I have $11, how many pens can I buy at most?
Ans: _____________________ 20. The following diagram is not drawn to scale. Find ∠ i, given that WSX and YSZ are
straight lines.
Ans: _____________________
i 87o
154o
W Z
X
Y
S
119
21. The average of the two numbers A and B is 80. The average of those two numbers and a third number C is 85. What is the value of C?
Ans: _____________________22. 9 x 5.6 = 5.6 + 5.6 + 5.6 + 5.6 x A
Find the value of A.
Ans: _____________________23. Benjamin received 72 marks for Mathematics, 83 marks for Physics and 67 marks
for Chemistry. What is his average score for the three subjects?
Ans: _____________________24. What are the common factors of 24 and 36?
Ans: _____________________
120
25. A convenience store collects an average of $5839 a day. How much does the store collect in a week?
Ans: _____________________ Questions 26 to 30 carry 2 marks each Show your working clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 26.
The sum of the area of all the faces of a solid cube is 54 cm2. What is the volume of the cube?
Ans: _____________________ 27. A journey 12.8 km long was divided into 9 parts. Of these 9 parts, there were 5 parts
that were 0.91 km long each and 3 parts that were 1.32 km each in length. What was the length of the remaining part?
Ans: _____________________
121
28. There are 10 200 people in a village. 30% of the villagers are children and the rest are adults. 40% of the adults are working outside the village. How many adults are working outside the village?
Ans: _____________________29. Calculate ∠ ABD in the figure below. Note that it was not drawn to scale.
Ans: _____________________30. Lucy bought 6 similar skirts and 4 similar shirts for $162. The price of 2 shirts is
equal to the price of 3 skirts. How much is a shirt?
Ans: _____________________
A
B C
D93o
43o37o
122
Semestral Assessment 2: Mock Paper 4 Paper 2 (Duration: 1 hr 40 mins)
Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. Stanley withdrew some money from the bank to purchase some goods. He spent
$1144 to buy a new laptop and 41 of the remainder on a game console. He still had
half of what he withdrew from the bank. How much did Stanley withdraw from the bank?
Ans: _____________________ 2. 5 similar bags of potatoes have a total mass of 86.25 kg. A porter can carry a
maximum of 60 kg. How many porters are needed to carry 20 of such bags?
Ans: _____________________ 3. The distance from Mary’s house to her grandmother’s house is 14 km. Mary had
cycled 3.115 km from her home to her grandmother’s. What percentage of the journey had she covered?
Ans: _____________________
123
4. In the figure below, there are two adjacent squares and the shaded shape overlaps both. The larger square has a side of 36 cm and the smaller square has a side of 20 cm. What is the area of the shaded shape?
Ans: _____________________5. The ratio of Charles’ stamps to Mark’s stamps to Shawn’s stamps is 3: 7: 9. Mark
has 168 stamps. a) How many stamps do the boys have altogether? b) After Mark gives some stamps to Charles, the two boys have the same number of stamps. How many stamps did Mark give Charles?
Ans: _____________________
124
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. There are some flowers in a garden. 0.2 of the flowers are daisies and the remaining
flowers are roses. 75 of the roses are red and the rest are white. There are 24 more red
roses than white roses. a) How many white roses are there? b) How many daisies are there?
Ans: _____________________[4] 7. In the figure below, AB = BC = CA. FCD, BCE and ACG are straight lines. The
figure is not to scale. Find a) ∠ CED b) ∠ ACF
Ans: _____________________[4]
A
F
C
E G
B
D
42o
31o
125
8. Mrs. Foo bought 3.3 kg of fish at $1.59 per 100g, 2.8 kg of beef at $4.89 per 500 g, and 7 packages of vegetable at $0.86 per package. How much did she pay for all the goods?
Ans: _____________________[4]9. The ratio of the number of curry puffs to the number of cakes in a shop is 1: 4. A
curry puff costs $2. Each cake is sold at $5. The total amount that the shop will receive from selling all the cakes and curry puffs is $1892. How many cakes are there?
Ans: _____________________[4]10. A shop had 280 pens. 70% of the pens were blue. A week later, a number of blue
pens were sold and 60% of the remaining pens were blue. How many pens altogether were there in the shop a week later?
Ans: _____________________[4]
126
11. A textbook and a bag cost $30. A textbook and a comic book cost $22.5. David bought 4 textbooks, 2 bags and 1 comic book for $100. What is the cost of a comic book?
Ans: _____________________[3] 12. Marion and Nina had some beads in the ratio 5: 7. If Marion gave Nina 24 beads,
Nina would have three times as many beads as Marion had. How many beads did Marion have at first?
Ans: _____________________[4] 13. What fraction of 4l is 350ml? Express your answer in the simplest form.
Ans: _____________________[3]
127
14. 40% of the fruits in an orchard are apples, 80% of the remainder is oranges and the rest are mangoes. There are 648 more oranges than apples. After some apples have been sold, 10% of the remaining fruits in the basket are apples. How many apples have been sold?
Ans: _____________________[4]15. A salesman’s salary is $1575 a month. Apart from the salary, he earns a commission
of $1.20 for every $5 of sales he makes. In 8 months, the total sales he makes is $72000. What is his average earning a month over these 8 months?
Ans: _____________________[4]16. A rectangular tank measures 60 cm by 43 cm by 24 cm is filled with water up to
31
its height. At 1.p.m, water from a tap started to flow into the tank at a rate of 1.8 l per minute. How much water is in the tank at 1.20 pm?
Ans: _____________________[4]
128
17. Three identical squares, each is made up of 9 identical squares, are overlapped as in the figure below. Find the ratio of the shaded portion to the total area of the figure.
Ans: _____________________[4] 18. Joanne thinks of a number. The difference between thrice that number and of that
same number is 36 more than that number. What is the number that Joanne thinks of?
Ans: _____________________[4]
129
Semestral Assessment 2: Mock Paper 5 Paper 1 (Duration: 50 mins)
Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided. 1. The figure below is made up of 2-cm cubes. How many more cubes are needed to
make it into a larger cube with sides 6 cm?
(1) 10 (2) 12 (3) 17 (4) 20 ( )2. Johan has some coins. 12.5% of them are 20 cent coins.
83 of them are 10 cent coins.
The remainders are 50 cent coins. All the 10 cent coins together are worth $2 more than all the 20 cent coins together. How many 50 cent coins does Johan have?
(1) 40 (2) 80 (3) 120 (4) 160 ( )
3. The ratio of the number of orangees to the number of mangoes in a basket is 4: 5. If there are 5 more mangoes than oranges, how many oranges are there in the basket?
(1) 20 (2) 25 (3) 45 (4) 5 ( ) 4. Which of the following statements is true?
(1) If one of the angles in an isosceles triangle is 60o, the triangle is equilateral.
(2) A rhombus has all the properties of a square.
(3) No angle can be 60o in a right-angled triangle. (4) The sum of all the angles in a four-
sided figure is always different. ( )
130
5. Three pupils shared a number of books. Katrina contributed 0.5 of the number of
books, Melisa contributed 103 and Patrick contributed the rest. What percentage of
the number of books is Patrick’s contribution? (1) 20% (2) 35% (3) 53% (4) 80% ( ) 6. Sally read 40% of her book and had 120 pages left. How many pages were there in
the book? (1) 200 (2) 280 (3) 300 (4) 520 ( ) The following graph shows the number of students in different grades in a secondary school. Study the graph carefully and answer the questions below.
7. What is the difference between the number of Sec 3 and the number of Sec 1
students? (1) 30 (2) 40 (3) 70 (4) 80 ( ) 8. What fraction of the total number of students is the number of Sec 1 students?
(1) 5714 (2)
5716
(3) 11429 (4)
11425
( )
131
9. Sabrina planned to complete her drawing in 54 hours. However, she only used
43 of
the time intended. How much time did she save?
(1) 201 h (2)
51 h
(3) 2011 h (4)
53 h
( ) 10. 3 boys shared 1
41 of a pizza equally. What fraction of a whole pizza did each boy
get?
(1) 125 (2)
512
(3) 121 (4)
415
( ) 11. Find the missing value
8.507 = ________ x 1000 ÷ 100 (1) 0.8507 (2) 8.507 (3) 85.07 (4) 850.7 ( ) 12. Which of the following is not equal to
95 ?
(1) 2715 (2)
8145
(3) 3625 (4)
6335
( ) 13. The average of 3 numbers is 27. Two of the numbers are 19 and 25. What is the third
number? (1) 17 (2) 37 (3) 59 (4) 81 ( ) 14. Find a number between 40 and 50 that has a remainder of 2 when divided by either 4
or 5. (1) 42 (2) 46 (3) 47 (4) 49 ( )
132
15. Study the figure below. ABC is an isosceles triangle at A, CDE is an isosceles triangle at D. Find the value of ∠x. The figure is not to scale.
(1) 25o (2) 36o (3) 55 o (4) 70 o ( ) Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 16. Alice bought some chocolates. She saved
31 of the chocolates for her brother. She
divided the rest of the chocolates equally among herself and her 5 friends. What fraction of the total number of chocolates did each of Alice’s friends get?
Ans: _____________________ 17. Mr. Smith had dinner at a restaurant. The cost of the food was $150. If he had to pay
7% GST and 10% service charge on the cost of the food, how much more did he have to pay?
Ans: _____________________
A
B C
D
E
144ox
133
18. Calculate the sum of the first 7 multiples of 9 that are larger than 90.
Ans: _____________________19. Express 20.08l in litres and millilitres.
Ans: ________l________ml20. A container measures 20 cm by 15 cm by 10 cm. Another container measures 15 cm
by 7 cm by 5 cm. What is the total volume of the two containers?
