18N.1.SL.TZ0.T_11

pestleMathematicsAISLPaper 118N· sl-5-4-tangents-and-normalsource ↗

Consider the curve y = 5x³− 3x.

The curve has a tangent at the point P(−1, −2).

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

[2]

Find the gradient of this tangent at point P.

[2]

Find the equation of this tangent. Give your answer in the form y = mx + c.

[2]

Markscheme / solution

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

15x² − 3 (A1)(A1) (C2)

Note: Award (A1) for 15x², (A1) for −3. Award at most (A1)(A0) if additional terms are seen.

[2 marks]

15 (−1)² − 3 (M1)

Note: Award (M1) for substituting −1 into their $\frac{{{\text{d}}y}}{{{\text{d}}x}}$ .

= 12 (A1)(ft) (C2)

Note: Follow through from part (a).

[2 marks]

(y − (−2)) = 12 (x − (−1)) (M1)

−2 = 12(−1) + c (M1)

Note: Award (M1) for point and their gradient substituted into the equation of a line.