108 pounds sterling is shared between Aaliyah and Finlay in the ratio 5:7. Work out how much each person receives.
(Total for Question 17 is 3 marks)
18
A library has 260 books. 3/10 of the books are non-fiction. Calculate how many books are non-fiction.
(Total for Question 18 is 2 marks)
19
A bicycle helmet costs 65 pounds sterling. In a sale its price is reduced by 40%. Work out the sale price.
(Total for Question 19 is 3 marks)
20
Solve 5x + 6 = 41.
(Total for Question 20 is 2 marks)
21
Work out 65% of 140.
(Total for Question 21 is 2 marks)
22
Write 5/8 as a decimal.
(Total for Question 22 is 1 mark)
23
Round 3.847 to 1 decimal place.
(Total for Question 23 is 1 mark)
24
Work out 150 - 7 x 8.
(Total for Question 24 is 2 marks)
25
A cinema sells tickets at 11 pounds sterling each. Calculate the total cost for 19 tickets.
(Total for Question 25 is 2 marks)
26
Zara buys 6 stickers at 35 pence each and a notebook for 1.80 pounds sterling. She pays with a 5 pound note. Calculate how much change she receives.
(Total for Question 26 is 4 marks)
27
Work out the highest common factor of 48 and 60.
(Total for Question 27 is 2 marks)
28
Work out the lowest common multiple of 8 and 10.
(Total for Question 28 is 2 marks)
29
A recipe for 4 people needs 260 g of couscous. Yusuf wants to make the recipe for 7 people.
(a)Work out the amount of couscous needed per person.(2)
(b)Work out the total amount of couscous needed for 7 people.(2)
(Total for Question 29 is 4 marks)
30
Elena has 9/25 of a bag of 200 marbles. Calculate how many marbles Elena has.
(Total for Question 30 is 2 marks)
31
Work out 4 1/4 + 1 5/6.
(Total for Question 31 is 2 marks)
32
Hassan saves 7 pounds sterling each week. Calculate how much he saves in 14 weeks.
(Total for Question 32 is 2 marks)
33
Grace invests 650 pounds sterling in a savings account paying simple interest at 5% per annum. Calculate the total amount in her account after 4 years.
(Total for Question 33 is 4 marks)
34
Marcus orders a tablet priced at 220 pounds sterling. The shop offers 20% off for signing up to the newsletter. There is also a delivery charge of 5.50 pounds sterling, which is not discounted. Calculate the total amount Marcus pays.
(Total for Question 34 is 4 marks)
35
Solve each equation.
(a)Solve 6y + 5 = 41.(2)
(b)Solve 8x - 9 = 4x + 19.(3)
(Total for Question 35 is 5 marks)
36
A school fete raises 480 pounds sterling from 3 stalls, shared in the ratio 3:5:8.
(a)Work out the largest of the three stalls' shares.(2)
(b)The organisers keep 15% of the total 480 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 48.6 x 6.3.
(Total for Question 37 is 2 marks)
38
A coach travels 175 km in 2.5 hours at a constant speed.
(a)Calculate the coach's average speed in km/h.(2)
(b)At this speed, calculate how far the coach would travel in 6 hours.(2)
(Total for Question 38 is 4 marks)
39
Fatima scored 63 out of 70 in a science test and 51 out of 60 in a geography 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 75 pounds sterling backpack by 20% in a summer sale. It is then reduced by a further 25% of the new, already reduced, price in a clearance sale. Calculate the final price of the backpack.
