Core Algebra
Manipulate expressions and formulae, solve equations and inequalities and interpret coordinates, graphs and sequences.
How to prepare for the current TMUA
Secure the shared mathematical specification, practise application in unfamiliar settings, then make every Paper 2 implication and proof step explicit.
Core concepts
Concept 1
Distinguish expressions, equations, identities, inequalities and formulae.
Exam cue: Simplify or factor before choosing a solution method.
Concept 2
Solve linear, quadratic and simultaneous systems algebraically or graphically.
Exam cue: Link a graph intersection to simultaneous equations.
Concept 3
Interpret gradients, intercepts, turning points, graph areas and sequence rules.
Exam cue: Read axes, units and interval restrictions before interpreting a graph.
Risk pitfalls and guardrails
Cancelling terms across a sum.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Forgetting to reverse an inequality after multiplying by a negative value.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Selecting a graph by shape while ignoring intercepts or scale.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Memory anchors
Identity
An identity is true for every permitted value.
Factor first
Factorisation exposes roots and valid cancellations.
Quadratic routes
Factorise, complete the square or use the formula.
Gradient
Vertical change divided by horizontal change.
Intersection
A shared point satisfies both equations.
Sequence check
Test an nth-term claim against more than one term.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Solve 3(2x−5)−2(x+4)=9. What is x?
If x−y=4 and xy=12, what is x²+y²?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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