KS3 Revision work. Level 6 + = 1

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1 KS3 Revision work Level 6 1. Thinking fractions Write the missing numbers in these fraction sums. 1 + = = Pi The value of correct to 7 decimal places is: (a) Write the value of correct to 4 decimal places. Hertfordshire La Schools 1

2 (b) Which value below is closest to the value of π? Put a ring round the correct one Cube Look at the cube. The area of a face of the cube is 9x 2 Area = 9x 2 Hertfordshire La Schools 2

3 Write an expression for the total surface area of the cube. Write your answer as simply as possible Walk I went for a walk. The distance-time graph shows information about my walk. Distance travelled Time taken Tick ( ) the statement below that describes my walk. I was walking faster and faster. I was walking slower and slower. I was walking north-east. I was walking at a steady speed. I was walking uphill. Hertfordshire La Schools 3

4 5. Tomatoes The graph shows information about the diameters and heights of a sample of three types of tomato. height, h diameter, d The dotted lines on the graph can be used to decide which type of tomato each point is likely to represent type A type B type C Height (cm) Diameter (cm) Hertfordshire La Schools 4

5 (a) The diameter of a tomato of type C is 11 cm. What would you expect its height to be?... cm (b) The diameter of a different tomato is 3.2 cm. Its height is 5.8 cm. Which of the three types of tomato is it most likely to be? A B C Explain your answer. (c) Which type of tomato is most nearly spherical in shape? A B C Explain your answer. Hertfordshire La Schools 5

6 6. Same area The triangle and the rectangle below have the same area. Not drawn accurately 6 cm w cm 4 cm 4 cm Work out the value of w Show your working. w... cm 2 marks 7. Newspaper In a survey, 60 people were asked: What kind of newspaper did you buy today? Hertfordshire La Schools 6

7 Here are the results. Type of newspaper Number of people Morning newspaper 35 Evening newspaper 10 No newspaper 15 Complete the pie chart to show this information. Morning newspaper 2 marks Hertfordshire La Schools 7

8 8. Vowels A computer is going to choose a letter at random from an English book. The table shows the probabilities of the computer choosing each vowel. Vowel A E I O U Probability What is the probability that it will not choose a vowel? 2 marks 9. Travelling by car A pupil investigated how the teachers at his school travel to work. The table shows the results. Number of teachers who travel by car Number of teachers who do not travel by car 18 7 (a) What percentage of these teachers travel by car?...% Hertfordshire La Schools 8

9 (b) 18 teachers travel by car. Some of these teachers travel together. Write the missing frequency in the table below. Number of teachers in one car Number of cars Points and rules (a) The grid shows six points labelled A, B, C, D, E and F y B A C x 1 F 2 D 3 4 E Hertfordshire La Schools 9

10 Complete the table to show which points have coordinates that match the rules below. The first one is done for you. Rule A B C D E F x 3 y 3 x y 2 marks Hertfordshire La Schools 10

11 (b) This grid shows six different points. One rule matches the coordinates of each of the six points. 6 y x Write a rule, using x and y, that matches all six points. Hertfordshire La Schools 11

12 11. Drawing Four cubes join to make an L-shape. The diagram shows the L-shape after quarter turns in one direction. On the paper below, draw the L-shape after the next quarter turn in the same direction. 2 marks Hertfordshire La Schools 12

13 12. Dice The diagrams show nets for dice. Each dice has six faces, numbered 1 to 6 Write the missing numbers so that the numbers on opposite faces add to Hertfordshire La Schools 13

14 13. Isosceles A teacher said: Use compasses to construct an isosceles triangle. One side must be 5 cm Another side must be 7 cm. Gill drew two different triangles. The first had sides 5 cm, 7 cm and 7 cm and looked like this: 7 cm 7 cm 5 cm Hertfordshire La Schools 14

15 The second had sides 5 cm, 5 cm and 7 cm. Complete the drawing of the triangle with sides 5 cm, 5 cm and 7 cm. One side of 5 cm has been drawn for you. 5 cm 2 marks 14. Same volume The drawing shows 2 cuboids that have the same volume. Cuboid A Cuboid B 4 cm 2 cm 5 cm 3 cm 5 cm x cm Not drawn accurately Hertfordshire La Schools 15

16 (a) What is the volume of cuboid A? Remember to state your units marks (b) Work out the value of the length marked x... cm Hertfordshire La Schools 16

