N4 Mathematics Non Calculator Added Value Practice DO NOT WRITE ON THESE SHEETS Percentages: Core skills (a) 30% of 450 (b) 2% of 1200 (c) 15% of 60 (d) 65% of 40 In Context: Q1: Last year a holiday was priced at £800. This year the same holiday has risen by 10%. What is the new cost of the holiday? Q2: A ship was sailing at 25km/hour. It increased its speed by 40%. What was its new speed? Q3: The temperature in the Sahara Desert was 40 ̊ at noon. By 4pm, it had dropped by 5% of this temperature. What is the new temperature? Q4: A tractor bought for £30 000 in 2002 has depreciated in value over the past few years. It is now worth 32% less than the original value. What is the tractor worth today? Q5: Zachar knows that the manufacturers of Raisin Flakes claim to have at least 20% raisins in every box of cereal. He discovers that a 550g packet of Raisin flakes has 100g of raisins in it. Has this box met with the manufacturers claim? From Linwood High School Website
48
Embed
N4 Mathematics Non Calculator Added Value Practice
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
N4 Mathematics Non Calculator Added Value Practice DO NOT WRITE ON THESE SHEETS Percentages: Core skills (a) 30% of 450 (b) 2% of 1200 (c) 15% of 60 (d) 65% of 40 In Context: Q1: Last year a holiday was priced at £800.
This year the same holiday has risen by 10%.
What is the new cost of the holiday?
Q2: A ship was sailing at 25km/hour.
It increased its speed by 40%.
What was its new speed?
Q3: The temperature in the Sahara Desert was 40 ̊ at noon.
By 4pm, it had dropped by 5% of this temperature.
What is the new temperature?
Q4: A tractor bought for £30 000 in 2002 has depreciated in value over the past few
years. It is now worth 32% less than the original value.
What is the tractor worth today?
Q5: Zachar knows that the manufacturers of Raisin Flakes claim to have at least 20% raisins in every box of cereal. He discovers that a 550g packet of Raisin flakes has 100g of raisins in it. Has this box met with the manufacturers claim?
From Linwood High School Website
Statistics - Mean:
Core skills
Find the Mean of (a) 2,6,1,2,4 (b) 12,8,14,6,0,1,8
In Context:
Q1: Calculate the mean of the following and round your answer to 2 decimal places.
£6, £9, £12, £27, £25, £3
Q2: Mr Gibson buys 9 jars of humbugs. There is supposed to be an average of 52 humbugs in each jar.
He finds that they contain the following number of humbugs
52, 52, 55, 52, 55, 52, 53, 51, 55, 51
(a) (i) Calculate the mean number of humbugs.
(ii) Should he complain?
(b) Find the median
(c) What is the mode?
Q3: The heights of seven children in Mr Bennett’s class are listed below.
172cm, 175cm, 183cm, 172cm, 187cm, 181cm, 183cm
Calculate the mean height.
Q4: The contents of nine boxes of chocolates are examined.
The boxes contain the following number of chocolates:-
a) 2.5 + 6.25 – 3.8 b) 5.18 + 2.6 – 3.12 c) 8.6 – 3.15 + 2.4
In context:
Q1: In a science experiment 4.5g of copper is mixed with 2.15g of sulphuric acid.
The reaction of these chemicals causes the overall mass to reduce by 3.85g.
What is the mass of the remaining chemical mix?
Q2: Bill the Busker made £ 4.85 in the morning and £ 12.50 in the afternoon.
If he spent £ 5 on a fish supper on the way home how much did he have left?
Q3: Emma timed herself completing the three levels of cup stacking. The first two levels are stacking and the total time taken to stack is the addition of these two times. The third level is unstacking back to the start.
Her separate times for the 2 stacking levels were 4.5 seconds and 8.22 seconds.
Her third level time for unstacking was 5.8 seconds.
How much longer did it take Emma to stack than unstack?
Q4: Mrs Lister is redecorating her flat.
She buys wallpaper costing £ 107.94 and paint costing £ 49.99.
From a budget of £ 200 calculate how much she has left.
Plot these points and find the length of the line AB.
Trigonometry: Core skills
In Context:
2.
3.
4.
5.
Co-ordinates 1. (a) On the grid below, plot the points A(2, 6), B(8, 2) and C(6, –1).
