O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2019 · Q68 Marks

The diagram shows the curve y = 3x²-2x+1 and the straight line y = 2x+5 intersecting at the points P and Q. Showing all your working, find the area of the shaded region.

The diagram shows the curve y = 3x²-2x+1 and the straight line y = 2x+5 intersecting at the points P and Q. Showing all your working, find the area of the shaded region.[8]

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Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

[M1] equating the equations of the line and the curve and rearranging to obtain a three term quadratic equated to zero
[A1] 3x²-4x-4=0
[A1] x = -2/3 and x = 2
[M1] subtraction (either way round)
[M1] integration to Ax + Bx² + Cx³
[A1] for 4x+2x² - x³ oe
[M1] Dep on preceding M1 correct use of limits
[A1] 256/27 or 9.48 or 9 13/27

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About this question

Topic

Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.

Source

O-Level Additional Mathematics, May/June 2019 Paper 1 Variant 1, question 6.

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