AQA GCSE Maths
Topic questions Pure mathematics Vectors in geometry
36 questions · 90 marks · about 1.5 hours
Write down the translation vector that maps shape A to shape B.
Describe fully a rotation that maps A to B.
ABCD is a quadrilateral. AC and BD intersect at P.
BP: PD = 3: 2 AP: PC = 1: k
Work out the value of k. You must show your working.
Write down the vector that translates B to A.
Write down the vector that translates B to A.
Prove that DEF is a straight line.
PQRS is a quadrilateral. PQ is not parallel to SR. X is a point on QR. QX: XR = 2: 3 
QX
= 2a + 4b
Prove that PQRS is a trapezium.
Also involves Vector arithmetic
m
4
15 a = 
b = 
3 
p 
The diagram shows the vector 2 a + b
Work out the values of m and p.
Write down the translation vector that maps shape A onto shape B .
Write down the translation vector that maps shape A onto shape B .
The diagram shows the vectors a and b.
What is b as a column vector?
Work out 4 a as a column vector.
Work out c as a column vector. Circle your answer.
The diagram shows the vectors a and b.
What is b as a column vector?
Work out 4 a as a column vector.
Work out c as a column vector. Circle your answer.
Two congruent parallelograms, PQRV and VRST, are joined.
X is the midpoint of VT. VW: WR = 1: 2 Prove that Q, W and X lie on a straight line.
Triangles ABC and DEF are shown on a grid.
Describe a single transformation that shows the triangles are congruent.
Work out the vector that translates shape A to shape B.
Five points are connected by vectors.
Work out 
FE
in terms of a and b.
Circle your answer.
Circle the vector that translates the point (โ 2, 7) to the point (3, โ 1)
Also involves Ratio
In the diagram
EX: XH = 3: 1 EF: FG = 1: 3
Is DXF a straight line? Show working to support your answer.
Here is a parallelogram.
The parallelogram is translated 4 squares to the left and 3 squares up. Draw the translated parallelogram.
Here is vector a.
Circle the column vector that represents a.
Also involves Ratio
In triangle JKL M is the midpoint of JK JN: NL = 3: 2
Work out 
JM
in terms of a and b. Give your answer in its simplest form.
3
1 
17 a = 
and b = 
2 
5
Work out a โ 3 b Circle your answer.
2
5 
30 a = 
b = 
7
2
Work out 3 a + b
Also involves Forming and solving equations ยท Similarity, lengths, areas and volumes
ABC and ACD are triangles. k is a constant.
Show that 
CD
= 6a + 4.5b
BCD is a straight line. Work out the value of k. You must show your working.
Vectors a and b are drawn on a grid.
Write b in terms of a.
Vectors c and d are drawn on a grid.
On the grid above, draw a vector representing c โ d
Also involves Vectors
Line AB is shown on the grid. A is the point (0, 2)
Work out the coordinates of the midpoint of the line AB.
C is another point on AB. C is closer to B than to A. The coordinates of C are whole numbers. Work out the coordinates of C.
On the grid, draw a line from point (0, 0) that is parallel to AB and two thirds as long as AB.
PQR is a straight line. PQ: QR = 3: 1 
PQ
= a Not drawn accurately
Circle the vector 
RQ
In which direction does the shape move? Circle your answer.
up down left right
Also involves Transformations
In which direction does the shape move? Circle your answer.
up down left right
Circle the vector that translates B to A.
Also involves Vector arithmetic
6 
โ1
โ4 30 a = 
b = 
c = 
โ10
2 
7
Work out a + b + c
Show that a + 2 c = k b, where k is an integer.
6 
โ1
โ4
11 a = 
b = 
c = 
โ10 
2 
7 
Work out a + b + c
Show that a + 2 c is parallel to b
4
3 
1 a = 
and b = 
1
1
Circle the vector 2 a + b
Memes
Laugh now. Cry in the exam hall later. Then come back and do a past paper.
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