Sample test questions All questions

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1 Ma KEY STAGE 3 LEVELS 3 8 Sample test questions All questions 2003

2 Contents Question Level Attainment target Page Completing calculations 3 Number and algebra 3 Odd one out 3 Number and algebra 4 Hexagon area 4 Shape, space and measures 5 Digit cards 4 Number and algebra 6 Number puzzle level 4 4 Number and algebra 7 Number puzzle level 5 5 Number and algebra 8 Wrapping paper 5 Shape, space and measures 9 Text messages 6 Handling data 10 Prime 6 Number and algebra 11 Rhombus tiles 6 Shape, space and measures 12 Different order 6 Number and algebra 13 Circle design 7 Number and algebra 14 Primary maths challenge 8 Handling data 15 2

3 Completing calculations 1. Write numbers to complete the calculation. = 50 1 mark Now write different numbers to complete the calculation. = 50 1 mark 3

4 Odd one out 1. Look at these diagrams diagram A diagram B diagram C Which diagram is the odd one out? Tick ( ) your answer. A B C Explain why. 1 mark 4

5 Hexagon area 1. The grid shown below is made of regular hexagons. On the grid, draw a rectangle with an area 6 times as big as the area of one hexagon. 1 mark 5

6 Digit cards 1. I have these number cards I place all the cards in a loop so that each side adds to the same total. Fill in the missing numbers on the cards marks 6

7 Number puzzle - level 4 1. Look at this number puzzle. You add two numbers to work out the number that goes on top of them = 10 so 10 goes on top of 4 and Complete the number puzzle below marks 7

8 Number puzzle - level 5 1. Look at this number puzzle. You add two numbers to work out the number that goes above them = 10 so 10 goes above 4 and Complete the number puzzle below marks 8

9 Wrapping paper 1. I have a present in a box, a cuboid measuring 10cm by 8cm by 5cm. Not drawn accurately 5cm 8cm 10cm I have one sheet of wrapping paper to wrap up the box. The sheet is a rectangle that measures 25cm by 30cm. Is the sheet of wrapping paper big enough to cover all the box? Show how you know. 2 marks 9

10 Text messages 1. Four boys and two girls received text messages. The mean number of messages received by the four boys was 20 The mean number of messages received by the two girls was 26 Use the information in the box to decide if each statement below is True or False. (a) The person who received the most messages must have been a girl. True False Explain your answer. 1 mark (b) The mean number of messages received by the six people was 23 True False Explain your answer. 1 mark 10

11 Prime 1. I am thinking of a six-digit square number with a units digit of 6 6 Could its square root be a prime number? Tick ( ) Yes or No. Yes No Explain your answer. 2 marks 11

12 Rhombus tiles 1. I have some tiles that are squares and some tiles that are equilateral triangles. The side lengths of the tiles are all the same. I arrange the tiles like this. I want to fill the gaps by making four tiles that are rhombuses. What should the angles in each rhombus be? Show calculations to explain your answer. 3 marks 12

13 Different order 1. (a) I think of a number, then I carry out these operations on my number. Multiply by 5 Add 8 When I carry out the operations in one order the answer is 105 When I carry out the operations in the other order the answer is 73 What is my number? Show your working. 2 marks (b) The difference between my two answers is 32 Prove that the difference will always be 32, no matter what my number is. 2 marks

14 Circle design 1. Here are three circles. Area a Area 4a Area 9a Parts of the circles are used to make the design below. What fraction of the design is shaded? You must show your working. 2 marks 14

15 Primary maths challenge 1. Here is some information about a maths competition for primary school pupils. In November 2001, more than pupils in 1175 schools took part in the main competition. Over 1100 high-scoring pupils reached the finals of the competition. The distributions of the marks for the main competition and the finals are shown on the following page. To reach the finals, pupils had to score at least x marks in the main competition. Estimate the value of x You must show your working. x = 3 marks 15

16 Main competition Percentage Marks Finals Percentage Marks Data: Primary maths challenge 2001/ Source: the Mathematical Association