Maths: Full Practice Paper (Additional, Level 3, Set 6) - Worksheets, Questions and Revision

22 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

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CE.M38 Maths: Full Practice Paper (Additional, Level 3, Set 6)

ISEB COMMON ENTRANCE CE.M38 · Calculator allowed · about 60 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
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

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22