(Total for Question 40 is 5 marks)
Mark scheme · CE.M18 Mental Arithmetic: Practice Set 4
Question 1
B1 93 cao
Answer: 93
Question 2
B1 33 cao
Answer: 33
Question 3
B1 72 cao
Answer: 72
Question 4
B1 11 cao
Answer: 11
Question 5
B1 49 cao
Answer: 49
Question 6
B1 15 cao
Answer: 15
Question 7
B1 7 cao
Answer: 7
Question 8
B1 -9 cao
Answer: -9
Question 9
B1 0.35 oe
Answer: 0.35
Question 10
B1 29 cao (correct order of operations)
Answer: 29
Question 11
B1 17/20 oe
Answer: 17/20
Question 12
M1 108 / 9 = 12 oe
A1 60 cao
Answer: 60
Question 13
M1 10% of 80 = 8 and 5% of 80 = 4, or equivalent valid method oe
A1 36 cao
Answer: £36
Question 14
M1 6 x 4 = 24 seen (correct order of operations)
A1 22 cao
Answer: 22
Question 15
M1 - (-11) = + 11 oe
A1 17 cao
Answer: 17
Question 16
(a) B1 36 cao
(a) Answer: 36
(b) B1 17 cao
(b) Answer: 17
(c) B1 64 cao
(c) Answer: 64
Question 17
M1 108 / 12 = 9 (value of one share) oe
A1 Aaliyah receives 45 (pounds sterling) cao
A1 Finlay receives 63 (pounds sterling) cao
Answer: Aaliyah: £45, Finlay: £63
Question 18
M1 260 / 10 = 26 oe
A1 78 cao
Answer: 78 books
Question 19
M1 10% of 65 = 6.5 oe
M1 6.5 x 4 = 26 (40% found), or equivalent valid method
A1 39 cao
Answer: £39
Question 20
M1 5x = 35 oe
A1 x = 7 cao
Answer: x = 7
Question 21
M1 10% of 140 = 14 and 5% of 140 = 7, or equivalent valid method oe
A1 91 cao
Answer: 91
Question 22
B1 0.625 oe
Answer: 0.625
Question 23
B1 3.8 cao
Answer: 3.8
Question 24
M1 7 x 8 = 56 seen (correct order of operations)
A1 94 cao
Answer: 94
Question 25
M1 11 x 19 oe
A1 209 cao
Answer: £209
Question 26
M1 6 x 0.35 = 2.10 oe
M1 2.10 + 1.80 = 3.90 (ft their 2.10)
M1 5.00 - 3.90 (ft their 3.90)
A1 1.10 cao
Answer: £1.10
Question 27
M1 factors of 48 and 60 listed or compared oe
A1 12 cao
Answer: 12
Question 28
M1 multiples of 8 and 10 listed or compared oe
A1 40 cao
Answer: 40
Question 29
(a) M1 260 / 4 oe
(a) A1 65 (g) cao
(a) Answer: 65 g
(b) M1 65 x 7 (ft their 65)
(b) A1 455 (g) cao
(b) Answer: 455 g
Question 30
M1 200 / 25 = 8 oe
A1 72 cao
Answer: 72 marbles
Question 31
M1 3/12 and 10/12 (common denominator used) oe
A1 6 1/12 cao
Answer: 6 1/12
Question 32
M1 7 x 14 oe
A1 98 cao
Answer: £98
Question 33
M1 5% of 650 = 32.50 oe
M1 32.50 x 4 = 130 (ft their 32.50)
M1 650 + 130 (ft their 130)
A1 780 cao
Answer: £780
Question 34
M1 20% of 220 = 44 oe
M1 220 - 44 = 176 (ft their 44)
M1 176 + 5.50 (ft their 176)
A1 181.50 cao
Answer: £181.50
Question 35
(a) M1 6y = 36 oe
(a) A1 y = 6 cao
(a) Answer: y = 6
(b) M1 4x = 28 oe (correct collection of terms)
(b) M1 x = 28 / 4 (ft their 28)
(b) A1 x = 7 cao
(b) Answer: x = 7
Question 36
(a) M1 480 / 16 = 30 (value of one part) oe
(a) A1 240 cao
(a) Answer: £240
(b) M1 15% of 480 = 72 oe
(b) M1 480 - 72 (ft their 72)
(b) A1 408 cao
(b) Answer: £408
Question 37
M1 50 x 6 oe (correct rounding to 1 significant figure)
A1 300 cao
Answer: 300
Question 38
(a) M1 175 / 2.5 oe
(a) A1 70 (km/h) cao
(a) Answer: 70 km/h
(b) M1 70 x 6 (ft their speed from part a)
(b) A1 420 (km) cao
(b) Answer: 420 km
Question 39
M1 63 / 70 = 90% oe
M1 51 / 60 = 85% oe
A1 Science test, with both percentages correctly stated