Practise questions · Salam Academy

SA-9709-P2-DF-0143 marksL1 FoundationCalculatorParametric

A curve has parametric equations

x=t^2

,

y=2t

. Find the gradient of the curve at the point where

t=2

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P2-DF-Q021 markL1 FoundationCalculatorParametric

If

x=f(t)

and

y=g(t)

, then

\dfrac{dy}{dx}=

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-D34-0032 marksL1 FoundationCalculatorCartesian form

A curve has parametric equations

x=t+1

,

y=t^2

. Find its Cartesian equation,

y

in terms of

x

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-D34-G012 marksL1 FoundationCalculatorParametric

A curve has parametric equations

x=2t

,

y=t^2

. Find the gradient of the curve at the point where

t=3

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DF-0113 marksL1 FoundationCalculatorParametric

A curve is given by

x=t^2

,

y=2t

. Find the gradient of the curve at the point where

t=3

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P2-DF-0153 marksL2 StandardCalculatorParametric

A curve has parametric equations

x=3\cos t

,

y=2\sin t

. Find the gradient at the point where

t=\tfrac\pi4

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-D34-0012 marksL2 StandardCalculatorParametric

A curve has parametric equations

x=\cos t

,

y=\sin t

. Find the exact gradient at the point where

t=\dfrac{\pi}{3}

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-D34-0022 marksL2 StandardCalculatorParametric

A curve has parametric equations

x=t^3

,

y=t^2

. Find the gradient at the point where

t=2

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P2-DF-0164 marksL3 ExamCalculatorTangents

A curve has parametric equations

x=e^t+1

,

y=e^{2t}

. Find the equation of the tangent at the point where

t=0

, in the form

y=mx+c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P2-DF-0174 marksL3 ExamCalculatorParametric

A curve has parametric equations

x=t+\dfrac1t

,

y=t-\dfrac1t

, for

t>0

. Find the gradient of the curve at the point where

t=2

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DF-0125 marksL3 ExamCalculatorTangents

A curve has parametric equations

x=2\cos\theta

,

y=3\sin\theta

. Find the equation of the tangent at the point where

\theta=\tfrac\pi4

, in the form

y=mx+c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DF-0134 marksL3 ExamCalculatorTangents

A curve has parametric equations

x=e^t+1

,

y=te^t

. Find the exact coordinates of the point where the gradient is

3

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P2-DF-0186 marksL4 ChallengingCalculatorTangents

A curve has parametric equations

x=\ln t

,

y=t^2-2t

, for

t>0

. Find the exact coordinates of the point on the curve where the gradient is

4

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-D34-0044 marksL4 ChallengingCalculatorTangents

A curve has parametric equations

x=t^2

,

y=t^3-3t

. Find the

y

-coordinates of the points where the tangent is parallel to the

x

-axis.

Salam Academy Original Practice · Proposed mark scheme

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