June 2025 Paper 2 Q5
5 The equation of a curve is \(\quad y = x^5 + px^4 \quad\) where \(p\) is a constant.
When \(\quad x = -1 \quad\) the gradient of the curve is \(-3\)
Work out the value of \(p\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(5x^4\) or \(4px^3\) | M1 | oe eg \(5 \times x^{5 - 1}\) or \(4 \times px^{4 - 1}\) |
| \(5(-1)^4 + 4p(-1)^3 = -3\) or \(5 - 4p = -3\) | M1dep | oe equation |
| 2 | A1 |
Additional guidance
| M1 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| \(y = 5x^4 + 4px^3\) is awarded 1st M1 and may be awarded up to full marks with further correct working | |
| Missing brackets must be recovered |