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Mathematics test Ma KEY STAGE 3 Paper 2 Calculator 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 may use a calculator in this test. I You will need: pen, pencil, rubber, ruler, a pair of compasses, an angle measurer or protractor 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. I Check your work carefully. I Ask your teacher if you are not sure what to do. For marker’s use only QCA/01/670 Sourced from SATs-Papers.co.uk Total marks Borderline check 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 may use a calculator to answer any question in this test. Formulae You might need to use these formulae. Trapezium b Area = (a p b) th 2 height (h) a Prism length Volume e area of cross-section t length KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk Drinks Machine 1. A drink from a machine costs 55p The table shows the coins that were put into the machine one day. Coins Number of coins 50p 31 20p 22 10p 41 5p 59 How many cans of drink were sold that day? Show your working. ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ cans ○ ○ ○ ○ ○ ○ ○ ○ ○ 3 marks KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 3 http://www.SATs-Papers.co.uk Advert 2. You can work out the cost of an advert in a newspaper by using this formula: C = 15n + 75 C is the cost in pounds n is the number of words in the advert (a) An advert has 18 words. Work out the cost of the advert. Show your working. ○ ○ ○ ○ ○ ○ ○ £ ○ 2 marks (b) The cost of an advert is £ 615 How many words are in the advert? Show your working. ○ ○ ○ ○ ○ ○ ○ ○ ○ http://www.SATs-Papers.co.uk ○ ○ ○ ○ ○ ○ ○ 4 ○ KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk words 2 marks Speed 3. (a) A coach travels 300 miles at an average speed of 40 mph. For how many hours does the coach travel? ○ ○ ○ ○ hours ○ ○ ○ ○ ○ ○ ○ 1 mark (b) An aeroplane flies 1860 miles in 4 hours. What is its average speed? ○ ○ ○ mph ○ ○ ○ ○ ○ ○ ○ ○ ○ 1 mark (c) 1 A bus travels for 2 2 hours at an average speed of 24 mph. How far does the bus travel? ○ ○ ○ ○ miles ○ ○ ○ ○ ○ ○ ○ 1 mark KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Trundle Wheel 4. A trundle wheel is used to measure distances. Imran makes a trundle wheel, of diameter 50 cm. (a) Calculate the circumference of Imran’s trundle wheel. Show your working. ○ ○ ○ ○ ○ ○ ○ cm ○ ○ ○ ○ ○ ○ ○ ○ 2 marks (b) Imran uses his trundle wheel to measure the length of the school car park. His trundle wheel rotates 87 times. What is the length of the car park, to the nearest metre? ○ ○ ○ m ○ ○ ○ ○ ○ ○ ○ ○ 1 mark KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk Algebra Pairs Draw lines to join any pairs of algebraic expressions that will always have the same value when a = b = c ○ ○ ○ ○ ○ ○ ○ ○ ○ 5. ○ ○ ○ 3 marks KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk Books 6. A teacher asked two different classes: ‘What type of book is your favourite?’ (a) Results from class A (total 20 pupils): Type of book Frequency Crime 3 Non-fiction 13 Fantasy 4 Complete the pie chart to show this information. Show your working and draw your angles accurately. Crime ○ ○ ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 8 http://www.SATs-Papers.co.uk (b) The pie chart below shows the results from all of class B. Each pupil had only one vote. Crime Romance Fantasy Non-fiction The sector for Non-fiction represents 11 pupils. How many pupils are in class B? Show your working. ○ ○ ○ ○ ○ ○ ○ ○ pupils ○ ○ ○ ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk Yoghurt 7. (a) The label on yoghurt A shows this information. How many grams of protein does 100 g of yoghurt provide ? Show your working. ○ ○ ○ ○ ○ ○ ○ g ○ ○ ○ ○ ○ ○ ○ ○ 2 marks (b) The label on yoghurt B shows different information. A boy eats the same amount of yoghurt A and yoghurt B. Which yoghurt provides him with more carbohydrate? Show your working. ○ ○ ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 10 http://www.SATs-Papers.co.uk Missing Side 8. (a) Calculate the length of the unknown side of this right-angled triangle. Show your working. Not drawn accurately ○ ○ ○ ○ ○ ○ ○ ○ cm ○ ○ ○ ○ ○ ○ ○ 2 marks (b) Calculate the length of the unknown side of the right-angled triangle below. Show your working. Not drawn accurately ○ ○ ○ ○ ○ ○ ○ ○ cm ○ ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 11 http://www.SATs-Papers.co.uk Goldcrests 9. The goldcrest is Britain’s smallest species of bird. On winter days, a goldcrest must eat enough food to keep it warm at night. During the day, the mass of the bird increases. The scatter diagram shows the mass of