Work out how much each person gets.
Jack £ ………..
Jill £ ………....
(Total 2 marks)
2. (a) Express the following numbers as products of their prime factors.
(i) 56
……….
(ii) 84
……….
(4) (b) Find the Highest Common Factor of 56 and 84.
………
(1) (Total 5 marks)
3. In a sale all the normal prices are reduced by 18%.
In the sale Mandy pays £12.71 for a hat.
Calculate the normal price of the hat.
£………..
(Total 3 marks)
4. pq
q x p
p = 4 × 105 q = 1.25 × 104
(a) Calculate the value of x.
Give your answer in standard form.
………
(2) (b) Make q the subject of the formula
pq q x p
q = ……….
5. (a) Express the following numbers as products of their prime factors.
(i) 60,
...
(ii) 96.
...
(4) (b) Find the Highest Common Factor of 60 and 96.
...
(1) (c) Work out the Lowest Common Multiple of 60 and 96.
...
(2) (Total 7 marks)
6. A garage keeps records of the costs of repairs to its customers’ cars.
The table gives information about the costs of all repairs which were less than £250 in one week.
Cost, (£C) Frequency
0 < C 50 4
50 < C 100 8
100 < C 150 7
150 < C 200 10
200 < C 250 11
(a) Find the class interval in which the median lies.
...
(2) There was only one further repair that week, not included in the table.
That repair cost £1000.
Dave says ‘The class interval in which the median lies will change.’
(b) Is Dave correct? Explain your answer.
...
...
(1) The garage also sells cars.
It offers a discount of 20% off the normal price for cash.
Dave pays £5200 cash for a car.
(c) Calculate the normal price of the car.
£...
(3) (Total 6 marks)
7.
x
x
A cuboid has a square base of side x cm.
The height of the cuboid is 1 cm more than the length x cm.
The volume of the cuboid is 230 cm3. (a) Show that x3 + x2 = 230
(2)
The equation x3 + x2 = 230 has a solution between x = 5 and x = 6.
(b) Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working.
x = ...
(4) (Total 6 marks)
8. y2 =
b a
ab
a = 3 × 108 b = 2 × 107 Find y.
Give your answer in standard form correct to 2 significant figures.
y = ...
(Total 3 marks)
9. A floppy disk can store 1 440 000 bytes of data.
(a) Write the number 1 440 000 in standard form.
………
(1)
A hard disk can store 2.4 × 109 bytes of data.
(b) Calculate the number of floppy disks needed to store the 2.4 × 109 bytes of data.
………
(3) (Total 4 marks)
10.
Diagrams accurately drawn
NOT
100° 100°
A
E
B F
C
G
D H
6 cm
5 cm
8 cm
4 cm
Shapes ABCD and EFGH are mathematically similar.
(i) Calculate the length of BC.
BC = ……… cm (ii) Calculate the length of EF.
EF = ……… cm
(Total 5 marks)
11. The table shows the number of computer games sold in a supermarket each month from January to June.
Jan Feb Mar Apr May Jun 147 161 238 135 167 250 (a) Work out the three month moving averages for this information.
... ... ... ...
(2) In a sale, a supermarket took 20% off its normal prices.
On Fun Friday, it took 30% off its sale prices.
Fred says, “That means there was 50% off the normal prices”.
(b) Fred is wrong. Explain why.
(2) (Total 4 marks)
12. The equation
x3 – 2x = 67 has a solution between 4 and 5
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show ALL your working.
x = ...
(Total 4 marks)
13. A nanosecond is 0.000 000 001 second.
(a) Write the number 0.000 000 001 in standard form.
...
(1)
A computer does a calculation in 5 nanoseconds.
(b) How many of these calculations can the computer do in 1 second?
Give your answer in standard form.
14. Use your calculator to work out the value of
63 . 9 81 . 4
52 . 4 27 . 6
(a) Write down all the figures on your calculator display.
...
(2) (b) Write your answer to part (a) to an appropriate degree of accuracy.
...
(1) (Total 3 marks)
15. A company bought a van that had a value of £12 000 Each year the value of the van depreciates by 25%.
(a) Work out the value of the van at the end of three years.
£ ...
(3)
The company bought a new truck.
Each year the value of the truck depreciates by 20%.
The value of the new truck can be multiplied by a single number to find its value at the end of four years.
(b) Find this single number as a decimal.
...
(2) (Total 5 marks)
16. The equation x3 + 4x = 100
has one solution which is a positive number.
Use the method of trial and improvement to find this solution.
Give your answer correct to 1 decimal place.
You must show ALL working.
x = ...
(Total 4 marks)
17. Nicola invests £8000 for 3 years at 5% per annum compound interest.
(a) Calculate the value of her investment at the end of 3 years.
£...
(3) Jim invests a sum of money for 30 years at 4% per annum compound interest.
Value
£
Value
£
Value
£
Value
£ O
O
O
O Years
Years
Years
Years A
C
B
D
(b) Write down the letter of the graph which best shows how the value of Jim’s investment changes over the 30 years.
...
(1)
Hannah invested an amount of money in an account paying 5% per annum compound interest.
After 1 year the value of her investment was £3885
(c) Work out the amount of money that Hannah invested.
£...
(3) (Total 7 marks)
18. Fred runs 200 metres in 21.2 seconds.
(a) Work out Fred’s average speed.
Write down all the figures on your calculator display.
... metres per second
(2) (b) Round off your answer to part (a) to an appropriate degree of accuracy.
... metres per second
(1)
19. Three woman earned a total of £36 They shared the £36 in the ratio 7:3:2 Donna received the largest amount.
(a) Work out the amount Donna received.
£….………..
(3)
A year ago, Donna weighed 51.5 kg.
Donna now weighs 8 2
1% less.
(b) Work out how much Donna now weighs.
Give your answer to an appropriate degree of accuracy.
……….kg
(4) (Total 7 marks)
20. The equation
x3 – 4x = 24 has a solution between 3 and 4.
Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working.
x = ………..
(Total 4 marks)
% less.
(b) Work out how much Donna now weighs.
Give your answer to an appropriate degree of accuracy.
……….kg
(4) (Total 7 marks)
21. In a sale, normal prices are reduced by 20%.
SALE 20% OFF
Andrew bought a saddle for his horse in the sale.
The sale price of the saddle was £220.
Calculate the normal price of the saddle.
£………
(Total 3 marks)
22. Work out (3.2 × 105) × (4.5 × 104)
Give your answer in standard form correct to 2 significant figures.
………..
(Total 2 marks)
23. Ann and Bob shared £240 in the ratio 3 : 5 Ann gave a half of her share to Colin.
Bob gave a tenth of his share to Colin.
What fraction of the £240 did Colin receive?
...
(Total 4 marks)
24. A garage sells cars.
It offers a discount of 20% off the normal price for cash.
Dave pays £5200 cash for a car.
Calculate the normal price of the car.
£ ...
(Total 3 marks)
