Time allowed: 60 minutes. Answer ALL 22 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 is a sixth practice paper covering a broader spread of topics from the Additional (Level 3) syllabus: order of operations and significant figures, fractions and percentages of amounts, simplifying expressions and solving equations, substituting into formulae, ratio, angles in a triangle, sequences, probability, averages and range, scale drawings, compound measures, volume, standard form, simultaneous equations by elimination, circles, direct proportion, transformations, and multi-step problem solving.
1
Work out 62 - 4 * (9 - 5) / 2. Show your working. (2 marks)
(Total for Question 1 is 2 marks)
2
Round 0.058239 correct to 3 significant figures. (2 marks)
(Total for Question 2 is 2 marks)
3
Mrs Okafor buys a printer priced at 268.00 pounds. In a sale she gets 3/8 off the price. Work out the sale price she pays. (3 marks)
(Total for Question 3 is 3 marks)
4
A gym membership costs 42.00 pounds per month. From 01/09/2026 the price increases by 12%. Work out the new monthly price. (3 marks)
(Total for Question 4 is 3 marks)
5
Simplify fully: 5x + 3y - 2x + 7y (2 marks)
(Total for Question 5 is 2 marks)
6
Solve 4(x + 3) = 2x + 26 (3 marks)
(Total for Question 6 is 3 marks)
7
The cost, C pounds, of hiring a bouncy castle for h hours is given by C = 35 + 12h. Freya hires a bouncy castle and pays 119.00 pounds. Work out how many hours she hired it for. (3 marks)
(Total for Question 7 is 3 marks)
8
Tariq, Priya and Kofi share a prize fund of 360.00 pounds in the ratio 2 : 3 : 4. Work out Kofi's share. (3 marks)
(Total for Question 8 is 3 marks)
9
A garden is in the shape of a 12 m by 9 m rectangle, with a 5 m by 4 m rectangular corner removed to leave an L-shape. Work out the area of the remaining garden. (4 marks)
(Total for Question 9 is 4 marks)
10
The three angles of a triangle are in the ratio 2 : 3 : 4. Work out the size of the largest angle. (3 marks)
(Total for Question 10 is 3 marks)
11
A sequence begins 5, 9, 13, 17, 21, ...
(a)Find an expression for the nth term of the sequence. (2 marks)(2)
(b)Determine whether 151 is a term in the sequence. Show your reasoning. (2 marks)(2)
(Total for Question 11 is 4 marks)
12
A bag contains 5 red counters, 3 blue counters and 4 green counters. Ffion takes one counter at random from the bag, notes its colour, and replaces it in the bag.
(a)Write down the probability that the counter Ffion takes is blue. (1 mark)(1)
(b)Ffion takes a counter, replaces it, then takes a second counter. Work out the probability that both counters are green. (2 marks)(2)
(Total for Question 12 is 3 marks)
13
The number of goals scored by a football team in its last 9 matches were: 0, 1, 1, 2, 2, 2, 3, 4, 5
(a)Find the median number of goals. (1 mark)(1)
(b)Find the mean number of goals, giving your answer correct to 2 decimal places. (2 marks)(2)
(c)Find the range of the number of goals. (1 mark)(1)
(Total for Question 13 is 4 marks)
14
A map is drawn to a scale of 1 : 25000. The distance between two villages on the map is 6.4 cm. Work out the real-life distance between the villages, giving your answer in kilometres. (3 marks)
(Total for Question 14 is 3 marks)
15
Rohan cycles from home to college, a distance of 8.4 km, at an average speed of 14 km/h. He needs to arrive by 08:15. Work out the latest time he must leave home. (3 marks)
(Total for Question 15 is 3 marks)
16
A water trough for horses is in the shape of a triangular prism, lying on its rectangular base. The cross-section is a right-angled triangle with base 40 cm and height 30 cm. The trough is 150 cm long. Work out the volume of the trough, in litres. (1 litre = 1000 cm3) (4 marks)
(Total for Question 16 is 4 marks)
17
(a) Write 47 200 000 in standard form. (b) Write 3.6 * 10-4 as an ordinary number.
(a)Write 47 200 000 in standard form. (2 marks)(2)
(b)Write 3.6 * 10-4 as an ordinary number. (1 mark)(1)
(Total for Question 17 is 3 marks)
18
Solve the simultaneous equations: 2x + 3y = 16, x - 3y = -1 (4 marks)
(Total for Question 18 is 4 marks)
19
A circular pond has a diameter of 5.6 m. Calculate the circumference of the pond, correct to 1 decimal place. (Use π = 3.14159) (3 marks)
(Total for Question 19 is 3 marks)
20
The cost of hiring a marquee is directly proportional to the number of days it is hired for. A 4-day hire costs 860.00 pounds. Nia needs the marquee for 7 days. Work out the cost of a 7-day hire. (3 marks)
(Total for Question 20 is 3 marks)
21
Triangle T has vertices at (1, 2), (1, 5) and (3, 2). Triangle T is reflected in the line x = 4 to give triangle T'. Write down the coordinates of the three vertices of T'. (3 marks)
(Total for Question 21 is 3 marks)
22
Zainab is organising a school fair. She buys 160 raffle tickets to sell at 1.20 pounds each, paying a printing cost of 18.00 pounds for the tickets. By the end of the fair she has sold 85% of the tickets. She also receives 45.00 pounds in cash donations. Zainab donates 40% of her total takings (ticket sales plus cash donations) to charity. Work out how much money she has left after paying the printing cost and making the charity donation. (5 marks)
(Total for Question 22 is 5 marks)
Mark scheme · CE.M38 Maths: Full Practice Paper (Additional, Level 3, Set 6)
Question 1
M1 evaluates the power and the bracket correctly: 36 and 4 seen
A1 28 cao
Answer: 28
Question 2
M1 identifies the first three significant figures as 5, 8, 2, using the 4th significant figure (3) to decide the rounding
A1 0.0582 cao
Answer: 0.0582
Question 3
M1 268 * 3/8 (=100.50) oe
M1 268 - their discount (dep)
A1 167.50 pounds cao
Answer: 167.50 pounds
Question 4
M1 42 * 0.12 (=5.04) oe, or 42 * 1.12
M1 42 + their 5.04 (dep, if the 12% was found separately)
A1 47.04 pounds cao
Answer: 47.04 pounds
Question 5
M1 collects the x terms or the y terms correctly
A1 3x + 10y cao
Answer: 3x + 10y
Question 6
M1 expands the bracket correctly: 4x + 12 seen
M1 collects terms onto one side: 2x = 14 oe
A1 x = 7 cao
Answer: x = 7
Question 7
M1 119 - 35 (=84) oe
M1 their 84 / 12 (dep)
A1 7 hours cao
Answer: 7 hours
Question 8
M1 2 + 3 + 4 = 9 seen, or 360 / 9 (=40)
M1 their 40 * 4 (dep)
A1 160.00 pounds cao
Answer: 160.00 pounds
Question 9
M1 12 * 9 (=108) oe
M1 5 * 4 (=20) oe
M1 their 108 - their 20 (dep on both previous method marks)
A1 88 m2 cao
Answer: 88 m2
Question 10
M1 2 + 3 + 4 = 9 seen, or 180 / 9 (=20)
M1 their 20 * 4 (dep)
A1 80 degrees cao
Answer: 80 degrees
Question 11
(a) M1 identifies the common difference of 4, or 4n seen
(a) A1 4n + 1 cao
(a) Answer: 4n + 1
(b) M1 sets their nth term equal to 151, e.g. 4n + 1 = 151, leading to n = 37.5 (ft their part a)
(b) A1 correct conclusion that 151 is not a term, since n is not a whole number (ft)
(b) Answer: No, since n = 37.5 is not a whole number
Question 12
(a) B1 3/12 oe (e.g. 1/4, 0.25, 25%) cao
(a) Answer: 1/4
(b) M1 4/12 * 4/12 oe
(b) A1 1/9 oe cao
(b) Answer: 1/9
Question 13
(a) B1 2 goals cao
(a) Answer: 2 goals
(b) M1 sum of the data = 20 seen, divided by 9
(b) A1 2.22 (2 d.p.) awrt cao
(b) Answer: 2.22 goals
(c) B1 5 goals cao
(c) Answer: 5 goals
Question 14
M1 6.4 * 25000 (=160000) oe
M1 converts their 160000 cm into km (dep), using 1 km = 100000 cm
A1 1.6 km cao
Answer: 1.6 km
Question 15
M1 8.4 / 14 (=0.6 hours) oe
M1 converts their 0.6 hours to 36 minutes (dep)
A1 07:39 cao
Answer: 07:39
Question 16
M1 0.5 * 40 * 30 (=600) oe, for the cross-sectional area
M1 their 600 * 150 (=90000), for the volume in cm3
M1 their 90000 / 1000 (dep)
A1 90 litres cao
Answer: 90 litres
Question 17
(a) M1 4.72 seen (correct digits, correctly placed decimal point)
(a) A1 4.72 * 107 cao
(a) Answer: 4.72 * 107
(b) B1 0.00036 cao
(b) Answer: 0.00036
Question 18
M1 adds the two equations to eliminate y: 3x = 15 oe
A1 x = 5
M1 substitutes their x into either equation
A1 y = 2 cao (ft their x)
Answer: x = 5, y = 2
Question 19
M1 identifies the correct formula: circumference = π * d oe
M1 3.14159 * 5.6 (=17.59...) oe
A1 17.6 m (1 d.p.) awrt cao
Answer: 17.6 m
Question 20
M1 860 / 4 (=215), for the cost per day
M1 their 215 * 7 (dep)
A1 1505.00 pounds cao
Answer: 1505.00 pounds
Question 21
B1 (7, 2) cao
B1 (7, 5) cao
B1 (5, 2) cao
Answer: (7, 2), (7, 5), (5, 2)
Question 22
M1 0.85 * 160 (=136), for the number of tickets sold
M1 their 136 * 1.20 (=163.20), for the ticket revenue
M1 their 163.20 + 45 (=208.20), for the total takings
M1 0.4 * their 208.20 (=83.28), for the charity donation