O-LevelAdditional MathematicsFunctions4037/12 · Oct/Nov 2015 · Q1110 Marks
A function f is such that f(x) = x² + 6x + 4 for x≥0.
- (a)(i)Show that x² + 6x + 4 can be written in the form (x + a)² + b, where a and b are integers.[2]
- (a)(ii)Write down the range of f.[1]
- (a)(iii)Find f⁻¹ and state its domain.[3]
- (b)Functions g and h are such that, for x ∈ R, g(x) = eˣ and h(x) = 5x + 2. Solve h²g(x) = 37.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.
- [B1, B1] B1 for 3, B1 for -5
- [B1] y ≥ 4 or f ≥ 4. Correct notation or statement must be used
- [M1] for a correct attempt to find the inverse function
- [A1] must be in the correct form and positive root only
- [B1FT] Follow through on their answer to (ii), must be using x
- [M1] for correct order (h²g(x))
- [M1] for dealing with h²
- [DM1] for solution of equation (dependent on both previous M marks)
- [A1] leading to x = 0
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