Time allowed: 60 minutes. Answer ALL 25 questions. Write your answers in the spaces provided. You ARE allowed to use a calculator. You must show all your working; marks are available for a correct method as well as for the final answer. The number of marks for each question, or part-question, is shown in brackets. This fourth Core (Level 2) calculator paper covers the whole Core syllabus: number, fractions/decimals/percentages, ratio, algebra, geometry, measures, coordinates, statistics and probability, using different questions from the first three Core calculator papers (CE.M15, CE.M21 and CE.M28).
1
One evening in Deepa's garden in Cambridge, the temperature at 8 pm was 3 degrees C. Overnight it fell by a further 10 degrees C. Work out the temperature by morning. (1 mark)
(Total for Question 1 is 1 mark)
2
Work out 693 + 248. (1 mark)
(Total for Question 2 is 1 mark)
3
Work out 850 - 467. (1 mark)
(Total for Question 3 is 1 mark)
4
Write these numbers in order of size, smallest first: 0.6, 0.16, 0.61, 0.06 (2 marks)
(Total for Question 4 is 2 marks)
5
Work out 3/5 of 245. (2 marks)
(Total for Question 5 is 2 marks)
6
A bike helmet in a shop in Bath costs 45 pounds. In a sale it is reduced by 20%. Work out the amount of the discount. (2 marks)
(Total for Question 6 is 2 marks)
7
Meera and Ben share 208 pounds in the ratio 5:3. Work out how much money Ben receives. (3 marks)
(Total for Question 7 is 3 marks)
8
Simplify 8m + 2n - 3m + 5n. (2 marks)
(Total for Question 8 is 2 marks)
9
Solve these two equations.
(a)Solve 7x - 15 = 41. (2 marks)(2)
(b)Solve x/6 + 4 = 11. (2 marks)(2)
(Total for Question 9 is 4 marks)
10
Two angles of a triangle are 57 degrees and 88 degrees. Work out the size of the third angle. (2 marks)
(Total for Question 10 is 2 marks)
11
A rectangle has length 18 cm and width 5 cm.
(a)Work out the area of the rectangle. (1 mark)(1)
(b)Work out the perimeter of the rectangle. (2 marks)(2)
(Total for Question 11 is 3 marks)
12
A cuboid has length 9 cm, width 4 cm and height 2 cm. Work out its volume. (3 marks)
(Total for Question 12 is 3 marks)
13
Convert 7500 metres into kilometres. (2 marks)
(Total for Question 13 is 2 marks)
14
On 22/07/2026, a ferry leaves a port in Portsmouth at 06:52 and arrives at a French port at 09:15. Work out how long the journey took. Give your answer in hours and minutes. (3 marks)
(Total for Question 14 is 3 marks)
15
A 350 g jar of jam costs 2.10 pounds and a 900 g jar of the same jam costs 5.13 pounds. Work out which jar gives better value for money. Show your working. (2 marks)
(Total for Question 15 is 2 marks)
16
The number of text messages sent by a group of six friends during a car journey were: 12, 18, 9, 15, 21, 15. Work out the mean number of text messages. (3 marks)
(Total for Question 16 is 3 marks)
17
A jar contains 9 orange marbles, 6 purple marbles and 5 white marbles. One marble is picked at random. Work out the probability that it is white. (2 marks)
(Total for Question 17 is 2 marks)
18
Here are the first four terms of a sequence: 5, 12, 19, 26, ... Find the 10th term of the sequence. (2 marks)
(Total for Question 18 is 2 marks)
19
Point G has coordinates (1, 8) and point H has coordinates (11, 2). Work out the coordinates of the midpoint of GH. (2 marks)
(Total for Question 19 is 2 marks)
20
A games console originally costs 385 pounds. The price is first reduced by 20% in a sale, and then a further 9 pounds is taken off the sale price. Work out the final price of the games console. (3 marks)
(Total for Question 20 is 3 marks)
21
A swimmer named Niamh trains near Leicester.
(a)Niamh swims 3.6 km in 1.2 hours. Work out her average speed in km/h. (1 mark)(1)
(b)Niamh then swims for a further 30 minutes at the same average speed. Work out the extra distance she swims. (2 marks)(2)
(Total for Question 21 is 3 marks)
22
A market stall in Hull buys leather belts for 10 pounds each and sells them for 13 pounds each.
(a)Work out the stall's profit as a percentage of the price they paid. (2 marks)(2)
(b)The stall then reduces the selling price by 20% for a clearance sale. Work out the sale price. (2 marks)(2)
(Total for Question 22 is 4 marks)
23
Harvey thinks of a number.
(a)He multiplies his number by 6, then subtracts 9. The result is 45. Write down an equation in h to represent this, where h is Harvey's number. (1 mark)(1)
(b)Solve your equation to find the value of h. (2 marks)(2)
(c)Harvey's friend Leah's number is 7 more than four times Harvey's number. Find Leah's number. (1 mark)(1)
(Total for Question 23 is 4 marks)
24
A patio belonging to Mrs Farrukh in Chester is made from two rectangles. The patio measures 11 m by 9 m overall, with a rectangular section measuring 3 m by 4 m removed from one corner for a shed base.
