A-LevelMathematicsDifferentiation9709/33 · Oct/Nov 2024 · Q78 Marks

The parametric equations of a curve are x = 3 sin 2t, y = tan t + cot t, for 0 < t < ¦π.

(a)Show that dy/dx = -2 / (3 sin² 2t).[5]
(b)Find the equation of the normal to the curve at the point where t = ¦π. Give your answer in the form py+qx+r = 0, where p, q and r are integers.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

[B1] (a) Obtain dx/dt = 6 cos 2t.
[B2] (a) Simplify y to 1/(sin t cos t) or 2/(sin 2t).
[M1] (a) Obtain dy/dt = -4 cos 2t / sin² 2t, and then use dy/dx = (dy/dt) ÷ (dx/dt).
[A1] (a) Obtain dy/dx = -2 / (3 sin² 2t) from full and correct working. AG
[B1] (b) Gradient of normal = 3/2.
[M1] (b) Use correct method to find the equation of the normal. E.g. (y-2) = (3/2)(x-3) or find c in y = (3/2)x + c.
[A1] (b) Obtain 2y -3x+5=0. Or k(2y-3x + 5) = 0, where k is an integer.

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Topic: Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source: A-Level Mathematics, Oct/Nov 2024 Paper 3 Variant 3, question 7.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content