IGCSEMaths: ExtendedCIETopic QuestionsAlgebra & SequencesSimultaneous Equations

Syllabus Edition

First teaching 2023

First exams 2025

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Simultaneous Equations (CIE IGCSE Maths: Extended)

Topic Questions

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1
Sme Calculator6 marks

Solve the simultaneous equations.
You must show all your working.

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 7 minus 3 y end cell row cell x squared minus y squared end cell equals 39 end table


        x equals .................... y equals ....................
x equals .................... y equals ....................

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2
Sme Calculator4 marks

Solve the simultaneous equations.
You must show all your working.

2 x plus 3 y equals negative 12 5 x plus 2 y equals 14
 

x = ................................................ 
y = ................................................ 

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3
Sme Calculator6 marks

Solve the simultaneous equations       x squared plus y squared equals 9 x plus y equals 2


Give your answers correct to 2 decimal places.

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4
Sme Calculator5 marks

Solve the equations

x squared plus y squared equals 36

x equals 2 y plus 6

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1
Sme Calculator3 marks

Solve the simultaneous equations.
You must show all your working.


1 half x minus 3 y equals 9 space space space 5 x plus y equals 28

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2
Sme Calculator4 marks

Solve the simultaneous equations     table row cell 2 x space plus space 7 y space end cell equals cell space 17 space end cell row cell 5 x space plus space 3 y space end cell equals cell space – 1 end cell end table

Show clear algebraic working.

table row cell x space end cell equals cell space.................................. end cell row cell y space end cell equals cell space.................................. space end cell end table 

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3
Sme Calculator3 marks

Solve the simultaneous equations

table row cell 5 a space plus space 2 c space end cell equals cell space 10 space end cell row cell 2 a space – space 4 c space end cell equals cell space 7 end cell end table

Show clear algebraic working.


             a space equals .......................................................       
c space equals .......................................................       

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4
Sme Calculator4 marks

Solve the simultaneous equations

table row cell 7 x space – space 2 y space end cell equals cell space 34 space end cell row cell 3 x space plus space 5 y space end cell equals cell space minus 3 end cell end table

Show clear algebraic working.

x space equals.............................................      

   y space equals.............................................      

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1
Sme Calculator6 marks

The straight line y space equals space 2 x space plus space 1 intersects the curve y space equals space x squared space plus space 3 x space – space 4 at the points A and B.

Find the coordinates of A and B.
Give your answers correct to 2 decimal places.

A ( .................... , .................... )
B ( .................... , .................... )

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2
Sme Calculator6 marks

The straight line y space equals space 3 x space plus space 2 intersects the curve y space equals space 2 x to the power of 2 space end exponent plus space 7 x space minus space 11 at two points.

Find the coordinates of these two points.
Give your answers correct to 2 decimal places.

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

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

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3
Sme Calculator7 marks

The graphs of space y equals open parentheses x minus 1 close parentheses squared space and space y equals fraction numerator 1 space over denominator 2 end fraction x plus 1 space intersect at A and B.
 
Find the length of AB.
 

AB = ................................................

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4
Sme Calculator6 marks

Solve the simultaneous equations.
You must show all your working.

table row y equals cell 4 minus x end cell row cell x squared plus 2 y squared end cell equals 67 end table
 

x equals.................... , space y equals.................... 
x equals.................... , space y equals.................... 

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5
Sme Calculator6 marks

Marco is making patterns with grey and white circular mats.
cie-igcse-2018-may-jun-1-p4-q12
The patterns form a sequence.
Marco makes a table to show some information about the patterns.

Pattern number 1 2 3 4
Number of grey mats 6 9 12 15
Total number of mats 6 10 15 21

Marco needs a total of 6 mats to make the first pattern.
He needs a total of 16 mats to make the first two patterns.
He needs a total of 1 over 6 n cubed plus a n squared plus b n mats to make the first n patterns.

Find the value of a and the value of b.

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

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