# B293B. MATHEMATICS B (MEI) Paper 3 Section B (Higher Tier) GENERAL CERTIFICATE OF SECONDARY EDUCATION. Tuesday 12 January 2010 Morning

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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 Sine rule a sin A = b sin B = c sin C b C a Cosine rule a 2 = b 2 + c 2 2bc cos A Area of triangle = ab sin C 1 2 A c B 4 3 Volume of sphere = πr 3 r Surface area of sphere = 4πr 2 Volume of cone = πr 2 h Curved surface area of cone = πrl 1 3 l h r The Quadratic Equation The solutions of ax 2 + bx + c = 0, where a 0, are given by x = b ± (b 2 4ac) 2a PLEASE DO NOT WRITE ON THIS PAGE

3 8 Mike drove down the motorway at a steady speed of 70 mph for 3 hours. (a) Work out the distance Mike travelled in 3 hours. 3 He then took another 2 hours to cover a further 40 miles. (b) Calculate his average speed for the whole journey. (a)... miles [1] (b)... mph [2] Turn over

4 9 A rectangular garden measures 95 m by 45 m. A path lies on a diagonal of the rectangle m Not to scale 95 m Calculate the length of the path.... m [3]

5 10 Tony and Gordon compared pizzas inch 15 inch 8 13 Tony said, The diameter of the big pizza is half as much again; it should only cost 12. Gordon said, No, the area of the big pizza is more than twice as much; it is very good value. Write down calculations to show that Gordon is right.... [4] Turn over

6 11 The table summarises the attendances at the home matches of a local football club. 6 Attendance (n) Number of matches Midpoint 500 n n n n n Calculate an estimate of the mean attendance.... [3] 12 Last year George received a pension of per week. This year his pension has increased to Calculate the percentage increase, correct to one decimal place....% [3]

7 13 The number of fish in a lake can be estimated by the capture/recapture method. One day 20 fish were caught. They were tagged and returned to the lake. The next day 20 fish were caught, 2 of which were already tagged. Using the information the probability that a fish that is caught is already tagged, the number of tagged fish, estimate the number of fish originally in the lake [3] Turn over

8 14 Josh and his sister Julia have an Uncle Peter. Each Christmas he gives them a sum of money to be shared in the ratio of their ages. (a) In 2008, when Josh was 11 and Julia was 14 years old, he gave them 200 to share. How much did each receive? 8 (a) Josh:... Julia:... [3] (b) The following year Uncle Peter gave them 243 to share. How much did they each receive in 2009? (b) Josh:... Julia:... [3]

9 15 (a) Complete the table for y = x 3 3x x y [2] (b) Draw the graph of y = x 3 3x +1 for 2 x 2. 4 y x [2] (c) Write down the roots of the equation x 3 3x +1 = 0, correct to one decimal place. (c)... [2] TURN OVER FOR QUESTION 16

10 16 A solid ornament has the shape of a pyramid with triangular base ABC and vertex V. The perpendicular height, VG, of the ornament is 12 cm. AB = 6 cm, BC = 7 cm and angle ABC = V 12 cm B 44 6 cm 7 cm G A C (a) Find the area of the base, ABC, of the ornament. (a)... cm 2 [2]

11 11 (b) (i) Hence find the volume of the ornament. [The volume of a pyramid = 1 base area height.] 3 (ii) The ornament is made of glass which has a density of 2.6 g/cm 3. Find the mass of the ornament. (b)(i)... cm 3 [1] (ii)... g [2]

### B293A. MATHEMATICS B (MEI) Paper 3 Section A (Higher Tier) GENERAL CERTIFICATE OF SECONDARY EDUCATION. Tuesday 12 January 2010 Morning WARNING

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### Wednesday 3 June 2015 Morning

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### Wednesday 3 June 2015 Afternoon

Oxford Cambridge and RSA H Wednesday 3 June 2015 Afternoon GCSE GEOGRAPHY B B563/02 Key Geographical Themes (Higher Tier) *4390586245* Candidates answer on the Question Paper. OCR supplied materials: OS

### Thursday 25 May 2017 Morning

Oxford Cambridge and RSA H Thursday 25 May 2017 Morning GCSE MATHEMATICS B J567/03 Paper 3 (Higher Tier) *4401106953* Candidates answer on the Question Paper. OCR supplied materials: None Other materials