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 third 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 two Core calculator papers (CE.M15 and CE.M21).
1
One evening in Freya's garden in Durham, the temperature at 9 pm was 4 degrees C. Overnight it fell by a further 9 degrees C. Work out the temperature by morning. (1 mark)
(Total for Question 1 is 1 mark)
2
Work out 547 + 368. (1 mark)
(Total for Question 2 is 1 mark)
3
Work out 723 - 458. (1 mark)
(Total for Question 3 is 1 mark)
4
Write these numbers in order of size, smallest first: 0.8, 0.08, 0.18, 0.81 (2 marks)
(Total for Question 4 is 2 marks)
5
Work out 2/3 of 156. (2 marks)
(Total for Question 5 is 2 marks)
6
A pair of headphones in a shop in Oxford costs 60 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
Rhys and Nadia share 168 pounds in the ratio 3:5. Work out how much money Nadia receives. (3 marks)
(Total for Question 7 is 3 marks)
8
Simplify 7p + 4q - 3p + 6q. (2 marks)
(Total for Question 8 is 2 marks)
9
Solve these two equations.
(a)Solve 6x - 11 = 37. (2 marks)(2)
(b)Solve x/5 + 3 = 9. (2 marks)(2)
(Total for Question 9 is 4 marks)
10
Two angles of a triangle are 63 degrees and 74 degrees. Work out the size of the third angle. (2 marks)
(Total for Question 10 is 2 marks)
11
A rectangle has length 14 cm and width 8 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 7 cm, width 4 cm and height 3 cm. Work out its volume. (3 marks)
(Total for Question 12 is 3 marks)
13
Convert 4.6 litres into millilitres. (2 marks)
(Total for Question 13 is 2 marks)
14
On 20/07/2026, a train leaves a station in Preston at 07:38 and arrives at a city station at 10:05. 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 400 g box of cereal costs 2.20 pounds and a 650 g box of the same cereal costs 3.51 pounds. Work out which box gives better value for money. Show your working. (2 marks)
(Total for Question 15 is 2 marks)
16
The number of goals scored by a hockey team in five matches were: 3, 5, 2, 6, 3. Work out the mean number of goals per match. (3 marks)
(Total for Question 16 is 3 marks)
17
A drawer contains 7 blue socks, 5 grey socks and 4 black socks. One sock is picked at random. Work out the probability that it is grey. (2 marks)
(Total for Question 17 is 2 marks)
18
Here are the first four terms of a sequence: 3, 8, 13, 18, ... Find the 11th term of the sequence. (2 marks)
(Total for Question 18 is 2 marks)
19
Point E has coordinates (2, 9) and point F has coordinates (10, 3). Work out the coordinates of the midpoint of EF. (2 marks)
(Total for Question 19 is 2 marks)
20
A washing machine originally costs 340 pounds. The price is first reduced by 10% in a sale, and then a further 12 pounds is taken off the sale price. Work out the final price of the washing machine. (3 marks)
(Total for Question 20 is 3 marks)
21
A cyclist named Idris trains near Winchester.
(a)Idris cycles 21 km in 1.75 hours. Work out his average speed in km/h. (1 mark)(1)
(b)Idris then cycles for a further 18 minutes at the same average speed. Work out the extra distance he cycles. (2 marks)(2)
(Total for Question 21 is 3 marks)
22
A market stall in Lincoln buys candles for 6 pounds each and sells them for 8.40 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 25% for a clearance sale. Work out the sale price. (2 marks)(2)
(Total for Question 22 is 4 marks)
23
Zainab thinks of a number.
(a)She multiplies her number by 5, then adds 7. The result is 47. Write down an equation in z to represent this, where z is Zainab's number. (1 mark)(1)
(b)Solve your equation to find the value of z. (2 marks)(2)
(c)Zainab's friend Connor's number is 4 more than three times Zainab's number. Find Connor's number. (1 mark)(1)
(Total for Question 23 is 4 marks)
24
A patio belonging to Mr Bello in Ipswich is made from two rectangles. The patio measures 10 m by 8 m overall, with a rectangular section measuring 4 m by 3 m removed from one corner for a pond.
