Further Parametric Equations (A Level only) | Edexcel A Level Maths: Pure Topic Questions 2018

1a

2 marks

Given

$x = e^{t}$ and $y = 2 t^{3} + 3 t$

find $\frac{d x}{d t}$ and $\frac{d y}{d t}$ .

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1b

2 marks

Hence, or otherwise, find $\frac{d y}{d x}$ in terms of t.

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1a

3 marks

Find an expression for $\frac{d y}{d x}$ in terms of t for the parametric equations

$x = \sin 2 t$ $y = e^{t}$

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1b

2 marks

Verify that the graph of x against y passes through the point (0 , 1) and find the gradient at that point.

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1a

3 marks

Find an expression for $\frac{d y}{d x}$ in terms of $t$ for the parametric equations

$x = e^{2 t}$ $y = 3 t^{2} + 1$

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1b

3 marks

The graph of y against x passes through the point P (1 , 1).

(i)

Find the value of t at the point P.

(ii)

Find the gradient at the point P.

(iii)

What does the value of the gradient tell you about point P?

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1

6 marks

The shaded area in the diagram below is bounded on three of its sides by the $x$ -axis, the $y$ -axis, and the line $x = 1$ . On the remaining side, the boundary is defined by the parametric equations

$x = 2 \cos t$ $y = \frac{9 t^{2}}{π^{2}}$ $0 \leq t \leq \frac{π}{2}$

q1-9-2-further-parametric-equations-very-hard-a-level-maths-pure

Show that the shaded area is not a trapezium.

In your work, you may use without proof the result

$\int_{\frac{π}{2}}^{\frac{π}{3}} t^{2} \sin t d t = - \frac{1}{18} π^{2} - (1 - \frac{\sqrt{3}}{3}) π + 1$

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Edexcel A Level Maths: Pure

Topic Questions

9.2 Further Parametric Equations (A Level only)