Unit 6
Algebra
About this unit
Solve equations, simultaneous conditions, and before-after ratio problems using systematic algebraic thinking. Translate word problems into equations confidently.
What types of questions will you face?
- 1Solve age problems where a future age equals a multiple of a past age — let the current age be the variable, write past and future expressions, set up one equation
- 2Translate two verbal operation sequences applied to the same unknown number into two algebraic expressions, set them equal, and solve for the unknown
- 3Solve simultaneous conditions — two people share a total and differ by a fixed amount — using the sum-and-difference shortcut or one-variable substitution
- 4Evaluate algebraic expressions by substituting a given value of the variable and simplifying step by step (applying order of operations correctly)
- 5Solve symbol or shape equations where each symbol represents an unknown number — use substitution or elimination across multiple equations
Skills you will build
- Anchoring on the current age as the single variable and expressing past and future ages as M − n and M + n before setting up any equation
- Translating verbal operation sequences word-by-word into algebraic expressions (e.g. 'multiply by 3 then add 8' → 3n + 8) without rearranging prematurely
- Collecting like terms across an equation: moving all variable terms to one side and all constants to the other before dividing
- Applying the sum-and-difference shortcut: if total = S and difference = D, then larger = (S + D) ÷ 2 and smaller = (S − D) ÷ 2
- Substituting a known symbol value back into another equation to find a second unknown — the core skill in multi-equation symbol problems
By the end of this unit, you will be able to
- Solve any age problem involving past and future time points by writing one equation in one variable and solving it
- Convert any 'think of a number' or verbal equation statement into algebra and solve for the unknown number
- Find both unknowns in any two-person sum-and-difference problem using either algebra or the shortcut
- Evaluate multi-step algebraic expressions correctly by substituting and following order of operations
- Solve systems of symbol equations by identifying which symbol to isolate first and cascading the substitution
Difficulty profile
Questions in this unit range from Very Easy to Difficult. Symbol substitution and simple equation solving are Very Easy to Easy. Age problems and think-of-a-number equations are Easy to Medium. Multi-step simultaneous equations applied to word problems reach Difficult.
Exam tip: Algebra
For age problems, never jump to the answer options — always let M = current age, write past and future ages in terms of M, and set up the equation first. For any verbal equation question, translate each clause into algebra before touching the numbers: left-hand side expression = right-hand side expression. Trying to solve in your head without writing the equation is the leading cause of errors on these questions.
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