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O-LevelAdditional MathematicsDifferentiation and integration4037/22 · Oct/Nov 2022 · Q36 Marks

In this question a and b are constants. The normal to the curve y = ax⁻³ + 3x - 2 at the point where x = 1 has equation y = -1/4 x + b. Find the values of a and b.

  1. In this question a and b are constants. The normal to the curve y = ax⁻³ + 3x - 2 at the point where x = 1 has equation y = -1/4 x + b. Find the values of a and b.[6]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

  1. [B1] [m_tangent =] -ax⁻² + 3 oe
  2. [B1] [When x = 1, m_normal = ] -1/(3-a) oe or gradient of tangent = 4 soi
  3. [M1] -1/(their(3-a)) = 1/4 oe
  4. [M1] or their (3-a) = 4 oe
  5. [A1] a = -1 nfww
  6. [M1] [When x = 1] their 0 = -1/4 [1] + b oe
  7. [A1] b = 1/4 nfww

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2022 Paper 2 Variant 2, question 3.

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