IGCSE Mathematics · 0580

IGCSE Mathematics: Quadratic Equations Practice Questions

Quadratics appear on every IGCSE Maths paper. These worked solutions show solving by factorising, using the quadratic formula when factorising fails, and handling the simple square-root case.

What you need to know

A quadratic equation has the form a x squared plus b x plus c equals 0.
If it factorises, set each bracket equal to zero to find the two solutions.
When it does not factorise, use the quadratic formula with the values of a, b and c.
Most quadratics have two solutions, which may be equal or, at IGCSE, sometimes only apply to real values.

Practice questions with answers

Question 13 marks

Solve x squared plus 5x plus 6 = 0 by factorising.

Find two numbers that multiply to 6 and add to 5: these are 2 and 3. So (x plus 2)(x plus 3) = 0. Setting each bracket to zero gives x = minus 2 or x = minus 3.

Mark schemeCorrect factorisation (x + 2)(x + 3) (1). Setting each bracket to zero (1). Both solutions x = -2 and x = -3 (1).

Common mistakeGiving only one solution, or getting the signs the wrong way round.

Exam tipCheck by expanding your brackets back out. It should return the original equation.

Question 24 marks

Solve 2x squared plus 3x minus 2 = 0 using the quadratic formula. Give exact answers.

Here a = 2, b = 3, c = minus 2. The formula gives x = (minus b plus or minus the square root of (b squared minus 4ac)) divided by 2a. So x = (minus 3 plus or minus the square root of (9 plus 16)) divided by 4 = (minus 3 plus or minus 5) divided by 4. This gives x = 0.5 or x = minus 2.

Mark schemeCorrect a, b, c substituted (1). Discriminant 9 + 16 = 25 (1). Simplify to (-3 +/- 5) over 4 (1). Both answers 0.5 and -2 (1).

Common mistakeSign errors with b, or forgetting the plus or minus giving only one root.

Exam tipWrite the values of a, b and c before substituting. It reduces sign slips and earns method marks.

Question 32 marks

Solve x squared = 9.

Take the square root of both sides, remembering both signs: x = plus or minus 3, so x = 3 or x = minus 3.

Mark schemex = 3 (1). x = -3 (1).

Common mistakeGiving only x = 3 and forgetting the negative solution.

Exam tipTaking a square root gives two answers. Always include the negative root.

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Frequently asked questions

What is the quadratic formula?

x equals minus b plus or minus the square root of (b squared minus 4ac), all divided by 2a, for a x squared plus b x plus c equals 0.

When should I use the quadratic formula?

Use it when the quadratic does not factorise easily, or when the question asks for answers to a number of decimal places.

How many solutions does a quadratic have?

Usually two. They can be two different values, two equal values, or in some cases the discriminant shows there are no real solutions.

How do I factorise a quadratic?

Find two numbers that multiply to give the constant term and add to give the coefficient of x, then write the two brackets.

More IGCSE Mathematics practice

Circle theorems Pythagoras theorem