Ans: _____________________21. Draw the corresponding height to base BC for the triangle ABC below.
22. Calculate 199 – 53 x 2 + 14 ÷ 7
Ans: _____________________
A
C B
134
23. What is the smallest positive common multiple of 36 and 48?
Ans: _____________________ 24. Calculate 2215 ÷ 9, corrected up to 2 decimal places.
Ans: _____________________ 25. How many seconds are there in 1
31 hours?
Ans: _____________________ Questions 26 to 30 carry 2 marks each Show your working clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 26.
Find the missing numbers. _____ : 18 : 22 = 28 : ______ : 77
Ans: _____________________
135
27. The table below shows the prices of air ticket to country X
AIR TICKET TO COUNTRY X
Ticket class Adult
(price per person)
Child (below 12 years old)
(price per person)
Economy $900 $450
Business $1200 $600
First class $1600 $800 Mr. Mohammed, his wife, 9-year-old daughter and 15-year-old son travelled to country X. How much did they pay altogether if they chose Business class?
Ans: _____________________ 28. 10% of a number is less than
52 of that number by 33. What is the number?
Ans: _____________________
136
29. Refer to the figure below. Three identical squares are arranged in a row. If the area of each square is 144 cm2, what is the perimeter of the rectangle that is made by the three squares?
Ans: _____________________ 30. The time on the clock is exactly 9 a.m. When the minute hand turns 450o clockwise,
what time will it be?
Ans: _____________________
137
Semestral Assessment 2: Mock Paper 5 Paper 2 (Duration: 1 hr 40 mins)
Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1. Swee Swee had a saving account of $30 000 in a bank. The interest rate is 3.75% per
year. How much interest will Swee Swee receive after a year?
Ans: _____________________2. Construct a line that goes through M and is perpendicular to AB.
3. Below is the menu at a restaurant: Appetizer Main course Dessert
Tom Yam soup Grilled fish Banana split Spring roll Beef stew Ice cream
Mango salad Roasted chicken Cheese cake How many different combinations could a person choose if he wanted to have an appetizer, a main course and a dessert?
Ans: _____________________
M .
A
B
138
4. What is the average of the first 8 multiples of 9?
Ans: _____________________ 5. Nicolas bought
54 kg of meat and cooked
107 kg for dinner. What is the quantity of
meat that has not been cooked? Give your answer in decimals.
Ans: _____________________ For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6. Mrs. Khoo mixed 6l grape syrup with 9l of water. After that, she used some
rectangular containers to store the drink. Each container measures 12 cm by 7 cm by 5 cm. Each container is filled completely. a) How many containers could be filled? b) What is the volume of the drink that was left over?
Ans: _____________________[4]
139
7. Find ∠ x in the figure below. AOB, COD, EOF are straight lines.
Ans: _____________________[4]8. In the figure below, the breadth of the rectangle is
43 its length. What is the area of
the shaded portion? The figure is not drawn to scale.
Ans: _____________________[4]
6.5 cm
17.5 cm
BA O
C
DE
F
78o 33o
x
140
9. Michael participated in a swimming competition. On average, he completed a lap in 3.2 minutes. He needed to swim 8 laps to complete the race. What was the total time he took to complete the race? Give your answer in minutes and seconds.
Ans: _____________________[3] 10. A farmer planted 400 flowers in his garden.
85 of them were roses. The farmer then
sold some roses. The remaining number of roses was then 83 of the total number of
flowers remained in the garden. How many roses were sold?
Ans: _____________________[3] 11. The figure below is made up of two adjacent squares and a shaded triangle. The
smaller square has an area of 16 cm2. The larger square has an area of 49 cm2. What is the area of the shaded triangle?
Ans: _____________________[4]
141
12. Find ∠z in the following figure. AOB and COD are straight lines. ∠y = ∠z. ∠x = 12o. The figure is not to scale.
Ans: _____________________[4]13. Peter studied Physics for 2
21 hours on Monday. On Tuesday he spent some time to
continue his Physics study. On Wednesday, he spent twice as many hours as on Tuesday to finish his Physics lesson. Over those 3 days, Peter spent an average of 138 minutes a day studying Physics. In how many hours did Peter study Physics on Wednesday?
Ans: _____________________[4]
A
B C
D
O
142o
xy z
142
14. Jordan is a basketball player. On the first match of the 2009 league he scored 7 goals. In every later match he scored 2 more goals than the previous match. He played 7 matches altogether in the league.
a) How many goals did he score in total? b) What is his average number of goals per match?
15. Nelson’s height is 152 cm. Nelson’s sister is 0.2 m shorter than he is. What fraction
of Nelson’s height is his sister’s height? Express your answer in the simplest form.
Ans: _____________________[4] 16. In a volleyball tournament, there are 10 school teams. Each team has to play one
match against each of the other teams. How many matches will be played between the teams?
Ans: _____________________[4]
143
17. Mr. Teo bought a table and two chairs for $300. The two chairs were sold at the same price. The table’s price is twice as much as a chair’s. What is the price of the table?
Ans: _____________________[4]18. Peter wrote all the number from 1 to 100 continuously
1234567891011121314……979899100 How many digits did he write?
Ans: _____________________[4]
144
Answers to Semestral Assessment 1: Mock Paper 1 Paper 1 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 3 4 4 3 2 3 3 1 2 2 2 3 1 4 2
16 Nine million eighty thousand and eleven 17 8 883 008, 8 880 003, 880 300, 88 380 18 3 906 = 3 000 + 900 + 6
7 503 906 = 7 000 000 + 500 000 + 3 906 The value of A is 500 000
19 The first 6 multiples of 7 are 0, 7, 14, 21, 28 and 35. 0 + 7 + 14 + 21 + 28 + 35 = 105 The sum of the first 6 multiples of 7 is 105
20 945 21 60
22 1095
24 5 976 201
25 3 147 682 26 If 90 pieces were in $100 notes, the money would be
90 x 100 = 9000 The number of $50 notes (9000 – 5250) ÷ 50 = 75 The cashier received 75 notes of $50 from Mr. Ben.
27 10 tables and 20 chairs cost $650 Thus 20 tables and 40 chairs cost $1300 20 tables and 10 chairs cost $850 Therefore 30 chairs cost $450 The cost of a chair is 450 ÷ 30 = 15 The cost of 1 table is (650 – 20 x 15) ÷ 10= 35 The cost of 1 table and 1 chair is 35 + 15 = 50 The cost of one table and one chair is $50
23
The two shaded triangles at the bottom are equal to the two unshaded triangle at the top. So they and the shaded trapezium add up to a rectangle that is
31
of the big square. The shaded area is 31
of the
total area.
28 850 + 620 + 930 = 2400
2400x41
=600, 2400 x121
=200
2400 – 600 – 200 = 1600 He had 1600 nails left.
29 90 x 1 ÷ (105 – 90) = 6 It takes 6 minutes.
30
One equal part is (2892 – 1572) ÷ 6 = 3112 Each of them had $3112 at first
Paper 2 1
Value of 1 equal crossed part (17245 – 12 795) ÷ 5 = 890 Team B collected $890 890 x 6 = 5340 Team D collected $5340
3
The total price of 1 kg of each type 99.60 ÷ 6 = 16.60 The price of 1 kg of chicken (16.60 – 5 – 2) ÷ 3 = 3.20 The price of 1 kg of beef 3.20 + 5 = 8.20 (3.20 + 8.20) x 6 = 68.40 She spent $68.40 on the beef and the chicken.
2 83
41
831 =−− ,
304114 83 =÷
The shop has 304 pairs of gloves in total.
4 One cheese cake: 6.90 ÷ 3 = 2.30 One curry puff: 5.20 ÷ 4 = 1.30 25 ÷ 2.30 = 10.87 => 10 cheese cakes 25 ÷ 1.30 = 19.23 => 19 curry puffs 19 – 10 = 9 (a) Timmy could buy 9 more curry puffs than cheese cakes. (b) number of cheese cakes and curry puffs altogether is =129.6 /(2.3+1.3) x 2 = 72
Equal areas
Equal areas
145
5 197g > 30g => $1.00 for the first 30g, left 197g – 30g = 167g. 167g > 50g => $1.70 for the next 50g, left 167g – 50g = 117g. 117 ÷ 25 = 4.68 => pay for 5 steps of 25g. $0.35 x 5 = $1.75 $1.00 + $1.70 + $1.75 = $4.45 Peter has to pay $4.45
7 Total of Peter’s and Jordan’s stickers: 924 x 2 = 1848Peter’s stickers: (1848 + 232) ÷ 2 = 1040 Jordan’s stickers: 1040 – 232 = 808 Albert’s stickers: 172 + 1040 = 1212
32
1212808 =
Jordan’s stickers are 32 of Albert’s.
6
8 Three years later:
Dan’s age: 34 ÷ (3 – 1) = 17 Dan’s father’s age: 17 x 3 = 51 Now: Dan’s father’s age: 51 – 3 = 48 Dan’s father is 48 years old now.
9 From 1 to 9: 9 x 1 = 9 From 10 to 99: 90 x 2 = 180 From 100 to 150: 51 x 3 = 153 9 + 180 + 153 = 342 342 steel digits are necessary.
10
A = 36 – 13 – 8 – 5 = 10 cm B = 7 + 9 – 4 – 5 = 7 cm 7 + 10 + 9 + 5 + 5 + 8 + 7 + 13 + 4 + 36 = 104 cm The perimeter is 104 cm
14
11 10 x 7 = 70 m2 70 x 15 = $1050
12 The difference in the number of bags 60 – 25 = 35 bags The mass of one bag (6790 – 4655) ÷ 35 = 61 g The mass of the box is 6790 – 60 x 61 = 3130g = 3.13 kg The box weights 3.13 kg.
