Algebra and Algebraic Processes
What you must understand
Algebra is the language in which the rest of the paper is written. You must simplify expressions by collecting like terms, expand single and double brackets, factorise (common factor, difference of two squares, quadratic trinomials), rearrange formulae, solve linear equations and inequalities, solve simultaneous equations by elimination or substitution, and solve quadratic equations by factorising or by formula. You should also handle algebraic fractions, substitution into expressions, and changing the subject of a formula.
Traps that appear in questions
- Signs when expanding. A minus before a bracket changes every sign inside it: −(2x − 5) = −2x + 5.
- Like terms only. 3x and 3x² cannot be combined.
- Inequalities and negative multipliers. Multiplying or dividing by a negative number reverses the inequality sign.
- Formula rearrangement. Whatever you do to one side, do to the other; if the subject appears twice, factorise it out first.
- Extraneous solutions. Always substitute back, especially with fractions or square roots.
- Simultaneous equations. Make coefficients match before eliminating, and subtract the whole equation including the constant.
Worked example
Solve 3x − 5 = 2(x + 4). Expand: 3x − 5 = 2x + 8. Subtract 2x from both sides: x − 5 = 8. Add 5: x = 13. Check: 3(13) − 5 = 34 and 2(13 + 4) = 34.
Rule of thumb
For any equation, do the same operation to both sides, keep the equals signs aligned in a column, and finish by substituting your answer back into the original equation.