1.10.5 Implicit and parametric differentiation (A-level only)

Medium Hard

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78

Question 51

A precision laser cutting tool follows a path defined by the relationship between its lateral displacement, $x$ mm, and the angle of its guide-rail, $y$ radians, given by

16\sin^2 y + 5, \quad 0 \leqslant y \leqslant \frac{\pi}{2}

The point $P(k,π3)P\left(k, \frac{\pi}{3}\right)$ lies on this path.

Verify that $k = 17$ .

[2]

bi.

Find $dxdy\frac{dx}{dy}$ in terms of $y$ .

[2]

bii.

Hence show that $dydx=12x−521−x\frac{dy}{dx} = \frac{1}{2\sqrt{x-5}\sqrt{21-x}}$ .

[3]

The normal to the path at $P$ cuts the $x$ -axis at the point $N$ .

Find the exact area of triangle $O P N$ , where $O$ is the origin. Give your answer in the form $aπ+bπ2a\pi + b\pi^2$ where $a$ and $b$ are constants.

[5]

1.10.5 Implicit and parametric differentiation (A-level only) Questions

A Level
Maths
1.10.5 Implicit and parametric differentiation (A-level only)

A Level
Maths AQA
Question bank