MODULE 3 - Homework 1H - Meden School€¦ · INTEGERS, RECIPROCALS, FACTORS, MULTIPLES AND PRIME NUMBERS MODULE 3 - Homework 1H GRADES : E,D BIDMAS Follow the correct order of operations

INTEGERS, RECIPROCALS, FACTORS, MULTIPLES AND PRIME NUMBERS

MODULE 3 - Homework 1H GRADES : E,D

BIDMAS Follow the correct order of operations to calculate the following: 1. 5 + 2 x 3 = ___ 2. 10 ÷ 2 + 7 = ___ 3. 7 + 9 ÷ 3 = ___ 4. 2 x 3 + 7 x 2 = ___ 5. 8 ÷ 4 – 2 x 1 = ___ 6. 5 x 10 + 9 ÷ 1 = ___ 7. 2 + 4 x 4 + 1 = ___ 8. (2 + 4) x 8 = ___ 9. (3 – 1) x (9 – 4) = ___ 10. 30 – (7 + 6) = ___ 11. 20 – (4 + 10) = ___ 12. (5 + 9) ÷ (2 x 1) = ___ BRACKETS Put brackets into the questions to make them correct. 1. 2 + 2 x 3 = 12 2. 4 – 1 x 7 = 21 3. 2 + 1 x 1 + 2 = 9 4. 9 ÷ 3 x 2 + 1 = 9 5. 50 ÷ 7 + 3 = 10 6. 6 + 2 x 4 + 3 = 51 1234 Use the digits 1, 2, 3, and 4 to make correct calculations. Use brackets where appropriate. 1 = ________________________________ 2 = _________________________________ 3 = ________________________________ 4 = _________________________________ 5 = ________________________________ 6 = _________________________________ 7 = ________________________________ 8 = _________________________________ 9 = ________________________________ 10 = _________________________________ EXAM QUESTION


MODULE 3 - Homework 2H GRADES : D,C

PRIME NUMBERS Answer TRUE or FALSE: 1. 2 is a prime number 2. 9 is a prime number 3. 15 is a prime number 4. 7 is a prime number 5. 19 is a prime number 6. 23 is a prime number 7. 21 is a prime number 8. 8 is a prime number 9. 27 is a prime number 10. 3 is the smallest prime number 11. There are four prime numbers between 1 and 10 12. 99 is a prime number 13. There are three primes between 20 and 30 PRIME FACTORS Write each number as a product of its’ prime factors: 1. 21 2. 12 3. 36 4. 50 5. 150 6. 54 7. 49 8. 84 RECIPROCALS Write down the reciprocal of each number

1. 3 2. 2 3. 5 4. 1

4

5. 1

2 6. 10 7.

1

8 8.

1

9

9. 5 10. 2

3 11.

3

4 12. 6

EXAM QUESTIONS 1.

2.

3.


MODULE 3 - Homework 3H GRADES : D, C

Multiples Write down the first six multiples of each number: 1. 4 2. 3 3. 7 4. 9 5. 15 6. 12 7. 8 8. 11 Highest Common Factor Find the Lowest Common Factor (HCF) for each pair of numbers. 1. 36 and 10 2. 50 and 30 3. 45 and 27 4. 100 and 36 5. 88 and 56 6. 36 and 32 Lowest Common Multiple Find the Highest Common Multiple (LCM) for each pair of numbers. 1. 6 and 9 2. 5 and 15 3. 12 and 8 4. 2 and 11 5. 12 and 8 6. 5 and 9 EXAM QUESTIONS 1.

2.

3.

4.

ROUNDING AND APPROXIMATIONS MODULE 3 - Homework 4H GRADES : E, D

ESTIMATING Copy the lists below and match up the questions to the estimated answers. The first one has been done for you.

QUESTIONS ESTIMATED ANSWERS

3.92 x 5.05

3

6.9 x 2.9

100

30.1 ÷ 9.91

11.4

√32

15

(8.8 + 11.11) x 4.9

40

50 ÷ 7.21

7

√103

8

4.05 x (6.9 + 2.9)

20

67 ÷ 8.12

12.2

√150

5.5 EXAM QUESTIONS 1.

2.

3.

