CIE IGCSE Maths: Extended

Topic Questions

IGCSEMaths: ExtendedCIETopic Questions2. Algebra & Graphs2.7 Simultaneous Equations

Syllabus Edition

First teaching 2021

Last exams 2024

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2.7 Simultaneous Equations

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1
Sme Calculator4 marks

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

table attributes columnalign right center left columnspacing 0px end attributes row cell 6 x plus 5 y end cell equals 27 row cell 5 x minus 3 y end cell equals 44 end table
 

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.
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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4
Sme Calculator5 marks

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

y space equals space 5 x squared space plus space 4 x space minus space 19 y space equals space 4 x space plus space 1

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

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

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5
Sme Calculator5 marks

Solve the equations

x squared plus y squared equals 36

x equals 2 y plus 6

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6
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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7
Sme Calculator5 marks

Solve algebraically the simultaneous equations

x squared plus y squared equals 25 y minus 2 x equals 5

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1
Sme Calculator2 marks

Solve the simultaneous equations.

2 x space plus space y space equals space 7 3 x space minus space y space equals space 8

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

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

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2
Sme Calculator3 marks

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

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x minus 8 y end cell equals 22 row cell x plus 4 y end cell equals 4 end table

x equals................................................  

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

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3
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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4
Sme Calculator3 marks

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

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 x plus 8 y end cell equals 4 row cell 1 half x plus 3 y end cell equals 7 end table
  

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

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5
Sme Calculator3 marks

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

table row cell 2 x plus 1 half y end cell equals 13 row cell 3 x plus 2 y end cell equals 17 end table


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

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1
Sme Calculator5 marks

cie-igcse-2020-oct-nov-p4-tz1-q5b


The diagram shows a curve with equation y space equals space 2 x to the power of 2 space end exponent minus space 2 x space minus 7.
The straight line with equation y space equals space 3 x space plus space 5 intersects the curve at the points A and B.

Find the coordinates of the points A and B.

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

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

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2
Sme Calculator5 marks

cie-igcse-2020-oct-nov-p4-tz1-q7

These are the first four diagrams of a sequence.
The diagrams are made from white dots and black dots.

T spaceis the total number of dots used to make all of the first  n diagrams.

T thin space equals space a n to the power of 3 space end exponent plus space b n squared 

Find the value of a and the value of b.
You must show all your working.


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

b space equals space................................................ 

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3
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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4
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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5
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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6
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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