(b) Plot a fourth point D so that ABCD is a rectangle.
(c) Find the length of the line AD to 1 decimal place. (Hint – Pythagoras) 2. The coordinates of 3 corners of a square are: ( 3 , 1 ), ( –1 , 1 ) and ( 3 , –3 ). (a) What are the coordinates of the 4th corner? (b) Calculate the length of the diagonal. (1dp) 3. The vertices of a shape have coordinates: A ( 3 , 3 ) ,B ( 5, –1 ) , C( 3 , –5 ) and D ( 1 , –1 ).
(a) Plot the points on a co-ordinate diagram and join them in order. (b) What is the name of the shape? (c) By considering the diagonals of this quadrilateral, calculate the length of each side.
Comparing Data Sets:
Core skills
Q1: For this set of data:
3, 4, 7, 3, 3, 8, 9, 5
Find a) the mean b) the mode c) the median d) the range
e) Which of the averages least represents the data, and why?
In context
Q1:
(a) The pie chart shows the favourite flavour of
crisps from a sample of 40 pupils.
Using the information in the table below calculate
Prawn cocktail Salt &
Vinegar
Plain
the sector angles of the pie chart.
Crisp flavour No of people Angle Salt and vinegar 22 Prawn cocktail 10 Plain 8
(b) If one of the pupils from the above sample was chosen at random, what would be the Probability that their favourite flavour of crisps was Plain?
Q2: The ages of children at Youth Club A are listed below:
7, 10, 11, 12, 9, 8, 7, 8, 10, 9, 9, 9, 7, 11, 8
a) Construct a frequency table showing these ages
b) What is the mean age of the children?
c) Youth Club B had the same number of children, but the mean age was 10. Make a comment comparing the two means.
ADDED VALUE ASSESSMENT - A
Paper 1 Time: 20 minutes Marks
x No calculator is permitted x Answers without explanation may receive no credit;
Make sure all your working is clear.
x All questions must be attempted.
1 Sports4u.com has a sale on all sports shoes.
Original Price £80
20% Discount!!
(a) How much money will be saved on the above sports shoes? (1) (b) What is the new price of these sports shoes? (1)
2 During one week in winter the midday temperatures in Edinburgh were recorded as shown in the table below.
Day Sun Mon Tue Wed Thurs Fri Sat Temp (oC) 1 2 4 1 1 4 3
Calculate the mean midday temperature for the week correct to 2 decimal places (3)
3 240 pupils are going on a school trip to Alton Towers. Only 83 of these pupils were brave
enough to ride the Nemesis rollercoaster.
(a) How many pupils had a ride on the Nemesis rollercoaster? (2)
(b) How many pupils did NOT have a ride on Nemesis? (1)
4 Laura collects her paper round money on a Sunday. She has to collect £12.75 in total from her Brown Street customers and £18.20 from her High Street customers.
(a) How much should she collect altogether? (2) (b) Including tips she received £40.
How much of this money was made up in tips? (2)
5 Paul cycles 2.3 miles for 6 days. What is the total distance he cycled? (3)
Total (15)
End of Paper 1
ADDED VALUE ASSESSMENT - A
Paper 2 Time: 40 minutes Marks
x You may use a calculator. x Answers without explanation may receive no credit;
Make sure all your working is clear.
All questions must be attempted.
1 It took Kate 5 hours and 20 minutes to drive from Edinburgh to Liverpool at an average speed of 45 miles per hour. How far is it from Edinburgh to Liverpool?
(3)
2 A hotel charges a set fee of £200 for the use of their function room AND an additional £15 per guest for weddings.
(a) Let x be the number of guests and write down a formula in x for the total cost of a wedding. (1)
(b) How much would it cost for a wedding with 55 guests? (1)
(c) Ian and Jill have £1400 to pay for their wedding function.
Form an equation in x and solve it to find the maximum number of guests they can invite. (3)
25m
10m
3.5m
1.5m 3
This swimming pool is 25m long and 10m wide.
It is 1.5m deep at the shallow end and 3.5m deep at the deep end.
