Revision NotesExam QuestionsTarget TestPast Papers
GCSEFurther MathsAQAExam Questions3. Coordinate GeometryCoordinate Geometry & Straight Lines

Coordinate Geometry & Straight Lines (AQA GCSE Further Maths): Exam Questions

58 mins19 questions
Medium
Hard
Very Hard
1
Sme Calculator3 marks

A sketch of the lines  y equals 2 x and  y equals 6 is shown.

q1-paper2-spec2020-aqa-gcse-furthermaths

Work out the area of triangle O P Q.

.................................. units2

How did you do?

2
Sme Calculator2 marks

M is the midpoint of the line A B.

q3-paper2-spec2020-aqa-gcse-furthermaths

Work out the values of p and r.

p space equals ............................ r space equals ............................

How did you do?

3
Sme Calculator3 marks

Work out the equation of the straight line that is parallel to the line  2 y equals x and intersects the x-axis at left parenthesis 4 comma space 0 right parenthesis.

How did you do?

4
Sme Calculator2 marks

Work out the distance between the points A left parenthesis – 3 comma space 7 right parenthesis andspace B spaceleft parenthesis 5 comma space 1 right parenthesis

........................ units

How did you do?

5
Sme Calculator1 mark

Here are four sketch graphs.

Circle the letter of the sketch graph that represents  3 x space plus space 2 y space equals space 5

q3-paper1-nov2021-aqa-gcse-furthermaths

How did you do?

6
Sme Calculator3 marks

A straight line passes through the points space left parenthesis negative 2 comma space 11 right parenthesis and left parenthesis 1 comma space 2 right parenthesis

Work out the equation of the line.

Give your answer in the form y equals m x plus c

How did you do?

7
Sme Calculator3 marks

P is the point left parenthesis negative 12 comma space b right parenthesis
Q is the point left parenthesis a comma space 4 right parenthesis
R is the point left parenthesis 6 comma space minus 2 right parenthesis

Q is the midpoint of P R.

Work out the values of a and b.

a space equals  .......................... b space equals ..........................

How did you do?

8a
Sme Calculator1 mark

L is a straight line with equation   a x plus b y equals c where a comma space b and c are non-zero integers.

At which point does L intersect the x-axis?

Circle your answer.

open parentheses a over c comma 0 close parentheses

open parentheses c over a comma 0 close parentheses

open parentheses b over c comma 0 close parentheses

open parentheses c over b comma 0 close parentheses

How did you do?

8b
Sme Calculator1 mark

What is the gradient of a line parallel to L?

Circle your answer.

negative b over a

b over a

negative a over b

a over b

How did you do?

9
Sme Calculator4 marks

Work out the point of intersection of the lines

2 x plus 3 y equals 11 and   2 y equals 13 minus 3 x

How did you do?

10
Sme Calculator3 marks

A triangle has vertices A open parentheses 2 comma space 5 close parentheses ,  B open parentheses 2 comma space 0 close parentheses   and   C open parentheses negative 4 comma space 3 close parentheses

Work out the area of triangle A B C.

You may use the grid to help you.

qp1-2016-paper-2-aqa-gcse-further-maths

............................ square units

How did you do?

1
Sme Calculator4 marks

A B C spaceis a straight line with A B colon B C equals 5 colon 2

q4-paper1-spec2018-aqa-gcse-furthermaths

Work out the coordinates of C.

How did you do?

2
Sme Calculator4 marks

A B C is a straight line.

A is the pointspace left parenthesis negative 4 comma space 5 right parenthesis
C is the point space left parenthesis 20 comma space minus 7 right parenthesis space
A B colon B C equals 5 colon 3

qp8-2019-paper-1-aqa-gcse-further-maths

Work out the coordinates of B.

How did you do?

3
Sme Calculator3 marks

Here is a sketch of quadrilateral P Q R S.

M is the midpoint of P S.

qp2-2019-paper-2-aqa-gcse-further-maths

Use gradients to show that M R is parallel to P Q.

How did you do?

4
Sme Calculator2 marks

P space left parenthesis – 3 comma space – 10 right parenthesis and Q space open parentheses a comma space b close parentheses space are points on a straight line with gradient 12

Work out one possible pair of integer values for a and b.

a space equals..................  b space equals....................

How did you do?

5
Sme Calculator3 marks

A open parentheses 1 1 fifth comma space 3 4 over 5 close parentheses comma space B open parentheses 2 comma 1 4 over 5 close parentheses and C open parentheses 5 comma 3 close parentheses are points on a coordinate grid.

Show that the line segments A B and B C are perpendicular.

How did you do?

6
Sme Calculator3 marks

D open parentheses negative 6 comma space 4 close parentheses and E open parentheses negative 2 comma space 9 close parentheses are joined by a straight line.

P is a point on D E.

D P space colon space P E space equals space 3 colon 5

Work out the coordinates of P.

How did you do?

1
Sme Calculator5 marks

A and space B spaceare points on the line y equals 3 x plus 2

B comma space C spaceand D (5, 0) are points on the line L.

space O A colon A C equals 1 colon 4 space

q12-paper2-nov2021-aqa-gcse-furthermaths

Work out the x-coordinate of B.

How did you do?

2
Sme Calculator4 marks

In the diagram,

A is the point left parenthesis 15 comma space 0 right parenthesis and B lies on the y-axis.

Anglespace A B C space equals space 90 degree and tan theta = 5 over 3

qp12-2018-paper-1-aqa-gcse-further-maths

Work out the equation of the line B C.

How did you do?

3
Sme Calculator4 marks

Here is a sketch of triangle ABC.

P is a point on AB.

q8-2018-paper-2-aqa-gcse-further-maths

AP : PB is 3 : 1

Work out the length PC.

Give your answer to 4 significant figures.

 ................................ units

How did you do?