260 pounds sterling is shared between Ahmed and Grace in the ratio 5:8. Work out how much each person receives.
(Total for Question 17 is 3 marks)
18
A library has 216 books. 5/9 of the books are fiction. Calculate how many books are fiction.
(Total for Question 18 is 2 marks)
19
A jacket costs 90 pounds sterling. In a sale its price is reduced by 30%. Work out the sale price.
(Total for Question 19 is 3 marks)
20
Solve 7x + 4 = 60.
(Total for Question 20 is 2 marks)
21
Work out 55% of 460.
(Total for Question 21 is 2 marks)
22
Write 3/8 as a decimal.
(Total for Question 22 is 1 mark)
23
Round 7.283 to 1 decimal place.
(Total for Question 23 is 1 mark)
24
Work out 312 - 7 x 8.
(Total for Question 24 is 2 marks)
25
A cafe sells sandwiches at 4 pounds sterling each. Calculate the total cost for 17 sandwiches.
(Total for Question 25 is 2 marks)
26
Marcus buys 7 pencils at 25 pence each and a ruler for 1.60 pounds sterling. He pays with a 5 pound note. Calculate how much change he receives.
(Total for Question 26 is 4 marks)
27
Work out the highest common factor of 36 and 84.
(Total for Question 27 is 2 marks)
28
Work out the lowest common multiple of 6 and 10.
(Total for Question 28 is 2 marks)
29
A recipe for 5 people needs 300 g of flour. Hassan wants to make the recipe for 8 people.
(a)Work out the amount of flour needed per person.(2)
(b)Work out the total amount of flour needed for 8 people.(2)
(Total for Question 29 is 4 marks)
30
Chidi has 5/12 of a box of 348 sweets. Calculate how many sweets Chidi has.
(Total for Question 30 is 2 marks)
31
Work out 3 5/6 + 1 3/4.
(Total for Question 31 is 2 marks)
32
Tariq saves 16 pounds sterling each week. Calculate how much he saves in 9 weeks.
(Total for Question 32 is 2 marks)
33
Sofia invests 800 pounds sterling in a savings account paying simple interest at 3% per annum. Calculate the total amount in her account after 4 years.
(Total for Question 33 is 4 marks)
34
Ben orders a laptop priced at 540 pounds sterling. The shop offers 15% off for students. There is also a delivery charge of 12.50 pounds sterling, which is not discounted. Calculate the total amount Ben pays.
(Total for Question 34 is 4 marks)
35
Solve each equation.
(a)Solve 5y + 9 = 39.(2)
(b)Solve 9x - 11 = 4x + 24.(3)
(Total for Question 35 is 5 marks)
36
A charity bake sale raises 540 pounds sterling from 3 stalls, shared in the ratio 4:5:6.
(a)Work out the largest of the three stalls' shares.(2)
(b)The organisers keep 20% of the total 540 pounds sterling for running costs, and the rest is given to charity. Calculate the amount given to charity.(3)
(Total for Question 36 is 5 marks)
37
By rounding each number to 1 significant figure, estimate the value of 62.3 x 4.8.
(Total for Question 37 is 2 marks)
38
A train travels 234 km in 3 hours at a constant speed.
(a)Calculate the train's average speed in km/h.(2)
(b)At this speed, calculate how far the train would travel in 5 hours.(2)
(Total for Question 38 is 4 marks)
39
Layla scored 42 out of 50 in a maths test and 51 out of 75 in a science test. By converting both scores to percentages, work out which test she scored more highly on.
(Total for Question 39 is 3 marks)
40
A shop reduces the price of a 120 pounds sterling bicycle by 30% in a spring sale. It is then reduced by a further 5% of the new, already reduced, price in a clearance sale. Calculate the final price of the bicycle.