ROUNDING AND APPROXIMATIONS MODULE 3 - Homework 5H GRADES : D,C

SIGNIFICANT FIGURES 1. Write each number correct to one significant figure. a) 27 b) 832 c) 8.12 d) 93 e) 77 f) 13.5 g) 95 2. Use a calculator to work out the answers and write them down correct to 1 significant figure. a) 50 x 23 b) 5.25 x 7 c) 910 x 12 d) 9.5 x 7.3 e) 93 x 77 3. Write each number correct to two significant figures. a) 275 b) 0.03451 c) 8.12 d) 0.956 e) 7.04 f) 7.05 g) 959 4. Write each number correct to three significant figures. a) 27589 b) 0.03451 c) 8.1254 d) 0.95621 e) 0.0704124 f) 7.05555 g) 959595 ESTIMATING CALCULATIONS By approximating each number, estimate the answers to these calculations. You must show how you reached your estimate.

1. 9.1

21.159.4 2.

03.905.1

2.589.19

3. 09.59.405.4

EXAM QUESTIONS

1.

2.

3.

ROUNDING AND APPROXIMATIONS MODULE 3 - Homework 6H GRADES : C, B

ROUNDING IN CALCULATIONS Give your final answer to each question correct to two decimal places. Remember not to round during the intermediate steps of the calculation.

1. 91.82.3

09.32.6

2. 8.32.1

9.4

3.

515.0

14.8

17.2

9

4. 00462.03.6

973.0054.9

5. 017.99.3

56.7 3

6. 1.12.91.22.35 2

HIGHEST AND LOWEST 1. The length of a pencil is given as 9cm to the nearest cm. What is the minimum length that the pencil could be? 2. The height of a door is 210cm to the nearest 10cm. What is the maximum height that the door could be? 3. The width of a piece of paper is given as 18.4cm correct to one decimal place. a) What is the minimum width that the paper could be? b) What is the maximum width that the paper could be? EXAM QUESTIONS 1.

2.

3.

ROUNDING AND APPROXIMATIONS MODULE 3 - Homework 7H GRADES : A

UPPER AND LOWER BOUNDS EXAM QUESTIONS 1.

2.

3.

4.

5.

WHOLE NUMBER AND DECIMAL CALCULATIONS


MULTIPLICATION AND DIVISION (WHOLE NUMBERS)

MULTIPLYING DECIMALS

DIVIDING WITH DECIMALS

EXAM QUESTION 1.

2.

FRACTIONS MODULE 3 - Homework 9H GRADES : D,C

ADDING AND SUBTRACTING FRACTIONS 1. Fill in the boxes by adding the fractions.

+ 1

3 2

5 3

8 2

7

1

2

2

3

2. Work out each question without a calculator. Show your working and write your answer in its’ simplest form.

a) 5

3

4

1 b)

3

1

5

3 c)

10

1

9

1 d)

6

1

4

3

3. Work out each question with a calculator.

a) 15

3

4

3 b)

3

2

10

7 c)

10

7

9

7 d)

20

9

15

13

EXAM QUESTIONS 1.

2.

3.

4.

5.

6.

7.

FRACTIONS MODULE 3 - Homework 10H GRADES : D,C

MULTIPLYING FRACTIONS Fill in the boxes by multiplying the fractions.

x 1

3 2

5 3

8 2

7

1

2

2

3

MIXED NUMBERS

1. 5

32

2

11 2.

2

11

5

23 3.

4

13

3

22

DIVIDING WITH FRACTIONS

1. 4

1

2

1 2.

10

1

5

2 3.

8

3

4

3 4.

5

1

10

3 5.

4

3

9

7

EXAM QUESTIONS 1.

2.

3.

, 4.

5.

6.

7.

,

FRACTIONS MODULE 3 - Homework 11H GRADES : B

RECURRING DECIMALS EXAM QUESTIONS 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

SQUARES, CUBES, POWERS AND ROOTS

MODULE 3 - Homework 12H GRADES : E, D,C

POWERS AND ROOTS ‘COLLECT A LETTER’

START 1000 8 32 49 64

P O U E T A 23 92 52 73 63 24

27 121 36 100 1 125

E D L N H I 43 25 53 103 62 02

216 16 343 0 25 81

I C R S T R 102 15 END 72 33 112

1) √25 3² √36 2³ √100 2) √100 4² 2² √81 √121 3) 5² 4² + 2² √144 √25+√36 1³ + 3³ 4) √36 - √4 4² - 2² 1³ + 2³ √100 - 3² 1³ + 1² EXAM QUESTIONS

1.

2.

3.

4.