17 15. Three straight lines The diagram shows three straight lines. b Not drawn accurately c a Hertfordshire La Schools 17

18 Work out the sizes of angles a, b and c Give reasons for your answers. a =... because b =... because c =... because Sizing (a) Put these values in order of size with the smallest first smallest largest 2 marks Hertfordshire La Schools 18

19 (b) Look at this information. 5 5 is 3125 What is 5 7?... 2 marks 17. Doubles I have two fair dice. Each of the dice is numbered 1 to 6. (a) The probability that I will throw double 6 (both dice showing number 6) is 1 36 What is the probability that I will not throw double 6? Hertfordshire La Schools 19

20 (b) I throw both dice and get double 6. Then I throw the dice again. Tick the box that describes the probability that I will throw double 6 this time. less than more than 36 1 Explain your answer. I start again and throw both dice. (c) What is the probability that I will throw double 3 (both dice showing 3)? Hertfordshire La Schools 20

21 (d) What is the probability that I will throw a double? (It could be double 1 or double 2 or any other double.) Hertfordshire La Schools 21

22 18. Enlarging Enlarge the shape by a scale factor of 2, using P as the centre of enlargement. P Isometric grid 2 marks Hertfordshire La Schools 22

23 19. Circle working Kevin is working out the area of a circle with radius 4 He writes: 4 Area = π 8 Explain why Kevin s working is wrong. Hertfordshire La Schools 23

24 20. Values (a) Here are two equations. k = a + b a + b + k = 30 What is the value of k? k =... (b) Look at this information. 10 = c + d c is one more than d What is the value of c? c =... Hertfordshire La Schools 24

25 21. Speed The line on the graph below represents a speed of 60km/hour km/hour Distance (km) Time (minutes) (a) Draw a line on the graph to represent a speed of 30 km/hour. Label the line by writing 30km/hour. (b) Now draw a line on the graph to represent a speed of 120 km/hour. Label the line by writing 120km/hour. Hertfordshire La Schools 25

26 22. Tiles This is a series of patterns with grey and white tiles. pattern number 1 pattern number 2 pattern number 3 The series of patterns continues by adding each time. (a) Complete this table: pattern number 5 16 number of grey tiles number of white tiles 2 marks (b) Complete this table by writing expressions: pattern number n expression for the number of grey tiles expression for the number of white tiles 2 marks Hertfordshire La Schools 26

27 (c) Write an expression to show the total number of tiles in pattern number n. Simplify your expression. 23. Error Kate asked people if they read a daily newspaper. Then she wrote this table to show her results. No 80 people 40% Yes 126 people 60% The values in the table cannot all be correct. The error could be in the number of people. Complete each table to show what the correct numbers could be. No 80 people 40% Yes... people 60% Hertfordshire La Schools 27

28 No... people 40% Yes 126 people 60% 24. Solving Solve these equations. Show your working. 8k 1 15 k... 2m m... 3t + 4 t + 13 t... 2 marks Hertfordshire La Schools 28

29 2(3n + 7) 8 n Straight lines The graph shows a straight line. y x 2 (a) Fill in the table for some of the points on the line. (x, y) (, ) (, ) (, ) x + y Hertfordshire La Schools 29

30 (b) Write an equation of the straight line.... (c) On the graph, draw the straight line that has the equation x + y Consideration (a) Give an example to show the statement below is not correct. When you multiply a number by 2, the answer is always greater than 2 (b) Now give an example to show the statement below is not correct. When you subtract a number from 2, the answer is always less than 2 Hertfordshire La Schools 30

31 27. Completing rules Look at the information. x = 4 y = 13 Complete the rules below to show different ways to get y using x. The first one is done for you. To get y, multiply x by and add This can be written as y =... 2x To get y, multiply x by... and add... This can be written as y =... To get y, multiply x by... and subtract... This can be written as y =... To get y, divide x by... and add... This can be written as y = Relationships Write the missing numbers. 6x + 2 = 10 so 6x + 1 =... Hertfordshire La Schools 31

32 1 2y = 10 so (1 2y) 2 = Equation Solve this equation. 2(2n + 5) = 12 n =... 2 marks 30. Tickets Ann, Ben, Carl, Donna and Eric are friends. They have four tickets for a concert. The order in which they sit at the concert does not matter. Ben must go to the concert. If Eric goes to the concert, Donna must go too. Hertfordshire La Schools 32

33 List all the different groups of four who could go to the concert. Remember, order does not matter. 2 marks Hertfordshire La Schools 33