Algebra, Equations and Functions
This topic covers linear equations, inequalities, systems, quadratic expressions, functions, graphs, substitutions, factoring, and algebraic modeling.
How to study for the GRE
Build every answer around the exact task: passage evidence, blank logic, argument structure, equation setup, units, data labels, and section-level timing.
Core concepts
Concept 1
Algebra, Equations and Functions questions test reasoning under the current GRE General Test structure.
Exam cue: Name the question type, then mark the evidence, blank logic, argument role, equation, table label, or writing goal.
Concept 2
The best answer identifies the task, evidence, relationship, equation, quantity, or writing move before comparing choices.
Exam cue: Check scope, contrast words, quantifiers, units, graph labels, variable definitions, and whether the answer fits every condition.
Concept 3
Eliminate choices that add outside assumptions, reverse the relationship, ignore wording, misuse units, or answer a nearby but different task.
Exam cue: Use review time to verify the exact prompt, not just the topic that first looked familiar.
Risk pitfalls and guardrails
Choosing a familiar word, formula, or claim without testing it against the exact context.
Guardrail: Use a 15-second safety pause before finalizing your action.
Treating a GRE reasoning item like a memorization item rather than a task about relationships.
Guardrail: Use a 15-second safety pause before finalizing your action.
Skipping the final reasonableness check for passage support, sentence meaning, or quantitative scale.
Guardrail: Use a 15-second safety pause before finalizing your action.
Memory anchors
Linear Equation
A linear equation represents a constant rate of change.
Inequality
An inequality describes a range and reverses direction when multiplied by a negative.
System
A system solution satisfies all equations or inequalities at once.
Function
A function assigns each input exactly one output.
Slope
Slope is change in output divided by change in input.
Intercept
An intercept is where a graph crosses an axis.
Quadratic
A quadratic expression has degree two and can often be factored or completed.
Substitution
Substitution replaces a variable with an equivalent expression or value.
Factoring
Factoring rewrites an expression as a product without changing value.
Domain
A domain is the set of input values allowed by the function or context.
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 3x − 5 = 16.
Which inequality is equivalent to −2x + 3 > 11?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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