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GCSE in Mathematics B Modular 2381 Unit 2 stage 2 Practice Paper B Higher (Calculator) EDEXCEL GCSE Mathematics 2540/2544 Formulae sheet — Higher tier Volume of prism = area of cross-section length Volume of sphere = 4 3 r 3 Surface area of sphere = 4 r2 Volume of cone = 4 2 r h 3 Curved surface area of cone = rl C In any triangle ABC b A a c B a b c = = sin A sin B sin C Sine Rule: Cosine Rule: a2 = b2 + c2 –2bc cos A Area of a triangle = 1 ab sin C 2 The Quadratic Equation b (b 2 4ac) The solutions of ax + bx + c = 0, where a 0, are given by x = 2a 2 This Publication may be reproduced only in accordance with Edexcel Limited copyright policy © 2007 Edexcel Limited 2 1. Work out 40.8 1 .2 ………… (2) (Total 2 marks) 2. (a) Factorise 3x + 6 ……………… (1) (b) Factorise completely 6a3 − 9a2 ……………… (2) (Total 2 marks) This Publication may be reproduced only in accordance with Edexcel Limited copyright policy © 2007 Edexcel Limited 3 3. Write an expression, in terms of m and c, for the total number of seats on m minibuses and c coaches ….………….……. (2) (Total 2 marks) This Publication may be reproduced only in accordance with Edexcel Limited copyright policy © 2007 Edexcel Limited 4 Diagram NOT accurately drawn 4. A O T B A and B are points on the circumference of a circle, centre 0. TA and TB are tangents to the circle. Calculate the size of the angle ATO when angle AOT = 56° Give a reason for each stage in your working. ………………….° (Total 3 marks) 5. x° 101° (a) Diagram NOT accurately drawn. 79° Find the size of the angle marked x° ………………..° (2) (b) Give a reason for your answer. …………………………………………………………………………………………………. (1) This Publication may be reproduced only in accordance with Edexcel Limited copyright policy © 2007 Edexcel Limited 5 (Total 3 marks) Mr Smith owns minibuses and coaches. Each minibus has 12 seats. (a) Write an expression, in terms of m, for the number of seats in m minibuses. ….………….……. (1) Each coach has 48 seats. (b) Write an expression, in terms of m and c, for the total number of seats on m minibuses and c coaches ….………….……. (2) (Total 3 marks) This Publication may be reproduced only in accordance with Edexcel Limited copyright policy © 2007 Edexcel Limited 6 6. Evaluate 3−2 ……………… (Total 1 mark) This Publication may be reproduced only in accordance with Edexcel Limited copyright policy © 2007 Edexcel Limited 7 7. Here is a right-angled triangle. 5x + 10 3x + 6 4x + 8 The lengths of the three sides of the triangle are 3x + 6, 4x + 8 and 5x + 10 (b) Find an expression, in terms of x, for the perimeter of the triangle. Give your answer in its simplest form. ……………… (2) (Total 2 marks) 8. Factorise 9x2 − 6x + 1 ….………..……. (Total 2 marks) This Publication may be reproduced only in accordance with Edexcel Limited copyright policy © 2007 Edexcel Limited 8 9. 35° Diagram NOT accurately drawn 50° x° (i) Work out the value of y°. (ii) Explain how you worked out your answer. y° y = ……….…… ……………………………………………………………………….……….… ……………………………………………………………………….….……… (2) (Total 2 marks) This Publication may be reproduced only in accordance with Edexcel Limited copyright policy © 2007 Edexcel Limited 9 10. (a) Use your calculator to work out the value of 6.27 4.52 4.81 9.63 Write down all the figures on your calculator display ........................ (2) (b) Write your answer to part (a) to an appropriate degree of accuracy. ........................ (1) (Total 3 marks) This Publication may be reproduced only in accordance with Edexcel Limited copyright policy © 2007 Edexcel Limited 10 11. B A C 35° Diagram NOT accurately drawn 94° D y E Find the size of the angle marked y. Give your reason for your answer. y = …….…….° ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. (Total 2 marks) This Publication may be reproduced only in accordance with Edexcel Limited copyright policy © 2007 Edexcel Limited 11 1. 40.8 408 = 408 12 = 34 1 .2 12 2. (a) 3x + 6 = 3(x + 2) (b) 3a² (2a – 3) 3. 4. 12m + 48c Angle between tangent and radius = 90° Angle T = 180 − 90 − 56 = 34° (angle in a triangle add up to 180°) Angle ATO = 34° 5. (i) x = 79° ii) alternate angles (a) 12m 6. (i) 7. 3x + 6 + 4x + 8 + 5x + 10 = 12x + 24 3−2 = 1 1 2 9 3 This Publication may be reproduced only in accordance with Edexcel Limited copyright policy © 2007 Edexcel Limited 12 8. 9x2 − 6x + 1 = (3x − 1)(3x − 1) 9. (a) (i) 180 − 50 = 130 130 2 = 65° The angles in a triangle add up to 180°, and the angles opposite the equal sides of an isosceles triangle are equal. (b) (i) 30° 10. 11. (ii) the exterior angle (x = 65°) of a triangle = the sum of the 2 interior opposites angles (a) 28.3404 = 1.962631579 14.44 (b) 1.96 or 2.0 35° (as all numbers in original sum have 2dp or 3sf) alternate angles This Publication may be reproduced only in accordance with Edexcel Limited copyright policy © 2007 Edexcel Limited 13