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 second 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 Core calculator paper (CE.M15).
1
One evening in Chidinma's garden in Sheffield, the temperature was -3 degrees C. Overnight it fell by a further 5 degrees C. Work out the temperature by morning. (1 mark)
(Total for Question 1 is 1 mark)
2
Work out 638 + 275. (1 mark)
(Total for Question 2 is 1 mark)
3
Work out 804 - 356. (1 mark)
(Total for Question 3 is 1 mark)
4
Write these numbers in order of size, smallest first: 0.72, 0.3, 0.35, 0.07 (2 marks)
(Total for Question 4 is 2 marks)
5
Work out 5/8 of 168. (2 marks)
(Total for Question 5 is 2 marks)
6
A pair of trainers in a shop in Coventry costs 72 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
Declan and Nia share 135 pounds in the ratio 4:5. Work out how much money Declan receives. (3 marks)
(Total for Question 7 is 3 marks)
8
Simplify 6a + 5b - 2a + 3b. (2 marks)
(Total for Question 8 is 2 marks)
9
Solve these two equations.
(a)Solve 5x - 9 = 26. (2 marks)(2)
(b)Solve x/4 + 5 = 12. (2 marks)(2)
(Total for Question 9 is 4 marks)
10
Two angles of a triangle are 48 degrees and 79 degrees. Work out the size of the third angle. (2 marks)
(Total for Question 10 is 2 marks)
11
A rectangle has length 15 cm and width 9 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 6 cm, width 5 cm and height 4 cm. Work out its volume. (3 marks)
(Total for Question 12 is 3 marks)
13
Convert 3.2 kg into grams. (2 marks)
(Total for Question 13 is 2 marks)
14
On 18/07/2026, a minibus leaves a school in Exeter at 08:55 and arrives at an activity centre at 11:40. 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 500 g jar of honey costs 3.20 pounds and a 750 g jar of the same honey costs 4.65 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 books read by seven pupils in a school library during the summer term were: 5, 8, 6, 11, 5, 7, 9. Work out the mean number of books read. (3 marks)
(Total for Question 16 is 3 marks)
17
A box contains 6 yellow pens, 4 black pens and 2 red pens. A pen is picked at random. Work out the probability that it is red. (2 marks)
(Total for Question 17 is 2 marks)
18
Here are the first four terms of a sequence: 6, 11, 16, 21, ... Find the 9th term of the sequence. (2 marks)
(Total for Question 18 is 2 marks)
19
Point C has coordinates (3, 7) and point D has coordinates (9, 1). Work out the coordinates of the midpoint of CD. (2 marks)
(Total for Question 19 is 2 marks)
20
A tablet computer originally costs 260 pounds. The price is first reduced by 15% in a sale, and then a further 8 pounds is taken off the sale price. Work out the final price of the tablet. (3 marks)
(Total for Question 20 is 3 marks)
21
A runner named Osman trains near Belfast.
(a)Osman runs 12 km in 1.5 hours. Work out his average speed in km/h. (1 mark)(1)
(b)Osman then runs for a further 24 minutes at the same average speed. Work out the extra distance he runs. (2 marks)(2)
(Total for Question 21 is 3 marks)
22
A market stall in Aberdeen buys scarves for 8 pounds each and sells them for 12.80 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 an end-of-season sale. Work out the sale price. (2 marks)(2)
(Total for Question 22 is 4 marks)
23
Tariq thinks of a number.
(a)He multiplies his number by 4, then subtracts 6. The result is 34. Write down an equation in y to represent this, where y is Tariq's number. (1 mark)(1)
(b)Solve your equation to find the value of y. (2 marks)(2)
(c)Tariq's brother Ellis's number is 3 less than twice Tariq's number. Find Ellis's number. (1 mark)(1)
(Total for Question 23 is 4 marks)
24
A patio belonging to Mrs Adeyemi in Plymouth is made from two rectangles. The patio measures 12 m by 7 m overall, with a rectangular section measuring 3 m by 2 m removed from one corner for a flower bed.
