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Module 5 Paper 2 Higher Tier June 2008

This document summarizes key mathematical concepts and problems from the June 2008 Higher Tier exam, including area calculations, volume of solids, angle measurements, algebraic equations, and the use of trigonometric functions. It covers topics such as the calculation of exterior angles in polygons, solving quadratic equations, employing the sine rule, and validating properties of geometric figures. Review these essential concepts to prepare for your mathematics assessments effectively.

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Module 5 Paper 2 Higher Tier June 2008

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  1. Module 5 Paper 2 Higher Tier June 2008

  2. Area: ½ x 10.4 x 5.5 = 28.6 cm2 2 Marks

  3. 5x - 3x = 7 + 4 2x = 11 x = 5.5 13 - 5y = 12 13 – 12 = 5y 5y = 1 13 - 5y = 4 x 3 6 Marks y = ⅕ or 0.2

  4. Y= 2 2 Marks

  5. 1 Mark

  6. 1 Mark Sum: 25 + 33 + 34 + 35 = 127

  7. n + 8 n + 9 n + 10 n + n + 8 + n + 9 + n + 10 = 4n + 27 4n is always even. 27 is an odd number Even + Odd = Odd 6 marks

  8. Exterior angle of regular Octagon = 360 ÷ 8 = 45⁰ Exterior angle of regular Pentagon = 360 ÷ 5 = 72⁰ Angle a = 45 + 72 = 117⁰ 4 Marks

  9. 5d = c - 2 2 Marks

  10. Need to extend line so it goes from x =-1 to x=5 X X X 5 Marks x = 3.3 y = 1.7

  11. A B Area of A is 3 x 2 = 6cm2 Area of B is 9 x 2 = 18cm2 Area of cross section is 18 + 6 = 24cm2 Volume of block is area of cross section x length: 24 x 65 = 1560 cm3 5 Marks

  12. Equidistant from P and Q 3 marks

  13. Answer : x4 Answer: 6y7z5 Answer: 8p9r6 5 Marks

  14. OPP Use TAN Adj A = Tan-1 0.6875 = 34.5⁰ 3 Marks

  15. Adj Hyp Use Cosine DF = 24 x cos 64 DF = 10.5cm DF = 10.5(209.....) 4 Marks

  16. 30 x 1.20 = 36 15 X 1.10 = 16.5 3 Marks New area = 36 x 16.5 = 594cm2

  17. Answer: ( 5x + 1 ) ( x + 7 ) Answer: 3 ( y2 - 4z2 ) = 3 ( y - 2z ) ( y + 2z) 5 Marks

  18. Use Sine Rule YZ = 14.65cm (14.7cm) 3 Marks

  19. MC = OA (=a) –equal and parallel Hence AC = OM (and parallel) If opposite sides are equal and parallel then OACM is a parallelogram 2 Marks

  20. Volume of cone: ⅓ πr2h = 2400 r2 = 81.85 r = 9.04cm (9.05cm) 3 Marks

  21. Multiply every term by x ( x – 2 ) 4 ( x – 2 ) + 3x = x ( x – 2 ) 4x - 8 + 3x = x2 - 2x Collect terms together on one side and simplify x2 - 9x + 8 = 0 x = 1 or x = 8 Factorise 5 Marks ( x - 1 ) ( x – 8 ) = 0

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