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Instructions Answers ✎ This means write down your answer or show your working and your answer. Calculators You may use a calculator in this test. Formulae You might need to use these formulae. Trapezium Area = (a + b) ×h 2 Prism Volume = area of cross-section × length KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 3 http://www.SATs-Papers.co.uk Lift 1. The graph shows my journey in a lift. I got in the lift at floor number 10 ✎ (a) The lift stopped at two different floors before I got to floor number 22 What floors were they? ✎ KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 floors . . . . . . . and . . . . . . . 4 . . . . 1 mark http://www.SATs-Papers.co.uk (b) For how long was I in the lift while it was moving? ✎ . . . . . . . seconds . . . . 1 mark (c) After I got out of the lift at floor number 22, the lift went directly to the ground floor. It took 45 seconds. On the graph, show the journey of the lift from floor 22 to the ground floor. KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 5 http://www.SATs-Papers.co.uk . . . . 1 mark Scores 2. (a) Paula played four games in a competition. In three games, Paula scored 8 points each time. In the other game she scored no points. ✎ What was Paula’s mean score over the four games? . . . . . . . points . . . . 1 mark (b) Jessie only played two games. Her mean score was 3 points. Her range was 4 points. ✎ What points did Jessie score in her two games? . . . . . . . and . . . . . . . . . . . 1 mark (c) Ali played three games. His mean score was also 3 points. His range was also 4 points. What points might Ali have scored in his three games? ✎ Show your working. . . . . . . . . . . . and . . . . . . . and . . . . . . . KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 6 http://www.SATs-Papers.co.uk . . . . 2 marks Polygons 3. (a) Any quadrilateral can be split into 2 triangles. ✎ Explain how you know that the angles inside a quadrilateral add up to 360° . . . . 1 mark (b) What do the angles inside a pentagon add up to? ✎ . . . . . . . ° . . . . . . . . . . . ° . . . . 1 mark (c) What do the angles inside a heptagon (7-sided shape) add up to? ✎ Show your working. . . . . 2 marks KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 7 http://www.SATs-Papers.co.uk Hedging 4. A garden centre sells plants for hedges. The table shows what they sold in one week. Plants Takings Beech 125 £212.50 Leylandii 650 £2437.50 Privet 35 £45.50 Hawthorn 18 £23.40 Laurel 5 £32.25 Total (a) Number of plants sold 833 £2751.15 What percentage of the total number of plants sold was Leylandii? Show your working. ✎ . . . . . . . . . . . % (b) . . . . 2 marks What percentage of the total takings was for Leylandii? Show your working. ✎ . . . . . . . . . . . % (c) ✎ . . . . 2 marks Which is the cheaper plant, Beech or Privet? Show working to explain how you know. . . . . 1 mark KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 8 http://www.SATs-Papers.co.uk Area 5. The diagram shows a circle and a square. Not drawn accurately (a) The radius of the circle is 12mm. What is the area of the circle to the nearest mm 2 ? ✎ Show your working. . . . . . . . . . . . mm 2 . . . . 2 marks (b) The ratio of the area of the circle to the area of the square is 2 :1 ✎ What is the area of the square to the nearest mm 2 ? . . . . . . . mm 2 . . . . 1 mark (c) What is the side length of the square? ✎ Show your working. . . . . . . . . . . . mm KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 9 http://www.SATs-Papers.co.uk . . . . 2 marks Pitch 6. A groundsman marks out a football pitch. (a) He makes the pitch 93 metres long, to the nearest metre. What is the shortest possible length of the pitch? ✎ . . . . . . . m . . . . 1 mark (b) He makes the pitch 50 metres wide, to the nearest metre. What is the shortest possible width of the pitch? ✎ . . . . . . . m . . . . 1 mark (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. . . . . . . . . . . . KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 10 http://www.SATs-Papers.co.uk . . . . 2 marks Dots 7. I am thinking of a point on the dotted grid below. The co-ordinates of my point are ( x , y ) You have 3 clues to find which of the dots is my point. (a) First clue: x > 0 and y > 0 Which dots cannot represent my point? On the grid below, cross them out like this ✎ . . . . . . . . 2 marks (b) Second clue: x + y < 4 Which other dots cannot represent my point? This time, put a square around them like this . . . . 1 mark (c) Third clue: x>y What are the co-ordinates of my point? ✎( , ) . . . . 1 mark KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 11 http://www.SATs-Papers.co.uk Families 8. A class collected information about the number of children in each of their families. The information was displayed in a frequency chart, but you cannot see all the information. Call the number of families that have two children n (a) ✎ Show that the total number of children in all the families is 55 + 2n . . . . 