General Certificate of Secondary Education Higher Tier

Transcription

1 Centre Number Surname Other Names Candidate Number For Examiner s Use Examiner s Initials Candidate Signature General Certificate of Secondary Education Higher Tier Pages Mark GCSE Mathematics Unit 3 Higher Tier Practice Paper Set 4 Specification 4360 For this paper you must have: mathematical instruments. You may use a calculator Time allowed 1 hour 30 minutes 43603H H TOTAL Instructions Use black ink or black ball-point pen. Draw diagrams in pencil. Fill in the es at the top of this page. Answer all questions. You must answer the questions in the space provided. around each page or on blank pages. Do all rough work in this book. Cross through any work that you do not want to be marked. If your calculator does not have a button, take the value of to be 3.14 unless another value is given in the question. Information The marks for questions are shown in brackets. The maximum mark for this paper is 80. The quality of your written communication is specifically assessed in questions 3, 4 and 9 These questions are indicated with an asterisk ( ) You may ask for more answer paper and graph paper. These must be tagged securely to this answer booklet. Advice In all calculations, show clearly how you work out your answer. Practice Paper Set 4/43603H

2 2 Formulae Sheet: Higher Tier a Area of trapezium = 2 1 (a + b)h h b Volume of prism = area of cross-section length crosssection length Volume of sphere = 3 4 r 3 r Surface area of sphere = 4 r 2 Volume of cone = 3 1 r 2 h l h Curved surface area of cone = r l r In any triangle ABC C Area of triangle = 2 1 ab sin C b a Sine rule a sin A = b sin B = c sinc A c B Cosine rule a 2 = b 2 + c 2 2bc cos A The Quadratic Equation The solutions of ax 2 + bx + c = 0, where a 0, are given by x = _ 2 b ± ( b 2a _ 4ac)

3 3 Answer all questions in the spaces provided. 1 The diagram shows a map of an island with roads joining four towns. N North Coast Beach Point Saltsea South Bay 1(a) Choose the correct bearing from the list to complete each sentence Saltsea is on a bearing of... from South Bay. Beach Point is on a bearing of... from South Bay. (2 marks) 1(b) A ring is hidden on one of the roads. Here are some clues to find it. The bearing of the ring from Saltsea is 260 The ring is closer to South Bay than to Beach Point. Mark with a cross, the approximate position of the ring on the map. (2 marks) Turn over 4

4 4 2 Boxes are packed into crates. Not drawn accurately The crate measures 210cm by 120 cm by 100 cm. Each measures 8.4 cm by 6 cm by 4cm. The es cost 4 each to make. When sold, each makes 50% profit. How much profit is made if a crate full of es is sold? Answer... (5 marks)

5 5 3 A newspaper uses this formula to work out the cost of an advert. C = 10n + 20A C is the cost in pence. n is the number of words. A is the area of any pictures in cm². 3 (a) Work out the cost of an advert that has 20 words and a picture of area 9 cm². Give your answer in pounds. Answer... (3 marks) 3(b) Work out the cost of this advert. Horse for sale A mare with top class breeding. Owner would like a quick sale. Contact Bramley Stables for the price and further details. Answer... (4 marks) 12 Turn over

6 6 4 4(a) A homeowner wants to know the percentage of cars speeding past his home. 23 out of 50 cars are speeding. What percentage are speeding? Answer... % (2 marks) 4(b) Signs are put up warning drivers of the 30 miles per hour speed limit. The homeowner times cars over 200 metres. Here is a summary of his results. Time taken, t (seconds) Number of cars 0 < t < t < t < t < t 25 6 Has the proportion of speeding cars decreased? You can use 30 mph = 13.3 metres per second You must show your working. Answer... (5 marks)

7 7 5 The diagram shows two shapes B and C Describe fully the single transformation which takes shape B to shape C. Answer... (3 marks) 10 Turn over

8 8 6 The diagram shows a cylinder. The diameter of the base is 14 cm. The height is 12 cm. Not drawn accurately Work out the volume of the cylinder. Give your answer to a suitable degree of accuracy. Answer...cm 3 (4 marks) 7 Here is a formula for converting F to C. 5 C ( F 9 32) You are given that x F is the same as x C. Work out the value of x. Answer x =... (4 marks)

9 9 8 The diagram shows a shape made from four congruent right-angled triangles. Not drawn accurately 15cm 6cm Work out the area of the shape. State the units of your answer. Answer... (6 marks) 14 Turn over

10 9 The diagram shows a quadrilateral ABCD. 10 x B Not drawn accurately A 3x 4x C 2x D Prove that AB is parallel to DC. (5 marks)

11 11 10(a) Complete the table of values for y = x 3 2x + 3 x y (b) Complete the graph of y = x 3 2x + 3 for values of x from 2 to 2. (1 mark) y O x -2 (2 marks) 10(c) Write down the number of solutions to the equation x 3 2x + 3 = 0 Answer... (1 mark) 9 Turn over

12 12 11(a) The diagram shows a circle, centre O. w Work out the value of w. Answer...degrees (1 mark) 11(b) The diagram shows a circle, centre O. AT and BT are tangents to the circle. x y 11(b)(i) Work out the value of x. Answer...degrees (1 mark) 11(b)(ii) Work out the value of y. Answer...degrees (2 marks)

13 13 12 ABC and XYZ are similar triangles. Work out the length of XZ. Answer...cm (3 marks) 13 Solve the quadratic equation x 2 + 5x 3 = 0 Give your answers to two decimal places. Answer x =..., x =... (3 marks) 10 Turn over

14 14 14 The diagram shows a triangle ABC. Show that the triangle has an obtuse angle. (5 marks)

15 15 15 The diagram shows a major sector of a circle of radius 8 cm. Work out the perimeter of the sector. Answer...cm (4 marks) 9 Turn over

16 16 16 The graph of the curve y = a + b x passes through points (1, 7) and (2, 13) where a > 0 and b > 0 Work out the values of a and b. Answer a =..., b =... (6 marks)

17 17 17 The diagram shows triangles ABD and BCD. Work out the size of angle BCD. Answer... degrees (6 marks) END OF QUESTIONS 12 Turn over

18 18 There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED Copyright 2011 AQA and its licensors. All rights reserved.