MODULE 3 - Homework 13H GRADES : C

INDEX LAWS 1. Write each of these as simply as possible using indices. a) 2x2x2x2x2 b) y x y x y x y c) 9x9x9 d) 8x8x8x8x8x8x8 2. Write down the value of the missing index. a) x222 32 b) 128 233 x c) 92 555 x d) 73 222 x

e) x2)2( 42 f) 186 2)2( x g) x33

32

9

h) 58

44

4

x

3. State whether each equation is TRUE or FALSE.

a) 862 777 b) 23

88

8 c) 624 5)5(

EXAM QUESTIONS 1.

5.

2.

6.

3.

7.

4.

8.


MODULE 3 - Homework 14H GRADES : A, A*

FRACTIONAL POWERS and NEGATIVE POWERS EXAM QUESTIONS 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.



IRRATIONAL NUMBERS AND SURDS EXAM QUESTIONS 1.

2.

3.

4.

5.

6.

7.

POWERS OF 10 AND STANDARD INDEX FORM


STANDARD INDEX FORM EXAM QUESTIONS 1.

2.

3.

4.

5.

6.

PERCENTAGES MODULE 3 - Homework 17H GRADES : D,C

PERCENTAGE INCREASE AND DECREASE 1. Increase £90 by 10% 2. Increase £110 by 50% 3. Increase £120 by 5% 4. Decrease £40 by 20% 5. Decrease £700 by 30% 6. Decrease £320 by 5% 7. Increase £620 by 25% 8. Decrease £180 by 60% EXAM QUESTIONS 1.

2.

How much do they pay for the washing machine?

3.

PERCENTAGES MODULE 3 - Homework 18H GRADES : B, A

COMPOUND PERCENTAGE EXAM QUESTIONS 1.

2.

3.

4.

5.

6.

7.

PERCENTAGES MODULE 3 - Homework 19H GRADES : B

REVERSE PERCENTAGE EXAM QUESTIONS 1.

2.

3.

4.

5.

6.

RATIO AND PROPORTION MODULE 3 - Homework 20H GRADES : D,C

EXAM QUESTIONS 1.

2.

3.

4.

5.

6.

RATIO AND PROPORTION MODULE 3 - Homework 21H GRADES : A

DIRECT PROPORTION EXAM QUESTIONS 1.

2.

3.

INVERSE PROPORTION EXAM QUESTIONS 1.

2.

ALGEBRAIC MANIPULATION MODULE 3 - Homework 22H GRADES : E,D,C

EXAM QUESTIONS 1.

12.

2.

13.

3.

14.

4.

15.

5.

6.

7.

8.

9.

10.

11.

ALGEBRAIC MANIPULATION MODULE 3 - Homework 23H GRADES : B

EXPANDING QUADRATIC EXPRESSIONS EXAM QUESTIONS 1.

2.

3.

FACTORISING QUADRATIC EXPRESSIONS EXAM QUESTIONS 1.

2.

3.

4.

ALGEBRAIC MANIPULATION MODULE 3 - Homework 24H GRADES : A

EXPANDING HARDER QUADRATIC EXPRESSIONS EXAM QUESTIONS 1.

2.

3.

4.

5.

FACTORISING HARDER QUADRATIC EXPRESSIONS EXAM QUESTIONS 1.

2.

3.

4.

a)

b)

NON-LINEAR GRAPHS AND GRAPHICAL SOLUTION OF EQUATIONS


EXAM QUESTION


MODULE 3 - Homework 26H GRADES : A

GRAPHICAL SOLUTION OF EQUATIONS 1 EXAM QUESTION 1.

below



GRAPHICAL SOLUTION OF EQUATIONS 2 EXAM QUESTIONS 1.

2.

3.

below

COLLECTING DATA MODULE 1 - Homework 1H GRADES : D, C

DATA COLLECTION SHEETS AND QUESTIONNAIRES Exam questions 1.

2.

3.

4.

COLLECTING DATA MODULE 1 - Homework 2H GRADES : A

STRATIFIED SAMPLING Exam questions 1.

2.

3.

PRESENTING DATA AND INTERPRETING INFORMATION

MODULE 1 - Homework 3H GRADES : D

STEM AND LEAF DIAGRAMS Exam questions 1.

2.

3.

(a) How many people were asked? (b) What was the median number of driving lessons? (c) Work out the range of the number of driving lessons.


MODULE 1 - Homework 4H GRADES : D

FREQUENCY DIAGRAMS Exam questions 1.

