Let f(x) = (2x² + 7x + 8) / ((1+x)(2 + x)²).

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

1. [B1] (a) State or imply the form A/(1+x) + B/(2+x) + C/(2+x)²
2. [M1] (a) Use a correct method to find a constant
3. [A1] (a) Obtain one of A= 3, B = -1 and C = -2
4. [A1] (a) Obtain a second value
5. [A1] (a) Obtain the third value
6. [M1] (b) Use a correct method to find the first two terms of the expansion of (1+x)⁻¹, (2+x)⁻¹, (1+x)⁻², (2+x)⁻² or (1+x)⁻¹, (1+x)⁻², (2+x)⁻¹ or (1+x)⁻¹, (2+x)⁻¹
7. [A3] (b) Obtain correct unsimplified expansions up to the term in x² of each partial fraction
8. [A1] (b) Obtain final answer 2 - 9/4 x + 5/2 x²