CAIE A-Level Mathematics AS 2.4.3 Differentiation Rules Questions

Practise statistical inference methods within the AS mathematics syllabus.

Exam points

use vector notation and operations
solve geometric problems with vectors
interpret vector relationships

[Maximum number: 3]

Figure for Question CAIE A-Level Mathematics AS 2.4.3 Differentiation Rules Questions question 1 — CAIE A-Level Mathematics AS

The diagram shows the curve with parametric equations

x=4 \mathrm{e}^{2 t}, \quad y=5 \mathrm{e}^{-t} \cos 2 t

for $-\frac{1}{4} \pi \leqslant t \leqslant \frac{1}{4} \pi$ . The curve has a maximum point M.

Find an expression for $\frac{\mathrm{d} y}{\mathrm{~d} x}$ in terms of t.

Use product rule to find $\frac{\mathrm{d} y}{\mathrm{~d} t}$
Obtain $\frac{\mathrm{d} y}{\mathrm{~d} t}=-5 \mathrm{e}^{-t} \cos 2 t-10 \mathrm{e}^{-t} \sin 2 t$
or (unsimplified) equivalent (do not condone poor use of
brackets.

Obtain $\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{-5 \mathrm{e}^{-t} \cos 2 t-10 \mathrm{e}^{-t} \sin 2 t}{8 \mathrm{e}^{2 t}}$
OE following their expression for $\frac{\mathrm{d} y}{\mathrm{~d} t}$ .

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CAIE A-Level Mathematics AS 2.4.3 Differentiation Rules Questions question 1