Write these integers in order, starting with the smallest: -8, 3, -1, 0, -5
(Total for Question 1 is 1 mark)
2
Write 6407 to the nearest hundred.
(Total for Question 2 is 1 mark)
3
Ryan is investigating the number 24 and the number 36.
(a)List all the factors of 24.(1)
(b)Find the highest common factor (HCF) of 24 and 36.(1)
(Total for Question 3 is 2 marks)
4
Work out 3/4 + 1/8, giving your answer as a fraction in its simplest form.
(Total for Question 4 is 2 marks)
5
Calculate 15% of 260.
(Total for Question 5 is 2 marks)
6
Work out (-3) + (-7) - (-4).
(Total for Question 6 is 2 marks)
7
Calculate the value of 5 + 3 x (8 - 2) / 6, showing your method.
(Total for Question 7 is 3 marks)
8
Priya buys 3 notebooks at £2.45 each and a pen at £1.20. She pays with a £10 note. Work out how much change she receives.
(Total for Question 8 is 3 marks)
9
Express 84 as a product of its prime factors.
(Total for Question 9 is 3 marks)
10
A school trip costs £960 in total, shared between Year 8 and Year 9 in the ratio 5 : 3.
(a)Work out how much Year 8 pays and how much Year 9 pays.(2)
(b)A discount voucher reduces Year 9's share by 10%. Work out the new amount Year 9 pays.(2)
(Total for Question 10 is 4 marks)
11
Freya is estimating a calculation.
(a)Round 3.14159 to 3 significant figures.(1)
(b)By rounding each number to 1 significant figure, estimate the value of (198 x 5.2) / 9.8(2)
(Total for Question 11 is 3 marks)
12
A recipe for 6 people needs 450g of flour. Work out how much flour is needed to make the recipe for 9 people.
(Total for Question 12 is 3 marks)
13
Chidi is converting numbers between standard form and ordinary numbers.
(a)Write 0.0000523 in standard form.(2)
(b)Write 3.6 x 104 as an ordinary number.(1)
(Total for Question 13 is 3 marks)
14
Calculate the value of √169 + 52 - 33
(Total for Question 14 is 3 marks)
15
A shop increases the price of a jacket from £45 to £54. Work out the percentage increase.
(Total for Question 15 is 3 marks)
16
After a 20% discount, a bicycle costs £192. Work out the original price of the bicycle.
(Total for Question 16 is 3 marks)
17
Jamal invests £2000 at 4% per annum compound interest. Work out the total amount in his account after 3 years, giving your answer to the nearest penny.
(Total for Question 17 is 4 marks)
18
Two warning lights flash at regular intervals. One flashes every 18 seconds and the other every 24 seconds. Both flash together at exactly 09:00:00.
(a)Find the lowest common multiple (LCM) of 18 and 24.(2)
(b)Work out the time at which the two lights will next flash together.(2)
(Total for Question 18 is 4 marks)
19
A charity's total income is split between Bake Sale, Sponsored Walk and Raffle in the ratio 3 : 5 : 2. The Raffle raised £180 less than the Sponsored Walk.
(a)Find the value of one part of the ratio.(2)
(b)Find the total amount raised by all three activities.(2)
(c)What percentage of the total was raised by the Bake Sale?(1)
(Total for Question 19 is 5 marks)
20
Calculate the value of (7 - 2 x 5)2 + √32 + 42
(Total for Question 20 is 4 marks)
21
The distance from Earth to the Moon is approximately 3.84 x 105 km. A spacecraft travels at an average speed of 3200 km/h.
(a)Estimate the time taken for the journey, in hours, giving your answer to 3 significant figures.(3)
(b)Convert your answer to part (a) into days, giving your answer to 1 decimal place.(2)
(Total for Question 21 is 5 marks)
22
A cafe's weekly takings are shared between ingredients, wages and profit in the ratio 4 : 5 : 3. In one week the total takings were £2880.
