Algebra
Algebra at Ordinary Level examines your ability to manipulate expressions, solve equations and inequalities, work with indices and logarithms, and translate a written problem into an equation. Questions often combine skills, so a sign slip in one line can cost several marks.
Core manipulation
- Expand brackets carefully; a minus sign before a bracket changes every sign inside.
- Factorise by taking out the highest common factor first. Recognise the difference of squares: a² − b² = (a − b)(a + b).
- For a quadratic ax² + bx + c, factorise into two brackets or use x = [−b ± √(b² − 4ac)]/(2a). The discriminant b² − 4ac tells you the number of real roots.
- Solve simultaneous equations by elimination or substitution; keep the equations aligned.
Indices and logs
Use a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m−n), (a^m)^n = a^(mn), a^0 = 1, a^(−n) = 1/a^n. Logs reverse powers: log(ab) = log a + log b, log(a/b) = log a − log b, log(a^n) = n log a.
Worked example
Solve 2x² − 5x − 3 = 0. Find two numbers whose product is 2 × (−3) = −6 and whose sum is −5: −6 and 1. Split the middle term: 2x² − 6x + x − 3 = 0. Factor by grouping: 2x(x − 3) + 1(x − 3) = 0, so (2x + 1)(x − 3) = 0. Therefore x = −1/2 or x = 3. Check by substituting one value back into the original equation.
Traps
- Reversing the inequality sign only when multiplying or dividing by a negative number.
- Cancelling terms across a plus or minus sign instead of factors.
- Forgetting that a denominator cannot be zero.
- Giving only one root of a quadratic.