210 pounds sterling is shared between Priya and Tomasz in the ratio 3:4. Work out how much each person receives.
(Total for Question 17 is 3 marks)
18
A theatre has 192 seats. 3/8 of the seats are in the balcony. Calculate how many seats are in the balcony.
(Total for Question 18 is 2 marks)
19
A coat costs 70 pounds sterling. In a sale its price is reduced by 20%. Work out the sale price.
(Total for Question 19 is 3 marks)
20
Solve 8x + 3 = 59.
(Total for Question 20 is 2 marks)
21
Work out 65% of 340.
(Total for Question 21 is 2 marks)
22
Write 5/8 as a decimal.
(Total for Question 22 is 1 mark)
23
Round 8.362 to 1 decimal place.
(Total for Question 23 is 1 mark)
24
Work out 205 - 8 x 9.
(Total for Question 24 is 2 marks)
25
A cinema sells tickets at 9 pounds sterling each. Calculate the total cost for 23 tickets.
(Total for Question 25 is 2 marks)
26
Fatima buys 6 stickers at 35 pence each and a magazine for 2.85 pounds sterling. She pays with a 10 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 12.
(Total for Question 28 is 2 marks)
29
A recipe for 4 people needs 260 g of rice. Priyanka wants to make the recipe for 10 people.
(a)Work out the amount of rice needed per person.(2)
(b)Work out the total amount of rice needed for 10 people.(2)
(Total for Question 29 is 4 marks)
30
Owen has 7/15 of a box of 225 marbles. Calculate how many marbles Owen has.
(Total for Question 30 is 2 marks)
31
Work out 4 3/8 + 2 5/6.
(Total for Question 31 is 2 marks)
32
Leilani saves 14 pounds sterling each week. Calculate how much she saves in 12 weeks.
(Total for Question 32 is 2 marks)
33
Idris invests 650 pounds sterling in a savings account paying simple interest at 4% per annum. Calculate the total amount in his account after 3 years.
(Total for Question 33 is 4 marks)
34
Nadia orders a tablet priced at 320 pounds sterling. The shop offers 20% off for loyalty members. There is also a delivery charge of 8.50 pounds sterling, which is not discounted. Calculate the total amount Nadia pays.
(Total for Question 34 is 4 marks)
35
Solve each equation.
(a)Solve 6y + 7 = 43.(2)
(b)Solve 12x - 8 = 7x + 27.(3)
(Total for Question 35 is 5 marks)
36
A school fair raises 720 pounds sterling from 3 stalls, shared in the ratio 2:3:7.
(a)Work out the largest of the three stalls' shares.(2)
(b)The organisers keep 15% of the total 720 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 38.7 x 5.2.
(Total for Question 37 is 2 marks)
38
A cyclist travels 171 km in 4.5 hours at a constant speed.
(a)Calculate the cyclist's average speed in km/h.(2)
(b)At this speed, calculate how far the cyclist would travel in 6 hours.(2)
(Total for Question 38 is 4 marks)
39
Zara scored 34 out of 40 in an English test and 39 out of 60 in a history 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 96 pounds sterling heater by 25% in a winter sale. It is then reduced by a further 10% of the new, already reduced, price in a clearance sale. Calculate the final price of the heater.
