Algebra, Equations and Graphs
Manipulate expressions, solve equations and inequalities, use sequences and interpret linear, quadratic, reciprocal, exponential and trigonometric graphs.
How to prepare for the current ESAT
Confirm your course combination, build no-calculator fluency from Mathematics 1 upward, and use official Pearson materials for authentic timing and interface rehearsal.
Core concepts
Concept 1
Move between expressions, equations, formulae, identities and inequalities.
Exam cue: Factor or simplify before choosing a solving method.
Concept 2
Solve linear, quadratic and simultaneous equations algebraically or graphically.
Exam cue: Link an intersection to a simultaneous solution.
Concept 3
Use gradients, intercepts, roots, turning points and areas to interpret models.
Exam cue: Read axes and units before interpreting a gradient or area.
Risk pitfalls and guardrails
Cancelling terms across addition.
Guardrail: Do not use calculator-dependent shortcuts, import a fact outside the annual specification or overlook a unit, sign, scale or course-module boundary.
Forgetting to reverse an inequality after multiplying by a negative value.
Guardrail: Do not use calculator-dependent shortcuts, import a fact outside the annual specification or overlook a unit, sign, scale or course-module boundary.
Selecting a graph by shape while ignoring scale or intercept.
Guardrail: Do not use calculator-dependent shortcuts, import a fact outside the annual specification or overlook a unit, sign, scale or course-module boundary.
Memory anchors
Identity
An identity is true for every permitted value.
Factor first
Expose roots and cancellations before expanding further.
Quadratic routes
Factorise, complete the square or use the formula.
Gradient
Change in vertical quantity divided by change in horizontal quantity.
Intersection
A common point solves both equations.
Sequence check
Test the nth-term rule 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
Expand (x+3)(x−5).
Factorise x²−9.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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