Let f(x) = (x²+2x-11) / ((3+x)(2+x²)).

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

1. [B1] State or imply the form A+ B/(3+x) + (Cx+D)/(2+x^2)
2. [M1] Use a correct method for finding a constant
3. [A1] Obtain one of A = 1, B = –4, C = 1 and D = -3
4. [A1] Obtain a second value
5. [A1] Obtain a third value
6. [A1] Obtain all four correct values
7. [M1] Use a correct method to find the first two terms in the expansion of (3 + x)⁻¹, (2 + x²)⁻¹ or (1 + x²/2)⁻¹
8. [A1 FT] Obtain correct unsimplified expansions up to the term in x² of each partial fraction
9. [A1 FT] Multiply (Cx + D) by the expansion of (1 + x²/2)⁻¹ up to the term in x² where CD ≠ 0
10. [M1]
11. [A1] Obtain final answer 11/6 - 17/18 x + 65/108 x²