O-Level Mathematics Algebra: 6 Techniques to Solve Any Problem

Algebra accounts for a significant portion of O-Level Mathematics marks and is the foundation for many other topics including coordinate geometry, functions, and calculus. Students who struggle with algebra often find the entire Mathematics paper difficult. Here are 6 techniques that our tutors teach at Sophia Education.

Technique 1: Factorisation — The Foundation

Every student must be fluent in all factorisation methods: common factor, grouping, difference of two squares (a²-b² = (a+b)(a-b)), perfect square trinomials (a²±2ab+b² = (a±b)²), and quadratic trinomials (ax²+bx+c). Practise factorising 20 expressions daily until it becomes automatic.

Technique 2: Solving Simultaneous Equations

For linear simultaneous equations, use elimination (multiply equations to make coefficients equal, then add/subtract) or substitution (make one variable the subject, substitute into the other equation). For one linear and one quadratic, always use substitution.

Technique 3: The Quadratic Formula

x = (-b ± √(b²-4ac)) / 2a. Use this when factorisation is not possible or when the question asks for answers to decimal places. The discriminant (b²-4ac) tells you the nature of roots: positive = 2 real roots, zero = 1 repeated root, negative = no real roots.

Technique 4: Algebraic Fractions

To add/subtract algebraic fractions, find the LCM of the denominators, convert each fraction, then combine. To multiply, factorise first and cancel common factors before multiplying. To divide, multiply by the reciprocal.

Technique 5: Completing the Square

Completing the square converts ax²+bx+c into a(x+p)²+q form. This is used to find the minimum/maximum value of a quadratic, the axis of symmetry, and to solve quadratic equations. The vertex of the parabola is at (-p, q).

Technique 6: Indices and Surds

Master all index laws: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1, a⁻ⁿ = 1/aⁿ, a^(1/n) = ⁿ√a. For surds, rationalise the denominator by multiplying by the conjugate.