Quadratic Equations (Cambridge International IGCSE Maths): Exam Questions

Solve $6x^{2}-7x+2=0.$ You must show all your working.

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

Use the quadratic formula to solve $9x^{2}-12x-23=0$. Give your answers correct to 2 decimal places.

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

Solve the equation $3x^{2}-2x-10=0.$ Show all your working and give your answers correct to 2 decimal places.

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

Use the quadratic formula to solve the equation $3x^{2}+7x-11=0.$ You must show all your working and give your answers correct to 2 decimal places.

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

Solve the equation $3x^{2}-2x-2=0$. Show all your working and give your answers correct to 2 decimal places.

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

Solve the equation $6m^{2}+25m+16=0$. Show all your working and give your answers correct to 2 decimal places.

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

Solve the equation $2x^{2}+7x-3=0$.

Show all your working and give your answers correct to 2 decimal places.

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

Nina runs 5 km at $y$ km/h and then walks 7 km at $( y - 7 )$ km/h. She takes a total of 2 hours.

Show that $2y^{2}-26y+35=0$.

Solve $2y^{2}-26y+35=0$.

$y=$.................. or $y=$ ..................

Extract:

Nina runs 5 km at ![y] km/h and then walks 7 km at ![open parentheses y minus 7 close parentheses] km/h.

Find Nina's walking speed

........................................ km/h

Solve by factorisation.

$3x^{2}-11x+6=0$

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

The $n$th term of a sequence is $4n^{2}+n+3.$ Find the value of $n$ when the $n$th term is 498.

$n=$..................................................

Solve by factorisation $10m^{2}-31m-14=0$.

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

Find all the solutions to the equation.

$( x^{2} - 4 x + 4 )^{( x^{2} - 9 x + 20 )} = 1$

Solve $2x^{2}+9x-7=0$

You must show all your working and give your solutions correct to 3 significant figures.

Extract:

Solve ![2 x squared plus 9 x minus 7 equals 0]

You must show all your working and give your solutions correct to 3 significant figures.

Use your answer to part (a) to solve $\frac{2}{y^{2}}+\frac{9}{y}-7=0$ Give your solutions correct to 3 significant figures.

The diagram shows a trapezium.

All the measurements are in centimetres.

The area of the trapezium is 351 cm².

Show that $2x^{2}+x-351=0$

Extract:

2 x squared plus x minus 351 equals 0

Work out the value of $x$.