(Total for Question 40 is 5 marks)
Mark scheme · CE.M34 Mental Arithmetic: Practice Set 8
Question 1
B1 134 cao
Answer: 134
Question 2
B1 57 cao
Answer: 57
Question 3
B1 54 cao
Answer: 54
Question 4
B1 18 cao
Answer: 18
Question 5
B1 169 cao
Answer: 169
Question 6
B1 16 cao
Answer: 16
Question 7
B1 18 cao
Answer: 18
Question 8
B1 -16 cao
Answer: -16
Question 9
B1 0.35 oe
Answer: 0.35
Question 10
B1 47 cao (correct order of operations)
Answer: 47
Question 11
B1 13/20 oe
Answer: 13/20
Question 12
M1 90 / 6 = 15 oe
A1 75 cao
Answer: 75
Question 13
M1 10% of 260 = 26 and 5% of 260 = 13, or equivalent valid method oe
A1 117 cao
Answer: £117
Question 14
M1 6 x 5 = 30 seen (correct order of operations)
A1 24 cao
Answer: 24
Question 15
M1 - (-14) = + 14 oe
A1 22 cao
Answer: 22
Question 16
(a) B1 49 cao
(a) Answer: 49
(b) B1 13 cao
(b) Answer: 13
(c) B1 64 cao
(c) Answer: 64
Question 17
M1 260 / 13 = 20 (value of one share) oe
A1 Ahmed receives 100 (pounds sterling) cao
A1 Grace receives 160 (pounds sterling) cao
Answer: Ahmed: £100, Grace: £160
Question 18
M1 216 / 9 = 24 oe
A1 120 cao
Answer: 120 books
Question 19
M1 10% of 90 = 9 oe
M1 9 x 3 = 27 (30% found), or equivalent valid method
A1 63 cao
Answer: £63
Question 20
M1 7x = 56 oe
A1 x = 8 cao
Answer: x = 8
Question 21
M1 10% of 460 = 46 and 5% of 460 = 23, or equivalent valid method oe
A1 253 cao
Answer: 253
Question 22
B1 0.375 oe
Answer: 0.375
Question 23
B1 7.3 cao
Answer: 7.3
Question 24
M1 7 x 8 = 56 seen (correct order of operations)
A1 256 cao
Answer: 256
Question 25
M1 4 x 17 oe
A1 68 cao
Answer: £68
Question 26
M1 7 x 0.25 = 1.75 oe
M1 1.75 + 1.60 = 3.35 (ft their 1.75)
M1 5.00 - 3.35 (ft their 3.35)
A1 1.65 cao
Answer: £1.65
Question 27
M1 factors of 36 and 84 listed or compared oe
A1 12 cao
Answer: 12
Question 28
M1 multiples of 6 and 10 listed or compared oe
A1 30 cao
Answer: 30
Question 29
(a) M1 300 / 5 oe
(a) A1 60 (g) cao
(a) Answer: 60 g
(b) M1 60 x 8 (ft their 60)
(b) A1 480 (g) cao
(b) Answer: 480 g
Question 30
M1 348 / 12 = 29 oe
A1 145 cao
Answer: 145 sweets
Question 31
M1 10/12 and 9/12 (common denominator used) oe
A1 5 7/12 cao
Answer: 5 7/12
Question 32
M1 16 x 9 oe
A1 144 cao
Answer: £144
Question 33
M1 3% of 800 = 24 oe
M1 24 x 4 = 96 (ft their 24)
M1 800 + 96 (ft their 96)
A1 896 cao
Answer: £896
Question 34
M1 15% of 540 = 81 oe
M1 540 - 81 = 459 (ft their 81)
M1 459 + 12.50 (ft their 459)
A1 471.50 cao
Answer: £471.50
Question 35
(a) M1 5y = 30 oe
(a) A1 y = 6 cao
(a) Answer: y = 6
(b) M1 5x = 35 oe (correct collection of terms)
(b) M1 x = 35 / 5 (ft their 35)
(b) A1 x = 7 cao
(b) Answer: x = 7
Question 36
(a) M1 540 / 15 = 36 (value of one part) oe
(a) A1 216 cao
(a) Answer: £216
(b) M1 20% of 540 = 108 oe
(b) M1 540 - 108 (ft their 108)
(b) A1 432 cao
(b) Answer: £432
Question 37
M1 60 x 5 oe (correct rounding to 1 significant figure)
A1 300 cao
Answer: 300
Question 38
(a) M1 234 / 3 oe
(a) A1 78 (km/h) cao
(a) Answer: 78 km/h
(b) M1 78 x 5 (ft their speed from part a)
(b) A1 390 (km) cao
(b) Answer: 390 km
Question 39
M1 42 / 50 = 84% oe
M1 51 / 75 = 68% oe
A1 Maths test, with both percentages correctly stated
Answer: Maths test (84% vs 68%)
Question 40
M1 30% of 120 = 36 oe
M1 120 - 36 = 84 (ft their 36)
dM1 5% of 84 = 4.20 oe, dependent on previous mark