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Mathematics test Ma KEY STAGE 3 Paper 1 Calculator not allowed TIER 5–7 2002 Please read this page, but do not open your 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, ruler and a pair of compasses. 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/02/838 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 Area = 1 (a + b)h 2 Prism Volume = area of cross-section t length KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 2 http://www.SATs-Papers.co.uk Spinning 1. (a) A spinner has eight equal sections. What is the probability of scoring 4 on the spinner? 1 mark What is the probability of scoring an even number on the spinner? 1 mark (b) A different spinner has six equal sections and six numbers. On this spinner, the probability of scoring an even number is The probability of scoring 4 is 1 3 2 3 Write what numbers could be on this spinner. 2 marks KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 3 http://www.SATs-Papers.co.uk Growing shapes 2. Four squares join together to make a bigger square. (a) Four congruent triangles join together to make a bigger triangle. Draw two more triangles to complete the drawing of the bigger triangle. 1 mark (b) Four congruent trapeziums join to make a bigger trapezium. Draw two more trapeziums to complete the drawing of the bigger trapezium. 1 mark KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 4 http://www.SATs-Papers.co.uk (c) Four congruent trapeziums join to make a parallelogram. Draw two more trapeziums to complete the drawing of the parallelogram. 1 mark KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 5 http://www.SATs-Papers.co.uk Interpreting algebra 3. Look at this table. Age (in years) Ann a Ben b Cindy c Write in words the meaning of each equation below. The first one is done for you. b = 30 Ben is 30 years old a + b = 69 1 mark b = 2c a+b+c 3 KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 1 mark = 28 1 mark 6 http://www.SATs-Papers.co.uk Halfway 4. (a) The number 6 is halfway between 4.5 and 7.5 Fill in the missing numbers below. The number 6 is halfway between 2.8 and 1 mark The number 6 is halfway between –12 and 1 mark (b) Work out the number that is halfway between 27 t 38 and 33 t 38 Show your working. 2 marks KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 7 http://www.SATs-Papers.co.uk Survey 5. Hakan asked 30 pupils which subject they liked best. Subject Number of boys Number of girls Maths 4 7 English 2 4 Science 3 3 History 0 1 French 1 5 total 10 total 20 (a) Which subject did 20% of boys choose? 1 mark (b) Which subject did 35% of girls choose? 1 mark (c) Hakan said: ‘In my survey, Science was equally popular with boys and girls’. Explain why Hakan was wrong. 1 mark (d) Which subject was equally popular with boys and girls? 1 mark KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 8 http://www.SATs-Papers.co.uk Solving 6. (a) When x = 5, work out the values of the expressions below. 2 x + 13 = 5x – 5 = 3 + 6x = 2 marks (b) When 2y + 11 = 17, work out the value of y Show your working. y = 2 marks (c) Solve the equation 9y + 3 = 5y + 13 Show your working. y = KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 9 2 marks http://www.SATs-Papers.co.uk Dropping litter 7. This advert was in a newspaper. It does not say how the advertisers know that 93% of people drop litter every day. Some pupils think the percentage of people who drop litter every day is much lower than 93%. They decide to do a survey. (a) Jack says: We can ask 10 people if they drop litter every day. Give two different reasons why Jack’s method might not give very good data. First reason: 1 mark Second reason: 1 mark KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 With permission from the Keep Britain Tidy Campaign 10 http://www.SATs-Papers.co.uk Dropping litter cont, Negatives (b) Lisa says: We can go into town on Saturday morning. We can stand outside a shop and record how many people walk past and how many of those drop litter. Give two different reasons why Lisa’s method might not give very good data. First reason: 1 mark Second reason: 1 mark 8. Fill in the missing numbers in the boxes using only negative numbers. – 5 – KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 = = –5 11 1 mark 1 mark http://www.SATs-Papers.co.uk Puzzle 9. You can often use algebra to show why a number puzzle works. Fill in the missing expressions. 