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Quadratic Equations (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

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Quadratic Equations

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1
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Solve x squared minus 2 x minus 6 equals 0.

Give your answer in the form a plus-or-minus square root of b where a and b are integers.

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2
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Factorise.

1 plus x minus y minus x y

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3a
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Write space 6 x squared space – 7 x minus 3 space in the form space open parentheses 2 x plus a close parentheses open parentheses 3 x plus b close parentheses, where a and b are integers.

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3b
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Hence, or otherwise, solve space 6 x squared minus 7 x minus 3 equals 0.

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4
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Solve.

6 x squared minus 5 x minus 6 equals 0

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

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5
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Solve.

8 x squared minus 2 x minus 3 equals 0

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

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1
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The solutions to the equation space x squared plus g x plus h equals 0 are fraction numerator 1 minus square root of 17 over denominator 2 end fraction and fraction numerator 1 plus square root of 17 over denominator 2 end fraction.

Find the value of gand the value of h.

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2
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Solve by factorisation 10 r squared minus 23 r plus 9 equals 0.    

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

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3
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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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1
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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
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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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3
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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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