IGCSEMaths: ExtendedCIETopic QuestionsCoordinate Geometry & GraphsLinear Graphs

Syllabus Edition

First teaching 2023

First exams 2025

|

Linear Graphs (CIE IGCSE Maths: Extended)

Topic Questions

DownloadView
Easy
Medium
Hard
Easy
Medium
Hard
1
Sme Calculator3 marks

Line L is drawn on the grid below.

q3-2-13-easy-cie-igcse-maths-extended

Find the equation for the straight line L.
Give your answer in the form y space equals space m x space plus space c

How did you do?

Did this page help you?

2
Sme Calculator3 marks

On the grid, draw the graph of y space equals space 8 space minus space 2 x for values of x from negative 1 to 4

q4-2-13-easy-cie-igcse-maths-extended

How did you do?

Did this page help you?

3
Sme Calculator2 marks

The equation of a straight line is 2 y equals 3 x plus 4.

i)
Find the gradient of this line. 

 

[1]

ii)
Find the co-ordinates of the point where the line crosses the y-axis. 
 
( ..................... , ..................... ) [1]

How did you do?

Did this page help you?

1
Sme Calculator4 marks

A is the point (7, 2) and B is the point (−5, 8).

Find the equation of the line that is perpendicular to AB and that passes through the point (−1, 3).
Give your answer in the form y space equals space m x space plus space c.

y = ..............................................

How did you do?

Did this page help you?

2
Sme Calculator5 marks

A line from the point (2, 3) is perpendicular to the line y space equals 1 third x space plus space 1.
The two lines meet at the point P.

Find the coordinates of P.


( ...................... , ...................... )

How did you do?

Did this page help you?

3
Sme Calculator4 marks

A is the point left parenthesis 2 comma space 3 right parenthesis and B is the point left parenthesis 7 comma negative 5 right parenthesis.

Find the equation of the line through A that is perpendicular to AB.
Give your answer in the form y equals m x plus c.
 

y equals....................................................

How did you do?

Did this page help you?

4
Sme Calculator4 marks

P is the point (16, 9) and Q is the point (22, 24).

Find the equation of the line perpendicular to PQ that passes through the point (5, 1).
Give your answer in the form y equals m x plus c.

y equals................................................

How did you do?

Did this page help you?

5a
Sme Calculator5 marks

A rhombus A B C D has a diagonal A C where A is the point left parenthesis negative 3 comma space 10 right parenthesis and C is the point left parenthesis 4 comma space minus 4 right parenthesis.

i)
Calculate the length A C.

[3]
ii)
Show that the equation of the line A C is  y equals negative 2 x plus 4.

[2]

How did you do?

5b
Sme Calculator4 marks

Find the equation of the line B D.

How did you do?

Did this page help you?

6a
Sme Calculator4 marks

The coordinates of P are left parenthesis negative 3 comma space 8 right parenthesis and the coordinates of Q are left parenthesis 9 comma negative 2 right parenthesis.

Find the equation of the perpendicular bisector of PQ.
 

How did you do?

6b
Sme Calculator3 marks

The coordinates of P are left parenthesis negative 3 comma space 8 right parenthesis and the coordinates of Q are left parenthesis 9 comma negative 2 right parenthesis.

Find the equation of the line parallel to PQ that passes through the point left parenthesis 6 comma negative 1 right parenthesis.
 

How did you do?

Did this page help you?

7a
Sme Calculator3 marks

A straight line joins the points A (-2, -3) and C (1, 9).

Find the equation of the line A C in the form y equals m x plus c.
 

y = ..............................................

How did you do?

7b
Sme Calculator5 marks

A B C D is a kite, where A C is the longer diagonal of the kite.
B is the point (3.5, 2).

i)
Find the equation of the line B D in the form y equals m x plus c.
 
y = .............................................. [3]
ii)
The diagonals A C and B D intersect at (-0.5, 3).
 
Work out the co-ordinates of D.
 
(...................... , ....................) [2]

How did you do?

Did this page help you?

8a
Sme Calculator1 mark

q4-2-13-very-hard-cie-igcse-maths-extended

Figure 1

The line l subscript 1 has equation 2 x space minus space 3 y space plus space 12 space equals space 0
Find the gradient of l subscript 1.

How did you do?

8b
Sme Calculator3 marks

The line l subscript 1 crosses the x-axis at the point A and the y-axis at the point B, as shown in Figure 1.

The line l subscript 2 is perpendicular to l subscript 1 and passes through B.

Find an equation of l subscript 2.

How did you do?

8c
Sme Calculator3 marks

The line l subscript 2 crosses the x-axis at the point C.

Find the area of triangle ABC.

How did you do?

Did this page help you?

1a
Sme Calculator2 marks

A straight line, l, has equation y equals 5 x plus 12.

Find the coordinates of the point where line l crosses the x-axis.
 

( ....................... , ......................)

How did you do?

1b
Sme Calculator1 mark

A line perpendicular to line l has gradient k.
 
Find the value of k.
 

k equals................................................

How did you do?

Did this page help you?

2
Sme Calculator2 marks

cie-igcse-2020-may-jun-p4-tz2-q9ci

On the diagram,

Sketch the graph of space y equals 1 half x plus 1.

How did you do?

Did this page help you?

3
Sme Calculator3 marks

A line joins A left parenthesis 1 comma space 3 right parenthesis to B left parenthesis 5 comma space 8 right parenthesis.

Find the equation of the line A B.

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

 

y = ...................................................

How did you do?

Did this page help you?