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Linear Graphs (Cambridge O Level Maths)

Exam Questions

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Linear Graphs

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Linear Graphs

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1
Sme Calculator1 mark

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

Write down the gradient of line l.

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2
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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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3a
Sme Calculator1 mark

Find the co-ordinates of the point where the line y equals 3 x minus 8 crosses the y-axis.
 

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

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3b
Sme Calculator1 mark

Write down the gradient of the line y equals 3 x minus 8.

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4
Sme Calculator3 marks

The line L is shown on the grid.

q5-2-13-easy-cie-igcse-maths-extended

Find an equation for L.

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5a
Sme Calculator2 marks

The equation of line P is space 5 x space plus space 2 y space equals space 13 space.

The equation of line Q is y space equals space 2 x space – space 7.

Find the gradient of line P.

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5b
Sme Calculator2 marks

Find the coordinates of the point of intersection of line space Q spacewith the x-axis.

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1
Sme Calculator2 marks

Find the gradient of a line that is perpendicular to 8 y space plus space 4 x space equals space 5.

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2
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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3
Sme Calculator2 marks

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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4
Sme Calculator1 mark

Sketch the graph of the function.

y equals x minus 3



cie-igcse-2020-march-p2-tz2-q10a-b

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5
Sme Calculator3 marks

Show that the line  4 y equals 5 x minus 10  is perpendicular to the line  5 y plus 4 x equals 35.

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6
Sme Calculator2 marks

Find the gradient of the line that is perpendicular to the line  2 y equals 3 plus 5 x.

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7
Sme Calculator3 marks

Line L passes through the points left parenthesis 0 comma negative 3 right parenthesis and left parenthesis 6 comma 9 right parenthesis.

Find the equation of line L.

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8
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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9a
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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9b
Sme Calculator3 marks

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

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9c
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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1
Sme Calculator4 marks

A is the point left parenthesis 3 comma space 5 right parenthesis and B is the point left parenthesis 1 comma space minus 7 right parenthesis.
Find the equation of the line perpendicular to A B that passes through the point A.
Give your answer in the form y equals m x plus c.


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

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2
Sme Calculator2 marks

Find the equation of the line that is perpendicular to the line y equals 2 x minus 3 and passes through the point left parenthesis 0 comma space 2 right parenthesis.

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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
Sme Calculator3 marks

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 Calculator4 marks

cie-igcse-2018-oct-nov-p2-tz2-q17

The diagram shows the points C(–1, 2) and D(9, 7).

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

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

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6
Sme Calculator3 marks

The line PQ has equation y equals 3 x minus 8 and point P has co-ordinates (6, 10).

Find the equation of the line that passes through P and is perpendicular to PQ.
Give your answer in the form y equals m x plus c.

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

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7
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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8a
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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8b
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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9
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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