2.


MODULE 1 - Homework 5H GRADES : B

CUMULATIVE FREQUENCY Exam questions 1.

2.



BOX PLOTS Exam questions 1.

2.


MODULE 1 - Homework 7H GRADES : A

HISTOGRAMS Exam questions 1.

2.

3.



TIME SERIES Exam questions 1.

Copy the graph and plot all the other moving averages.

2.

MEASURES OF AVERAGE AND SPREAD MODULE 1 - Homework 9H GRADES : C

AVERAGES FROM TABLES Exam questions 1.

2.

3.

SCATTER DIAGRAMS AND CORRELATION

MODULE 1 - Homework 10H GRADES : C

SCATTER DIAGRAMS AND CORRELATION Exam questions 1.

2.

3.

PROBABILITY MODULE 1 - Homework 11H GRADES : B

RELATIVE FREQUENCY - Exam questions 1.

2.

PROBABILITY MODULE 1 - Homework 12H GRADES : C, B

TREE DIAGRAMS - Exam questions 1.

2.

PROBABILITY MODULE 1 - Homework 13H GRADES : B

COMBINED PROBABILITIES (AND RULE / OR RULE) Exam questions 1.

2.

3.

4.

PROBABILITY MODULE 1 - Homework 14H GRADES : A

DEPENDENT EVENTS Exam questions 1.

2.

3.

4.

1) Find the area and perimeter of each shape.

Compound area + perimeter (mathswatch clip 73)

MODULE 5 - Homework 1H GRADE : D

Circumference of circles (mathswatch clip 72)

MODULE 5 - Homework 2H GRADE : D

Area of circles (mathswatch clip 71)

MODULE 5 - Homework 3H GRADE : D,C

Volume of cuboids + prisms(mathswatch clip 34 + 122)

MODULE 5 - Homework 4H

GRADE : D - C

2)

3)

4)

1) Find the volume of the following cuboids

3cm

5cm 7cm

7cm

12cm 4cm

5) A cuboid has a volume of 80cm3 a width of 5cm and a depth of 2 cm find it’s height?

Surface area (mathswatch clip 121)

MODULE 5 - Homework 5H GRADE : C -B

2)

3)

1) Find the surface area of the following cuboids

3cm

5cm

7cm

7cm

12cm 4cm

5) A cuboid has a surface area of 36cm2 a width of 5cm and a depth of 2 cm find it’s height?

Volume of Spheres and Cones (mathswatch clip 177)

MODULE 5 - Homework 6H GRADE : A-A*

4) A marble paperweight consists of a cuboid and a hemisphere as shown in the diagram. The hemisphere has a radius of 4 cm.

10 cm 10 cm

5 cm

4 cm

Volume of Spheres and Cones (mathswatch clip 177)


4) A marble paperweight consists of a cuboid and a hemisphere as shown in the diagram. The hemisphere has a radius of 4 cm.

10 cm 10 cm

5 cm

4 cm

Length / Area of arcs, sectors


2) A giant paper clip is placed alongside a centimetre ruler. The curved ends are semicircles.

Not drawn accurately

0 1 2 3 4 5 6 7 8 9 10cm

Calculate the length of wire used to make the clip.

3) A circle fits inside a semicircle of diameter 10 cm as shown.

10 cm

Calculate the shaded area.

1) The diagram shows a sector of a circle of radius 9 centimetres.

80º9 cm

Not drawn accurately

Find the perimeter of the sector.

Polygons (mathswatch clip 70)

MODULE 5 - Homework 8H GRADE : C

2)

3)

1) find angle x if the following shape is a rhombus

32o

x

Sequences MODULE 5 - Homework 9H GRADE : C

2) Find the nth term of the following; 3, 8, 13, 18, 23, …. 20, 13, 6, -1, …. 2, 8, 18, 32, 50, ….. ½ , 1, 4 ½ , 8, 12 ½ , ……

A sequence of numbers is shown.

5 9 13 17 21

(a) Find an expression for the nth term of the sequence.

(b) Explain why 83 will not be a term in this sequence.

(a) Part of a number grid is shown below.

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 30 31 32 33 34 35

The shaded cross is called C11 because it has the number 11 at the centre.

This is Cn

n – 7

n

Fill in the empty boxes.

(b) Kevin notices the following number sequence in the grid.

1, 9, 17, 25, 33,...

Write down the nth term of this sequence.

