IGCSEMaths: ExtendedCIETopic Questions2. Algebra & Graphs2.13 Linear Graphs

Syllabus Edition

First teaching 2021

Last exams 2024

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Linear Graphs (CIE IGCSE Maths: Extended)

Topic Questions

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1
Sme Calculator3 marks

The equation of line L is space 3 x minus 8 y plus 20 equals 0.

i)

Find the gradient of line L.
 

[2]

ii)

Find the coordinates of the point where line L cuts the y-axis.
 

( ................... , ................... ) [1]

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2
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Write down the function shown in the graph.

cie-igcse-2020-may-jun-p4-tz3-q10ai 

straight f open parentheses x close parentheses equals..............................................

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3a
Sme Calculator6 marks

The diagram shows a straight line L.

cie-igcse-2019-may-jun-p4-tz2-q4b

Find the equation of line L.

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3b
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Find the equation of the line perpendicular to line L that passes through left parenthesis 9 comma 3 right parenthesis.

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4
Sme Calculator2 marks

cie-igcse-2018-oct-nov-p4-tz1-q8a

Write down the equation of the line parallel to line l that passes through the point B.

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5
Sme Calculator3 marks

Find the equation of the straight line that is perpendicular to the line  y equals 1 half x plus 1  and passes through the point left parenthesis 1 comma space 3 right parenthesis.

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6a
Sme Calculator4 marks

The point P has co-ordinates open parentheses 10 comma space 12 close parentheses and the point Q has co-ordinates open parentheses 2 comma negative 4 close parentheses.
 
Find

i)

the co-ordinates of the mid-point of the line PQ,
 

(....................... , .......................) [2]

ii)

the gradient of the line PQ,
 

 [2]

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6b
Sme Calculator3 marks

Find the equation of a line perpendicular to PQ that passes through the point open parentheses 2 comma space 3 close parentheses.

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1
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The line space y equals 3 x minus 2 space crosses the y-axis at G.
 
Write down the coordinates of G.
 

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

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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.

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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]

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4a
Sme Calculator2 marks

cie-igcse-2018-oct-nov-p4-tz3-q1b

B is the  mid-point of the line A C.
 

Find the co-ordinates of C.

 

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

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4b
Sme Calculator3 marks

Find the equation of the straight line that passes through A and B.

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4c
Sme Calculator1 mark

The straight line that passes through Aand B cuts the y-axis at D.

 

Write down the co-ordinates of D.

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

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5
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 = ...................................................

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6
Sme Calculator3 marks

cie-igcse-2018-oct-nov-p4-tz1-q8a 

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

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

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1a
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]

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1b
Sme Calculator4 marks

Find the equation of the line B D.

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2
Sme Calculator3 marks

cie-igcse-2018-oct-nov-p4-tz1-q8aC is the point (8, 14).

Write down the equation of the line perpendicular to line l that passes through the point C.

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3a
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 = ..............................................

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3b
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]

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4a
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.
 

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4b
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.
 

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5a
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.

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5b
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.

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5c
Sme Calculator3 marks

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

Find the area of triangle ABC.

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