Maths: Full Practice Paper (Additional, Level 3, Set 4) - 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.M27 Maths: Full Practice Paper (Additional, Level 3, Set 4)

ISEB COMMON ENTRANCE CE.M27 · 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 fourth practice paper covering stretch and scholarship-track topics from the Additional (Level 3) syllabus: index laws (including negative indices), expanding and factorising harder expressions, solving simultaneous equations by substitution, Pythagoras' theorem, right-angled trigonometry, compound measures, and harder probability.
1
Write 43 * 46 as a single power of 4. (1 mark)
(Total for Question 1 is 1 mark)
2
Simplify r15 / r8, giving your answer as a single power of r. (1 mark)
(Total for Question 2 is 1 mark)
3
Work out the value of 60 + 3-2, giving your answer as a fraction. (2 marks)
(Total for Question 3 is 2 marks)
4
Simplify (w4)3 / w5, giving your answer as a single power of w. (2 marks)
(Total for Question 4 is 2 marks)
5
Expand and simplify (x + 5)(x - 3). (2 marks)
(Total for Question 5 is 2 marks)
6
Expand and simplify (5x - 2)(3x + 4). (3 marks)
(Total for Question 6 is 3 marks)
7
Factorise x2 - x - 20. (2 marks)
(Total for Question 7 is 2 marks)
8
Factorise 2x2 + 9x + 4. (3 marks)
(Total for Question 8 is 3 marks)
9
Solve the simultaneous equations using substitution. y = 3x - 1 and x + 2y = 19 (3 marks)
(Total for Question 9 is 3 marks)
10
Solve the simultaneous equations using substitution. 2y = 3x + 2 and x + y = 11 (4 marks)
(Total for Question 10 is 4 marks)
11
A right-angled triangle has two shorter sides of length 7 cm and 24 cm. Calculate the length of the hypotenuse. (3 marks)
(Total for Question 11 is 3 marks)
12
A right-angled triangle has a hypotenuse of length 26 cm and one shorter side of length 10 cm. Calculate the length of the other shorter side. (3 marks)
(Total for Question 12 is 3 marks)
13
A groundsman wants to mark a straight diagonal path across a rectangular playing field. The field is 20 m wide. The diagonal path, from one corner to the opposite corner, is planned to be 29 m long. Calculate the length of the field. (4 marks)
(Total for Question 13 is 4 marks)
14
In a right-angled triangle, one of the angles is 35 degrees. The side adjacent to this angle has length 14 cm. Calculate the length of the side opposite this angle, correct to 1 decimal place. (3 marks)
(Total for Question 14 is 3 marks)
15
In a right-angled triangle, the side opposite an angle x has length 11 cm and the side adjacent to x has length 4 cm. Calculate the size of angle x, correct to the nearest degree. (3 marks)
(Total for Question 15 is 3 marks)
16
Freya walks 7.2 km in 48 minutes at a constant speed. Work out her average speed in km/h. (3 marks)
(Total for Question 16 is 3 marks)
17
A brick exerts a force of 45 N on the ground through a base with an area of 0.05 m2. Work out the pressure the brick exerts on the ground, in N/m2. (3 marks)
(Total for Question 17 is 3 marks)
18
A box contains 9 white counters, 6 black counters and 5 orange counters. A counter is picked at random from the box. Work out the probability that the counter is orange. Give your answer as a fraction in its simplest form. (2 marks)
(Total for Question 18 is 2 marks)
19
A pencil case contains 5 blue pens and 7 black pens. Two pens are taken from the pencil case at random, one after the other, without replacement. Work out the probability that the two pens are different colours. (4 marks)
(Total for Question 19 is 4 marks)
20
From a point P on level ground, David measures the angle of elevation to the top of a radio mast as 22 degrees. Point P is 95 m from the base of the mast.
(a)Calculate the height of the mast, correct to 1 decimal place. (3 marks)(3)
(b)David then walks towards the mast until he reaches a point Q, where the angle of elevation to the top of the mast has increased to 39 degrees. Using your answer to part (a), calculate the distance PQ, correct to 1 decimal place. (2 marks)(2)
(Total for Question 20 is 5 marks)
21
A garden centre sells plant pots and bags of compost. Four plant pots and three bags of compost cost 30.50 pounds in total. One bag of compost costs 2.00 pounds more than one plant pot.
(a)Using p for the cost of one plant pot, in pounds, write down an expression for the cost of one bag of compost, in pounds. (1 mark)(1)
(b)Form and solve a pair of simultaneous equations to find the cost of one plant pot and the cost of one bag of compost. (4 marks)(4)
(Total for Question 21 is 5 marks)
22
The three sides of a right-angled triangle have lengths x cm, (x + 2) cm and (x + 4) cm, where (x + 4) cm is the hypotenuse.
(a)Use Pythagoras' theorem to form an equation in x. (1 mark)(1)
(b)Expand and simplify your equation to show that it can be written as x2 - 4x - 12 = 0. (2 marks)(2)
(c)Factorise your equation and hence find the value of x, giving a reason for rejecting the other solution. (2 marks)(2)
(Total for Question 22 is 5 marks)
Mark scheme · CE.M27 Maths: Full Practice Paper (Additional, Level 3, Set 4)

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