13 $1 215 x 116 = $140 940 The agency received $140 940
15
If Alex had 224 more stamps, there would be five equal parts. Value of one equal part (2151 + 224) ÷ 5 = 475 Carl had 475 stamps.
16 The figure has 5 lines of symmetry
17 Tank’s volume: 90 x 40 x 15 = 54000 cm3 = 54l 18112 2
1 =× l 54 – 18 = 36l Rate of tap B l412 3
1 =× in a minutes Total rate 12 + 4 = 16l in a minute Time taken: 36 ÷16 = 2.25 minutes = 2 minutes 15 seconds.
18 4 trees in the corners. Along the length: 49 ÷ 7 – 1 = 6 trees. Along the breadth: 35 ÷ 7 – 1 = 4 trees. Total: 6 x 2 + 4 x 2 + 4 = 24 trees. There were 24 trees in total
5 cm
8 cm
13 cm
36 cm
9 cm
7 cm
4 cm
A B
5 cm
146
Answers to Semestral Assessment 1: Mock Paper 2 Paper 1 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 3 1 3 2 1 2 2 4 4 2 3 2 2 3 1
17
Cost of a child ticket 49 ÷ (2 + 5) x 2 = 14 A child ticket costs $14
18 $179 501 19 965312 20
107
41
53
41 )1( =−−
He spent 107 of his money
16
21 Number of children: 144 ÷ 3 = 48
Total: 48 x 5 = 240 There were 240 people in the audience
22
12 x 9 ÷ 2 = 54 cm2 The area is 54 cm2
24 0.14 + 0.8 + 5 + 0.032 = 5.972
23277
97 3 =÷
Each child got 277 of the cake
25 13:5:12:1 513
53 ==
27 The first team will play 3 matches with the 3 remaining teams. The second team already played 1 match with the first team, so it will play only 2 matches with 2 remaining teams. Similarly, the third team will play 1 match with the last team. The last team already played 3 matches with the 3 teams. 3 + 2 + 1 = 6, There are 6 matches in total.
26
28
1253 hours = 3 hours 25 minutes
7:45 + 3:25 = 11:10 Selina finished the task at 11:10 PM
30 x = 180o – 90o – 58o = 32o y = 180o – 33o – 80o = 67o y – x = 67 o – 32o = 35o , The difference is 35o
29 5:25 – 3:40 = 1:45 Vanessa parked her car for 1 hour 45 minutes. So she will pay $2.50 for the first hour and $1.90 for the second hour. $2.50 + $1.90 = $4.40 Vanessa paid $4.40
Paper 2 1 Total audience: 4500180 25
1 =÷ People came by train:
3195)1(4500 41
251 =−−×
There were 3195 people who came by train
2 108 ÷ 9 = 12 (12 + 9) x 2 = 42 The perimeter is 42m 126 ÷ 42 = 3 She paid $3 for each meter of the fence.
4 First finish line: 30m, Second line: 60m Third line: 120m, Fourth line: 240m Peter ran (30 + 60 + 120 + 240) x 2 = 900 m in total.
3 From Mon to Fri (5 days), Harry travelled on route 1. Total distance on route 1: 4.3 x 5 = 21.5 km Length of route 2: 8.2 – 4.3 = 3.9 km. Total distance travelled on route 2: 3.9 x 2 = 7.8 km Total distance: 21.5 + 7.8 = 29.3 km Harry travels 29.3 km to the basketball court in a week.
6 a) Length: 7 + (7 + 3 + 7) + 7 = 31 cm b) Breadth: 7 cm Area: 31 x 7 = 217 cm2
5 a) Least visited month: Sep, 1200 visitors. Most visited month: Dec, 1900 visitors. Fraction 1912
19001200 =
b) Children visitors in July: 12001800 32 =× . Number of girls: 1200 ÷ 3 = 400
M
N
147
7 Cost of a toy robot is 2 times that of a cake. Cost of 18 cakes is 18 ÷ 2 = 9 times that of a toy robot. Therefore, with the amount spent, Jeffery could have bought 21 + 9 = 30 toy robots. With 5
3 of his money, he could by 30 toy robots
With 52 of his money, the number of toy robots he
could buy is 30 ÷ 53 x 5
2 = 20 Jeffery could buy 20 more toy robots with the remaining money.
8 If each girl had 7 strawberries, there would be 4 strawberries extra. To give each girl one more strawberry so that each would have 8 strawberries, the 4 extra strawberries would be given to 4 girls first. There were 4 strawberries short so there were 4 girls left. Therefore, there were 8 girls. Number of strawberries 7 x 8 + 4 = 60 a) There were 60 strawberries b) There were 8 girls
9 Total number of toy cars that Jason and Malik had 56 x 14
11 = 44 Number of toy cars that Jason had 44 ÷ (7 + 15) x 15 = 30 Number of toy cars that Malik had 44 – 30 = 14 Total number of toy cars 30 + 14 + 56 = 100 a) Jason had 30 toy cars b) They have 100 toy cars altogether
10 Each notepad is $1.1 more than a pen. So 7 notepads is $7.7 more than 7 pens Cost of a pen (33.3 – 7.7) ÷ (7 + 9) = 1.6 9 x 1.6 = 14.4 Mary paid $14.40 for the pens.
11 1 notebooks = 3 files 10 notebooks = 30 files Cost of a file 85 ÷ (30 + 4) = 2.5 Cost of a notebook 2.5 x 3 = 7.5 The price of a notebook is $7.50
12 a) Area of the shaded part: 30 x 10 ÷ 2 = 150 cm2
Total area: 30 x (10 + 18) ÷ 2 = 420 cm2
Area of the shaded part: 420 – 150 = 270 cm2 b) 14
51810
10 =+ of the whole figure is shaded. 13
Value of one equal part (90 + 30) ÷ 3 = 40 Number of apples 40 x 2 + 30 = 110 110 – 90 = 20, There were 20 more apples than oranges.
14
Body = Head + Tail, 3B = 8 + B + 8 = B + 16 B = 8 Body = 8 x 3 = 24, Tail = 8 + 8 = 16 8 + 16 + 24 = 48m The whale skeleton is 48m long
16 Total amount of sugar: 500 + 600 + 800 + 900 + 1000 = 3800g The total mass of sugar in the sold packages must be a multiple of 3. Mrs. Liu did not keep packet A since she kept more than 500. So she must have kept packet C.
15 At Clementi: Number of girls 114 ÷ 2 = 57 Number of boys 57 x 3 = 171
Number of children 171 + 57 = 228 Number of adults 228 ÷ 6 x 5 = 190 Number of men 190 ÷ 5 = 38 Number of women 38 x 4 = 152 Total number of passengers 228 + 190 = 418 At Dover: The number of male passengers. 171 +5 + 38 = 204 a) There were 418 passengers altogether when the train left Clementi Station b) There were 204 male passengers when the train left Dover station.
18
From the diagram 7 = 13u ÷ 2 – 3u, u = 2 Mrs. Goh’s age 7 years ago 2 x 16 = 32, 32 + 7 = 39 Mrs. Goh is 39 years old now.
17 There are 3 ways to arrange the first pupil: Alex, Carol and Dean (Benny does not stand at the first position). If Alex is at the first position, there are 2ways to arrange the second position (Benny and Carol) since Alex is not standing next to Dean. For each of the case, there are 2 ways to arrange the remaining 2 pupils. If Carol is at the first position, Benny cannot be at the second position since Alex and Dean have to be next to each
148
other then. Therefore, there are only two ways to arrange the second position (Alex and Dean). For each of the case, there are only one way to arrange the third and last position, since the third position must be Benny. If Dean is at the first position, there are two ways to arrange the second position (Benny or Carol). For each of the case, there are two ways to arrange the remaining pupils. The number of possible ways is 1 x 2 x 2 + 1 x 2 x 1 + 1 x 2 x 2 = 10 There are 10 ways to arrange these pupils.
Answers to Semestral Assessment 1: Mock Paper 3
Paper 1 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 3 4 1 2 3 3 2 3 3 2 1 3 2 3 4
16
72
751 =− , 35
272
51 =× , 35
8352
721 =−−
490112 358 =÷ , 28490 35
2 =× The calculator cost $28
17 Area of one square: 32 ÷ 8 = 4m2
Side of each square is 2m. Perimeter 32m
18 600 = 2 x 2 x 2 x 3 x 5 x 5 The two page numbers are two continuous factors of 600. 2 x 2 x 2 x 3 = 24, 5 x 5 = 25 The two pages are 24 and 25
19 Total cost 300 – 41 = 259 Cost of 5 boxes of shuttlecocks 259 – 199 = 60 Cost of 1 box, 60 ÷ 5 = 12. Each box is $12.
20 8 + 5 = 13 65 ÷ 13 x 5 = 25 Elizabeth had 25 sweets.
21 X + 1 = Y, Y + Y = 10 + X X + 1 + X + 1 = 10 + X X = 8, Y = 9, 89 + 9 = 98
22
Total number of crayons at first (10 – 4) x 5 = 30 They had 30 crayons altogether at first.
23 300 ÷ 15 = 20 There were 20 pupils. 10 x 20 = 200 Miss Lisa gave the class 200 toy bricks.
24 After David gave Gupta, the amount that Gupta had was 300 ÷ (2 + 1) = 100 The amount Gupta had at first was 100 – 18 = 82 Gupta had $82 at first.