1 mark (b) ✎ Write an expression for the total number of families. . . . . 1 mark KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 12 http://www.SATs-Papers.co.uk (c) The mean number of children per family is 3 What is the value of n ? ✎ Show your working. n=. . . . . . . . . . . . . . . 2 marks KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 13 http://www.SATs-Papers.co.uk Triangles 9. ABC and ACD are both right-angled triangles. Not drawn accurately (a) ✎ Explain why the length of AC is 10 cm. . . . . 1 mark (b) ✎ Calculate the length of AD Show your working. . . . . . . . . . . . cm KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 14 http://www.SATs-Papers.co.uk . . . . 2 marks Not drawn accurately y x (c) ✎ By how many degrees is angle x bigger than angle y ? Show your working. . . . . . . . . . . . . . . . ° KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 15 . . . . 3 marks http://www.SATs-Papers.co.uk Counters 10. I have two bags of counters. Bag A contains 12 red counters and A 18 yellow counters. Bag B contains 10 red counters and B 16 yellow counters. I am going to take one counter at random from either bag A or bag B I want to get a red counter. Which bag should I choose? ✎ Show working to explain your answer. . . . . . . . . 2 marks KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 16 http://www.SATs-Papers.co.uk Satellites 11. Two satellites circle around the Earth. The distance from the centre of the Earth is: 1.53 × 107 m Satellite A 9.48 × 10 6 m Satellite B Not drawn accurately (a) What is the minimum distance apart the satellites could be? ✎ Show your working and give your answer in standard form. . . . . . . . . . . . . . . . . . . . . m . . . . 2 marks (b) What is the maximum distance apart the satellites could be? ✎ Show your working and give your answer in standard form. . . . . . . . . . . . . . . . . . . . . m KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 17 http://www.SATs-Papers.co.uk . . . . 2 marks Homework 12. A teacher asked fifty pupils in Year 9: How much time did you spend on homework last night? Results: Time spent on homework (minutes) Frequency 0 ≤ time ≤ 30 6 30 < time ≤ 60 14 60 < time ≤ 90 21 90 < time ≤ 120 9 Total (a) ✎ 50 Show that an estimate of the mean time spent on homework is 64.8 minutes. . . . . . . . . 2 marks KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 18 http://www.SATs-Papers.co.uk The teacher used the data to draw a cumulative frequency diagram. ✎ (b) ✎ Use the diagram to estimate the median time pupils spent on their homework. Show on the diagram how you get your answer. . . . . . . . . . . . minutes (c) . . . . 2 marks Use the diagram to estimate how many pupils spent more than 100 minutes on their homework. Show how you get your answer. ✎ . . . . . . . . . . . pupils KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 19 http://www.SATs-Papers.co.uk . . . . 2 marks Pyramid 13. The formula for the volume, V, of a square-based pyramid is V= 1 2 bh 3 b is the base length, h is the perpendicular height. (a) A square-based pyramid has base length 5cm and perpendicular height 6cm. What is its volume? ✎ V = . . . . . . . cm3 (b) . . . . 1 mark A different square-based pyramid has base length 4cm. Its volume is 48cm 3 What is its perpendicular height? ✎ h= KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 20 . . . . . . . cm http://www.SATs-Papers.co.uk . . . . 1 mark (c) The volume of another square-based pyramid is 25cm3 Its perpendicular height is 12cm. What is its base length? ✎ Show your working. . . . . b= (d) . . . . . . . cm . . . . 2 marks The diagram shows a triangular-based pyramid. The base is an isosceles, right-angled triangle. The perpendicular height is m Write a formula, in terms of m, for the volume, V, of the pyramid. ✎ . . . . 1 mark KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 21 http://www.SATs-Papers.co.uk Pots 14. John makes two clay pots. Each pot is fired independently. The probability that a pot cracks while being fired is 0.03 (a) ✎ Calculate the probability that both of John’s pots crack while being fired. Show your working. . . . . 1 mark (b) ✎ Calculate the probability that only one of John’s pots cracks while being fired. Show your working. . . . . . . . . 2 marks (c) John has enough clay for 80 pots. He receives an order for 75 pots. Does he have enough clay to make 75 pots without cracks? ✎ Explain your answer. . . . . 1 mark KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 22 http://www.SATs-Papers.co.uk END OF TEST KS3/00/Ma/Tier from SATs-Papers.co.uk Sourced 6-8/P2 23 http://www.SATs-Papers.co.uk