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Mathematics test Ma KEY STAGE 3 Paper 1 Calculator not allowed TIER 6–8 2001 Please read this page, but do not open the booklet until your teacher tells you to start. Write your name and the name of your school in the spaces below. If you have been given a pupil number, write that also. First name Last name School Pupil number Remember I The test is 1 hour long. I You must not use a calculator for any question in this test. I You will need: pen, pencil, rubber and a ruler. I Some formulae you might need are on page 2. I This test starts with easier questions. I Try to answer all the questions. I Write all your answers and working on the test paper – do not use any rough paper. I Check your work carefully. I Ask your teacher if you are not sure what to do. For marker’s use only QCA/01/669 Sourced from SATs-Papers.co.uk Total marks http://www.SATs-Papers.co.uk Instructions Answers This means write down your answer or show your working and write down your answer. Calculators You must not use a calculator to answer any question in this test. Formulae You might need to use these formulae. Trapezium b Area = height (h) (a p b) th 2 a Prism length Volume = area of cross-section t length KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 2 http://www.SATs-Papers.co.uk Glasses 1. There are 60 pupils in a school. 6 of these pupils wear glasses. (a) The pie chart is not drawn accurately. What should the angles be? Show your working. ○ ○ ○ ○ ○ O ○ ○ ○ ○ ○ ○ ○ ○ ○ and ○ O ○ ○ ○ ○ ○ ○ ○ 2 marks (b) Exactly half of the 60 pupils in the school are boys. From this information, what percentage of boys in this school wear glasses? Tick () the correct box below. 10% 50% not possible to tell ○ 20% ○ 6% ○ 5% ○ 1 mark KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 3 http://www.SATs-Papers.co.uk Bags 2. Ali, Barry and Cindy each have a bag of counters. They do not know how many counters are in each bag. They know that Barry has two more counters than Ali. Cindy has four times as many counters as Ali. (a) Ali calls the number of counters in her bag a Write expressions using a to show the number of counters in Barry’s bag and in Cindy’s bag. Ali’s bag Barry’s bag Cindy’s bag a ○ ○ ○ ○ 1 mark (b) Barry calls the number of counters in his bag b Write expressions using b to show the number of counters in Ali’s bag and in Cindy’s bag. Cindy’s bag ○ ○ ○ ○ b ○ Barry’s bag ○ Ali’s bag ○ ○ 2 marks KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 4 http://www.SATs-Papers.co.uk (c) Cindy calls the number of counters in her bag c Ali’s bag Barry’s bag Cindy’s bag c Which of the expressions below shows the number of counters in Barry’s bag? Circle the correct one. cp2 cm2 4 4 5 http://www.SATs-Papers.co.uk ○ KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 4 p2 ○ 4 m 2 c ○ c 4c m 2 1 mark ○ 4c p 2 Finding Angles 3. The diagram shows two isosceles triangles inside a parallelogram. Not drawn accurately (a) On the diagram, mark another angle that is 75 O ○ ○ ○ ○ Label it 75 O 1 mark (b) Calculate the size of the angle marked k Show your working. ○ ○ ○ ○ ○ ○ O ○ ○ ○ ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 6 http://www.SATs-Papers.co.uk Now look at the triangle drawn on the straight line PQ Q P Write x in terms of y ○ ○ ○ (c) ○ 1 mark (d) Now write x in terms of t and w ○ ○ ○ ○ 1 mark (e) Use your answers to parts (c) and (d) to show that y e t p w ○ ○ ○ ○ 1 mark KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 7 http://www.SATs-Papers.co.uk Statistics, Lambs 4. Here are three number cards. ? The numbers are hidden. ? ? The mode of the three numbers is 5 The mean of the three numbers is 8 What are the three numbers? Show your working. ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ , ○ ○ ○ ○ ○ ○ ○ ○ , ○ ○ ○ ○ ○ ○ ○ 2 marks 5. On a farm 80 sheep gave birth. 30% of the sheep gave birth to two lambs. The rest of the sheep gave birth to just one lamb. In total, how many lambs were born? Show your working. ○ ○ ○ ○ ○ ○ ○ ○ lambs ○ ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 8 http://www.SATs-Papers.co.uk Tiles 6. Two parts of this square design are shaded black. Two parts are shaded grey. Show that the ratio of black to grey is 5 : 3 ○ ○ ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 9 http://www.SATs-Papers.co.uk Thinking Equations 7. (a) Solve this equation. 7 p 5 k e 8k p 1 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ k e 1 mark (b) Solve these equations. Show your working. 10y p 23 e 4 y p 26 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ y e 2 marks 3(2y p 4) e 1 14 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 10 ○ KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 ○ y e 2 marks http://www.SATs-Papers.co.uk Comparing Powers 8. (a) Look at these numbers. Which is the largest? ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 1 mark Which is equal to 9 2 ? ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 1 mark (b) Which two of the numbers below are not square numbers ? ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ and ○ ○ ○ ○ ○ ○ 1 mark KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 11 http://www.SATs-Papers.co.uk Evens or Odds 9. (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. ( m – 1)( m + 1) ○ ○ ○ ○ 3m – 1 ○ m2 2m ○ ○ ○ 2 marks (b) m is an odd number. Is the number m +1 odd, or even, or is it not possible to tell? 2 Tick () the correct box. odd not possible to tell even Explain your answer. ○ ○ ○ ○ 1 mark KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 12 http://www.SATs-Papers.co.uk Computer Game 10. (a) Alan has a guessing game on his computer. He estimates that the probability of winning each game is 0.35 Alan decides to play 20 of these games. How many of these games should he expect to win? ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 1 mark (b) Sue played the same computer game. She won 12 of the games she played, and so she estimated the probability of winning each game to be 0.4 How many games did Sue play? Show your working. ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 2 marks (c) The manufacturers of another guessing game claim that the probability of winning each game is 0.65 Karen plays this game 200 times and wins 124 times. She says: ‘The manufacturers must be wrong’. Do you agree with her? Tick () Yes or No. Yes No Explain your answer. ○ ○ ○ ○ 1 mark KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 13 http://www.SATs-Papers.co.uk Graphing 11. Here are six different equations, labelled A to F A B C D E F Think about the graphs of these equations. (a) Which graph goes through the point (0, 0)? ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 1 mark (b) Which graph is parallel to the y -axis? ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 1 mark (c) Which graph is not a straight line? ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 1 mark (d) Which two graphs pass through the point ( 3, 7 ) ? ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ and ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 14 http://www.SATs-Papers.co.uk (e) The diagram shows the graph of the equation y e 4 m x 2 What are the coordinates of the points where the graph of this equation meets the graph of equation E ? y e 4 m x2 ○ ○ ○ ○ ○ ○ ○ ) ○ ○ , ○ ) and ( ○ , ○ ( 3 marks KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 15 http://www.SATs-Papers.co.uk True or False 12. Equations may have different numbers of solutions. For example: x p 2 e 7 has only one solution, x e 5 but x p 1 p 2 e x p 3 is true for all values of x Tick () the correct box for each algebraic statement below. Correct for no values of x Correct for one value of x Correct for two values of x Correct for all values of x 3x p 7 e 8 3(x p 1) e 3 x p 3 x p 3 e x m 3 5 p x e 5 m x x2 e 9 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 3 marks KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 16 http://www.SATs-Papers.co.uk Congruent 13. The diagram shows five triangles. All lengths are in centimetres. (a) Write the letters of two triangles that are congruent to each other. ○ ○ ○ ○ ○ and ○ ○ ○ ○ ○ Explain how you know they are congruent. ○ ○ ○ ○ 1 mark (b) Write the letters of two triangles that are mathematically similar to each other but not congruent. ○ ○ ○ ○ ○ and ○ ○ ○ ○ ○ Explain how you know they are mathematically similar. ○ ○ ○ ○ 1 mark KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 17 http://www.SATs-Papers.co.uk Thomas the Tank Engine 14. The first ‘Thomas the Tank Engine’ stories were written in 1945. In the 1980s, the stories were rewritten. The cumulative frequency graph shows the numbers of words per sentence for one of the stories. KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 18 http://www.SATs-Papers.co.uk There are 58 sentences in the old version. There are 68 sentences in the new version. (a) Estimate the median number of words per sentence in the old version and in the new version. Show your method on the graph. ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ new ○ old 3 marks (b) What can you tell from the data about the number of words per sentence in the old version and in the new version ? ○ ○ ○ ○ 1 mark (c) Estimate the percentage of sentences in the old version that had more than 12 words per sentence. Show your working. ○ ○ ○ ○ ○ ○ ○ % ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 19 http://www.SATs-Papers.co.uk Scores 15. (a) A fair coin is thrown. When it lands it shows heads or tails. Game: Throw the coin three times. Player A wins one point each time the coin shows a head. Player B wins one point each time the coin shows a tail. 1 8 ○ ○ ○ Show that the probability that player A scores three points is ○ 1 mark (b) What is the probability that player B scores exactly two points? Show your working. ○ ○ ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 20 http://www.SATs-Papers.co.uk Writing Numbers 1 is equal to 0.0004 2500 16. (a) Write 0.0004 in standard form. ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 1 mark 1 in standard form. 25000 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ (b) Write ○ 1 mark (c) Work out 1 1 + 2500 25000 Show your working, and write your answer in standard form. ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 21 http://www.SATs-Papers.co.uk BLANK PAGE KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 22 http://www.SATs-Papers.co.uk END OF TEST KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8 /P1 23 http://www.SATs-Papers.co.uk Sourced from SATs-Papers.co.uk © Qualiﬁcations and Curriculum Authority 2001 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA 00-6651/8 http://www.SATs-Papers.co.uk