25 225 ÷ 15 = 15 15 x 12.30 = 184.5 Mrs. Tan earned $184.50
26 Area of one triangle: 3 x 4 ÷ 2 = 6 cm2+
Area of 3 triangles:3x6=18 cm2 Area of the square: 4 x 4 = 16 cm2 Area of the rectangle: 4 x 7 = 28 cm2
Total area: 18+ 16 + 28 = 62 cm2
27 Fraction of $10 notes 21
61
311 =−−
Ratio of $2 notes to $5 notes to $10 notes 2 : 1 : 3 Ratio of total amount $2 to that of $5 to that of $10 4 : 5 : 30 Amount of $5 notes 1794 ÷ 39 x 5 = 230 The total value of $5 notes Ali saved is $230
28 89.55410 98
91 ≈=−
Darren had to run 5.89 km more.
29 After 2 hours, Jimmy already made 30 x 2 = 60 paper birds So the time that Philip would take is 60 ÷ (50 – 30) = 3 hours
30 108 ÷ 15 = 7.2, 98 ÷ 15 = 6.53, Therefore the bigger number is 15 x 7 = 105. The smaller number is 105 ÷15 x 2 = 14
Paper 2 1
2419
85
32 47 =× , 8
72419
32 247 =−
The difference in their distances is 2 87 km
2 CN = 96 ÷ 4 x 3 = 72 cm Area of triangle MNC is 72 x 24 ÷ 2 = 864 cm2
3 60 ÷ 4 x 7 = 105l (105 + 60) x 2.50 = 412.50 Mr. Quek paid $412.50
4 Volume of strawberry syrup needed 24 ÷ 6 = 4l Volume of strawberry syrup short: 4 – 1.5 = 2.5l Original volume of water 24 – 4 = 20l New ratio (4 + 2) : 20 = 6 : 20 = 3 : 10
149
5 Ratio of number of units of product A to that of
product B 14 : 3 Ratio of total amount received from product A to that of product B 14 x 10 : 3 x 4 = 35 : 3 Total amount from selling product A 11400 ÷ (35 + 3) x 35 = 10500 Total amount from selling product B 10500 ÷ 35 x 3 = 900 Number of product A 10500 ÷ 10 = 1050 10500 – 900 =9600 a) He sold 1050 units of product A b) The difference between the amount of money collected from product A and B is $9600
6 Fraction of stickers left after making scrapbooks
32
311 =−
Fraction of stickers given to friends 94
32
32 =×
Fraction of stickers each friend received 274
94 3 =÷
Fraction of stickers left 92
94
311 =−−
Number of stickers at first 42 ÷ (9 – 2) x 9 = 54 Each friend received 854 27
4 =× stickers
8 189 x 55 + 17 = 10 412 The number is 10 412
9 31
125
31 324 =××
3 hrs 20 mins Mr. Ong worked with his computer for 3 hours 20 minutes
7 Number of 20-cent coins that Suriyana had 192 ÷ (3 + 5) x 3 = 72 Number of 50-cent coins that Suriyana had 192 – 72 = 120 Suriyana had 72 twenty-cent coins and 120 fifty-cent coins. Fahan’s total number of coins:
48192 41 =× coins
Number of 20-cent coins Fahan had 48 ÷ 3 = 16 coinsNumber of 50-cent coins Fahan had 16 x 2 = 32 coinsa) Ratio of the number of 20-cent coins Suriyana had to the number of 50-cent coins that Fahan had 72 ÷ 32 = 9:4 b) Ratio of the amount of money that Suriyana had to the amount of money that Fahan had (72 x 20 + 120 x 50) : (16 x 20 + 32 x 50) = 31 : 8
10
1 equal part = 5 x 4 = 20 Tom: 20 + 5 = 25 Jerry: 20 x 2 – 5 = 35 a) Tom had $25 b) Jerry had $35
11 Cost of a pen in box A: 14.70 ÷ 16 ≈0.92 Cost of a pen in box B: 22.50 ÷ 24 ≈ 0.94 Box A is the cheaper buy
13 The length of the shortest side: 300 ÷ 5 x 2 = 120 cm The length of the last side: 300 ÷ 5 x 4 = 240 cm Perimeter 120 + 240 + 300 = 660 cm
14 2019
154
143
132
1 ... ×××× ++++
209
201
21
201
191
51
41
41
31
31
21 ... =−=−+−+−+−=
12 a) The first person shakes hand with the other 2 people. There are 2 handshakes. The second person already shook hand with the first, so there is one more handshake. The last person already shook hand with the other two people. The number of handshakes is 2 + 1 = 2 b) Similarly, the number of handshakes when there are 5 people is 4 + 3 + 2 + 1 = 10 c) N umber of handshakes when there are 10 people is 9 + 8 + 7 + 6 + 5 + 4+ 3 +2 + 1 = 45
15 85
831 =− , 768480 8
5 =÷ The total distance from A to B is 768 km
16 Base area: 5 x 7 = 35 m2 Depth: 105 ÷ 35 = 3 m The tank’s depth is 3 m.
17 (14 + 26) x 11 ÷ 2 = 220 cm2
18 If all the animals were dogs, the number of legs would
have been 4 x 36 = 144 Number of chickens (144 – 100) ÷ 2 = 22 There are 22 chickens.
150
Answers to Semestral Assessment 1: Mock Paper 4 Paper 1 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 2 1 2 2 2 3 3 2 3 4 4 2 3 4 2
16 Apples : oranges = 2 : 3 = 4 : 6
Apples : bananas = 4 : 9 Oranges : bananas = 6 : 9 = 2 : 3
17
Sylvia made (221 – 121) ÷ 4 = 25 stars Alan made 121 – 25 = 96 stars
18 Fraction of red pens 161
21
81 )1( =−
Fraction of black pens 167
161
211 =−−
Ratio of blue pens to red pens to black pens 8 : 1 : 7 Number of red pens 210 ÷ (7 – 1) = 35 Number of black pens 35 x 7 = 245 Number of blue pens 35 x 8 = 280 Total number of pens 35 + 245 + 280 = 560
19 The difference in the number of cans of coke and soda at first was 48 + 48 = 96 cans Number of cans of coke 96 ÷ (7 – 3) x 3 = 72 There were 72 cans of coke at first.
20 Area of the triangle XYZ 9 x 9 ÷ 2 = 40.5 cm2
Area of the unshaded part (9 – 4.5) x (9 – 2) ÷ 2 = 15.75 cm2 Area of the shaded part 40.5 – 15.75 = 24.75 cm2
2257
45
54
75 ,,, 21 If each boy was given $8, the total of their money
would be 54 + 8 + 8 = 70 Amount that Fahan had at the end 70 ÷ (3 + 4) x 4 = 40 Amount Fahan had at first 40 – 8 = 32 Fahand had $32 at first.
23 2718 32 =÷
There are 27 two-thirds in 18.
24 154254 43 =×
Betsy had 154 slices of fruit in 432 months.
2532
128 =
The value of the box is 3.
27 6 x 7 x 8 = 336, Mr. Lee had 336 boxes. 28 A= 63
2941
125 52 =÷
26 The number of candies in the box is a common multiple of 4 and 7. The smallest multiple of 4 and 7 is 4 x 7 = 28 We have 28 x 2 = 56 < 60 28 x 3 = 84 and 60 < 84 < 100 28 x 4 = 112 > 10 So the number of candies in the box is 84.
29 32 x 7 = 224 224 ÷ 25 = 8.96 9 buses are needed.
30 In one hour pump A can fill 31 the pool and pump B can fill 2
1 the pool.
The time taken for both pump to fill the pool completely is 1 / (1/2 + 1/3)= 1.2 hours。 Paper 2
2 1440 ÷ 80 x 5 = 90 Daniel had worked for 90 hours.
1 The fraction of the number of questions remained after the second day
52
101
211 =−−
Number of days to answer these questions:
410
1
5
2=÷ days
So on the sixth day he finishes all the questions.
3 The shaded area can be divided into two parts: a triangle at the top and a rectangle at the bottom. The area of the shaded part is 3 x 3 ÷ 2 + 3 x 1 = 7.5 squares The area of each square is 3 x 3 = 9 cm2 So the area of the shaded part is 9 x 7.5 = 67.5 cm2
4 Fraction of the area of the smaller piece is
125
1271 =−
Area of the bigger piece 138 ÷ (7 - 5) x 7 = 483 The area of the bigger piece is 483 cm2
6 Total perimeter 59 x 2 = 118 cm Perimeter of the triangle 30 + 12 + 28 = 70 cm Perimeter of the square 118 – 70 = 48 cm Side of the square 48 ÷ 4 = 12 cm Area of the square 12 x 12 = 144 cm2
5
151
8 (89 + 115) x 5 = 1020 (117 + 258) x 12 = 4500 So (205 + 397) x ? = 4816 ? = 4816 ÷ 602 = 8, The missing value is 8.
7
Volume of barrel A at first 24 x 3 ÷ 2 = 36 Volume of barrel B in the end 36 x 2 + 24 x 2 = 120 There is 120l of petrol in barrel B in the end.
9 Number of dolls sold: 900 ÷ 50 = 18 Number of dolls more than toy robots at the end 23 – 18 = 5 Number of dolls in the end 5 ÷ (1.5 – 1) x 1.5 = 15 Number of dolls at first 15 + 18 = 33 There were 33 dolls at first
11 The number of cards Fred had: 104 ÷ 2 = 52 Total number of cards that George and Harry had 52 ÷ 11
4 = 143 Number of cards Harry had 143 – 104 = 39 The total number of cards three of them had: 104 + 52 + 39 = 195 cards
12 400 = 2 x 2 x 2 x 2 x 5 x 5 We have 2 x 5 = 10 2 x 2 x 2 x 5 = 40 Therefore Jane had $10 and her brother had $40
10
From the figure we can see that 1 equal part in Joey’s money is 2 equal parts in Zhong Ren’s money (2 squares) and 1 equal part in Suriya’s money is equal to 3 equal parts in Zhong Ren’s money. Total number of squares 2 x 5 + 7 + 3 x 3 = 26 Value of one square 1326 ÷ 26 = 51 Joey spent 51 x 2 x 2 = 204 Zhong Ren spent 51 x 1 = 51 Suriya spent 51 x 1 x 3 = 153 Total amount spent 204 + 51 + 153 = 408 They spent $408 altogether.
