Unit 3 : Number, Algebra, Geometry 2 (Calculator) Higher Tier Paper A Time : 1 hour 45 minutes

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1 Name Class For Edexcel GCSE Mathematics Unit 3 : Number, Algebra, Geometry 2 (Calculator) Higher Tier Paper A Time : 1 hour 45 minutes You must have: Ruler, protractor, compasses, pen, pencil, eraser, calculator. Total Marks Instructions and Information Write your name in the box at the top of the page. Answer all the questions in the spaces provided. The total mark for this paper is 80. The marks for each question are shown in brackets. Calculators may be used. If your calculator does not have a button, take the value of to be unless the question instructs otherwise. Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed. Advice Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end. Written by Shaun Armstrong Only to be copied for use in the purchaser's school or college 2012 EHA Unit 3 Page 1 Churchill Maths Limited Turn over

2 GCSE Mathematics Formulae: Higher Tier You must not write on this formulae page. Volume of prism = area of cross section length Area of trapezium = 1 (a + b)h 2 a cross section length h b Volume of sphere = 4 3 πr3 Surface area of sphere = 4πr 2 Volume of cone = 1 3 πr2 h Curved surface area of cone = πrl r l h r In any triangle ABC C The Quadratic Equation The solutions of ax 2 + bx + c = 0 where a 0, are given by b a x = b± b2 4ac 2a A c B Sine Rule a sin A = b sin B = c sin C Cosine Rule a 2 = b 2 + c 2 2bc cos A Area of triangle = 1 2 ab sin C 2012 EHA Unit 3 Page 2 Churchill Maths Limited

3 Answer ALL questions. Write your answers in the spaces provided. You must write down all stages in your working. 1 Eight 5p coins weigh 26 g. Work out the weight of three 5p coins. 2 Calculate g (Total for Question 1 is 2 marks) (a) (b) giving your answer correct to 3 significant figures. (3) (Total for Question 2 is 4 marks) 2012 EHA Unit 3 Page 3 Churchill Maths Limited Turn over

4 3 This conversion graph can be used to change between degrees fahrenheit (ºF) and degrees celsius (ºC). ºC ºF 20 (a) (b) (c) Use the graph to change 140 ºF into degrees celsius. Use the graph to change 80 ºC into degrees fahrenheit. Water freezes at 0 ºC. ºC ºF At what temperature does water freeze in degrees fahrenheit? ºF (Total for Question 3 is 3 marks) 2012 EHA Unit 3 Page 4 Churchill Maths Limited

5 *4 Fran wants to save up 75 before she goes on holiday on the 19 th June. She starts saving 50p a day on the 1 st April. On 16 th April she increases the amount she saves each day to 80p. On 12 th May Fran increases the amount again to 1.20 On 18 th June, after adding 1.20 for the day, she counts her savings. Has Fran reached her target? Show how you decide. (Total for Question 4 is 4 marks) 5 (a) 4 < n 2 n is an integer. Write down all the possible values of n. (b) Solve the inequality 6 2x > 3 (Total for Question 5 is 4 marks) 2012 EHA Unit 3 Page 5 Churchill Maths Limited Turn over

6 6 (a) Convert 0. 6 to a fraction. (b) Write the reciprocal of 50 as a decimal. (c) Work out the difference between 1 80 and (Total for Question 6 is 4 marks) 7 Use a ruler and pair of compasses to construct the bisector of this angle. Leave in your constuction lines. (Total for Question 7 is 2 marks) 2012 EHA Unit 3 Page 6 Churchill Maths Limited

7 8 On the grid, draw the graph of y = x y O x (Total for Question 8 is 4 marks) 2012 EHA Unit 3 Page 7 Churchill Maths Limited Turn over

8 9 Dhakwan has an empty metal barrel. The barrel is in the shape of a cylinder. The height of the barrel is 1.2 m. The diameter of the base of the barrel is 80 cm. Dhakwan fills the barrel with water from a tap. The tap fills the barrel at the rate of 1 litre per second. 1.2 m Find how long it takes to fill the barrel. Give your answer to the nearest minute. 80 cm minutes (Total for Question 9 is 5 marks) 2012 EHA Unit 3 Page 8 Churchill Maths Limited

9 10 14 cm Diagram NOT accurately drawn 10 cm The diagram shows a sail from a design model of a boat. (a) Work out the length of the longest side of the model sail. (3) cm The model sail will be enlarged by a scale factor of 100 to make the sail of the boat. (b) How many times larger will the area of the sail of the boat be than the area of the model sail? (Total for Question 10 is 5 marks) 2012 EHA Unit 3 Page 9 Churchill Maths Limited Turn over

10 11 T = 5(n m) (a) Find the value of T when m = 3 and n = 4. (b) Rearrange the formula to make n the subject. (Total for Question 11 is 4 marks) 12 Nena wants to find out how much a taxi to the airport will cost. The distance to the airport is 35 miles to the nearest 5 miles. The cost will be 1.60 per mile to the nearest 10p. What is the most that the taxi to the airport will cost? (Total for Question 12 is 3 marks) 2012 EHA Unit 3 Page 10 Churchill Maths Limited

11 13 y A O x Triangle A is shown on the grid. (a) Translate triangle A using the vector 6 1. Label the image B. (b) Enlarge triangle A by scale factor 2 with centre of enlargement (0, 0). Label the image C. (Total for Question 13 is 4 marks) 2012 EHA Unit 3 Page 11 Churchill Maths Limited Turn over

12 14 (a) Solve (i) 4p 7 = 37 (ii) 3(1 2y) = 15 4y (3) *(b) Anna orders 2 cups of coffee and 4 cups of tea. She is charged 11. When Anna looks at her receipt she sees that she's been charged for 4 cups of coffee and 2 cups of tea. The cost should have been 10 so she is refunded 1. Work out the cost of a cup of coffee and the cost of a cup of tea. (5) Coffee Tea (Total for Question 14 is 10 marks) 2012 EHA Unit 3 Page 12 Churchill Maths Limited

13 15 E A b Diagram NOT accurately drawn B 120º a D 76º C The points A, B, C, D and E lie on the circumference of a circle as shown. AC is parallel to ED. (a) (i) Work out the size of angle a. º (ii) Give a reason for your answer. (b) Work out the size of angle b. º (Total for Question 15 is 4 marks) 2012 EHA Unit 3 Page 13 Churchill Maths Limited Turn over

14 16 (a) Factorise a 2 6a + 8 (b) Solve 2y 2 + 9y 2 = (y + 2)(y + 7) (3) (Total for Question 16 is 5 marks) 2012 EHA Unit 3 Page 14 Churchill Maths Limited

15 17 C D A Diagram NOT accurately drawn E O B F The diagram shows triangle OCF. OA = a, OC = 3a, OB = 2b and OF = 3b. (a) Express CF in terms of a and b. Given that CD = 1 3 CF and that CE = 5 6 CF, *(b) use vectors to prove that AD and BE are parallel. (5) (Total for Question 17 is 6 marks) 2012 EHA Unit 3 Page 15 Churchill Maths Limited Turn over

16 18 A Diagram NOT accurately drawn Q N 100 km A plane leaves an airport, A, and flies for 100 km on a bearing of 140º. The plane then turns and flies on a bearing of 045º until it is due East of A. The plane then flies directly back to A. Work out the total distance travelled by the plane. km (Total for Question 18 is 7 marks) TOTAL FOR PAPER IS 80 MARKS 2012 EHA Unit 3 Page 16 Churchill Maths Limited