IGCSEMaths: ExtendedCIEExam QuestionsCoordinate Geometry & GraphsLinear Graphs

Syllabus Edition

First teaching 2023

First exams 2025

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Linear Graphs (CIE IGCSE Maths: Extended)

Exam Questions

2 hours36 questions

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Linear Graphs

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Linear Graphs

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1
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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

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2
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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

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3
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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]

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1a
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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.
 

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

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1b
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A line perpendicular to line l has gradient k.
 
Find the value of k.
 

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

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2
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cie-igcse-2020-may-jun-p4-tz2-q9ci

On the diagram,

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

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3
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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 = ...................................................

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1
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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 = ..............................................

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2
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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.


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

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3
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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....................................................

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4
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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................................................

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5a
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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]

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5b
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Find the equation of the line B D.

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6a
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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.
 

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6b
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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.
 

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7a
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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 = ..............................................

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7b
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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]

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8a
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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.

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8b
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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.

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8c
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The line l subscript 2 crosses the x-axis at the point C.

Find the area of triangle ABC.

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