O-LevelAdditional MathematicsSimultaneous equations4037/21 · May/June 2017 · Q99 Marks

The curve 3x² + xy - y² + 4y – 3 = 0 and the line y = 2(1 – x) intersect at the points A and B.

(i)Find the coordinates of A and of B.[5]
(ii)Find the equation of the perpendicular bisector of the line AB, giving your answer in the form ax + by = c, where a, b and c are integers.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[M1] Substitution of y = 2(1-x) Must be attempt at full substitution. Condone one sign error in substitution. Condone omission of = 0 or incorrect rhs
[A1] -3x² + 2x + 1 = 0 oe (3x² - 2x - 1 = 0) Terms collected
[M1] Solving their quadratic found from eliminating one variable (3x+1)(1-x) or (3x+1)(x-1) can be implied by a correct pair of x values
[A2] ( -1/3, 8/3 ) oe and (1, 0) oe isw nfww A1 for each or A1 for a correct pair of x-coordinates or a correct pair of y-coordinates
[B1] [m=] -2/3 cao
[B1] (1/3, 4/3) FT
[M1] y - their (4/3) = their (-2/3) (x - their (1/3)) or y = their (-2/3)x + c and substitutes their midpoint and reaches c = ...
[A1] 6y - 3x = 7 allow any equivalent form with integer coeffs/constant

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