Calculate the volume of water in cubic metres in the pool when it is full. (5)
4 The sides of a bridge are constructed by joining sections. The sections are made of steel girders.
3 sections 2 sections 1 section
Number of Sections (s) 1 2 3 4 ………. s Number of Girders (g) 3 7
(a) Write down a formula for the number of girders, g, required when the number of sections, s, is known. (2)
(b) How many girders will be needed for 10 sections? (1)
(c) How many sections can be constructed from 87 girders? (2)
5 ABCD is a RHOMBUS with an area of 24 square units. What are the coordinates of B and D?
(2)
6 A banner for a parade is to be edged all around with gold braid.
The banner (shown above) is in the shape of a rectangle with an isosceles
triangle below it.
Calculate the total length of gold braid needed. (6)
32cm
56cm 86cm
7 Alice, whose eyes are 4.5 feet above ground level, is attempting to measure the height of a clock tower. She is standing 23 feet away from the clock tower looking at the top at an angle of 67o to the horizontal.
Calculate the height of the clocktower correct to 2 decimal places.
(4)
Total (30)
End of Paper 2
ADDED VALUE ASSESSMENT - B
Paper 1 Time: 20 minutes Marks
x You may use a calculator. x Answers without explanation may receive no credit;
Make sure all your working is clear.
All questions must be attempted.
Q1 : Mrs Young bought a new Volkswagen Polo for £9000. In the first year it lost 20% of its value.
(a) How much did it loose in the first year? (1) (b) What is it now worth? (1)
Q2 : Harry downloads music each week to his MP3 player. The number of downloads is shown for the first 6 weeks is shown in the table below:
Week 1 2 3 4 5 6
Downloads 9 7 12 10 15 5
Calculate the mean number of downloads per week correct to 2 decimal places. (3)
Q3 : A brown bear weighs 900kg before it hibernates for the winter.
During the winter it loses 103 of its body weight.
(a) How much weight did the bear loose during hibernation? (2) (b) How much did he weigh at the end of his hibernation period? (1)
Q4 : A decorator knows that he usually he can get 3 strips from a roll of wallpaper. For a hallway he uses 2 strips of length 2.3m and 2.75m. The roll of wallpaper is 7.4metres long.
(a) What length of wallpaper has he used in the first two strips? (2) (b) Does he have enough left in the same roll to cover a length of 2.2m? (2)
Q5 : For a chemistry experiment each group of pupils needs to measure 24.4ml of an acid. If there are 6 groups in the class, how many millilitres of acid is used altogether? (3)
END OF PAPER 1
ADDED VALUE ASSESSMENT - B
Paper 2 Time: 40 minutes Marks
x You may use a calculator. x Answers without explanation may receive no credit;
Make sure all your working is clear.
All questions must be attempted.
Q1: Mr Campbell takes his family on a holiday to York. If he drives the 180 miles in 4 hours 30 minutes, what is his average speed for the journey?
(3)
Q2: A BMX start ramp is shown opposite:
(a) Calculate the area of paint needed to cover side A. (3) (b) What volume of concrete would be needed to create the whole of the start ramp?
(2)
Q3: Triangle ABC is shown below. A is the point (-2, -1) and B is the point (4, -1).
Find the co-ordinates of C.
(5)
(-2,-1) (4,-1)
Q4: In a Greek café the tables are triangular in shape.
Tables (T) 1 2 3 4 5
People (P) 3 4
(a) Copy and complete the table above. (1)
(b) Write down a formula which will give P, the number of people, when you have T, the number of
tables. (1)
(c) How many people can be seated at 13 tables? (1)
(d) How many tables would be needed for 21 people? (2)
Q5: A Swedish home store sells glasses in packs of 3.
Each shelf in the warehouse can hold x number of packs.
(a) Make an expression in x for the number glasses that can be held on each shelf.
(1)
(b) If there are 5 shelves in each warehouse stocking these glasses, write another
expression in x for the number of glasses that are held in the warehouse.
(1)
(c) If the warehouse knows that in total there are 1800 individual glasses in stock,
(i) Form an equation in x (1)
(ii) Solve it to find the number of packs of glasses in the warehouse.
(1)
Q6: The plan for a section of a church 50 metres high and 10 metres wide is shown opposite.
Regulations state that the angle xo of the steeple cannot exceed 70o.
(a) Calculate the angle and state whether this complies with regulations. (3) (b) Find the length, l, of the slanted roof. (3)
Q7 : The time of a swimmer’s race over 50m for two swim teams is shown below.