13 Ratio of the cost of 1 pair of shoes and 1 pair of socks is 9 : 1 Ratio of the cost of 3 pairs of shoes and 5 pairs of socks is 27 : 5 Cost of 3 pairs of shoes 192 ÷ (27 + 5) x 27 = 162 Cost of 1 pair of shoes 162 ÷ 3 = 54 A pair of shoes costs $54.
14 Area of the shaded parts 2 x 4 ÷ 2 + 3 x 4 ÷ 2 = 10 squares Area of each square 4 x 4 = 16 cm2 Area of the shaded part 16 x 10 = 160 cm2
15 Total mass of the two bags 33.25 x 2 = 66.5 kg The mass of the powder bag
19)12(25.66 21 =+÷ kg
16 Number of pens 36 ÷ (7 – 3) x 7 = 63 There were 63 pens at first.
17 Area of the rectangle 15 x 19 = 285 cm2 Area of the triangle 19 x (15 – 7) ÷ 2 = 76 cm2 Area of the shaded part 285 – 76 = 209 cm2
18 6 ÷ 3 x 7 = 14, 14 – 9 = 5, Alice bought 5 more notepads.
Answers to Semestral Assessment 1: Mock Paper 5 Paper 1 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q154 3 4 4 3 1 1 2 3 4 1 4 2 2 4
16 Eight million six thousand five hundred. 17 3 18
5013
50001300 = 19
53
523 4= It is 4600metres.
20 Area MQH = area KNP = 41 area MNPQ
=> Area MKPH = 21 area MNPQ
Shaded area = 21 area MKPH = 4
1 area MNPQ.
2183
41
21 2)( =÷+
Jing Jing had done 83 of the homework.
22 40 ÷ 8 = 5 5 carpenters are required.
23 50502100)1100( == ×+A
24 4 hours 40 minutes – 2 hours 45minutes = 1 hour 55 minutes. The carpenter started at 1.55 pm.
25 Feng Xue and Ann each had (181 – 37) ÷ 2 = 72 stamps. Ann later had 72 + 29 = 101 stamps Ann had 101 stamps in the end.
152
26 (148.5 + 43.5) ÷ 2 = 96 (148.5 – 43.5) ÷ 2 = 52.5 The two numbers are 96 and 52.5
27 DH = 30 ÷ (7 + 3) x 7 = 21 cm Area BDH = 21 x 30 ÷ 2 = 315 cm2
28
95 of the apples is equal to 7
5 of the pears Ratio of apples to pears is 9 : 7 Number of pears at first 592 ÷ (9 + 7) x 7 = 259 Number of pears sold 74259 7
2 =× 74 pears were sold.
30 Women : adults = 3 : 4 = 9 : 12 Adults : children = 3 : 7 = 12 : 28 Women : children = 9 : 28 Number of children 114 ÷ (28 – 9) x 28 = 168 There were 168 children at the concert.
29 Fraction of the full water volume taken from the tank
31
21
65 =−
Mass of the water taken out 81.74 – 59.8 = 21.94 kg
Mass of the full water volume kg82.6594.21 3
1 =÷ Mass of half of the water volume
kg91.3282.65 21 =×
Mass of the tank 59.8 – 32.91 = 26.89 kg
Paper 2 1 3.25 kg = 3250 g
3250 ÷ 250 x 0.65 = 8.45 Mr. Khoo paid $8.45
2 Area ABC = 22 x 16 ÷ 2 = 176 cm2
Area BCD = 22 x 7 ÷ 2 = 77 cm2 Area ACD = 176 – 77 = 99 cm2
3 Total mass of 3 packets 903.6 x 3 = 2710.8 g Apple : strawberry : mango = 2 : 1 : 5
4 = 10 : 5 : 4 Mass of the packet of apple candies 2710.8 ÷ (10 + 5 + 4) x 10 ÷ 1000 = 1.43 kg
5 In every minute, tank X receives 8l more than tank Y 54 – 22 = 32 Time taken so that tank X is 32l more than tank Y 32 ÷ 8 = 4 minutes Rate of water flowing in tank Y 22 ÷ 4 + 56.5 = 62 After 1 hour, the volume of water in tank Y is (62 – 56.5) x 60 = 330l
4 2 boxes of candies and 3 boxes of cookies is 5 x 3.84 = 19.2 kg Therefore 4 boxes of candies and 6 boxes of cookies is 19.2 x 2 = 38.4 kg 3 boxes of candies and 2 boxes of cookies is 5 x 3.7 = 18.5 kg Therefore 9 boxes of candies and 6 boxes of cookies is 18.5 x 3 = 55.5 kg So 5 boxes of candies is 55.5 – 38.4 = 17.1 kg 1 boxes of candies is 17.1 ÷ 5 = 3.42 kg 1 boxes of cookies is (19.2 – 2 x 3.42) ÷ 3 = 4.12 kg The total mass of 2 boxes of candies and 1 box of cookies is 2 x 3.42 + 4.12 = 10.96 kg
6 The remainder before Tom bought the computer: (846 + 27) x 2 = 1746 The remainder before Tom paid his bills: (1746 + 54) ÷ 7
6 = 2100
Tom’s salary is 2100 ÷ 43 = 2800
Tom’s salary is $2800
7 Number of plastic pieces 64 x 2 = 128 Number of chairs (128 + 64) ÷ 8 x 5 = 120 Number of tables 120 ÷ 5 x 3 = 72 Number of plastic chairs 120 – 32 = 88 Number of plastic tables 128 – 88 = 40 Number of wooden tables 72 – 40 = 32 Ratio of the number of plastic chairs to that of wooden tables 88 : 32 = 11 : 4
8
m58.112)11(11
127
32
21
32
61
21
≈=÷+
=+
The average height of the two children is 1.58m.
9 Fraction of the magazine: read on Saturday (1- 5
1 )x 41 = 5
1
read on Sunday 51 x2= 5
2 Fraction of the magazine that was not read 1- 5
1 - 51 - 5
2 = 51
10 Cost of the LCD 900 ÷ (9/4) = 400 Average cost (400 + 900) ÷ 2 = 650 The average cost of the two devices is $650.
11 A pair of jeans cost $5 more than a pair of shirts. Therefore, if Ken bought 2 pairs of jeans instead of 2 shirts, he would have to pay 5 x 2 = 10 more The cost of 1 pairs of jeans (90 + 10) ÷ 5 = 20 A pair of jeans costs $20.
12 Indian : Chinese = 2 : 7 = 8 : 28 Malay : Chinese = 3 : 4 = 21 : 28 Indian : Malay : Chinese = 8 : 21 : 28
13 172000 x 0.68% = 1169.6 Interest that Bill would earn after a year is $1169.60
153
14 After giving money, the total would not change. Amount that Margaret had in the end 630 ÷ (8 + 1) = 70 Amount that Margaret had at first 70 + 52.70 = 122.70 Amount that Soo Hui had at first 630 – 122.70 = 507.30 507.30 – 122.70 = 384.60 The difference is $384.60
16 3290 x 80% = 2632 2632 x 107% = 2816.24 Mr. Tay paid $2816.24 for the furniture.
17 263790
15
Value of one equal part (400 + 30) ÷ 8 = 53.75l The initial volume of water in tank B was 53.75l
18 128 ÷ 2 = 64, 64 ÷ 2 = 32, 32 ÷ 2 = 16, 16 ÷ 2 = 8, 8 ÷ 2 = 4, 4 ÷ 2 = 2, 2 ÷ 2 = 1, 1 ÷ 2 = 0.5 It took 8 times 12 minutes for the bacteria to reach 128 mg. Time taken is 12 x 8 = 96 minutes. So the starting time was 5 hours – 96 minutes = 3 hours 24 minutes. The starting time was 3:24 pm.
Answers to Semestral Assessment 2: Mock Paper 1
Paper 1 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q153 2 1 1 4 1 2 3 2 4 1 1 1 4 4
16 3256 = 19 x 191 + 7
The remainder is 7 17 680 795
19 261 18
3023
52
61 23 =−
20 1l 25 ml = 1025 cm3
22 3045 32 =×÷=x 21
95
31
65 )1( =−×
The volume of milk left in the bottle is l95 23 63.08l = 63 080 ml
24 2 x 3.65 + 3 x 5.99 = 25.27 Uncle Tiong spent $25.27
25 5 : 9 = 35 : 63 => Y = 35 7 : 35 = 1 : 5 => X = 1
26 If each pupil gets 7 pens, there will be 3 pens extra. To give each pupil 8 pens, the 3 extra pens can be given to 3 pupils. There are 4 pens short. So the number of pupil is 4 + 3 = 7 Number of pens 7 x 7 + 3 = 52 a) There are 7 pupils b) There are 52 pens.
27 100% - 75% = 25% , 25% x 40% = 10% 100% - 75% - 10% = 15% , 15%= 20
3 Total number of candies 20 ÷ 10% = 200 Number of chocolate candies: 200 x 75% = 150 Number of strawberry candies: 200 x 15% = 30 a) The number of strawberry flavored candies is 20
3 of the total. b) 150 – 30 = 120 There are 120 more chocolate candies than strawberry candies.