(Total for Question 40 is 5 marks)
Mark scheme · CE.M26 Mental Arithmetic: Practice Set 7
Question 1
B1 147 cao
Answer: 147
Question 2
B1 54 cao
Answer: 54
Question 3
B1 56 cao
Answer: 56
Question 4
B1 18 cao
Answer: 18
Question 5
B1 144 cao
Answer: 144
Question 6
B1 18 cao
Answer: 18
Question 7
B1 -15 cao
Answer: -15
Question 8
B1 -13 cao
Answer: -13
Question 9
B1 0.45 oe
Answer: 0.45
Question 10
B1 55 cao (correct order of operations)
Answer: 55
Question 11
B1 7/20 oe
Answer: 7/20
Question 12
M1 108 / 4 = 27 oe
A1 81 cao
Answer: 81
Question 13
M1 10% of 180 = 18 and 5% of 180 = 9, or equivalent valid method oe
A1 63 cao
Answer: £63
Question 14
M1 7 x 4 = 28 seen (correct order of operations)
A1 24 cao
Answer: 24
Question 15
M1 - (-11) = + 11 oe
A1 16 cao
Answer: 16
Question 16
(a) B1 64 cao
(a) Answer: 64
(b) B1 14 cao
(b) Answer: 14
(c) B1 125 cao
(c) Answer: 125
Question 17
M1 210 / 7 = 30 (value of one share) oe
A1 Priya receives 90 (pounds sterling) cao
A1 Tomasz receives 120 (pounds sterling) cao
Answer: Priya: £90, Tomasz: £120
Question 18
M1 192 / 8 = 24 oe
A1 72 cao
Answer: 72 seats
Question 19
M1 10% of 70 = 7 oe
M1 7 x 2 = 14 (20% found), or equivalent valid method
A1 56 cao
Answer: £56
Question 20
M1 8x = 56 oe
A1 x = 7 cao
Answer: x = 7
Question 21
M1 10% of 340 = 34 and 5% of 340 = 17, or equivalent valid method oe
A1 221 cao
Answer: 221
Question 22
B1 0.625 oe
Answer: 0.625
Question 23
B1 8.4 cao
Answer: 8.4
Question 24
M1 8 x 9 = 72 seen (correct order of operations)
A1 133 cao
Answer: 133
Question 25
M1 9 x 23 oe
A1 207 cao
Answer: £207
Question 26
M1 6 x 0.35 = 2.10 oe
M1 2.10 + 2.85 = 4.95 (ft their 2.10)
M1 10.00 - 4.95 (ft their 4.95)
A1 5.05 cao
Answer: £5.05
Question 27
M1 factors of 48 and 60 listed or compared oe
A1 12 cao
Answer: 12
Question 28
M1 multiples of 8 and 12 listed or compared oe
A1 24 cao
Answer: 24
Question 29
(a) M1 260 / 4 oe
(a) A1 65 (g) cao
(a) Answer: 65 g
(b) M1 65 x 10 (ft their 65)
(b) A1 650 (g) cao
(b) Answer: 650 g
Question 30
M1 225 / 15 = 15 oe
A1 105 cao
Answer: 105 marbles
Question 31
M1 9/24 and 20/24 (common denominator used) oe
A1 7 5/24 cao
Answer: 7 5/24
Question 32
M1 14 x 12 oe
A1 168 cao
Answer: £168
Question 33
M1 4% of 650 = 26 oe
M1 26 x 3 = 78 (ft their 26)
M1 650 + 78 (ft their 78)
A1 728 cao
Answer: £728
Question 34
M1 20% of 320 = 64 oe
M1 320 - 64 = 256 (ft their 64)
M1 256 + 8.50 (ft their 256)
A1 264.50 cao
Answer: £264.50
Question 35
(a) M1 6y = 36 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 720 / 12 = 60 (value of one part) oe
(a) A1 420 cao
(a) Answer: £420
(b) M1 15% of 720 = 108 oe
(b) M1 720 - 108 (ft their 108)
(b) A1 612 cao
(b) Answer: £612
Question 37
M1 40 x 5 oe (correct rounding to 1 significant figure)
A1 200 cao
Answer: 200
Question 38
(a) M1 171 / 4.5 oe
(a) A1 38 (km/h) cao
(a) Answer: 38 km/h
(b) M1 38 x 6 (ft their speed from part a)
(b) A1 228 (km) cao
(b) Answer: 228 km
Question 39
M1 34 / 40 = 85% oe
M1 39 / 60 = 65% oe
A1 English test, with both percentages correctly stated
Answer: English test (85% vs 65%)
Question 40
M1 25% of 96 = 24 oe
M1 96 - 24 = 72 (ft their 24)
dM1 10% of 72 = 7.20 oe, dependent on previous mark