16N.1.SL.TZ0.T_14

pestleMathematicsAASLPaper 116N· sl-5-3-differentiating-polynomials-n-e-zsource ↗

The equation of a curve is $y = \frac{1}{2}{x^4} - \frac{3}{2}{x^2} + 7$ .

The gradient of the tangent to the curve at a point P is $- 10$ .

Find $\frac{{{\text{d}}y}}{{{\text{d}}x}}$ .

[2]

Find the coordinates of P.

[4]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$2{x^3} - 3x$ (A1)(A1) (C2)

Note: Award (A1) for $2{x^3}$ , award (A1) for $- 3x$ .

Award at most (A1)(A0) if there are any extra terms.

[2 marks]

$2{x^3} - 3x = - 10$ (M1)

Note: Award (M1) for equating their answer to part (a) to $- 10$ .

$x = - 2$ (A1)(ft)

Note: Follow through from part (a). Award (M0)(A0) for $- 2$ seen without working.

$y = \frac{1}{2}{( - 2)^4} - \frac{3}{2}{( - 2)^2} + 7$ (M1)

Note: Award (M1) substituting their $- 2$ into the original function.

$y = 9$ (A1)(ft) (C4)

Note: Accept $( - 2,{\text{ }}9)$ .

[4 marks]

Examiners’ report

[N/A]