O-LevelAdditional MathematicsDifferentiation and integration4037/22 · Oct/Nov 2016 · Q58 Marks

The curve with equation y = x³ + 2x²-7x+2 passes through the point A (-2, 16). Find

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.

[B1] (i) dy/dx = 3x² + 4x-7
[M1] x = -2→ dy/dx = 12-8-7 = -3 insert x = -2 into their gradient and use (−2, 16) and their gradient of tangent in equation of line.
[A1] Equation of tangent : (y-16)/(x+2) = -3 → y = -3x+10
[M1] (ii) Tangent cuts curve again x³+2x²-7x+2 = -3x+10 equate curve and their linear answer from (i).
[A1] x³+2x²-4x-8=0
[M1] (x+2)(x+2)(x-2) = 0 factorise: (x+2) and a two or three term quadratic is sufficient. Allow long division
[A1A1] x = 2, y = 4 withhold final A1 if (2, 4) not clearly identified as their sole answer.

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Topic: Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2016 Paper 2 Variant 2, question 5.

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