O-LevelAdditional MathematicsFunctions4037/21 · May/June 2012 · Q1210 Marks
Answer only one of the following two alternatives. EITHER The equation of a curve is y = 2x² – 20x + 37.
- (i)Express y in the form a(x + b)² + c, where a, b and c are integers.[3]
- (ii)Write down the coordinates of the stationary point on the curve.[1]
- (iii)A function f is defined by f : x → 2x² – 20x + 37 for x > k. Given that the function f⁻¹(x) exists, write down the least possible value of k,[1]
- (iv)sketch the graphs of y = f(x) and y = f⁻¹(x) on the axes provided,[2]
- (v)obtain an expression for f⁻¹.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.
- [3] (i) y = 2(x-5)² -13 or a = 2, b = -5, c = -13 B1+B1+B1
- [1] (ii) (5,-13) B1^
- [1] (iii) 5 B1^
- [2] (iv) Positive quadratic curve; correct position B1+B1
- [1] (v) Method for inverse M1
- [2] 5 + √((x+13)/2) A2, 1, 0
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