Double Award GCSE Mathematics GCSE 1. Exemplar Paper 3 Section A (Higher Tier)

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1 Double Award GCSE Mathematics GCSE 1 Exemplar Paper 3 Section A (Higher Tier) Time allowed: 1 hour for section A Paper total: 120 marks (60 for section A; 60 for section B) Calculator not allowed for section A This paper is one of a set of 6 exemplar papers written by MEI, covering the Foundation and Higher Tiers of GCSE 1 and 2. The aim of these papers is to inform public discussion. They do not contribute to any existing GCSE qualification. June 2006 Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 1 of 19

2 Section A: No calculator allowed on this section To be collected in after 1 hour A1. In a raffle, tickets numbered 44 to 138 are sold. These are my tickets: What is the probability that I win the first prize? A2. 7cm 5cm A cylindrical tin, with diameter 7cm and height 5 cm, has a label that overlaps by 1 cm so it can stick to itself. What is the approximate area of the label? (4 marks) Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 2 of 19

3 A3. s ( u + v) t 2 = is a formula for an object travelling with constant acceleration. It calculates the distance from the starting point, s, using the starting velocity, u, the final velocity, v, and the time, t. (a) Calculate the distance from the starting point for an object that starts with velocity 10 m/s and finishes with a velocity of 15 m/s, 20 seconds later. (b) A runner starts with zero speed and travels 20m in 5 seconds. Assuming she is travelling with constant acceleration, how fast is she running at the end of the 5 seconds? (c) Rearrange the formula to make u the subject. Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 3 of 19

4 A4. Sylvie is planning to sell her house. She intends to paint the walls and ceiling of her front room with two coats of magnolia emulsion. Her front room is 4.2m wide, 4.8m long and 2.6m high. Each litre of paint covers 14 m² and the paint is available in 5l tins at or 2.5l tins at (a) Estimate the area she needs to paint (you must show working). (4 marks) (b) How many tins should she buy (and of which size) and how much will it cost her? (4 marks) Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 4 of 19

5 A5. The graph below shows the number of special school teachers by age in Scotland in 2004 (source: (a) Write down two features of the data that are shown by this graph. (b) What could happen from 2010 onwards? You must give a reason for your answer. Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 5 of 19

6 A6. Ali is making a scale model. The front elevation, side elevation and plan are drawn below. Make an isometric drawing of the shape on the grid provided. (4 marks) Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 6 of 19

7 A7. (a) Winston needs to make a fence 10 metres long following the pattern shown above. How many planks will he need? (b) Find a formula for the number of planks, P, needed for n metres of fence. A8. A fifth of my wages go in taxes. Housing costs me another third. I spend half of the rest on food. What fraction do I spend on food? (4 marks) Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 7 of 19

8 A9. The diagram shows 2 points A and B and the perpendicular bisector of the line joining them. Write a brief description of a situation in life that could be represented by the diagram. Your description should say: (a) What is at point A? (b) What is at point B? (c) What does the perpendicular bisector represent? A10. The dawn temperatures on Monday to Friday of a week have a mean of -2ºC and a range of 12ºC. The temperatures on Monday to Wednesday are: 3ºC, -8ºC, -1ºC What are the temperatures on Thursday and Friday? (4 marks) Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 8 of 19

9 A11. Alex is doing a probability experiment. He has a tube with 7 beads in it: 1 red, 2 yellow and 4 blue. They fall in this pattern when he puts the tube down. (a) What is the probability that all the blue ones are on the outside of the circle? (b) We call getting the red in the centre place a win. Three people have these results from doing the experiment: Alex Bob Carl Number of times doing the experiment Number of wins 0 10 About how many wins do you expect Carl to have? (You must show working) A12. I have returned from my holiday and want to change some Euros back into pounds. I know a Euro is worth less than a pound and I see these commission-free rates: Travel Agent Bank Euro Euro We buy at We buy at We sell at We sell at Where should I go to change my Euros into pounds? (You must give reasons for your answer) Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 9 of 19

10 A13. The diagram shows a design for a pencil shaped pencil case. The measurements shown on the diagram will affect the volume of the pencil case. Could this be a formula for the volume of the pencil case? (You must give a reason for your answer) π 2 d + 12 ( 3x h) A14. Miss, how much money do you have in your purse? I have four times as much as Mr Brown, but if I gave him 5, he would have more than me. How much money does Mr Brown have? (You must show working/ reasoning) (4 marks) Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 10 of 19

