O-LevelAdditional MathematicsEquations, inequalities and graphs4037/22 · May/June 2014 · Q86 Marks

The line y=x-5 meets the curve x² + y² + 2x – 35 = 0 at the points A and B. Find the exact length of AB.

The line y=x-5 meets the curve x² + y² + 2x – 35 = 0 at the points A and B. Find the exact length of AB.[6]

Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

[M1] Substitution of either x - 5 or y + 5 into equation of curve and brackets expanded condone one sign error in either equation of curve or expansion of brackets; condone omission of = 0, BUT x – 5 or y + 5 must be correct
[A1] 2x² - 8x -10[= 0] or 2y² +12y[= 0] obtained
[M1] Solving their quadratic dep on a valid substitution attempt
[A1*+A1*] (-1, -6) oe and (5, 0) oe isw or A1 for correct pair of x coordinates or correct pair of y coordinates
[B1dep*] √72 or 6√2 cao isw

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Topic: Equations, inequalities and graphs, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source: O-Level Additional Mathematics, May/June 2014 Paper 2 Variant 2, question 8.

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