June 2025 Paper 1 Q17
17 The expansions of \(\ (4a + x)^4\ \) and \(\ (5 - 2x)^3\ \) have the same coefficient of \(x^3\)
Work out the value of \(a\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(4 \times 4a\ \ (\times x^3)\) or \((-2x)^3\) or \(-8(x^3)\) | M1 | oe 4 could be written as \(\dbinom{4}{3}\) or \(\dbinom{4}{1}\) \(x^3\) doesn’t need to be seen |
| \(4 \times 4a = -8\) or \((-2)^3\) or \(16a = -8\) | M1dep | oe both terms correct \(x^3\) needs to be on both sides of the equation or neither |
| \(-0.5\) | A1 | oe |
Additional guidance
| Coefficients must be part of a correct term eg \(16a + x^3\) | M0 |
| Errors in negatives can be recovered | |
| Condone correct terms seen in full expansions (even if there are other errors in the expansions) |