28 Percentage of the breadth to half-perimeter 15% x 2 = 30% Percentage of the length to half-perimeter 100% - 30% = 70% Ratio of breadth to length is 3 : 7 The breadth is 760 ÷ (7 – 3) x 3 = 570 cm = 5.7m The length is 760 + 570 = 1330 cm = 13.3m Area = 5.70 x 13.30 = 75.81 m2
570 ÷ 30 = 19 1330 ÷ 30 =44.33 The maximum number of cartons that can be stored is19 x 44 = 836 cartons
30 Number of Peter’s books: 4832 32 =÷
Number of Fahan’s books: 48 ÷ 2 = 24 Total number of books: 48 + 24 + 32 = 104.
29 In January Charges for first 40 units: 1.17 x 40 = 46.80 Charges for the remaining units 1.40 x (56 – 40) = 22.40 Total bill: 46.80 + 22.40 = 69.20 In February Charges for the units above the first 40 units: 135 – 46.80 = 88.20 Number of units above the first 40 units: 88.20 ÷ 1.40 = 63 Total consumption in February 40 + 63 = 103 Average consumption: (56 + 40 + 63) ÷ 2 = 79.5 Average bill (69.20 + 135) ÷ 2 = 102.1 a) 103 units b) 79.5 units c) $102.10
154
Paper 2 1 Four other pupils each can have a maximum score of
50 marks. Highest possible average is (50 + 50 + 50 + 50 + 15) ÷ 5 = 43 marks.
2 George folded 100% - 35% = 65% of the birds. The difference between them is 65% -35% = 30% of the birds. Total number of birds: 90 ÷ 30% = 300. George folded 300 x 65% = 195 birds.
3 Mary : Andy = 0.4 : 1 , Mary : Bob = 1 : 2 Mary : Andy : Bob = 2 : 5 : 4 660 ÷ (2 + 5 + 4) x 5 = 300, Andy donated $300.
4 ABD = (180° - 116°) ÷ 2 = 32° ABE = 180° - 32° = 148°
5 12 ÷ 30% = 40
He had 40 stamps at first. 6 7 + 16 + 5 = 28 , 5 + 9 + 28 = 42
28 ÷ 42 x100% = 66.67% 7 Number of males: 2500 – 1100 = 1400
1400 ÷ 1100 x 100% = 127.27% There are 27.27% more males than females.
8 2 : 4 : 5 = 6 : 12 : 15 Total number of questions done is 6 + 12 + 15 = 33
9 The largest possible difference is when the number of adults is largest and the number of children is smallest. The largest possible number of adults is 3349. The smallest possible number of children is 1651. The largest difference is 3349 – 1651 = 1698
10 Triangle SQR and triangle PQR have the same base QR and their heights are in the ratio of 1 : 4. Therefore there areas are also in the ratio of 1 : 4. Therefore the ratio of the shaded area to that of triangle PQR is 3 : 4 Area of triangle PQR is 54 ÷ 3 x 4 = 72 cm2
12 Number of students remained 36 – 9 = 27 Number of extra lollipops 27 x 3 = 81 Ratio of the number of student left to the total number of students 9 : 36 = 1 : 4 Number of lollipops 81 x 4 = 324 Miss Chua bought 324 lollipops.
11
From the figure, the unshaded area of Square B is 27 x 2 ÷ (5 – 3) = 27 cm2+
Area of the square is 27 + 27 = 54 cm2 The area of the square is 54 cm2
13 AC = 9 cm BC = 12 cm Side of the small square inside: 12 – 9 = 3 cm Area of triangle ABC 9 x 12 ÷ 2 = 54 cm2
Area of the small square 3 x 3 = 9 cm2 Area of the square MNPQ 54 x 4 + 9 = 225 cm2
14 Height of triangle D is the width of the rectangle, so it is 6 cm. The base of triangle D is 30 x 2 ÷ 6 = 10 cm Triangles A and D have the same height. Therefore the base of triangle A is 10 x 3 ÷ 5 = 6 cm Triangles A and B also have the same height. So the base of triangle B is 6 x 3 = 18 cm The length of the rectangle is 18 + 10 = 28 cm The perimeter of the rectangle is (28 + 6) x 2 = 68 cm
16
(45 + 6 + 3) ÷ 2 = 27 Lucy had $27 at first.
15 Ratio of story books to comic books is 1.5 : 1 = 3 : 2 Ratio of story books sold to comic books sold (3 x 3
2 ) : (2 x 1) = 2 : 2 = 1 : 1 Ratio of money received from selling story books to comic books (1 x 12) : (1 x 8) = 12 : 8 = 3 : 2 Money received from selling story books 6400 ÷ (3 + 2) x 3 = 3840 Money the shop would received from selling the remaining 3
1 of the story books 3840 ÷ 2 = 1920 Money the shop would receive at the end 6400 + 1920 = 8320 When all the books were sold, the shop would receive $8320.
17 From the figure, 53 of Joey’s marbles is 7
2 that of Thomas. Ratio between Joey’s marbles and Thomas’s marbles is 10 : 21 Ratio between Joey’s marbles to the difference between them is 10 : 11 Ratio between Joey’s marbles to Ben’s marbles is 10 : 22 = 5 : 11 Joey’s marbles is 48 ÷ (11 – 5) x 5 = 40 Thomas’s marbles is 40 / 10 x 21 = 84 Ben’s marbles is 40 ÷ 5 x 11 = 88 , 84 + 40 + 88 = 212. They have 212 marbles altogether.
18 Volume of tank A 4 x 6 x 1 = 24 m3 , Volume of tank B 5 x 3 x 2 = 30 m3
The volume of water in each tank is 4 x 6 x 0.5 = 12 m3. The height of water in tank B is 12 ÷ (5 x 3) = 0.8 m
155
Answers to Semestral Assessment 2: Mock Paper 2 Paper 1 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q152 1 4 1 3 1 2 2 2 1 1 2 4 2 4
16 9 : (5 + 9) = 9 : 14
The ratio is 9 : 14 17 12.42 + 2.07 = 14.49
The volume of juice drink is 14.49 l 19 0.064 20
121
18 Number of squares: 3 x 3 = 9 Each triangle is 2
1 of a square, so each triangle is
181
91
21 =× of the figure
So the fraction shaded is 92
181 4 =× of the figure.
i.e. 22.22% of the figure is shaded
21 3 years ago Mohammed was 15 – 3 = 12 years old. His brother’s age was 1812 3
2 =÷ His brother’s age now is 18 + 3 = 21 years old.
22 2009 is a normal year so there are 365 days. There are 30 days in September. 30 ÷ 365 x 100% = 8.22%
2310051
1000105 ,501.0,,051.0
24 26
252516
26 2100 x 107% = 2247 The price is $2247
27 1.25 + 2.125 + 0.786 = 4.161 ≈ 4.16 The total volume is 4.16
28 1053 ÷ (5 + 8) x 5 = 405 Kavitha’s saving is $405
29 Volume of the pool 20 x 10 x 1.5 = 300 m2 Volume of water to be filled 300 ÷ 2 = 150 m2 Total volume of water that can be filled in a minute 0.375 x 4 = 1.5 m3 Total time required 150 ÷ 1.5 = 100 minutes
30 8.5 – 5 = 3.5 An adult ticket cost 3.5 more than a child ticket. 126 ÷ 2 = 63 If there were 126 more child tickets sold, the cinema would received 2907 + 126 x 5 = 3537 By then there would be an equal amount of adult and child ticket. Ratio of the money received from selling adult tickets to child tickets would be 8.5 : 5 Amount received from selling adult tickets 3537 ÷ (8.5 + 5) x 8.5 = 2227 Number of adult tickets 2227 ÷ 8.5 = 262. There were 262 adults.
Paper 2 1 Total money saved by all children: 604 x 10 = 6040
Total money saved by the boys 592 x 2 = 1184 Total money saved by the girls 6040 – 1184 = 4856 Average of savings of the girls 4856 ÷ 8 = 607 On average, each girl saved $607.
2 Number of Indian pupils 1200 x 20% = 240 Percentage of Chinese pupils (100% - 20%) x 65% = 52% Number of Chinese pupils 1200 x 52% = 624 Percentage of Malay pupils 100% - 20% - 52% = 28%a) 624 Chinese pupils b) 28% of the pupils are Malay.
3 Fraction of the balloons sold on the last two days:
54
511 =−
Fraction of the balloons sold on the last day
2512
54 35 =×÷
Fraction of the balloons sold on the second day
258
54 25 =×÷
Ratio of the number of balloons sold on the first day to the second day to the last day 5 : 8 : 12 Number of balloons sold on the last day 92 ÷ (12 – 8) x 12 = 276 Number of balloons sold on the second day 276 – 92 = 184 Number of balloons sold on the first day 184 ÷ 8 x 5 = 115 Total number of balloons 115 + 184 + 276 = 575 Money received 575 x 1.2 = 690 Mr Chan earned $690 in total.
4
2u + 2v = 858 => 6u + 6v = 2574 5v – 3u = 225 => 10v – 6u = 450 => 16v = 3024 => v = 189 Number of tulips 189 x 5 = 945 Number of roses 945 – 225 = 720 945 + 720 = 1665 There were 1665 flowers at first.