(a)Work out the area of the patio. (3 marks)(3)
(b)Decking costs 7.20 pounds per square metre. Work out the cost of decking 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 18 pupils, the mean mark in a French test was 58%. In a second class of 22 pupils, the mean mark was 71%. 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.M28 Maths: Full Practice Paper (Core, Calculator, Set 3)
Question 1
B1 -5 (degrees C) cao
Answer: -5 degrees C
Question 2
B1 915 cao
Answer: 915
Question 3
B1 265 cao
Answer: 265
Question 4
M1 evidence of comparing place value, e.g. writing 0.80, 0.08, 0.18, 0.81
A1 0.08, 0.18, 0.8, 0.81 all in correct order cao
Answer: 0.08, 0.18, 0.8, 0.81
Question 5
M1 156 / 3 (= 52) oe
A1 104 cao
Answer: 104
Question 6
M1 10% of 60 pounds = 6 pounds, or equivalent method (e.g. 60 x 0.15)
A1 9 pounds cao
Answer: 9 pounds
Question 7
M1 identifies 8 total parts (3 + 5)
M1 168 / 8 (= 21), the value of one part
A1 105 pounds cao
Answer: 105 pounds
Question 8
M1 correctly collects p terms or q terms (4p or 10q seen)
A1 4p + 10q cao
Answer: 4p + 10q
Question 9
(a) M1 6x = 48 (adds 11 to both sides)
(a) A1 x = 8 cao
(a) Answer: x = 8
(b) M1 x/5 = 6 (subtracts 3 from both sides)
(b) A1 x = 30 cao
(b) Answer: x = 30
Question 10
M1 180 - 63 - 74 oe
A1 43 (degrees) cao
Answer: 43 degrees
Question 11
(a) B1 112 cm2 cao
(a) Answer: 112 cm2
(b) M1 2 x (14 + 8) oe
(b) A1 44 cm cao
(b) Answer: 44 cm
Question 12
M1 correct method/setup, e.g. 7 x 4 x 3
M1 7 x 4 (= 28), then 28 x 3 (or equivalent order of multiplying)
A1 84 cm3 cao
Answer: 84 cm3
Question 13
M1 4.6 x 1000 oe
A1 4600 ml cao
Answer: 4600 ml
Question 14
M1 correct method to find elapsed time, e.g. 07:38 to 08:00 = 22 minutes
M1 adds the remaining time from 08:00 to 10:05 (2 hours 5 minutes)
A1 2 hours 27 minutes cao
Answer: 2 hours 27 minutes
Question 15
M1 finds a correct unit price for at least one box, e.g. 2.20 / 4 = 0.55 pounds per 100 g, or 3.51 / 6.5 = 0.54 pounds per 100 g
A1 correct conclusion with supporting unit prices: the 650 g box is better value (0.54 pounds per 100 g compared with 0.55 pounds per 100 g)
Answer: The 650 g box is better value for money
Question 16
M1 total of the five numbers = 19
M1 19 / 5
A1 3.8 goals cao
Answer: 3.8 goals
Question 17
M1 total number of socks = 16
A1 5/16 oe (accept 0.3125 or 31.25%) cao
Answer: 5/16
Question 18
M1 correct method, e.g. continuing the pattern +5 each time to the 11th term, or using nth term = 5n - 2
A1 53 cao
Answer: 53
Question 19
M1 ((2+10)/2 , (9+3)/2) oe
A1 (6, 6) cao
Answer: (6, 6)
Question 20
M1 10% of 340 pounds = 34 pounds (or 340 x 0.9)
M1 340 - 34 (= 306 pounds), the sale price
A1 294 pounds cao
Answer: 294 pounds
Question 21
(a) B1 12 km/h cao
(a) Answer: 12 km/h
(b) M1 18/60 (= 3/10) hours, or equivalent method using their (a)
(b) A1 3.6 km cao
(b) Answer: 3.6 km
Question 22
(a) M1 profit = 8.40 - 6.00 (= 2.40 pounds)
(a) A1 40% cao
(a) Answer: 40%
(b) M1 25% of 8.40 pounds = 2.10 pounds, or equivalent method (e.g. 8.40 x 0.75)
(b) A1 6.30 pounds cao
(b) Answer: 6.30 pounds
Question 23
(a) B1 5z + 7 = 47 oe
(a) Answer: 5z + 7 = 47
(b) M1 5z = 40 (subtracts 7 from both sides)
(b) A1 z = 8 cao
(b) Answer: z = 8
(c) B1 28, follow through 3 x their z + 4
(c) Answer: 28
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 490 pounds, follow through their (a) x 7.20, rounded to the nearest 10 pounds
(b) Answer: 490 pounds
Question 25
M1 total marks for the class of 18 = 18 x 58 (= 1044)
M1 total marks for the class of 22 = 22 x 71 (= 1562)
M1 (1044 + 1562) / 40, combining both totals and dividing by 40 pupils