Maths: Full Practice Paper (Core, Non-Calculator, Set 4) - Worksheets, Questions and Revision

25 original exam-style questions - 7 pages of questions with a full mark scheme - free printable PDF.

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CE.M31 Maths: Full Practice Paper (Core, Non-Calculator, Set 4)

ISEB COMMON ENTRANCE CE.M31 · Calculators not allowed · about 60 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Time allowed: 60 minutes. Answer ALL 25 questions. Write your answers in the spaces provided. You are NOT 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 fourth Core (Level 2) paper covers the same breadth as Papers 1, 2 and 3: number, fractions/decimals/percentages, ratio, algebra, geometry, measures, coordinates, statistics and probability, with entirely different questions.
1
Write the number eight hundred and thirteen thousand and forty-two in figures. (1 mark)
(Total for Question 1 is 1 mark)
2
Work out 8005 - 4728 (1 mark)
(Total for Question 2 is 1 mark)
3
Find 5/8 of 96 (1 mark)
(Total for Question 3 is 1 mark)
4
Two angles lie on a straight line. One angle is 134 degrees and the other is w degrees. Work out the size of angle w (1 mark)
(Total for Question 4 is 1 mark)
5
Simplify 8h + 3k - 5h + 6k (1 mark)
(Total for Question 5 is 1 mark)
6
One evening in Fort William, the temperature was -5 degrees C. Overnight it fell by 8 degrees C. Work out the temperature after it fell. (2 marks)
(Total for Question 6 is 2 marks)
7
Convert 17/25 to a percentage. (2 marks)
(Total for Question 7 is 2 marks)
8
Simplify the ratio 72:96 fully. (2 marks)
(Total for Question 8 is 2 marks)
9
Solve 4x - 9 = 23 (2 marks)
(Total for Question 9 is 2 marks)
10
A triangle has a base of 16 cm and a perpendicular height of 11 cm. Work out its area. (2 marks)
(Total for Question 10 is 2 marks)
11
Bilal is making a smoothie and needs 900 ml of milk. He has three cartons of milk, each containing 250 ml. Show working to decide whether he has enough milk, and if not, say how much more he needs. (2 marks)
(Total for Question 11 is 2 marks)
12
Point G has coordinates (5, 12) and point H has coordinates (13, 4). Find the coordinates of the midpoint of GH. (2 marks)
(Total for Question 12 is 2 marks)
13
In a charity quiz, five teams scored the following points: 34, 41, 29, 38, 33. Work out the mean score. (2 marks)
(Total for Question 13 is 2 marks)
14
A box contains 6 red pens, 4 blue pens and 10 black pens. Freya takes one pen from the box at random.
(a)Find the probability that it is blue. (1 mark)(1)
(b)Find the probability that it is NOT black. (1 mark)(1)
(Total for Question 14 is 2 marks)
15
Write down all the factors of 105 that are also prime numbers. (2 marks)
(Total for Question 15 is 2 marks)
16
Expand and simplify 6(3x + 4) - 5(x - 3) (3 marks)
(Total for Question 16 is 3 marks)
17
In triangle XYZ, angle X = 41 degrees, angle Y = (4x + 13) degrees and angle Z = 3x degrees.
(a)Form an equation in x and solve it. (2 marks)(2)
(b)Work out the size of angle Z. (1 mark)(1)
(Total for Question 17 is 3 marks)
18
Priya and Callum share 117 conkers in the ratio 4:9. Work out how many conkers Callum receives. (3 marks)
(Total for Question 18 is 3 marks)
19
A tablet computer costs 320 pounds. In a sale, the price is reduced by 15%. Work out the sale price. (3 marks)
(Total for Question 19 is 3 marks)
20
Mr Kowalski's garden in Preston is a rectangle measuring 18 m by 11 m. A rectangular patio measuring 5 m by 4 m has been built in one corner of the garden (the patio is not lawn).
(a)Work out the area of the whole rectangular garden. (1 mark)(1)
(b)Work out the area of the patio. (1 mark)(1)
(c)Work out the area of the garden that is lawn (not patio). (2 marks)(2)
(Total for Question 20 is 4 marks)
21
A pie chart was used to show how 108 students travel to a school open evening. It shows that they go by Walking (angle 120 degrees), by Car (angle 90 degrees), and by Bicycle (angle 70 degrees). The rest go by Bus.
(a)Work out the angle for the Bus sector of the pie chart. (2 marks)(2)
(b)Work out how many of the 108 students go by Bus. (2 marks)(2)
(Total for Question 21 is 4 marks)
22
Tunde is x years old. His grandmother Ngozi is 6 years older than five times Tunde's age. The sum of their ages is 78.
(a)Write down an equation in x to represent this information. (1 mark)(1)
(b)Solve your equation to find Tunde's age. (2 marks)(2)
(c)Find Ngozi's age. (1 mark)(1)
(Total for Question 22 is 4 marks)
23
A craft shop sells buttons for 55p each and ribbons for 85p each. Grace buys 6 buttons and 4 ribbons, and pays with a 10 pound note.
(a)Work out the total cost of the buttons. (1 mark)(1)
(b)Work out the total cost of the ribbons. (1 mark)(1)
(c)Work out how much change Grace should receive from her 10 pound note. (3 marks)(3)
(Total for Question 23 is 5 marks)
24
A circular flower bed in a park in Durham has a diameter of 112 cm. Take π = 22/7.
(a)Work out the radius of the flower bed. (1 mark)(1)
(b)Work out the circumference of the flower bed. (2 marks)(2)
(c)A low edging strip needs to sit 9 cm out from the edge of the flower bed all the way round. Work out the diameter of the circle that the edging forms. (2 marks)(2)
(Total for Question 24 is 5 marks)
25
At a summer fete, a profit of 720 pounds is shared between the PTA fund and the school trip fund in the ratio 5:7.
(a)Work out how much money the PTA fund receives. (2 marks)(2)
(b)The PTA fund then spends 25% of its share on new equipment. Work out how much money is spent on equipment. (2 marks)(2)
(c)Work out how much money the PTA fund has left after this spending. (2 marks)(2)
(Total for Question 25 is 6 marks)
Mark scheme · CE.M31 Maths: Full Practice Paper (Core, Non-Calculator, 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

Question 23

Question 24

Question 25