We have almost every SATs paper within our archives including KS1 *Money Problems* and many other KS1, KS2 and KS3 SATs papers and worksheets. SATs papers are fantastic practise tools, especially for literacy, problem solving and maths. Alternative sources for study include the Bitesize resources and Revisewise for more SATs practice, SATs revision and SATs preparation!

KS3 P2 5-7_254651.qxd Ma KEY STAGE 3 19/2/03 10:03 am Page 1 Mathematics test Paper 2 Calculator allowed TIER 5–7 2003 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. First name Last name School Remember I The test is 1 hour long. I You may use a calculator for any question in this test. I You will need: pen, pencil, rubber, ruler and a scientific or graphic calculator. 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. Marks may be awarded for working. I Check your work carefully. I Ask your teacher if you are not sure what to do. For marker’s use only QCA/03/969 Sourced from SATs-Papers.co.uk Total marks Borderline check http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 2 Instructions Answers This means write down your answer or show your working and write down your answer. Calculators You may 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 KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 3 Drawing 1. In this question, the grids are centimetre square grids. (a) Draw a rectangle that has an area of 12cm2 1 mark (b) Draw a triangle that has an area of 6cm2 1 mark KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 3 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 4 Ages 2. (a) It is Tina’s birthday. We do not know how old Tina is. Call Tina’s age, in years, n The expressions below compare Tina’s age to some other people’s ages. Use words to compare their ages. The first one is done for you. Tina’s age n Ann is Ann’s age n+3 Tina’s age n 3 years older than Tina Barry is Barry’s age n–1 Tina’s age n Carol’s age 2n Carol is 2 marks (b) In one year’s time Tina’s age will be n + 1 Write simplified expressions to show the ages of the other people in one year’s time. Tina Ann Barry Carol Age now n n+3 n–1 2n Age in one year’s time n+1 2 marks KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 4 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 5 (c) When n = 30, find the value of 2 n + 1 1 mark When n = 30, find the value of 2( n + 1) 1 mark KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 6 Grid percentages 3. Each diagram below was drawn on a square grid. (a) Write what percentage of each diagram is shaded. The first one is done for you. 75 % % 1 mark % 1 mark (b) Explain how you know that 12 1 % of the diagram below is shaded. 2 1 mark 1 2 (c) Shade 37 % of the diagram below. 1 mark KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 7 Data collection 4. Some pupils plan a survey to find the most common types of tree in a wood. The pupils will only use one design. (a) Choose a design they should not use. Design Explain why it is not a good design to use. 1 mark (b) Choose the design that is the best. Design Explain why it is the best. 1 mark KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 8 Coins 5. (a) Jo has these 4 coins. Jo is going to take one of these coins at random. Each coin is equally likely to be the one she takes. Show that the probability that it will be a 10p coin is 1 2 1 mark (b) Colin has 4 coins that total 33p. He is going to take one of his coins at random. What is the probability that it will be a 10p coin? You must show your working. 1 mark KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 8 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 9 Explaining why 6. Look at the diagram. Triangle ABD is the reflection of triangle ABC in the line AB. Not drawn accurately Fill in the gaps below to explain how to find angle x The length of AC is 12 cm. The length of AD is cm. The length of CD is cm. ACD is an equilateral triangle because 1 mark so angle y is ° because so angle x is ° because KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 1 mark 1 mark 9 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 10 Water 7. (a) A glass holds 225ml. An adult needs about 1.8 litres of water each day to stay healthy. How many glasses is that? Show your working. 2 marks (b) An adult weighs 80kg. 60% of his total mass is water. What is the mass of this water? kg 1 mark KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 10 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 11 Ratio of ages 8. Paul is 14 years old. His sister is exactly 6 years younger, so this year she is 8 years old. This year, the ratio of Paul’s age to his sister’s age is 14 : 8 14 : 8 written as simply as possible is 7 : 4 (a) When Paul is 21, what will be the ratio of Paul’s age to his sister’s age? Write the ratio as simply as possible. : 1 mark (b) When his sister is 36, what will be the ratio of Paul’s age to his sister’s age? Write the ratio as simply as possible. : 1 mark (c) Could the ratio of their ages ever be 7 : 7? Tick ( ) Yes or No. Yes No Explain how you know. 1 mark KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 11 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 12 Sizing 9. The information in the box describes three different