(a)Work out the area of the patio. (3 marks)(3)
(b)Paving costs 6.50 pounds per square metre. Work out the cost of paving the whole patio, giving your answer to the nearest 10 pounds. (1 mark)(1)
(Total for Question 24 is 4 marks)
25
In a class of 24 pupils, the mean mark in a history test was 55%. In a second class of 16 pupils, the mean mark was 70%. Work out the mean mark for all 40 pupils, giving your answer correct to 1 decimal place. (4 marks)
(Total for Question 25 is 4 marks)
Mark scheme · CE.M32 Maths: Full Practice Paper (Core, Calculator, Set 4)
Question 1
B1 -7 (degrees C) cao
Answer: -7 degrees C
Question 2
B1 941 cao
Answer: 941
Question 3
B1 383 cao
Answer: 383
Question 4
M1 evidence of comparing place value, e.g. writing 0.60, 0.16, 0.61, 0.06
A1 0.06, 0.16, 0.6, 0.61 all in correct order cao
Answer: 0.06, 0.16, 0.6, 0.61
Question 5
M1 245 / 5 (= 49) oe
A1 147 cao
Answer: 147
Question 6
M1 10% of 45 pounds = 4.50 pounds, or equivalent method (e.g. 45 x 0.2)
A1 9 pounds cao
Answer: 9 pounds
Question 7
M1 identifies 8 total parts (5 + 3)
M1 208 / 8 (= 26), the value of one part
A1 78 pounds cao
Answer: 78 pounds
Question 8
M1 correctly collects m terms or n terms (5m or 7n seen)
A1 5m + 7n cao
Answer: 5m + 7n
Question 9
(a) M1 7x = 56 (adds 15 to both sides)
(a) A1 x = 8 cao
(a) Answer: x = 8
(b) M1 x/6 = 7 (subtracts 4 from both sides)
(b) A1 x = 42 cao
(b) Answer: x = 42
Question 10
M1 180 - 57 - 88 oe
A1 35 (degrees) cao
Answer: 35 degrees
Question 11
(a) B1 90 cm2 cao
(a) Answer: 90 cm2
(b) M1 2 x (18 + 5) oe
(b) A1 46 cm cao
(b) Answer: 46 cm
Question 12
M1 correct method/setup, e.g. 9 x 4 x 2
M1 9 x 4 (= 36), then 36 x 2 (or equivalent order of multiplying)
A1 72 cm3 cao
Answer: 72 cm3
Question 13
M1 7500 / 1000 oe
A1 7.5 km cao
Answer: 7.5 km
Question 14
M1 correct method to find elapsed time, e.g. 06:52 to 07:00 = 8 minutes
M1 adds the remaining time from 07:00 to 09:15 (2 hours 15 minutes)
A1 2 hours 23 minutes cao
Answer: 2 hours 23 minutes
Question 15
M1 finds a correct unit price for at least one jar, e.g. 2.10 / 3.5 = 0.60 pounds per 100 g, or 5.13 / 9 = 0.57 pounds per 100 g
A1 correct conclusion with supporting unit prices: the 900 g jar is better value (0.57 pounds per 100 g compared with 0.60 pounds per 100 g)
Answer: The 900 g jar is better value for money
Question 16
M1 total of the six numbers = 90
M1 90 / 6
A1 15 cao
Answer: 15
Question 17
M1 total number of marbles = 20
A1 5/20 oe (accept 1/4, 0.25 or 25%) cao
Answer: 1/4
Question 18
M1 correct method, e.g. continuing the pattern +7 each time to the 10th term, or using nth term = 7n - 2
A1 68 cao
Answer: 68
Question 19
M1 ((1+11)/2 , (8+2)/2) oe
A1 (6, 5) cao
Answer: (6, 5)
Question 20
M1 20% of 385 pounds = 77 pounds (or 385 x 0.8)
M1 385 - 77 (= 308 pounds), the sale price
A1 299 pounds cao
Answer: 299 pounds
Question 21
(a) B1 3 km/h cao
(a) Answer: 3 km/h
(b) M1 30/60 (= 1/2) hours, or equivalent method using their (a)
(b) A1 1.5 km cao
(b) Answer: 1.5 km
Question 22
(a) M1 profit = 13.00 - 10.00 (= 3.00 pounds)
(a) A1 30% cao
(a) Answer: 30%
(b) M1 20% of 13 pounds = 2.60 pounds, or equivalent method (e.g. 13 x 0.8)
(b) A1 10.40 pounds cao
(b) Answer: 10.40 pounds
Question 23
(a) B1 6h - 9 = 45 oe
(a) Answer: 6h - 9 = 45
(b) M1 6h = 54 (adds 9 to both sides)
(b) A1 h = 9 cao
(b) Answer: h = 9
(c) B1 43, follow through 4 x their h + 7
(c) Answer: 43
Question 24
(a) M1 11 x 9 (= 99 m2), the area of the full rectangle
(a) M1 3 x 4 (= 12 m2), the area removed
(a) A1 87 m2 cao
(a) Answer: 87 m2
(b) B1 570 pounds, follow through their (a) x 6.50, rounded to the nearest 10 pounds
(b) Answer: 570 pounds
Question 25
M1 total marks for the class of 24 = 24 x 55 (= 1320)
M1 total marks for the class of 16 = 16 x 70 (= 1120)
M1 (1320 + 1120) / 40, combining both totals and dividing by 40 pupils