CAMBRIDGE IGCSE MATHS (0580)

Question 1:
Solve the equation \( 2x^2 + 6x - 3 = 0 \)
Show your working and give your answers correct to 2 decimal places.

Question 2:
Simplify fully:
\( \frac{x^2 - x - 20}{x^3 - 10x^2 + 25x} \)

Question 3:
Simplify the following:
\( \frac{h^2 - h - 20}{h^2 - 25} \)

Question 4:
a) Factorise \( x^2 + x - 30 \)
b) Simplify \( \frac{(x - 5)(x + 4)}{x^2 + x - 30} \)

Question 5:
Use the quadratic equation formula to solve:
\( 2x^2 + 7x - 3 = 0 \)
Show all your working and give your answer correct to 2 decimal places.

Question 6:
The solutions of the equation \( x^2 - 6x + d = 0 \) are both integers. \( d \) is a prime number.
Find \( d \).

Question 7:
Simplify:
\( \frac{x^2 + 6x - 7}{3x + 21} \)

Question 8:
a) Factorise \( 3x^2 + 2x - 8 \)
b) Solve the equation \( 3x^2 + 2x - 8 = 0 \)

Question 9:
Simplify:
\( \frac{4x^2 - 16x}{2x^2 + 6x - 56} \)

Question 10:
Factorise \( 2x^2 - 5x - 3 \)

Question 11:
\( f(x) = x^2 + 4x - 6 \)
\( f(x) \) can be written in the form \( (x + m)^2 + n \).
Find the value of \( m \) and the value of \( n \).

Question 12:
Use your answer to Question 11 to find the positive solution to \( x^2 + 4x - 6 = 0 \).

Question 13:
Solve the equation:
\( 2x^2 + x - 2 = 0 \)
Show your working and give your answer correct to 2 decimal places.

Question 14:
Simplify:
\( \frac{x^2 - 16}{x^2 - 3x - 4} \)

Question 15:
Solve the equation:
\( 5x^2 - 6x - 3 = 0 \)
Show all your working and give your answers correct to 2 decimal places.

Question 16:
Solve the equation:
\( 3x^2 + 4x - 5 = 0 \)
Show all your working and give your answers correct to 2 decimal places.

Question 17:
Simplify:
\( \frac{4 + 10w}{8 - 50w^2} \)

Question 18:
\( y = x^2 + 7x - 5 \) can be written in the form:
\( y = (x + a)^2 + b \)
Find the value of \( a \) and the value of \( b \).

Question 19:
Solve the equation:
\( 2x^2 + 3x - 3 = 0 \)
Show all your working and give your answers correct to 2 decimal places.

Question 20:
Factorise:
a) \( m^3 + m \)
b) \( 25 - y^2 \)
c) \( x^2 + 3x - 28 \)

Question 21:
Write as a single fraction in its simplest form:
\( \frac{x^2 - 3x}{x^2 - 9} \)

Question 22:
Solve the equation:
\( 5x^2 + 10x + 2 = 0 \)
Show all your working and give your answers correct to 2 decimal places.

Question 23:
Factorise completely:
a) \( x^2 - x - 132 \)
b) \( x^3 - 4x \)

Question 24:
Use the quadratic formula to solve the equation:
\( 3x^2 + 7x - 11 = 0 \)
Show all your working and give your answers correct to 2 decimal places.

Question 25:
\( x^2 - 12x + a = (x + b)^2 \)
Find the values of \( a \) and \( b \).

Question 26:
Solve the equation:
\( 3x^2 - 2x - 2 = 0 \)
Show all your working and give your answers correct to 2 decimal places.