M7.2 Simultaneous Equations, Functions and Proportion
Algebraic simultaneous equations, two-variable inequalities, complex formula rearrangement, non-linear sequences, function graphs and direct proportion.
How to study for CCEA GCSE Mathematics
Secure fluent methods, explain mathematical reasoning and solve unfamiliar problems with a route-aware balance of non-calculator and calculator practice.
Core concepts
Concept 1
Simultaneous equations seek values satisfying both relationships and can be solved by elimination or substitution.
Exam cue: Confirm the CCEA unit, tier and calculator condition before selecting a method.
Concept 2
Linear, quadratic, cubic and reciprocal graph shapes support interpretation and approximate intersection solutions.
Exam cue: Define variables, find and use the constant of proportionality, and verify simultaneous solutions in both original relationships.
Concept 3
Direct proportion has a constant ratio and an algebraic form such as y = kxⁿ.
Exam cue: Show a complete mathematical chain, use appropriate notation and check that the answer is sensible in context.
Risk pitfalls and guardrails
Assuming every increasing relationship is directly proportional or omitting the constant k.
Guardrail: Do not import an England 9-1 convention, omit cumulative prerequisites or present a calculator display as mathematical reasoning.
Importing a topic boundary, formula sheet or paper convention from an England 9-1 board.
Guardrail: Do not import an England 9-1 convention, omit cumulative prerequisites or present a calculator display as mathematical reasoning.
Giving a calculator display or unsupported answer without the reasoning, units or accuracy the question requires.
Guardrail: M5-M8 Paper 1 is non-calculator; Paper 2 and every M1-M4 assessment use a permitted calculator.
Memory anchors
Simultaneous equations
Equations solved together for values satisfying every equation.
Elimination
A method that combines equations to remove one variable.
Reciprocal function
A function such as y = a/x, with x not equal to zero.
Direct proportion
A relationship with a constant quotient after accounting for the stated power.
Constant of proportionality
The fixed multiplier k in a proportional relationship.
Non-linear sequence
A sequence whose first differences are not constant.
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 x+y=11, x-y=3. Find x.
Solve 2x+y=13, x-y=2. Find y.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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