m =... n =... Ks3 Revision material Level 7 1. Powers Work out the values of m and n = 5 m = 5 n 2. Multiplication grids

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1 Ks3 Revision material Level 7 1. Powers Work out the values of m and n = 5 m m = = 5 n n = Multiplication grids Write the missing numbers in these multiplication grids Hertfordshire La Schools 1

2 marks 3. Quiz In a quiz game two people each answer 100 questions. They score one point for each correct answer. The quiz game has not yet finished. Each person has answered 90 questions. The table shows the results so far. Person A 60% of the first 90 questions correct Person B 50% of the first 90 questions correct Can person B win the quiz game? Explain your answer. Hertfordshire La Schools 2

3 Tick ( ) your answer. B can win. B cannot win but can draw. B cannot win or draw. 4. Random numbers Chris read the first 55 numbers from a book of random numbers. As he read each number he recorded it in the diagram below Key 1 3 represents (a) What was the largest number he recorded?... Hertfordshire La Schools 3

4 (b) Explain how Chris could change the diagram to make it easier for him to find the median of his data set. 5. 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 4

5 (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 (c) What is the mean number of teachers in each car?... Hertfordshire La Schools 5

6 6. Sweets Altogether, I have 10 bags of sweets. The mean number of sweets in the bags is 41 The table shows how many sweets there are in 9 of the bags. Number of sweets in a bag Frequency Calculate how many sweets there are in the 10th bag. You must show your working.... Hertfordshire La Schools 6

7 ... (b) Explain how Chris could change the diagram to make it easier for him to fid the median of his data set. 7. 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. (a) 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 7

8 No... people 40% Yes 126 people 60% (b) The error could be in the percentages. Complete the table with the correct percentages. No 80 people... % Yes 126 people... % Hertfordshire La Schools 8

9 8. Which pupil? The table shows the number of boys and girls in two different classes. Class 9A Class 9B Boys Girls A teacher is going to choose a pupil at random from each of these classes. In which class is she more likely to choose a boy? You must show your working. Tick ( ) your answer. Class 9A Class 9B Hertfordshire La Schools 9

10 9. Pitch A groundsman marks out a football pitch. 93 metres 50 metres (a) He makes the pitch 93 metres long, to the nearest metre. What is the shortest possible length of the pitch?... m (b) He makes the pitch 50 metres wide, to the nearest metre. What is the shortest possible width of the pitch?... m Hertfordshire La Schools 10

11 (c) Des wants to know how many times he should run around the outside of this pitch to be sure of running at least 3km. Use your answer to parts (a) and (b) to find how many times Des should run around the pitch. You must show your working. 10. Counters A bag contains counters that are red, black, or green. 1 of the counters are red 3 1 of the counters are black 6 Hertfordshire La Schools 11

12 There are 15 green counters in the bag. How many black counters are in the bag?... Hertfordshire La Schools 12

13 11. x and y Solve these simultaneous equations using an algebraic method. 3x + 7y 18 x + 2y 5 You must show your working. x =... y =... 3 marks 12. Triangles ABC and ACD are both right-angled triangles. D 6 cm C Not drawn accurately 6 cm B 8 cm A Hertfordshire La Schools 13

14 (a) Explain why the length of AC is 10 cm. (b) Calculate the length of AD Show your working.... cm Hertfordshire La Schools 14

15 13. Area The diagram shows two circles and a square, ABCD. A and B are the centres of the circles. The radius of each circle is 5 cm. A 5 cm B 5 cm D C Not drawn accurately Calculate the area of the shaded part of the square marks Hertfordshire La Schools 15

16 14. Sequences (a) Draw lines to match each nth term rule to its number sequence. nth term Number sequence 4n 4, 7, 12, 19, (n + 1) 2 4, 8, 12, 16, n , 9, 16, 25, n ( n + 3) 4, 10, 18, 28, (b) Write the first four terms of the number sequence using the nth term rule below. n 3 + 3,,, Hertfordshire La Schools 16

17 15. Fence plan Here is a plan of some land. There will be a fence that is always the same distance from tree A as from tree B, going all the way from one road to the other road. Use compasses and a straight edge to show accurately on the plan where the fence will go. You must leave in your construction lines. Road Tree A Tree B Road Hertfordshire La Schools 17

18 16. Running machine Kali uses a running machine to keep fit. The simplified distance-time graph shows how she used the machine during one run. 4 3 Distance (km) Time Use the graph to answer these questions. (a) Between 0930 and 0940, what was her speed in kilometres per hour?... km/h Hertfordshire La Schools 18

19 (b) Throughout the run, for how many minutes did she travel at this speed?... minutes (c) At 0940, she increased her speed. By how many kilometres per hour did she increase her speed?... km/h 17. Sixty (a) Each of these calculations has the same answer, 60 Fill in each gap with a number = Hertfordshire La Schools 19

20 (b) Solve these equations to find the values of a, b and c. 5 a 40 4 b + 80 = 60 2 c + 24 a... b... c... 3 marks 18. Graphing Here are six different equations, labelled A to F A y = 3 x 4 B y = 4 C x = 5 D x + y = 10 E y = 2 x + 1 F y x = 2 Think about the graphs of these equations. (a) Which graph goes through the point (0, 0)?... Hertfordshire La Schools 20

21 (b) Which graph is parallel to the y-axis?... (c) Which graph is not a straight line?... (d) Which two graphs pass through the point ( 3, 7 )?... and... Hertfordshire La Schools 21

22 (e) The diagram shows the graph of the equation y 4 x 2 What are the coordinates of the points where the graph of this equation meets the graph of equation E? 5 y x y 2 = 4 x (, ) and (, ) 3 marks Hertfordshire La Schools 22

23 19. Bracket multiplication Multiply out the brackets in these expressions. y (y 6)... (k + 2)(k + 3) Evens or Odds (a) m is an odd number. Which of the numbers below must be even, and which must be odd? Write odd or even under each one. 2m m 2 3m 1 (m 1)(m + 1) Hertfordshire La Schools 23

24 (b) m is an odd number. Is the number m 1 2 odd, or even, or is it not possible to tell? Tick ( ) the correct box. odd even not possible to tell Explain your answer. 21. Triangle Look at the triangle. a 2b Not drawn accurately a b Hertfordshire La Schools 24

25 Work out the value of a a =... 3 marks Hertfordshire La Schools 25

26 22. Two semicircles This shaded shape is made using two semicircles. One semicircle has a diameter of 20cm. The other has a diameter of 30cm. 30cm 20cm Not drawn accurately Calculate the perimeter of the shaded shape.... cm Hertfordshire La Schools 26

27 23. Thinking diagonally The diagram shows a square with side length 5 cm. y cm Not drawn accurately The length of the diagonal is y cm. Show that the value of y is Brackets (a) Jenny wants to multiply out the brackets in the expression 3(2a+ 1) She writes: 3 (2a + 1) = 6a + 1 Show why Jenny is wrong. Hertfordshire La Schools 27

28 (b) Sandeep wants to multiply out the brackets in the expression (k + 4) (k + 7) He writes (k + 4) (k + 7)= K Show why Sandeep is wrong. Hertfordshire La Schools 28

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