156
5 AFD = FGD = 80° ADE = (180° - AFD) ÷ 2 = 50° EDC = 90° - 50° = 40° DAE = ADE = 50°
6 83 x4500g=1687.5g=1.6875 kg
48%x18 kg=8.64 kg Total mass 1.6875 + 8.64 = 10.3275 ≈10.33 kg
7 There are 4 spaces between the third tree and the seventh tree. Distance between any two trees 7920 ÷ 4 = 1980 cm = 19.8 m Distance from the 15th tree to the first tree: 19.8 x 14 = 277.2 m
8 Distance travelled when the ball hit the ground the first time: 15m Distance bounced up 15x 5
4 =12 m Distance travelled to hit the ground the second time: 12 m Total distance: 15 + 12 + 12 = 39 m
10 If all trucks were small trucks, the number of wheels would be 10 x 32 = 320 Number of wheels extra 408 – 320 = 88 Number of large trucks 88 ÷ (14 – 10) = 22 There are 22 large trucks.
9
Age of the last child (193 – 3 – 3 x 2 – 3 x 3) ÷ 7 = 25Age of the first child 25 + 9 = 34 The first child is 34 years old.
11 Francis’s money before he gave to his sister (443+53) 5
2÷ =1240 Francis’s money before he bought the book
1240 + 61 = 1301 Francis’s money before he bought the furniture
(1301 + 49) ÷ 75% = 1800 Francis’s salary (1800 + 100) x 2 = 3800 Francis’s salary is $3800.
12 The ratio of the mass of an elephant to that of a zebra is 5.5 : 1 The ratio of the mass of 2 elephants to that of 3 zebras is 5.5 x 2 : 1 x 3 = 11 : 3 Mass of 2 elephants 1260 ÷ (11 + 3) x 11 = 990 Mass of an elephant 990 ÷ 2 = 495 Mass of a zebra 495 ÷ 5.5 = 90 Mass of an elephant and 4 zebras 495 + 4 x 90 = 855 The total mass of one elephant and 4 zebras is 855 kg.
13 Total money earned from January to August 2 340 x 8 = 18 720 Total money earned for the year 3 290 x 12 = 39 480 Total money earned from September to December 39 480 – 18 720 = 20 760 Average earning during that period 20 760 ÷ 4 = 5 190
15 Number of roses 954 ÷ (9 – 3) x 3 = 477 Number of lilies 477 ÷ 3 x 5 = 795 795 – 477 = 318 There were 318 more lilies than roses.
14
(1459 + 296) ÷ (4 + 4 + 1) = 195 Kathy raised $195
16 The total number of pages in 1 book of each type 10 000 ÷ 20 = 500 pages The number of pages in a Physics book (500 – 20 – (20 + 70)) ÷ 3 = 130 There are 130 pages in a Physics book
17 Perimeter of the rectangle (75 + 33) x 2 = 216 cm That is also the total perimeter of the two triangles. The base of each triangle is (216 – 39 x 4) ÷ 2 = 30 cm The area of one triangle is 36 x 30 ÷ 2 = 540 cm2
18 Derek’s money after buying stationeries 150 + 246 = 396 Fraction of Derek’s money that he spent on toys on
stationary The amount of money that Derek had:
The amount of money that Josh had 720 ÷ 5 x 3 = 432. Josh had $432.
157
Answers to Semestral Assessment 2: Mock Paper 3 Paper 1 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q151 1 2 2 2 2 1 1 4 1 3 3 2 1 3
16 48% 17 480 cm2
18 6 ÷ 4 x 24 = 36 Two dozen cans cost $36
19 x = 162° ÷ 2 = 81°
21 390 ÷ 12 = 32.5 33 pencil cases are needed.
22158
1571 =− , 7:8: 15
7158 =
The ratio is 8 : 7 23 Number of $5 notes 45 ÷ (1 + 1.5) = 18
Number of $2 notes 18 x 1.5 = 27 Total amount of money 27 x 2 + 18 x 5 = 144 Brian has $144
24 18 = 2 x 3 x 3 45 = 3 x 3 x 5 The common factors are 3, 9
25 55 x 18 = 990 Kiara’s school is 990m from her home.
20
The shaded area on the right = 21 MBJH =
41 MBCN
The shaded area on the left = 21 IHND = 4
1 AMND Ratio of the total shaded area to the area of ABCD is
41
26 At some times later, the difference in ages will still remain the same Raphael’s age then 38 ÷ (3 – 1) = 19 The number of years is 19 – 10 = 9 After 10 years, Raphael’s father‘s age will be three times his age.
27 72 ÷ 36% = 200 ml The bottle is 200 ml
29 4750 g = 4.75 kg 42.5 + 4.75 = 47.25 The scale indicates 47.25 kg
28 500 ÷ 40 = 12.5 600 ÷ 40 = 15 300 ÷ 40 = 7.5 The maximum number of boxes that can be stored is 12 x 15 x 7 = 1260 boxes
30 1 52 km = 1.4 km = 1400 m, 4
3 km = 0.75 km = 750 m, 1400 – 750 = 650, Antoine had walked 650 m
Paper 2 1 60 x 25 x 30 = 45000, 45000 cm3 = 45 l
45 ÷ 3 = 15, Uncle Tiong has to fill 15 times. 2 Area IBK = (25 – 18) x (25 – 2) ÷ 2 = 80.5 cm2
Remaining area = 25 x 25 – 2 x 80.5 = 464 cm2
3 Price at which Mrs. Choo bought the grapes 3.20 – 0.70 = 2.50 per 100 g Amount that Mrs. Ong paid 2000 ÷ 100 x 3.20 = 64 Amount of grapes that Mrs. Choo bought 64 x 100 ÷ 2.50 ÷ 1000 = 2.56, 2.56 – 2 = 0.56 Mrs. Choo bought 0.56 kg more than Mrs. Ong.
4 1 = 1 x 1 4 = 2 x 2 9 = 3 x 3 25 = 5 x 5 So the missing value is 16, since 16 = 4 x 4
5 Total distance of the first 3 attempts 155 x 3 = 465 cm Total distance of all attempts 145 x 5 = 725 cm Total distance of the last 2 attempts 725 – 465 = 260 cm Average distance of the last 2 attempts = 130 cm
6 NMQ = 180° - 29° x 2 = 122° QNP = MNQ = 29° ONP = 180° - 29° = 151° NOP = (180° - 151°) ÷ 2 = 14.5°
8 1.4 ÷ (2 + 5) x 2 = 0.4 l = 400 ml The volume of syrup needed is 400 ml
7 Fraction of the milk that Guo Qi drank on the next 2 days (1- 5
1 )x75%= 53
Fraction of the remaining milk 1- 5
1 - 53 = 5
1 Volume of the carton
lml 75.33750750 51 ==÷
9 Number of toothpicks needed to make n shapes is 6 + 4(n – 1) To make 5 shapes, the number of toothpicks needed is 6 + 4(5 – 1) = 22 Using 258 toothpicks 6 + 4 (n – 1) = 258 n = 64 64 shapes can be made.
CD
J
A B
I
M
H
N
158
10 952 ÷ (0.4 + 1) = 680 The number of stickers that Zoe had is 680
11 Total mass 44 x 3 = 132 kg Chek Khoon’s mass is (132 + 4) ÷ (5 + 6 + 6) x 6 = 48 kg
12
Number of black pepper chickens 90 ÷ 5 x 2 = 36 Number of honey roasted chickens 36 x 3 = 108 a) 108 honey roasted chickens were sold. b) 36 black pepper chickens were sold.
13 If Andy only bought 3 comic books and 3 story books, he would save 18 x 2 = 36 Amount left after buying 3 comic books and 3 story books 36 + 24 = 60 With this $60, if he buys 2 more story books, he will need $16 more. Therefore, cost of a comic book is (60 – 16) ÷ 2 = 38 Amount of money that Andy had 3 x 38 + 5 x 18 + 24 = 228 Andy has $228
14 Area of 2, 3, 4 and 5 is 1 unit Area of 1 is 4 x 4 = 16 units Area of 1 and 2 is 16 + 1 = 17 units The ratio is 17 : (16 + 4) = 17 : 20
15 Amount received from selling plastic tables 75 x 150 = 11250 Number of wooden tables (12850 – 11250) ÷ 80 = 20 20 wooden tables were sold.
16 Fraction of the pupils who like chess (1- 3
1 )x 41 = 6
1
Total number of pupils 6010 61 =÷
Number of pupils who like basketball 60x 31 =20
Number of pupils who like either chess or basketball 20 + 10 = 30 pupils
17 Ratio of the amount paid for safe delivery to amount received for broken products 9 x 16.5 : 1 x 66 = 9 : 4 Amount received for broken products 15015 ÷ (9 – 4) x 4 = 12012 Number of broken products 12012 ÷ 66 = 182 There were 182 products broken on the way.
18 149 – 53 = 96 Each day Ryan ate 8 more cookies than Mindy. Number of days taken to eat 96 more cookies: 96 ÷ 8 = 12 Number of cookies each of them had at first 149 + 23 x 12 = 425 a) 12 days b) 425 cookies.
Answers to Semestral Assessment 2: Mock Paper 4
Paper 1 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 4 3 4 3 2 2 3 2 1 3 2 1 2 2 1
16 Goldfish : clownfish = 2 : 7 = 10 : 35
Clownfish : angelfish = 5 : 2 = 35 : 14 Goldfish : angelfish = 10 : 14 = 5 : 7
1761
18 31
65
21 311 =+
There was 3 31 l of milk in the fridge at first
19 11 ÷ 1.20 = 9.17 At most, 9 pens can be bought
20 i = 154° - 87° = 67° 22 A = 9 – 1 – 1 – 1 = 6
21 A + B = 80 x 2 = 160 , A + B + C = 85 x 3 = 255 C = 255 – 160 = 35
23 (72 + 83 + 67) ÷ 3 = 74 Benjamin’s average mark is 7
24 24 = 2 x 2 x 2 x 3, 36 = 2 x 2 x 3 x 3 The common factors are 2, 4, 6, 12
25 5 839 x 7 = 40 873
27 12.8 – 0.91 x 5 – 1.32 x 3 = 4.29 km
26 Area of one face 54 ÷ 6 = 9 cm2
Since 9 = 3 x 3, the sides of the cube are 3 cm. Volume of the cube 3 x 3 x 3 = 27 cm3
28 Percentage of adults 100% - 30% = 70% Number of adults 10 200 x 70% = 7140 Number of adults working outside 7140 x 40% = 2856 There are 2856 adults working outside the village.
