CAIE IGCSE Mathematics Extended 7 Transformations and Vectors Topic Practice

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Covered syllabus points

E7.1 TransformationsE7.2 Vectors in two dimensionsE7.3 Magnitude of a vectorE7.4 Vector geometry

Question 1

[Maximum number: 5]
Figure for Question 1 — CAIE IGCSE Mathematics Extended

Question (a)

(a)

On the diagram, draw the image of

[ 5 ]

Question (i)

(i)

shape A after a translation by the vector (1−7)\binom{1}{-7}

[ 2 ]

Question (ii)

(ii)

shape A after a reflection in the line y=x+1.

[ 3 ]

Question 2

[Maximum number: 1]
Figure for Question 2 — CAIE IGCSE Mathematics Extended

Write AB→\overrightarrow{AB} as a column vector.
AB→=(   )\overrightarrow{AB}=\begin{pmatrix}\ \ \\ \ \end{pmatrix}

Question 3

[Maximum number: 5]

F is the point (1,-4), FG→=(8−3)\overrightarrow{FG}=\binom{8}{-3} and GH→=(−1235)\overrightarrow{GH}=\binom{-12}{35}.
Find

Question (a)

(a)

3FG→3\overrightarrow{FG}

[ 1 ]

Question (b)

(b)

FG→+GH→\overrightarrow{F G}+\overrightarrow{G H}

[ 1 ]

Question (c)

(c)

the coordinates of the point G

[ 1 ]

Question (d)

(d)

the magnitude of vector GH→\overrightarrow{G H}.

[ 2 ]

Question 4

[Maximum number: 6]

The diagram shows triangle OPT.

Figure for Question 4 — CAIE IGCSE Mathematics Extended

NOT TO
SCALE

In the diagram OT→=t\overrightarrow{O T}=\mathbf{t} and OP→=p\overrightarrow{O P}=\mathbf{p}.
O K: K T=2: 1 and T L: L P=2: 1.

Question (a)

(a)

Find, in terms of t and p, in its simplest form

[ 4 ]

Question (i)

(i)

PL→\overrightarrow{P L}

[ 2 ]

Question (ii)

(ii)

KL→\overrightarrow{K L}.

[ 2 ]

Question (b)

(b)

KL is extended to the point M.
KM→=−23t+43p\overrightarrow{K M}=-\frac{2}{3} \mathbf{t}+\frac{4}{3} \mathbf{p}.

Show that M lies on OP extended.

[ 2 ]
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