squares, A, B and C. The area of square A is 36cm2 The side length of square B is 36 cm The perimeter of square C is 36cm Put squares A, B and C in order of size, starting with the smallest. You must show calculations to explain how you work out your answer. smallest KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 2 marks largest 12 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 13 Nets 10. The squared paper shows the nets of cuboid A and cuboid B. (a) Do the cuboids have the same surface area? Show calculations to explain how you know. 1 mark (b) Do the cuboids have the same volume? Show calculations to explain how you know. 2 marks KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 14 Beaches 11. Two beaches are very similar. A survey compared the number of animals found in one square metre on each beach. One beach had not been cleaned. The other beach had been cleaned. (a) The data for the beach that had not been cleaned represent 1620 animals. Complete the table to show how many of each animal were found. 2 marks KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 15 (b) The data for the beach that had been cleaned represent 15 animals. Complete the table to show how many of each animal were found on the cleaned beach. 2 marks (c) Cleaning the beach changes the numbers of animals and the proportions of animals. Write a sentence to describe both these changes. 1 mark KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 16 Equations 12. Find the values of t and r 2 t = 3 6 t= 1 mark 2 5 = r 3 r= KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 16 1 mark http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 17 Star design 13. This pattern has rotation symmetry of order 6 (a) What is the size of angle w ? Show your working. Not drawn accurately ° 2 marks (b) Each quadrilateral in the pattern is made from two congruent isosceles triangles. What is the size of angle y ? Show your working. Not drawn accurately ° 2 marks KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 18 Ks and ms 14. On the square grids below you can join dots with two different length lines. Length m is greater than length k (a) Draw a shape with each perimeter shown below. The first one is done for you. Perimeter 4k + 3 m Perimeter 4k + m 1 mark Perimeter 2 ( 2 k + m ) 1 mark KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 19 (b) What is the area of this triangle? Write it in terms of m 1 mark (c) This is the same triangle and grid. What is the area of the triangle? Write it in terms of k 1 mark (d) Using your answers to (b) and (c), explain why m 2 = 2 k 2 1 mark KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 20 Giraffe 15. A book gives this information: A baby giraffe was born that was 1.58 metres high. It grew at a rate of 1.3 centimetres every hour. Suppose the baby giraffe continued to grow at this rate. About how many days old would it be when it was 6 metres high? Show your working. days old 3 marks KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 20 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 21 Long-eared owls 16. Owls eat small mammals. They regurgitate the bones and fur in balls called pellets. The table shows the contents of 62 pellets from long-eared owls. Number of mammals found in the pellet 1 2 3 4 5 6 Frequency 9 17 24 6 5 1 (a) Show that the total number of mammals found is 170 1 mark (b) Calculate the mean number of mammals found in each pellet. Show your working and give your answer correct to 1 decimal place. 2 marks (c) There are about 10 000 long-eared owls in Britain. On average, a long-eared owl regurgitates 1.4 pellets per day. Altogether, how many mammals do the 10 000 long-eared owls eat in one day? Show your working and give your answer to the nearest thousand. 2 marks KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 22 Pictures 17. Here are four pictures, A, B, C and D. They are not to scale. (a) Picture A can be stretched horizontally to make picture B. Show that the horizontal factor of enlargement is 1.5 1 mark (b) Picture A can be stretched vertically to make picture C. The vertical factor of enlargement is 1.25 What is the height, h, of picture C? cm KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 22 http://www.SATs-Papers.co.uk 1 mark KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 23 Coffee 18. A cup of coffee costs £ 1.75 The diagram shows how much money different people get when you buy a cup of coffee. Not drawn accurately Complete the table to show what percentage of the cost of a cup of coffee goes to retailers, growers and others. Show your working. Retailers % Growers % Others % 2 marks KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 23 http://www.SATs-Papers.co.uk PLEASE TURN OVER KS3 P2 5-7_254651.qxd 19/2/03 10:03 am Page 24 Cissoid of Diocles 19. The equation of the curve shown is When x = 2.5 calculate the positive value of y Show all the digits on your calculator display. 1 mark When x = 2.5 give both values of y correct to 3 significant figures. and KS3/03/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk END OF TEST © Qualifications and Curriculum Authority 2003 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA 2 marks http://www.SATs-Papers.co.uk 254651