29 ABC = 180° - 93° - 43° = 44° ABD = 44° - 37° = 7°
30 The price of 2 shirts is equal to the price of 3 skirts. Therefore the price of 4 shirts is equal to the price of 6 shirts. The price of 4 shirts 162 ÷ 2 = 81. The price of a shirt 81 ÷ 4 = 20.25. A shirt costs $20.25
159
Paper 2 2 5 bags weigh 86.25 Kg.
1 bag weighs 17.25 Kg. Each porter can lift Maximum of 60/17.25 =3.47 that is 3 bags. For lifting 20 bags we need 20/3=6.666 That is 7 porters.
1
Amount left after spending 1144 ÷ 2 x 3 = 1716 Amount withdrawn 1716 x 2 = 3432
3 3.115 ÷ 14 x 100% = 22.25%
4 Area of unshaded triangle at the bottom left 20 x (20 + 36) ÷ 2 = 560 cm2 Area of the unshaded triangle at the top right 36 x 36 ÷ 2 = 648 cm2 Total area 20 x 20 + 36 x 36 = 1696 cm2 Area of the shaded part 1696 – 560 – 648 = 488 cm2
5 Total number of stamps 168 ÷ 7 x (3 + 7 + 9) = 456 Number of Charlie’s stamp 168 ÷ 7 x 3 = 72 Number of stamps that Mark gave Charlie (168 – 72) ÷ 2 = 48
6 Number of red roses 24 ÷ 3 x 5 = 40 Number of white roses 24 ÷ 3 x 2 = 16 Total number of flowers (40 + 16) ÷ (1 – 0.2) = 70 Number of daisies 70 x 0.2 = 14
7 CED = 42° - 31° = 11° FCB = 180° - 42°= 138° ACF = 138° - 60° = 78°
8 Cost of the fish 3300 ÷ 100 x 1.59 = 52.47 Cost of the beef 2800 ÷ 500 x 4.89 = 27.38 Cost of the vegetable 0.86 x 7 = 6.02 Total cost 52.47 + 27.38 + 6.02 = 85.87 Mrs. Foo paid $85.87
9 Ratio of the amount the shop received from selling curry puffs to that from selling cakes 1 x 2 : 4 x 5 = 1 : 10 Amount from selling cakes 1892 ÷ (10 + 1) x 10 = 1720 Number of cakes 1720 ÷ 5 = 344 There are 344 cakes.
10 The number of pens at first was 280 x 70% = 196 Number of other pens 280 – 196 = 84 After selling some blue pens, the number of other pens was 40% total. Total number of pens in the end 84 ÷ 40% = 210 Number of blue pens sold 280 – 210 = 70
11 A textbook and a bag cost $30. A textbook and a comic book cost $22.5. 2 textbooks and a bag and a comic book cost 30 + 22.5 = 52.5 4 textbooks, 2 bags and 1 comic book for $100 2 textbooks and 1 bag cost 100 – 52.5 = 47.5 Cost of 1 text book 47.5 – 30 = 17.5 Cost of 1 comic book 22.5 – 17.5 = 5 A comic book cost $5
12
24 ÷ 12 x 5 = 60 Marion had 60 beads at first.
13 350 ÷ 4000 x 100% = 8.75% 15 Earning from sales 72 000 ÷ 5 x 1.2 = 17280
Average earning from sale a month 17 280 ÷ 8 = 2160 Average earning a month 2160 + 1575 = 3735
16 Initial water volume 60 x 43 x 24 x 3
1 = 20 640 cm3 = 20.64 l After 20 minutes, volume of water flowed into the tank is 1.8 x 20 = 36 l Total volume of water in the tank 20.64 + 36 = 56.64 l
17 Total area: 21 squares Shaded area: 6 squares Ratio: 6 : 21 = 2 : 7
18 3N - 32 N = N + 36
N = 27 The number is 27.
14 Fraction of apples: 2/5 Fraction of oranges: (1- 5
2 )x 2512
54 =
Fraction of mangoes:
253
2512
521 =−−
Ratio of the number of apples to that of oranges to that of mangoes 10 : 12 : 3 Total number of fruits 648 ÷ (12 – 10) x (10 + 12 + 3) = 8100 Number of apples 8100 x 5
2 = 3240
8100 x 253 = 972
Total of oranges and mangoes 8100 – 3240 = 4860 After some apples have been sold, the total of oranges and mangoes is 90% of the total fruits. Number of fruits at the end 4860 ÷ 90% = 5400 Number of apples sold 8100 – 5400 = 2700 2700 apples have been sold.
160
Answers to Semestral Assessment 2: Mock Paper 5 Paper 1 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 3 2 1 1 1 1 3 4 2 1 1 3 2 1 2
17 150 x (1 + 0.07 + 0.1) = 175.5
Mr. Smith had to pay $175.50 18 99 + 108 + 117 + 126 + 135 + 144 + 153 = 882
16 1- 31 = 3
2 , 91
32 6 =÷
Each friend got 91 of the chocolates.
19 20.08 l = 20 l 80 ml 20 Volume of container 1: 20 x 15 x 10 = 3000 cm3
Volume of container 2: 15 x 7 x 5 = 525 cm3 Total volume 3000 + 525 = 3525 cm3
22 95 23 36 = 2 x 2 x 3 x 3, 48 = 2 x 2 x 2 x 2 x 3
The smallest common factor is 2 x 2 x 2 x 2 x 3 x 3 = 144
24 246.11 25 1 3
1 x 60 x 60 = 4800 There are 4800 seconds.
21
26 18 : 22 = 63 : 77
28 : 63 = 8 : 18 Therefore 8 : 18 : 22 = 28 : 63 : 77
27 Ticket price for the 9-year-old daughter: $600. Ticket price for each of other family members: $1200 Total ticket cost 600 + 1200 x 3 = 4200 The family paid $4200 altogether.
28 0.1N = 52 N– 33
N = 110 The number is 110
29 144 = 12 x 12 The side of each square is 12 cm The perimeter of the large rectangle is (12 x 3 + 12) x 2 = 96 cm
30 450° = 360° + 90° Therefore 1 hour and 15 minutes have passed. The time then will be 10.15 am. Paper 2 1 30 000 x 3.75% = 1125
Swee Swee will receive $1125 of interest after a year
3 There are 3 options for the appetizer, 3 options for main course, and 3 options for dessert. Total number of options is 3 x 3 x 3 = 27
4 5.31
8)( 2
879
87969...1909 ==
×××+×++×+×
5
101
107
54 =−
0.1 kg of meat has not been cooked.
2
7 x = 180° - 78° - 33° = 69° 6 Total volume: 6 + 9 = 15 l Volume of a container 12 x 7 x 5 = 420 cm3 = 0.42 l 15 ÷ 0.42 = 35.71 35 containers could be filled completely. Volume of drink left over: 15 – 35 x 0.42 = 0.3 l
8 Length of the rectangle 6.5 + 17.5 = 24 cm Breadth of the rectangle 24 x 4
3 = 18 cm Area of the shaded part (17.5 x 18) ÷ 2 = 157.5 cm2
9 Total time 3.2 x 8 = 25.6 minutes = 25 minutes 36 seconds.
10 Number of roses 400 x 85 = 250
Number of other flowers 400 – 250 = 150 Total number of flowers after selling
375)1(150 53 =−÷
Number of roses sold 400 – 375 = 25 25 roses were sold
11 16 = 4 x 4, 49 = 7 x 7 The side of the smaller square is 4 cm and that of the larger square is 7 cm. Total area 16 + 49 = 65 cm2 Area of the large triangle at the bottom (4 + 7) x 7 ÷ 2 = 38.5 cm2 Area of the triangle on top of the smaller square 4 x 4 ÷ 2 = 8 cm2 Area of the triangle on top of the larger square (7 – 4) x 7 ÷ 2 = 10.5 cm2 Area of the shaded part 65 – 38.5 – 8 – 10.5 = 8 cm2
M .
A
B
A
C
161
12 x + y + z = 142° z = (142° - 12°) ÷ 2 = 65°
14 a) Number of goals scored on the last match 7 + 2 x 6 = 19 Total number of goals
7 + 9 + … + 17 + 19 = 27)719( x+ = 91
b) Average number of goals per match 91 ÷ 7 = 13
13 Total time spent 138 x 3 = 414 minutes = 10
96 hours Total time spent on Tuesday and Wednesday
52
21
109 426 =− hours
Time spent on Wednesday 1514
52 2234 =×÷ hours
15 Nelson’s sister’s height 1.52 – 0.2 = 1.32 m
1.32 ÷ 1.52 = 3833
17 The price of the table 300 ÷ 4 x 2 = 150 The price of the table is $150
16 The first team has to play 9 matches again 9 other teams. The second team already played one match with the first team, so it has to play 8 matches more with 8 remaining teams. Similar reasoning can be applied for the other teams. Total number of matches : 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 +1 =45 There are 45 matches altogether.
18 Number of digits to write from 1 to 9: 9 x 1 = 9 Number of digits to write from 10 to 99: 90 x 2 = 180 Number of digits to write 100: 3 Total number of digits: 9 + 180 + 3 = 192 Peter wrote 192 digits.