Find the coefficient of x³ in the expansion of (3 – x)(1 + 3x)⅓ in ascending powers of x.

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

1. [B1] State unsimplified term in x², or its coefficient in the expansion of (1+3x)⅓: ⅓x(-2/3)/2 (3x)²
2. [B1] State unsimplified term in x³, or its coefficient in the expansion of (1+3x)⅓: ⅓x(-2/3)x(-5/3)/6 (3x)³
3. [M1] Multiply by (3 – x) to give 2 terms in x³, or their coefficients (3x × 10/6 + 1) Ignore errors in terms other than x³. 3x x³ coeff – x³ coeff and no other term in x³
4. [A1] Obtain answer 6 (Not 6x³)