CIE IGCSE Maths: Extended

Topic Questions

IGCSEMaths: ExtendedCIETopic Questions2. Algebra & Graphs2.5 Quadratic Equations

Syllabus Edition

First teaching 2021

Last exams 2024

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2.5 Quadratic Equations

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1
Sme Calculator2 marks

Write  x squared plus 10 x plus 14  in the form  open parentheses x plus a close parentheses squared space plus b.

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2
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i)

Write x squared plus 8 x minus 9 space in the form space open parentheses x plus k close parentheses squared plus h.
 

[2]

ii)

Use your answer to part (i) to solve the equation space x squared plus 8 x minus 9 equals 0.
 

x equals................... or x equals................... [2]

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3a
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Write space x squared minus 18 x minus 27 space in the form space open parentheses x plus k close parentheses squared plus h.

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3b
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Use your answer to part (a) to solve the equation space x squared minus 18 x minus 27 equals 0.
 

x equals.................... or x equals....................

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4
Sme Calculator3 marks

x squared plus 4 x minus 9 equals left parenthesis x plus a right parenthesis squared plus b

Find the value of a and the value of b.
 

  a = ............................................
b = ............................................

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5
Sme Calculator3 marks

Solve by factorisation 10 r squared minus 23 r plus 9 equals 0. 
  

r = ................... or r = ................... 

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6
Sme Calculator3 marks

Solve  10 m squared plus 9 m minus 162 equals 0. 

 

 

m = .................... or m = .................... 

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7
Sme Calculator3 marks

x squared minus 12 x plus a equals left parenthesis x plus b right parenthesis squared
 
Find the value of a and the value of b.
 

a = ...............................................
b = ...............................................

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8
Sme Calculator3 marks

The nth term of a sequence is space 4 n squared plus n plus 3.

Find the value of n when the nth term is 498.
 

n equals.................................................. 

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1
Sme Calculator4 marks

Use the quadratic formula to solve 9 x squared minus 12 x minus 23 equals 0.
Give your answers correct to 2 decimal places.


x equals ............................ or x equals ............................

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2
Sme Calculator4 marks

Solve the equation 3 x squared minus 2 x minus 10 equals 0.
Show all your working and give your answers correct to 2 decimal places. 
 

x = ..................... or x = ..................... 

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3
Sme Calculator4 marks

Use the quadratic formula to solve the equation  3 x squared plus 7 x minus 11 equals 0.
You must show all your working and give your answers correct to 2 decimal places.
 

x = .................... or x = ....................

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4
Sme Calculator4 marks

Solve the equation  3 x squared minus 2 x minus 2 equals 0.
Show all your working and give your answers correct to 2 decimal places.
 

x = ........................... or x = ........................... 

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5
Sme Calculator4 marks

Solve the equation 6 m squared plus 25 m plus 16 equals 0.
Show all your working and give your answers correct to 2 decimal places.


m equals ..................... or m equals..................... 

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6
Sme Calculator4 marks

Solve the equation 2 x squared plus 7 x minus 3 equals 0.
Show all your working and give your answers correct to 2 decimal places.


x = ..................... or x = ..................... 

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1
Sme Calculator3 marks

The solutions of the equation space x squared plus b x plus c equals 0 space are fraction numerator negative 7 plus square root of 61 over denominator 2 end fraction and fraction numerator negative 7 minus square root of 61 over denominator 2 end fraction.
 
Find the value of b and the value of c.
 

b equals ................................................  
c equals ................................................  

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2
Sme Calculator7 marks

cie-igcse-2019-may-jun-p4-tz1-q7b 
The difference between the areas of the two rectangles is 62 cm2.

i)
Show that x squared plus 2 x minus 63 equals 0.
 
[3]
ii)
Factorise x squared plus 2 x minus 63.
 
[2]
iii)
Solve the equation x squared plus 2 x minus 63 equals 0 to find the difference between the perimeters of the two rectangles.
 
.............................................. cm [2]

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3a
Sme Calculator3 marks

Solve 2 x squared plus 9 x minus 7 equals 0

Give your solutions correct to 3 significant figures.

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3b
Sme Calculator2 marks

Solve        2 over y squared plus 9 over y minus 7 equals 0
Give your solutions correct to 3 significant figures.

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4
Sme Calculator5 marks

Given that

2 x minus 1 space colon space x minus 4 equals 16 x plus 1 space colon space 2 x minus 1

find the possible values of x.

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5a
Sme Calculator2 marks

The diagram shows a trapezium.

q5-veryhard-2-5-quadratic-equations-cie-igcse-maths-extended

All the measurements are in centimetres.

The area of the trapezium is 351 cm2.

Show that  2 x squared plus x minus 351 equals 0

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5b
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Work out the value of x.

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6
Sme Calculator5 marks

q6-veryhard-2-5-quadratic-equations-cie-igcse-maths-extended

The lengths of the sides are in centimetres.
The area of triangle T1 is equal to the area of triangle T2.
Work out the value of x, giving your answer in the form a plus square root of b where a and b are integers.

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