Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

TopicSkillDifficulty

12 questions

SA-FP-CE-0011 markL1 FoundationNon-calculatorEccentricity

For the same ellipse, find the positive

x

-coordinate of a focus.

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SA-FP-CE-Q011 markL1 FoundationNon-calculatorEccentricity

A conic with eccentricity

1.5

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SA-FP-CE-X021 markL1 FoundationNon-calculatorEccentricity

Find the positive

x

-coordinate of a focus of

\frac{x^2}{16}+\frac{y^2}9=1

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SA-FP-CE-X051 markL1 FoundationNon-calculatorParametric forms

The ellipse

(5\cos\theta,3\sin\theta)

is at the point with

\theta=\frac\pi2

. Find

y

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SA-FP-CE-0021 markL2 StandardNon-calculatorEccentricity

For the same ellipse, find the positive directrix

x=k

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SA-FP-CE-0032 marksL2 StandardNon-calculatorParametric forms

Find the positive gradient of the asymptotes of

\frac{x^2}{16}-\frac{y^2}9=1

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SA-FP-CE-G012 marksL2 StandardNon-calculatorEccentricity

Find the eccentricity of

\frac{x^2}{25}+\frac{y^2}9=1

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SA-FP-CE-X012 marksL2 StandardNon-calculatorEccentricity

Find the eccentricity of

\frac{x^2}{16}+\frac{y^2}9=1

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SA-FP-CE-X032 marksL2 StandardNon-calculatorEccentricity

Find the eccentricity of the hyperbola

\frac{x^2}9-\frac{y^2}{16}=1

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SA-FP-CE-X041 markL2 StandardNon-calculatorEccentricity

For the same hyperbola, the positive directrix is

x=k

. Find

k

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SA-FP-CE-0043 marksL3 ExamNon-calculatorTangents

Find the

x

-intercept of the tangent to

\frac{x^2}{25}+\frac{y^2}9=1

\left(3,\frac{12}5\right)

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SA-FP-CE-0052 marksL3 ExamNon-calculatorEccentricity

A point

P

moves on

\frac{x^2}{25}+\frac{y^2}9=1

. Find the sum of its distances to the two foci.

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