11 Double Award GCSE Mathematics GCSE 1 Exemplar Paper 3 Section B (Higher Tier) Time allowed: 1 hour for section B Paper total: 120 marks (60 for section A; 60 for section B) Calculator allowed for section B This paper is one of a set of 6 exemplar papers written by MEI, covering the Foundation and Higher Tiers of GCSE 1 and 2. The aim of these papers is to inform public discussion. They do not contribute to any existing GCSE qualification. June 2006 Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 11 of 19

12 Section B Time allowed: 1 hour A Calculator is ESSENTIAL for this section of the paper. Tracing paper is available on request. B1. To celebrate their 60 th anniversary, a furniture store, founded in 1946, offers 19.46% discount in the year How much would you expect to pay for a sofa that cost 695 before the offer? B2. Someone with a suspected eye disease might be referred for a hospital appointment with an ophthalmologist. These are the number of months people had been waiting in Barnsley before being seen in the first quarter of 2004/5: (source: Months waiting No of patients 0 m < m < m < m < and over 0 (a) Find an estimate of the mean waiting time. (4 marks) (b) Comment on the class intervals that have been used for the data. Could they be improved? (1 mark) (c) If there had been patients in the 21 and over group, how would this have affected the mean? (You must give a reason for your answer) Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 12 of 19

13 B3. Sam is conducting a scientific experiment. He has a tall thin tube full of water, which is slowly emptying. He measures the height of water in cm every 5 seconds. Time (secs) Height (cm) (a) Plot the data below. (b) Sam wants to find an equation connecting height, h, with time, t. He decides to draw a straight line of best fit; draw this line on your graph. (c) Work out the gradient of your line of best fit. Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 13 of 19

14 (d) Work out the equation of your line of best fit. (e) Is a straight line the best way to represent this data, or would a different kind of graph be better? (1 mark) (f) Sam s science teacher suggests that the equation connecting the height, h, in cm with the time, t, in seconds should be h 2 = 0.024t 2.635t + 73 Calculate the height suggested by this equation at a time of 50 seconds. (g) Do you think the new equation will fit the experimental results better than the equation of your line of best fit? You must give reasons for your answer. Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 14 of 19

15 B4. The regulations for office space require each person to have at least 11 cubic metres of space. A union representative works in an office with a rectangular floor and constant height. To the nearest metre, the office measures 7m wide, 9m long and 3m high. (a) Based on these measurements, how many people should be able to work in the office? (b) The union representative measures the office accurately and discovers that the number of people that could work there is less than this. How low could it be? B5. Sixteen million tonnes of rain fall to earth every second. (from How to Make a Camel Smoothie by Gary Rimmer). 1 kg of water has a volume of 1 litre. The population of the world is If we could collect all the rain that fell to earth in a minute and share the water out, how many litres would each person get? Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 15 of 19

16 B6. A kaleidoscope is a children s toy. It has two mirrors at an angle. Coloured shapes, between the mirrors, are reflected repeatedly to make a symmetrical pattern. The diagram on the right shows a kaleidoscope pattern, with the mirrors at 45º. mirror mirror The diagram below shows a kaleidoscope with the mirrors at 60º. (a) Reflect the pattern of triangles in the thick mirror lines. (b) Finish the kaleidoscope pattern. Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 16 of 19

17 B7. Carlo and Andrea are helping to make the refreshments for a children s party. They are diluting some orange squash with water. The instructions on the bottle are to mix the concentrate with water in the ratio 1:4. They do not follow the instructions. Carlo mixes 500 ml of concentrated squash with 1500 ml of water. It is too strong. Andrea mixes 500 ml of concentrated squash with 4 l of water. It is too weak. (a) How much water should have been added to 500 ml of concentrated squash? They have no more squash left in the bottle. They do not want to waste their mixtures. They decide to add some of Andrea s mixture to Carlo s mixture to make it weaker. (b) Will adding 500 ml of Andrea s mixture to all of Carlo s mixture make the drink too strong, too weak or just right? (You must give reasons for your answer) (c) How much of Andrea s mixture should be added to Carlo s mixture to get the right strength of drink? (6 marks) Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 17 of 19

18 B8. Bob orders equipment usually priced at 650 for his business. This price includes VAT at 17.5%. The firm he orders it from gives him a 10% discount on the usual price. He can claim the VAT back. How much will the equipment cost him? (4 marks) Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 18 of 19

19 B9. In a biscuit factory, round biscuits 7cm in diameter are cut from a long strip of dough. The diagram above shows how many biscuits fit across the strip of dough. To reduce waste, they decide to change to regular hexagonal biscuits. The following diagram shows how many biscuits fit across the strip of dough. The strip of dough is the same width. How long is each side of the hexagonal biscuits? (7 marks) Double Award Mathematics GCSE 1, MEI Exemplar Paper 3A Page 19 of 19