1) Write the first five terms of the following sequences whose nth terms are

n+3 n2+3 3n 8n -2 2n2 n3 n2-5

Straight lines ( mathswatch clip 114 + 143 )


GRADE : C

6 ) Find the midpoints of the following co-ordinates i ) (0,4) (3, 13) ii) (0,7) (2, -1) iii) (10,5) (22, 18)

Solving Equations (Mathswatch clip 105)


GRADE :D-B

11) 2

5

3

3

6

12

xx

12) 164

6

3

2

yy

1) 4y + 3 = 2y + 10

2) 2x + 17 = 5x – 4

3) 2x + 7 = 16 – 4x

4) 20x -15 = 18x -7

5) 5(x + 3) = 2 (x + 6)

6) 4 (2y + 1) = 2 (12 - y)

7) 7 - 3x = 2 ( x + 1)

8) 52

3

x

9) 73

42

x

10) xx

43

40

Reflections and rotations (Mathswatch clip 74 + 75)


GRADE :D-C

Circle theorems (Mathswatch clip 150)


GRADE :B

Trial and improvement (Mathswatch clip 110)


GRADE :C

Translation (Mathswatch clip 77)


GRADE :C

Enlargement (Mathswatch clip 76)


GRADE :C

Transformations (Mathswatch clip 74,75,76,77)


GRADE :C-B

y

x

6

5

4

3

2

1

–1

–2

–3

–4

–5 –4 –3 –2 –1 1 2 3 4 5O

A

(i) Describe fully the single transformation that takes the shaded triangle to triangle A.

(ii) On the grid above translate the shaded triangle by 2 squares to the right and

–6 –4 –2 2 4 60 x

y6

4

2

–2

–4

–6

Draw the Final position of the rectangle after these transformations.

The rectangle is rotated 90’ clockwise about the point ( 1, 0) and then translated by

vector

5

4

(b) Triangle P is an enlargement of the shaded triangle. Find the scale factor and centre of enlargement.

y

x

6

5

4

3

2

1

–1

–2

–3

–4

–5 –4 –3 –2 –1 1 2 3 4 5O

P

The diagram shows four shapes, A, B, C and D.

–4 –3 –2 –1 1 2 3 4 5 6 7 8

6

5

4

3

2

1

–1

–2

–3

–4

O

A

B

C

D

(a) Describe fully the single transformation that takes shape A onto shape B.

(b) Describe fully the single transformation that takes shape B onto shape C.

(c) Describe fully the single transformation that takes shape C onto shape D.

Similar Shapes (Mathswatch clip 123)


GRADE :C-B

Two similar bottles are shown below. The smaller bottle is 20 cm tall and holds 480 ml of water. The larger bottle is 30 cm tall.

20 cm

30 cm

Not to scale

How much water does the larger bottle hold?

Dimensions of Formulae (Mathswatch clip 124)


GRADE :C-B

2) a, b, and c represent lengths combine a, b, c, to find five formulae that could represent

i) volume

ii) area

Compound Measures (Mathswatch clip 126)


GRADE :C-B

Bounds (Mathswatch clip 125)


GRADE : B

6) Sameera runs 100m (to the nearest 10m) in 12 seconds (correct to the nearest second).

Last time she ran the race her maximum possible speed was 8.2 metres per second – can she be sure that she has run faster his time? Give a reason for this answer

Real life graphs (Mathswatch clip 117)


GRADE : C

Real life graphs (Mathswatch clip 117)


GRADE : C

Mr Smith leaves the home at 10 am to go to the shopping mall. He walks to the station where he catches a train. He gets off the train at the mall. The travel graph shows his journey.

15

10

5

010 am 11 am 12 am 1pm 2 pm

Time

Distancefrom home(km)

After shopping Mr Smith goes home by taxi. The taxi leaves the mall at 1 pm and arrives at his home at 1.45 pm.

(a) Complete the travel graph. (2)

(b) Calculate the average speed of the taxi.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Answer .......................................................km per hour (2)

Substitution (Mathswatch clip 65)


GRADE : C

Forming Equations (Mathswatch clip 106)


GRADE : C

GRADE : C

Changing the subject of a formulae (Mathswatch clip 107)


MODULE 3 - Homework 1H - Meden School€¦ · INTEGERS, RECIPROCALS, FACTORS, MULTIPLES AND PRIME NUMBERS MODULE 3 - Homework 1H GRADES : E,D BIDMAS Follow the correct order of operations

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