(a)Work out the area of the patio. (3 marks)(3)
(b)Paving costs 6.20 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 15 pupils, the mean mark in a science test was 64%. In a second class of 12 pupils, the mean mark was 79%. Work out the mean mark for all 27 pupils, giving your answer correct to 1 decimal place. (4 marks)
(Total for Question 25 is 4 marks)
Mark scheme · CE.M21 Maths: Full Practice Paper (Core, Calculator, Set 2)
Question 1
B1 -8 (degrees C) cao
Answer: -8 degrees C
Question 2
B1 913 cao
Answer: 913
Question 3
B1 448 cao
Answer: 448
Question 4
M1 evidence of comparing place value, e.g. writing 0.72, 0.30, 0.35, 0.07
A1 0.07, 0.3, 0.35, 0.72 all in correct order cao
Answer: 0.07, 0.3, 0.35, 0.72
Question 5
M1 168 / 8 (= 21) oe
A1 105 cao
Answer: 105
Question 6
M1 10% of 72 pounds = 7.20 pounds, or equivalent method (e.g. 72 x 0.2)
A1 14.40 pounds cao
Answer: 14.40 pounds
Question 7
M1 identifies 9 total parts (4 + 5)
M1 135 / 9 (= 15), the value of one part
A1 60 pounds cao
Answer: 60 pounds
Question 8
M1 correctly collects a terms or b terms (4a or 8b seen)
A1 4a + 8b cao
Answer: 4a + 8b
Question 9
(a) M1 5x = 35 (adds 9 to both sides)
(a) A1 x = 7 cao
(a) Answer: x = 7
(b) M1 x/4 = 7 (subtracts 5 from both sides)
(b) A1 x = 28 cao
(b) Answer: x = 28
Question 10
M1 180 - 48 - 79 oe
A1 53 (degrees) cao
Answer: 53 degrees
Question 11
(a) B1 135 cm2 cao
(a) Answer: 135 cm2
(b) M1 2 x (15 + 9) oe
(b) A1 48 cm cao
(b) Answer: 48 cm
Question 12
M1 correct method/setup, e.g. 6 x 5 x 4
M1 6 x 5 (= 30), then 30 x 4 (or equivalent order of multiplying)
A1 120 cm3 cao
Answer: 120 cm3
Question 13
M1 3.2 x 1000 oe
A1 3200 g cao
Answer: 3200 g
Question 14
M1 correct method to find elapsed time, e.g. 08:55 to 11:00 = 2 hours 5 minutes
M1 adds the remaining 40 minutes (11:00 to 11:40)
A1 2 hours 45 minutes cao
Answer: 2 hours 45 minutes
Question 15
M1 finds a correct unit price for at least one jar, e.g. 3.20 / 5 = 0.64 pounds per 100 g, or 4.65 / 7.5 = 0.62 pounds per 100 g
A1 correct conclusion with supporting unit prices: the 750 g jar is better value (0.62 pounds per 100 g compared with 0.64 pounds per 100 g)
Answer: The 750 g jar is better value for money
Question 16
M1 total of the seven numbers = 51
M1 51 / 7
A1 7.3 books (1 dp), accept 7.29 or 51/7, cao
Answer: 7.3 books (1 dp)
Question 17
M1 total number of pens = 12
A1 1/6 oe (accept 2/12 or 0.166... or 16.7%) cao
Answer: 1/6
Question 18
M1 correct method, e.g. continuing the pattern +5 each time to the 9th term, or using nth term = 5n + 1
A1 46 cao
Answer: 46
Question 19
M1 ((3+9)/2 , (7+1)/2) oe
A1 (6, 4) cao
Answer: (6, 4)
Question 20
M1 15% of 260 pounds = 39 pounds (or 260 x 0.85)
M1 260 - 39 (= 221 pounds), the sale price
A1 213 pounds cao
Answer: 213 pounds
Question 21
(a) B1 8 km/h cao
(a) Answer: 8 km/h
(b) M1 24/60 (= 2/5) hours, or equivalent method using their (a)
(b) A1 3.2 km cao
(b) Answer: 3.2 km
Question 22
(a) M1 profit = 12.80 - 8 (= 4.80 pounds)
(a) A1 60% cao
(a) Answer: 60%
(b) M1 20% of 12.80 pounds = 2.56 pounds, or equivalent method (e.g. 12.80 x 0.8)
(b) A1 10.24 pounds cao
(b) Answer: 10.24 pounds
Question 23
(a) B1 4y - 6 = 34 oe
(a) Answer: 4y - 6 = 34
(b) M1 4y = 40 (adds 6 to both sides)
(b) A1 y = 10 cao
(b) Answer: y = 10
(c) B1 17, follow through 2 x their y - 3
(c) Answer: 17
Question 24
(a) M1 12 x 7 (= 84 m2), the area of the full rectangle
(a) M1 3 x 2 (= 6 m2), the area removed
(a) A1 78 m2 cao
(a) Answer: 78 m2
(b) B1 480 pounds, follow through their (a) x 6.20, rounded to the nearest 10 pounds
(b) Answer: 480 pounds
Question 25
M1 total marks for the class of 15 = 15 x 64 (= 960)
M1 total marks for the class of 12 = 12 x 79 (= 948)
M1 (960 + 948) / 27, combining both totals and dividing by 27 pupils