O-LevelAdditional MathematicsFunctions4037/22 · Oct/Nov 2025 · Q95 Marks
It is given that f(x) = ln(2x+5) for x > a, where a is a constant. It is also given that g(x) = x² +1 for x ∈ R.
- (a)Write down the least possible value of a.[1]
- (b)Using your value of a, write down the range of f.[1]
- (c)Using your value of a, solve the equation fg(x) = 4. Give your answers in exact form.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- [B1] (a) -5/2 oe
- [B1] (b) f ∈ ℝ oe
- [B1] (c) ln(2(x²+1)+5) [= 4] oe, soi
- [M1] (c) 2(x²+1)+5=e⁴ or their (2x² + 7) = e⁴
- [A1] (c) x = ±√( (e⁴-7)/2 ) or exact equivalent
- [M1] (c) Alternative method: for solving f(x) = 4 to find x = k and states g(x)=k, where k is a constant OR for stating g(x)=f⁻¹(4)
- [A1] (c) x² + 1 = (e⁴-5)/2 → x=±√( ((e⁴-5)/2)-1 ) or exact equivalent
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →