O-LevelAdditional MathematicsLogarithmic and exponential functions4037/22 · Oct/Nov 2025 · Q46 Marks
Variables x and y are such that when eʸ is plotted against x³, a straight-line graph is obtained. This line passes through the points (1, 13.5) and (7.5, 0.5).
- (a)Find y in terms of x.[4]
- (b)Find the values of x for which your equation is valid.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- [B1] (a) eʸ = mx³ + c soi
- [M1] (a) Correct method to find m e.g. (13.5-0.5)/(1-7.5) or 13=6.5m OR m = -2 soi
- [M1] (a) Correct method to find c e.g. 13.5 = their(–2)[1] + c oe or 0.5 = their(–2)(7.5) + c oe or 0.5 = 7.5(13.5 – c ) + c oe OR c = 15.5 soi
- [A1] (a) y = ln(15.5-2x³) mark final answer
- [M1 FT for 15.5−2x³ > 0 oe, soi; FT a+bx³ > 0 from y = ln(a + bx³)] (b) x < √7.75 oe, nfww
- [A1] (b) implied by 2 marks
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