# Monday 11 June 2012 Afternoon

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2 2 Formulae Sheet: Higher Tier a Area of trapezium = 1 2 (a + b)h h b Volume of prism = (area of cross-section) length crosssection length In any triangle ABC a sin A = b sin B = c Sine rule sin C b C a Cosine rule a 2 = b 2 + c 2 2bc cos A 1 2 Area of triangle = ab sin C A c B Volume of sphere = 4 3 π r 3 Surface area of sphere = 4 π r 2 r Volume of cone = 1 3 π r 2 h Curved surface area of cone = π r l l h r The Quadratic Equation The solutions of ax 2 + bx + c = 0, where a = 0, are given by b ± (b 2 4ac) x = 2a PLEASE DO NOT WRITE ON THIS PAGE

3 1 (a) Work out. 5 (i) (a)(i) [2] (ii) Give your answer as a mixed number in its simplest form. (ii) [3] (b) Work out the reciprocal of (b) [1] Turn over

4 2 Last year, one week s holiday in Spain cost 660. This year, the cost has increased by 15%. Calculate the cost of the holiday this year. 4 [3]

5 3 (a) Solve this inequality. 5 x 4 5 < 10 (b) Represent your solution to part (a) on this number line. (a) [2] [1] 4 Calculate angle p. 210 Not to scale p [3] Turn over

6 5 Lizzie and Sam discuss where to go on holiday. They collect this data about cities in the Northern Hemisphere from the Internet. City Latitude (degrees) 6 Average June temperature ( C) Height above sea level (m) Oslo Copenhagen Dijon Madrid Rome Athens Cairo Khartoum Freetown Bangui Libreville (a) Lizzie wants to go to somewhere that is near to sea level as she thinks places that are higher will be cooler. Lizzie draws a scatter graph of average June temperature against height above sea level for these cities Average June temperature ( C) Height above sea level (m)

7 (i) 7 Describe the relationship between height above sea level and average June temperature shown on the scatter diagram. (a)(i) [1] (ii) Does the scatter diagram support Lizzie s view about the relationship between temperature and height above sea level? Explain your answer. because [1] (b) Sam wants to go somewhere near the equator as he thinks these places will be warmer. Latitude gives information about how far from the equator you are. So Libreville, at latitude 0 degrees, is on the equator and Oslo, at latitude 59 degrees, is a long way north of the equator. (i) Use Latitude and Average June temperatures to draw and label another scatter diagram to test Sam s idea. [4] (ii) Does your scatter diagram support Sam s view about the relationship between temperature and distance from the equator? Explain your answer. because [2] Turn over

8 6 Wibke buys satsumas from the market each week. She keeps a record of how many satsumas she gets and how much they cost her. She plots this information on a grid Cost (y pence) Number of satsumas (x) (a) Draw a line of best fit. [1] (b) Calculate the gradient of your line. Give your answer to the nearest whole number. (c) What information about satsumas does the gradient represent? (b) [2] (d) Write down the equation of your line in terms of y and x. (c) [1] (d) [2]

9 7 Write down the inequality represented by each of these shaded regions. 9 (a) y O 5 x (a) [1] (b) y 2 O x (b) [1] (c) y y = x O x (c) [1] Turn over

10 10 8 (a) The diagram shows a small circle and a large circle. AB is a tangent to both circles. AD and BC are diameters. AD = 2 cm, BC = 5 cm. (i) Find the scale factor of the enlargement from the small circle to the large circle. C D Not to scale 5 cm 2 cm A B Any two circles of different size are mathematically similar. (a)(i) [1] (ii) Name another shape where all sizes of the shape will be mathematically similar to each other. (ii) [1] (iii)* Prove that ABCD is a trapezium. [3]

11 (b) (i)* 11 Show that these two triangles are not similar. Not to scale 5 cm 8 cm 9 cm 12 cm [3] (ii) Change one measurement on one triangle so that the triangles will be similar. (b)(ii) Change the cm side to cm [3] Turn over

12 12 9 Martha and Sukh are doing a task on area. They have a rectangle with the information shown. Area = 3.0 cm cm Not to scale length Martha works out the length and writes down her answer as cm. Sukh says she must be wrong. (a) Complete Sukh s explanation is clearly the wrong size. I know the answer should be close to 6 because [1] (b) Sukh s calculator gives the answer as Martha now rounds this answer to 4 decimal places. (i) Round correct to 4 decimal places. (b)(i) [1] Sukh says that 4 decimal places is not to an appropriate degree of accuracy. (ii) To what degree of accuracy should the answer be given? (ii) [1] (iii) Use your answer to part (ii) to write the length to an appropriate degree of accuracy. (iii) cm [1]

13 13 10 Enlarge shape J using scale factor - 2 and centre (0, 2). Label your image K. 5 4 y 3 2 J x [3] Turn over

14 14 11 (a) Simplify. (3a 3 b 4 ) 2 (a) [3] (b) Given that f(x) = 3x 5, evaluate f(3) f(1). (b) [3] (c) Evaluate (c) [2] (d) Rationalise the denominator and simplify (d) [2]

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