2 marks KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 12 http://www.SATs-Papers.co.uk Rectangle rest 10. The diagram shows a rectangle that just touches an equilateral triangle. Not drawn accurately (a) Find the size of the angle marked x Show your working. ° 2 marks (b) Now the rectangle just touches the equilateral triangle so that ABC is a straight line. Not drawn accurately Show that triangle BDE is isosceles. 2 marks KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 13 http://www.SATs-Papers.co.uk Mice 11. Three types of mice might come into our homes. Some mice are more likely to be found in homes far from woodland. Others are more likely to be found in homes close to woodland. The bar charts show the percentages of mice that are of each type. KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 14 http://www.SATs-Papers.co.uk Use the bar charts to answer these questions. (a) About what percentage of mice in homes close to woodland are wood mice? % 1 mark (b) About what percentage of mice in homes far from woodland are not wood mice? % 1 mark (c) The black bars show the percentages for house mice. One of the black bars is taller than the other. Does that mean there must be more house mice in homes far from woodland than in homes close to woodland? Tick ( ) Yes or No. Yes No Explain your answer. 1 mark KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 15 http://www.SATs-Papers.co.uk Straight lines 12. The graph shows a straight line. The equation of the line is y = 3x (a) Does the point ( 25, 75 ) lie on the straight line y = 3x ? Tick ( ) Yes or No. Yes No Explain how you know. 1 mark KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 16 http://www.SATs-Papers.co.uk (b) Write the coordinates of the point that lies on both the straight lines y = 4 x + 1 and y = 6 x – 4 You must show your working. ( , ) 3 marks (c) Explain how you can tell there is no point that lies on both the straight lines y = 1 x + 3 and 2 y = 1x + 5 2 1 mark KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 17 http://www.SATs-Papers.co.uk Egyptians 13. 1 1 1 , , are all examples of unit fractions. 3 8 5 All unit fractions must have a numerator that is 1 1 3 a denominator that is an integer greater than 1 The ancient Egyptians used only unit fractions. For 1 3 1 , they wrote the sum + 4 2 4 (a) For what fraction did they write the sum 1 1 + ? 2 5 Show your working. 1 mark 9 as the sum of two unit fractions. 20 1 One of them was 4 (b) They wrote What was the other? Show your working. 1 mark 1 mark KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 18 http://www.SATs-Papers.co.uk Egyptians cont, Rearrange (c) What is the biggest fraction you can make by adding two different unit fractions? Show your working. 2 marks 14. The subject of the equation below is p p = 2( e + f ) Rearrange the equation to make e the subject. e = KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 2 marks 19 http://www.SATs-Papers.co.uk Locus 15. The diagram shows the locus of all points that are the same distance from A as from B. The locus is one straight line. (a) The locus of all points that are the same distance from ( 2, 2 ) and ( – 4, 2 ) is also one straight line. Draw this straight line. 1 mark (b) The locus of all points that are the same distance from the x-axis as they are from the y-axis is two straight lines. Draw both straight lines. 1 mark KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 20 http://www.SATs-Papers.co.uk (c) Look at points C and D below. Use a straight edge and compasses to draw the locus of all points that are the same distance from C as from D. Leave in your construction lines. 2 marks KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 21 http://www.SATs-Papers.co.uk MOT 16. Cars more than three years old must pass a test called an MOT. The testers measure the right and left front wheel brakes, and give each brake a score out of 500 Then they use the graph. For example: A car has R = 300, L = 350 ( 300, 350 ) is in the white region, so the car passes this part of the test. KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 22 http://www.SATs-Papers.co.uk (a) A man takes his car to be tested. L = 200 Approximately, between what values does R need to be for his car to pass this test? and 1 mark A different part of the test uses R + L To pass, R + L ≥ 400 (b) On the graph, draw the straight line R + L = 400 1 mark Then shade the region where the car fails, R + L < 400 1 mark (c) If L = 200, between what values does R need to be to pass both parts of the test? and KS3/02/Ma/Tier from SATs-Papers.co.uk Sourced 5–7/P1 23 1 mark http://www.SATs-Papers.co.uk END OF TEST Sourced from SATs-Papers.co.uk © Qualifications and Curriculum Authority 2002 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA http://www.SATs-Papers.co.uk 01-8633/6