O-LevelAdditional MathematicsFunctions4037/11 · May/June 2022 · Q310 Marks
A function f is such that f(x) = ln (2x+1), for x > -1/2. A function g is such that g(x) = 5x-7, for x ∈ R.
- (a)Write down the range of f.[1]
- (b)Find the exact solution of the equation gf(x) = 13.[3]
- (c)Find the solution of the equation f'(x) = g⁻¹(x).[6]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [1] B1 Must be using correct notation, allow y ∈ (for f(x) ∈ R oe)
- [3] M1 For correct order (for 5(ln(3x + 1)) - 7 = 13)
- M1 for a correct attempt to solve to get x =, allow one sign error
- Dep on previous M mark
- A1 all correct must be exact (for x = (e^4 - 1)/2)
- [6] M1 for a/(2x+1) (for (f'(x) =) 2/(2x+1))
- A1 all correct
- B1 soi (for (g⁻¹(x) =) (x+7)/5)
- M1 for equating and forming a 3-term quadratic equation = 0 (for 2x² + 15x - 3 = 0)
- M1 For solution of their 3-term quadratic (for x = 0.195, -7.69)
- A1 For discounting negative root. (for x = 0.195)
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