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O-LevelAdditional MathematicsCircular measure4037/21 · May/June 2010 · Q1112 Marks

Answer only one of the following two alternatives.

  1. EITHER (i)The diagram represents a company logo ABCDA, consisting of a sector OABCO of a circle, centre O and radius 6 cm, and a triangle AOD. Angle AOC = 0.8π radians and C is the mid-point of OD. Find the perimeter of the logo,[7]
  2. EITHER (ii)the area of the logo.[5]
  3. OR (i)The diagram shows part of the curve y = x³ – 6x² + 8x + 5. The tangent to the curve at the point P(1, 8) cuts the curve at the point Q. Show that the x-coordinate of Q is 4.[6]
  4. OR (ii)Find the area of the shaded region.[6]

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Mark scheme

Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.

  1. [M1] EITHER (i) Sector angle = 1.2π
  2. [A1] OD = 12
  3. [M1] AD² = 12² + 6² - 2×12×6 cos 0.8π
  4. [A1] AD=17.2
  5. [M1] Uses s = 6×(1.2π)= (7.2π) (or 22.6)
  6. [M1] Complete plan (AD+re+6) or (17.2+7.2π + 6)
  7. [A1] 45.8
  8. [M1] EITHER (ii) AOD = 1/2 × 6 × 12 sin 0.8π
  9. [A1] 21.2
  10. [M1] Uses A = 1/2 × 6² × (1.2π)
  11. [A1] 21.6π or 67.8 or 67.9
  12. [A1] 89.0 or 89
  13. [M1A1] OR (i) dy/dx = 3x² - 12x +8
  14. [A1] gradient tangent = -1
  15. [A1] tangent y - 8 = −1(x – 1) or x + y = 9
  16. [M1] Valid method (e.g. substitute x = 4 in both)
  17. [A1] Valid conclusion (e.g. y = 5 in both)
  18. [M1A1] OR (ii) ∫y dx = x⁴/4 - 2x³ + 4x² + 5x
  19. [M1] Uses limits F(4) – F(1)
  20. [A1] 12.75
  21. [B1] Subtracts from area of trapezium (19.5)
  22. [A1] 6.75

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About this question

Topic
Circular measure, O-Level Additional Mathematics (syllabus 4037). Structured question, 12 marks.
Source
O-Level Additional Mathematics, May/June 2010 Paper 2 Variant 1, question 11.

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