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A-LevelMathematicsDifferentiation9709/12 · Feb/Mar 2023 · Q34 Marks

A curve has equation y = (1/60)(3x + 1)² and a point is moving along the curve. Find the x-coordinate of the point on the curve at which the x- and y-coordinates are increasing at the same rate.

  1. (a)Find the x-coordinate of the point on the curve at which the x- and y-coordinates are increasing at the same rate.[4]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2023). The mark or mark type is shown in brackets.

  1. [B1 B1] dy/dx = {1/60 (3x+1)×2}×{3} May see 1/60 (18x+6).
  2. [M1] 1/10(3x+1)=1 Equate their dy/dx to 1.
  3. [A1] x=3

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About this question

Topic
Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source
A-Level Mathematics, Feb/Mar 2023 Paper 1 Variant 2, question 3.

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