Freestyle Time over 50 metres
Team South Team North
5 2 3 7
4 4 2 0 3 0 4 8
7 5 2 1 4 1 6 9 9
1 5 6
2 7 means 27seconds
(a) What is the modal swim time ? (1) (b) Which team has the fastest time ? (1) (c) What is the median swim time for each team ? (3)
Added Value Practice A Paper 1: Non-calculator Q1. (a) Find 5% of 340 kilograms. 1 (b) Find of £144 1
Q2. The amount of fish food required is proportional to the number of fish. Anna has a fish tank containing 8 goldfish. She finds that 24 grams of fish food will feed her fish for 1 day. How many grams of fish food will she need for 1 day if she has 12 fish?
2
Q3. You joined a queue for a rock concert. The speed of the queue was 0·1 metres per second. It took you 20 minutes to reach the front of the queue. How long was the queue, in metres, when you joined it? 3 Q4 Find a formula connecting the variables in the table below
ans : 17 1 mark •1 finds percentage of a quantity ans : 64 1 mark •1 finds a fraction of a quantity
•1 5 × (340 ÷ 100) = 17 •1 (144 ÷ 9) × 4 = 64
2
ans : 36 grams 2 marks •1 calculates food for 1 fish •2 calculates food for 12 fish
•1 24 ÷ 8 = 3 •2 3 × 12 = 36
3 ans : 120 metres 3 marks •1 knows how to calculate distance •2 changes minutes to seconds •3 calculates distance
•1 D = S × T •2 20 × 60 = 1200 •3 D = 0·1 × 1200 = 120
4 Ans: F = 3a +1 •1 Correct multiplier •2 Correct addition NB: to be awarded 2nd mark formula must be written with the correct letters in the correct places with an ‘equals’ sign
Added Value Practice A Paper 2: Calculator Q1. Peter and Arif are playing a Word Puzzle board game. The game contains 30 consonants and 20 vowels. The letters are put together in a bag and letters are picked out at random by each player in turn. Arif wins the toss to choose the first letter. (a) What is the probability that the first letter chosen by Arif is a vowel? 2 (b) Arif keeps his first letter, which is a vowel, and Peter now picks his first letter. What is the probability that Peter’s first letter is a consonant? 2
Q2. Jack is building a robot for a competition. The sloping edges are to be mounted with sensor strips. Calculate the length of each strip, x. 4
Q4. A driveway leading up to a garage is 3 m long and at an angle of 18o to the horizontal. Calculate the height of the driveway, h. 3
Q5. The area above the front entrance of Newtonville town hall is to be covered with marble. The area is a rectangle with three semicircles removed. Calculate the area of marble needed. 5
Q6. The graph shows the height above sea-level, in metres, of eight places in Scotland and the corresponding temperatures.
(a) Draw a line of best fit through the points on the graph. 1 (b) Use your line of best fit to estimate the temperature of a place which is 800metres above sea-level.
Q7. Aaron is a salesman. He earns £350 per month plus 5·5% commission on all his sales. Calculate his monthly salary in a month when his sales total £6400. 3 Q8. The roof on Tom’s house is in the shape of an isosceles triangle. The slope of the roof is 3·6 metres and the height is 2 metres. 2 m Calculate the angle, xo, at the top of the roof. 4
ans : 2/5 2 marks •1 calculates probability •2 simplifies answer ans : 30/49 2 marks •1 calculates new total •2 calculates probability
•1 P(vowel) = 20/50 •2 2/5
•1 number of letters = 49 •2 30/49
2
ans : 25 cm 4 marks •1 identifies rt ∠d triangle •2 knows to use Pythagoras •3 substitutes values •4 calculates x
•1 •2 a2 + b2 = c2 •3 202 + 152 = x2 •4 x = 25
3 ans : x = 7 3 marks •1 collects like terms •2 simplifies both sides •3 solves equation
•1 6x − 3x = 34 – 13 •2 3x = 21 •3 x = 7
4
ans : 0·97 m 3 marks •1 knows to use tan ratio •2 substitutes values •3 evaluates correctly
•1 tan = opp/adj •2 tan 18o =h/3 •3 h = 0·97
5
ans : 5·43 m2 5 marks •1 calculates area of rectangle •2 calculates 2 smaller semi-circles •3 calculates larger semi-circles •4 knows how to calculate area •5 calculates area