Algebra Worked Examples for IGCSE Maths
Working through solved examples is one of the most effective ways to master algebra in IGCSE Mathematics. These worked examples, curated by Teacher Rig, cover the most common question types you will e
Working through solved examples is one of the most effective ways to master algebra in IGCSE Mathematics. These worked examples, curated by Teacher Rig, cover the most common question types you will encounter in the Cambridge IGCSE 0580 exam. Each solution shows every step of working with clear explanations of the reasoning behind each step.
Example 1: Solving a quadratic by factorising
Question
Solve x squared + 5x - 14 = 0.
Solution
- 1
Find two numbers that multiply to -14 and add to +5
Factors of -14: (7, -2) since 7 x (-2) = -14 and 7 + (-2) = 5
For x squared + bx + c = 0, we need two numbers that multiply to c and add to b.
- 2
Write the factorised form
(x + 7)(x - 2) = 0
Place each number into a bracket with x.
- 3
Solve each bracket
x + 7 = 0, so x = -7. Or x - 2 = 0, so x = 2.
If two things multiply to give zero, at least one must be zero.
Final Answer: x = -7 or x = 2
Exam Tip
Always check by expanding your brackets: (x+7)(x-2) = x squared -2x + 7x -14 = x squared + 5x - 14. Correct!
Example 2: Solving simultaneous equations
Question
Solve: 3x + 2y = 16 and 5x - 2y = 24.
Solution
- 1
Add the equations to eliminate y
3x + 2y + 5x - 2y = 16 + 24, so 8x = 40
Since one equation has +2y and the other -2y, adding eliminates y.
- 2
Solve for x
x = 40 / 8 = 5
Divide both sides by 8.
- 3
Substitute to find y
3(5) + 2y = 16, so 15 + 2y = 16, 2y = 1, y = 0.5
Substitute x = 5 back into either original equation.
- 4
Check in the other equation
5(5) - 2(0.5) = 25 - 1 = 24. Correct.
Always verify your answer in the equation you did not use.
Final Answer: x = 5, y = 0.5
Exam Tip
If adding does not eliminate a variable, try subtracting. If coefficients do not match, multiply one or both equations first.
Example 3: Simplifying algebraic fractions
Question
Simplify (x squared - 9) / (x squared + 5x + 6).
Solution
- 1
Factorise the numerator
x squared - 9 = (x + 3)(x - 3)
This is a difference of two squares: a squared - b squared = (a+b)(a-b).
- 2
Factorise the denominator
x squared + 5x + 6 = (x + 2)(x + 3)
Find two numbers that multiply to 6 and add to 5: that is 2 and 3.
- 3
Cancel common factors
(x + 3)(x - 3) / (x + 2)(x + 3) = (x - 3) / (x + 2)
(x + 3) appears in both numerator and denominator so it cancels.
Final Answer: (x - 3) / (x + 2)
Exam Tip
You can only cancel FACTORS, never individual terms. Always factorise completely before cancelling.
Example 4: Using the quadratic formula
Question
Solve 2x squared - 3x - 7 = 0. Give answers to 2 decimal places.
Solution
- 1
Identify a, b, c
a = 2, b = -3, c = -7
Compare with ax squared + bx + c = 0.
- 2
Substitute into the quadratic formula
x = (-b plus or minus sqrt(b squared - 4ac)) / 2a = (3 plus or minus sqrt(9 + 56)) / 4
x = (-(-3) plus or minus sqrt((-3) squared - 4(2)(-7))) / (2 times 2)
- 3
Calculate the discriminant
b squared - 4ac = 9 + 56 = 65
The discriminant tells us there are two real solutions since 65 > 0.
- 4
Find both solutions
x = (3 + sqrt(65)) / 4 = (3 + 8.062) / 4 = 11.062 / 4 = 2.77. Or x = (3 - 8.062) / 4 = -5.062 / 4 = -1.27.
Calculate each solution separately using plus then minus.
Final Answer: x = 2.77 or x = -1.27
Exam Tip
Write down the formula before substituting. Show the discriminant calculation separately. This earns method marks even if arithmetic goes wrong.
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Frequently Asked Questions
How many algebra questions appear in the IGCSE exam?
Algebra typically appears in both Paper 2 (non-calculator) and Paper 4 (calculator). You can expect 2-4 questions on algebra across both papers, worth a combined 15-25 marks depending on the session.
What is the best way to practise algebra for IGCSE?
Start by understanding the methods through worked examples like these, then practise past paper questions under timed conditions. Teacher Rig recommends working through at least 20 algebra past paper questions before your exam, checking your method against mark schemes.
Should I memorise algebra formulas for the exam?
Some formulas are given on the formula sheet in the exam, but you should still be very familiar with them. Key formulas that are NOT on the sheet should be memorised. Practice using the formulas so that applying them becomes automatic.
Need Help with Algebra?
Book a free 60-minute trial class with Teacher Rig. Work through Algebra problems together and build your confidence.