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 paper covers the whole Core (Level 2) syllabus: number, fractions/decimals/percentages, ratio, algebra, geometry, measures, coordinates, statistics and probability, using different questions from the non-calculator Core paper (CE.M13).
1
One morning in Sarah's garden in York, the temperature at 6am was -4 degrees C. By midday it had risen by 9 degrees C. Work out the temperature at midday. (1 mark)
(Total for Question 1 is 1 mark)
2
Work out 456 + 287. (1 mark)
(Total for Question 2 is 1 mark)
3
Work out 900 - 364. (1 mark)
(Total for Question 3 is 1 mark)
4
Write these numbers in order of size, smallest first: 0.6, 0.45, 0.5, 0.09 (2 marks)
(Total for Question 4 is 2 marks)
5
Work out 3/4 of 148. (2 marks)
(Total for Question 5 is 2 marks)
6
A jacket in a shop in Leeds costs 84 pounds. In a sale it is reduced by 15%. Work out the amount of the discount. (2 marks)
(Total for Question 6 is 2 marks)
7
Aisha and Priya share 96 pounds in the ratio 5:3. Work out how much money Priya receives. (3 marks)
(Total for Question 7 is 3 marks)
8
Simplify 5x + 3y - 2x + 7y. (2 marks)
(Total for Question 8 is 2 marks)
9
Solve these two equations.
(a)Solve 4x - 7 = 21. (2 marks)(2)
(b)Solve x/3 + 2 = 9. (2 marks)(2)
(Total for Question 9 is 4 marks)
10
Two angles of a triangle are 52 degrees and 67 degrees. Work out the size of the third angle. (2 marks)
(Total for Question 10 is 2 marks)
11
A rectangle has length 12 cm and width 7 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 5 cm, width 4 cm and height 3 cm. Work out its volume. (3 marks)
(Total for Question 12 is 3 marks)
13
Convert 2.5 km into metres. (2 marks)
(Total for Question 13 is 2 marks)
14
On 14/07/2026, a coach leaves a school in Bristol at 09:45 and arrives at a ski centre at 12:20. 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 750 g bag of pasta costs 1.80 pounds and a 1.2 kg bag of the same pasta costs 2.64 pounds. Work out which bag gives better value for money. Show your working. (2 marks)
(Total for Question 15 is 2 marks)
16
The ages, in years, of seven cousins at a birthday party are: 8, 11, 9, 14, 8, 10, 12. Work out the mean age. (3 marks)
(Total for Question 16 is 3 marks)
17
A bag contains 5 red counters, 3 blue counters and 2 green counters. A counter is picked at random. Work out the probability that it is blue. (2 marks)
(Total for Question 17 is 2 marks)
18
Here are the first four terms of a sequence: 4, 9, 14, 19, ... Find the 8th term of the sequence. (2 marks)
(Total for Question 18 is 2 marks)
19
Point A has coordinates (2, 5) and point B has coordinates (8, 1). Work out the coordinates of the midpoint of AB. (2 marks)
(Total for Question 19 is 2 marks)
20
A laptop originally costs 420 pounds. The price is first reduced by 10% in a sale, and then a further 15 pounds is taken off the sale price. Work out the final price of the laptop. (3 marks)
(Total for Question 20 is 3 marks)
21
A cyclist named Ffion trains near Cardiff.
(a)Ffion travels 45 km in 2.5 hours. Work out her average speed in km/h. (1 mark)(1)
(b)Ffion then cycles for a further 40 minutes at the same average speed. Work out the extra distance she travels. (2 marks)(2)
(Total for Question 21 is 3 marks)
22
A charity shop in Norwich buys a bicycle for 60 pounds and sells it for 96 pounds.
(a)Work out the shop's profit as a percentage of the price they paid. (2 marks)(2)
(b)The shop then reduces the selling price by 25% for a weekend sale. Work out the sale price. (2 marks)(2)
(Total for Question 22 is 4 marks)
23
Kofi thinks of a number.
(a)He multiplies his number by 3, then adds 8. The result is 50. Write down an equation in x to represent this, where x is Kofi's number. (1 mark)(1)
(b)Solve your equation to find the value of x. (2 marks)(2)
(c)Kofi's sister Aaliyah's number is 5 more than twice Kofi's number. Find Aaliyah's number. (1 mark)(1)
(Total for Question 23 is 4 marks)
24
An L-shaped garden belonging to Mr Osei in Nottingham is made from two rectangles. The garden measures 10 m by 8 m overall, with a rectangular section measuring 4 m by 3 m removed from one corner.
