Unit 11
Algebraic / Equation Reasoning
About this unit
Set up and solve real-world algebra problems without formal algebraic notation. You will work with simultaneous equations, age relationships, work rates, maximisation problems, and counting arrangements — all presented as practical word problems that require systematic equation thinking.
What types of questions will you face?
- 1Simultaneous equations from word problems (e.g. pens + notebooks at two prices)
- 2Maximisation: given limited quantities of multiple resources, find how many complete items can be made
- 3Work rate problems: if one worker takes X hours, another takes Y hours, how long do they take together?
- 4Age problems: relationships between ages now and in the past/future
- 5Counting arrangements: how many ways can items be arranged given restrictions?
- 6Shape equation puzzles: shapes represent numbers — find the value of each shape to make all equations true
Skills you will build
- Translating a word problem into one or two equations
- Solving simultaneous equations using substitution or elimination
- Using the "limiting resource" principle for maximisation problems
- Applying the combined work rate formula (1/A + 1/B = 1/total)
- Setting up and solving age equations with a single unknown
- Calculating permutations and combinations with restrictions
By the end of this unit, you will be able to
- Solve any two-variable simultaneous equation from a word problem
- Calculate how many complete items can be made from given resource quantities
- Solve work rate and shared task problems efficiently
- Answer age and relationship problems using clear algebraic thinking
Difficulty profile
Medium difficulty (avg 3.07). Shape equation puzzles are Easy; work rate and age problems are Medium; complex maximisation and counting problems with multiple restrictions are Difficult.
Exam tip: Algebraic / Equation Reasoning
For simultaneous equations: label your unknowns clearly (pen = p, notebook = n), write both equations, then subtract or substitute to eliminate one variable. For maximisation: divide your supply of each resource by what one item needs — the smallest result is your answer.
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