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-VP-G012 marksL1 FoundationNon-calculatorCross product

Find the

x

-component of

\begin{pmatrix}1\\2\\3\end{pmatrix}\times\begin{pmatrix}0\\1\\4\end{pmatrix}

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SA-FP-VP-Q011 markL1 FoundationNon-calculatorCross product

The vector

\mathbf a\times\mathbf b

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SA-FP-VP-X011 markL1 FoundationNon-calculatorCross product

Find the

\mathbf k

-component of

\mathbf i\times\mathbf j

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SA-FP-VP-0012 marksL2 StandardNon-calculatorPlanes

The plane through

(1,2,3)

with normal

\begin{pmatrix}2\\-1\\1\end{pmatrix}

2x-y+z=d

. Find

d

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SA-FP-VP-0023 marksL2 StandardNon-calculatorIntersections

Find the

x

-coordinate where

\mathbf r=\begin{pmatrix}1\\0\\2\end{pmatrix}+t\begin{pmatrix}1\\1\\1\end{pmatrix}

meets

x+2y+z=11

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SA-FP-VP-X022 marksL2 StandardNon-calculatorCross product

Find the

\mathbf i

-component of

(\mathbf i+2\mathbf j+3\mathbf k)\times(4\mathbf i+5\mathbf j+6\mathbf k)

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SA-FP-VP-X032 marksL2 StandardNon-calculatorPlanes

The plane through

(1,2,3)

with normal

2\mathbf i-\mathbf j+\mathbf k

2x-y+z=d

. Find

d

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SA-FP-VP-X042 marksL2 StandardNon-calculatorIntersections

The line

\mathbf r=t(\mathbf i+\mathbf j+\mathbf k)

meets the plane

x+y+z=6

. Find

t

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SA-FP-VP-0033 marksL3 ExamCalculatorIntersections

Find the acute angle between the line with direction

\begin{pmatrix}1\\1\\1\end{pmatrix}

and the plane

x+2y+z=5

, in degrees to 1 d.p.

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SA-FP-VP-0043 marksL3 ExamCalculatorCross product

Find the area of the triangle formed by vectors

\mathbf a=\begin{pmatrix}2\\1\\0\end{pmatrix}

and

\mathbf b=\begin{pmatrix}1\\3\\2\end{pmatrix}

from a common vertex (to 3 s.f.).

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SA-FP-VP-X052 marksL3 ExamCalculatorIntersections

Find, in degrees, the acute angle between the planes

x=0

and

x+y=0

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SA-FP-VP-0054 marksL4 ChallengingNon-calculatorIntersections

The line of intersection of

x+y+z=6

and

x-y+2z=5

has direction

\begin{pmatrix}3\\b\\c\end{pmatrix}

. Find

b

and

c

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