(a)Work out the area of the garden. (3 marks)(3)
(b)Turf costs 5.50 pounds per square metre. Work out the cost of turfing the whole garden, giving your answer to the nearest 10 pounds. (1 mark)(1)
(Total for Question 24 is 4 marks)
25
In a class of 20 pupils, the mean mark in a maths test was 64%. In a second class of 15 pupils, the mean mark was 72%. Work out the mean mark for all 35 pupils, giving your answer correct to 1 decimal place. (4 marks)
(Total for Question 25 is 4 marks)
Mark scheme · CE.M15 Maths: Full Practice Paper (Core, Calculator)
Question 1
B1 5 (degrees C) cao
Answer: 5 degrees C
Question 2
B1 743 cao
Answer: 743
Question 3
B1 536 cao
Answer: 536
Question 4
M1 evidence of comparing place value, e.g. writing 0.60, 0.45, 0.50, 0.09
A1 0.09, 0.45, 0.5, 0.6 all in correct order cao
Answer: 0.09, 0.45, 0.5, 0.6
Question 5
M1 148 / 4 (= 37) oe
A1 111 cao
Answer: 111
Question 6
M1 10% of 84 pounds = 8.40 pounds, or equivalent method (e.g. 84 x 0.15)
A1 12.60 pounds cao
Answer: 12.60 pounds
Question 7
M1 identifies 8 total parts (5 + 3)
M1 96 / 8 (= 12), the value of one part
A1 36 pounds cao
Answer: 36 pounds
Question 8
M1 correctly collects x terms or y terms (3x or 10y seen)
A1 3x + 10y cao
Answer: 3x + 10y
Question 9
(a) M1 4x = 28 (adds 7 to both sides)
(a) A1 x = 7 cao
(a) Answer: x = 7
(b) M1 x/3 = 7 (subtracts 2 from both sides)
(b) A1 x = 21 cao
(b) Answer: x = 21
Question 10
M1 180 - 52 - 67 oe
A1 61 (degrees) cao
Answer: 61 degrees
Question 11
(a) B1 84 cm2 cao
(a) Answer: 84 cm2
(b) M1 2 x (12 + 7) oe
(b) A1 38 cm cao
(b) Answer: 38 cm
Question 12
M1 correct method/setup, e.g. 5 x 4 x 3
M1 5 x 4 (= 20), then 20 x 3 (or equivalent order of multiplying)
A1 60 cm3 cao
Answer: 60 cm3
Question 13
M1 2.5 x 1000 oe
A1 2500 m cao
Answer: 2500 m
Question 14
M1 correct method to find elapsed time, e.g. 09:45 to 12:00 = 2 hours 15 minutes
M1 adds the remaining 20 minutes (12:00 to 12:20)
A1 2 hours 35 minutes cao
Answer: 2 hours 35 minutes
Question 15
M1 finds a correct unit price for at least one bag, e.g. 1.80 / 7.5 = 0.24 pounds per 100 g, or 2.64 / 12 = 0.22 pounds per 100 g
A1 correct conclusion with supporting unit prices: the 1.2 kg bag is better value (0.22 pounds per 100 g compared with 0.24 pounds per 100 g)
Answer: The 1.2 kg bag is better value for money
Question 16
M1 total of the seven ages = 72
M1 72 / 7
A1 10.3 years (1 dp), accept 10.29 or 72/7, cao
Answer: 10.3 years (1 dp)
Question 17
M1 total number of counters = 10
A1 3/10 oe (accept 0.3 or 30%) cao
Answer: 3/10
Question 18
M1 correct method, e.g. continuing the pattern +5 each time to the 8th term, or using nth term = 5n - 1
A1 39 cao
Answer: 39
Question 19
M1 ((2+8)/2 , (5+1)/2) oe
A1 (5, 3) cao
Answer: (5, 3)
Question 20
M1 10% of 420 pounds = 42 pounds (or 420 x 0.9)
M1 420 - 42 (= 378 pounds), the sale price
A1 363 pounds cao
Answer: 363 pounds
Question 21
(a) B1 18 km/h cao
(a) Answer: 18 km/h
(b) M1 40/60 (= 2/3) hours, or equivalent method using their (a)
(b) A1 12 km cao
(b) Answer: 12 km
Question 22
(a) M1 profit = 96 - 60 (= 36 pounds)
(a) A1 60% cao
(a) Answer: 60%
(b) M1 25% of 96 pounds = 24 pounds, or equivalent method (e.g. 96 x 0.75)
(b) A1 72 pounds cao
(b) Answer: 72 pounds
Question 23
(a) B1 3x + 8 = 50 oe
(a) Answer: 3x + 8 = 50
(b) M1 3x = 42 (subtracts 8 from both sides)
(b) A1 x = 14 cao
(b) Answer: x = 14
(c) B1 33, follow through 2 x their x + 5
(c) Answer: 33
Question 24
(a) M1 10 x 8 (= 80 m2), the area of the full rectangle
(a) M1 4 x 3 (= 12 m2), the area removed
(a) A1 68 m2 cao
(a) Answer: 68 m2
(b) B1 370 pounds, follow through their (a) x 5.50, rounded to the nearest 10 pounds
(b) Answer: 370 pounds
Question 25
M1 total marks for the class of 20 = 20 x 64 (= 1280)
M1 total marks for the class of 15 = 15 x 72 (= 1080)
M1 (1280 + 1080) / 35, combining both totals and dividing by 35 pupils