O-LevelAdditional MathematicsStraight line graphs4037/12 · Oct/Nov 2015 · Q129 Marks

The line 2x - y + 1 = 0 meets the curve x² + 3y = 19 at the points A and B. The perpendicular bisector of the line AB meets the x-axis at the point C. Find the area of the triangle ABC.

The line 2x - y + 1 = 0 meets the curve x² + 3y = 19 at the points A and B. The perpendicular bisector of the line AB meets the x-axis at the point C. Find the area of the triangle ABC.[9]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.

[M1] for attempt to obtain a 3 term quadratic in terms of one variable only
[DM1] for attempt to solve quadratic equation
[A1, A1] A1 for each 'pair' of values.
[B1] Midpoint (-3, -5)
[M1] for attempt at straight line equation, must be tangent using their gradient and y
[M1] for use of y = 0 in their line equation (but not 2x - y + 1 = 0)
[M1] for correct attempt to find area, may be using their values for A, B and C (C must lie on the x-axis)
[A1] = 125

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Topic: Straight line graphs, O-Level Additional Mathematics (syllabus 4037). Structured question, 9 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2015 Paper 1 Variant 2, question 12.

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