Let f(x) = (14 - 3x + 2x²) / ((2 + x)(3 + x²))

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. [B1] State or imply the form A/(2+x) + (B+Cx)/(3+x²)
2. [M1] Use a correct method for finding a constant
3. [A1] Obtain one of A = 4, B = 1 and C = −2
4. [A1] Obtain a second value
5. [A1] Obtain the third value
6. [M1] Use correct method to find the first two terms of the expansion of (2+x)⁻¹, (1+½x)⁻¹, (3+x²)⁻¹ or (3(1+x²/3))⁻¹
7. [A1FT] Obtain correct unsimplified expansions up to the term in x² of each partial fraction
8. [A1FT] Obtain correct unsimplified expansions up to the term in x² of each partial fraction
9. [M1] Multiply out, up to the terms in x², by B + Cx, where BC ≠ 0
10. [A1] Obtain final answer 7/3 − 5/3 x + 7/18 x²