(a)Work out the profit for that week.(2)
(b)The following week, takings increase by 12% but the ratio stays the same. Work out the new profit, giving your answer to the nearest penny.(3)
(Total for Question 22 is 5 marks)
Mark scheme · CE.M1 Number and Calculation
Question 1
B1 -8, -5, -1, 0, 3 in this order, cao
Answer: -8, -5, -1, 0, 3
Question 2
B1 6400 cao
Answer: 6400
Question 3
(a) B1 1, 2, 3, 4, 6, 8, 12, 24 all listed, oe
(a) Answer: 1, 2, 3, 4, 6, 8, 12, 24
(b) B1 12 cao
(b) Answer: 12
Question 4
M1 converts 3/4 to 6/8, or common denominator of 8 seen, oe
A1 7/8 cao (already in simplest form)
Answer: 7/8
Question 5
M1 finds 10% (26) and 5% (13), or 0.15 x 260, oe
A1 39 cao
Answer: 39
Question 6
M1 correctly rewrites as -3 - 7 + 4, oe
A1 -6 cao
Answer: -6
Question 7
M1 evaluates bracket: (8 - 2) = 6
M1 evaluates 3 x 6 / 6 = 3, using correct order of operations
A1 8 cao
Answer: 8
Question 8
M1 3 x 2.45 = 7.35
M1 total cost 7.35 + 1.20 = 8.55, then 10 - 8.55
A1 £1.45 cao
Answer: £1.45
Question 9
M1 divides by 2 twice: 84 = 2 x 42 = 2 x 2 x 21
M1 divides 21 by 3 and 7 to reach all prime factors
A1 22 x 3 x 7 oe
Answer: 22 x 3 x 7
Question 10
(a) M1 finds one share of the ratio: 960 / 8 = 120
(a) A1 Year 8 = £600 and Year 9 = £360, both cao
(a) Answer: Year 8 = £600, Year 9 = £360
(b) M1 10% of 360 = 36, or 360 x 0.9, ft from part (a)
(b) A1 £324 cao
(b) Answer: £324
Question 11
(a) B1 3.14 cao
(a) Answer: 3.14
(b) M1 rounds correctly to 200, 5 and 10
(b) A1 100 cao
(b) Answer: 100
Question 12
M1 finds the amount for 1 person: 450 / 6 = 75
M1 multiplies by 9: 75 x 9
A1 675g cao
Answer: 675g
Question 13
(a) M1 5.23 seen
(a) A1 5.23 x 10-5 cao
(a) Answer: 5.23 x 10-5
(b) B1 36000 cao
(b) Answer: 36000
Question 14
M1√169 = 13 and 52 = 25 both correctly evaluated
M1 33 = 27 correctly evaluated, and 13 + 25 = 38
A1 11 cao
Answer: 11
Question 15
M1 finds the increase: 54 - 45 = 9
M1 divides by the original amount: 9 / 45
A1 20% cao
Answer: 20%
Question 16
M1 recognises £192 represents 80% of the original price
M1 divides 192 by 0.8, oe
A1 £240 cao
Answer: £240
Question 17
M1 year 1: 2000 x 1.04 = 2080.00, oe
M1 year 2: 2080 x 1.04 = 2163.20, oe
M1 year 3: 2163.20 x 1.04 = 2249.728, oe (or use of 2000 x 1.043)
A1 £2249.73 cao, rounded to the nearest penny
Answer: £2249.73
Question 18
(a) M1 18 = 2 x 32 and 24 = 23 x 3, or lists multiples correctly
(a) A1 72 cao
(a) Answer: 72
(b) M1 uses LCM = 72 seconds, ft from part (a)
(b) A1 09:01:12 cao
(b) Answer: 09:01:12
Question 19
(a) M1 recognises (5 - 2) parts = 3 parts = £180
(a) A1 £60 cao
(a) Answer: £60
(b) M1 total parts = 3 + 5 + 2 = 10, ft from part (a)
(b) A1 £600 cao
(b) Answer: £600
(c) B1 30% cao, ft from parts (a) and (b)
(c) Answer: 30%
Question 20
M1 evaluates the bracket: 7 - 2 x 5 = -3, using correct order of operations
M1 squares the bracket: (-3)2 = 9
M1 evaluates √32 + 42 = √25 = 5
A1 14 cao
Answer: 14
Question 21
(a) M1 converts 3.84 x 105 to 384000, oe
(a) M1 divides distance by speed: 384000 / 3200
(a) A1 120 hours cao, awrt 3 sf
(a) Answer: 120 hours
(b) M1 divides by 24, ft from part (a)
(b) A1 5.0 days cao
(b) Answer: 5.0 days
Question 22
(a) M1 total parts = 4 + 5 + 3 = 12, one part = 2880 / 12 = 240