goldcrests at different times during winter days. It also shows the line of best fit. 6.0 5.5 5.0 Mass (g) 4.5 4.0 3.5 0 7am 8am 9am 10am 11am 12pm 1pm 2pm 3pm Time (GMT) (a) Estimate the mass of a goldcrest at 11 : 30 am. ○ ○ ○ ○ g ○ ○ ○ ○ ○ ○ ○ 1 mark KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 12 http://www.SATs-Papers.co.uk (b) Estimate how many grams, on average, the mass of a goldcrest increases during one hour. ○ ○ ○ ○ g ○ ○ ○ ○ ○ ○ ○ 1 mark (c) Which goldcrest represented on the scatter diagram is least likely to survive the night if it is cold? Show your answer by circling the correct point on the scatter diagram, then explain why you chose that point. ○ ○ ○ ○ 1 mark KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Triangles 10. (a) On the cm2 grid below, draw a right-angled triangle with an area of 12 cm2 Use line AB as one side of the triangle. ○ ○ ○ ○ 1 mark (b) Now draw an isosceles triangle with an area of 12 cm2 Use line AB as one side of the triangle. ○ ○ ○ ○ 1 mark KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk (c) Use Pythagoras’ theorem to prove that AC is the same length as AB Show your working. ○ ○ ○ ○ ○ ○ ○ ○ 2 marks (d) Calculate the size of angle ABC Show your working. ○ ○ ○ ○ ○ ○ O ○ ○ ○ ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Tree 11. A gardener wants to plant a tree. She wants it to be more than 8 m away from the vegetable plot. She wants it to be more than 18 m away from the greenhouse. The plan below shows part of the garden. The scale is 1 cm to 4 m. Show accurately on the plan the region of the garden where she can plant the tree. Label this region R. ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 3 marks KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 16 http://www.SATs-Papers.co.uk Earnings 12. The table shows the average weekly earnings for men and women in 1956 and 1998. 1956 1998 Men £ 11.89 £ 420.30 Women £ 6.16 £ 303.70 (a) For 1956, calculate the average weekly earnings for women as a percentage of the average weekly earnings for men. Show your working and give your answer to 1 decimal place. ○ ○ ○ ○ ○ ○ ○ % ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 2 marks (b) For 1998, show that the average weekly earnings for women were a greater proportion of the average weekly earnings for men than they were in 1956. ○ ○ ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk Sale 13. A shop had a sale. All prices were reduced by 15% Sale 15% off A pair of shoes cost £ 38.25 in the sale. What price were the shoes before the sale? Show your working. ○ ○ ○ ○ ○ ○ ○ £ ○ 2 marks KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk Parabolas 14. The diagram shows a sketch of the curve y = 16 – x 2 (a) What are the coordinates of points A, B and C? , ) ○ C ( ○ ) ○ , ○ B ( ○ ) ○ , ○ A ( ○ 2 marks The curve y = 16 – x 2 is reflected in the line y = 12 (b) B1 is the reflection of B What are the coordinates of B1? ○ ) ○ ○ , ○ B1 ( 1 mark (c) What is the equation of the new curve? ○ ○ ○ KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk ○ 1 mark Which is Bigger? 15. The diagram shows parts of two circles, sector A and sector B 1 8 1 5 of a circle of a circle (a) Which sector has the bigger area? Show working to explain your answer. ○ ○ ○ ○ ○ ○ ○ ○ 2 marks (b) The perimeter of a sector is made from two straight lines and an arc. Which sector has the bigger perimeter? Show working to explain your answer. ○ ○ ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 20 http://www.SATs-Papers.co.uk (c) A semi-circle, of radius 4 cm, has the same area as a complete circle of radius r cm. Not drawn accurately What is the radius of the complete circle? Show your working. ○ ○ ○ ○ ○ ○ ○ cm ○ ○ ○ ○ ○ ○ ○ r = 2 marks KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk Music Concert 16. Each year a school has a concert of readings and songs. In 1999 the concert had 3 readings and 9 songs. It lasted 120 minutes. In 2000 the concert had 5 readings and 5 songs. It lasted 90 minutes. In 2001 the school plans to have 5 readings and 7 songs. Use simultaneous equations to estimate how long the concert will last. Call the time estimated for a reading x minutes, and the time estimated for a song y minutes. You must show your working. ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ minutes ○ ○ ○ ○ ○ ○ ○ ○ Estimated time = 4 marks KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 22 http://www.SATs-Papers.co.uk END OF TEST KS3/01/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 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 00-6651/9 http://www.SATs-Papers.co.uk