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GRE Math · Learn
35 lessons in 10 units, about 41 h 5 min of reading and core practice. Each lesson ends with a quick check.
Unit 1
Single-variable differential calculus and the precalculus it rests on: limits and continuity, every differentiation technique, and applications to graphs, extrema, rates and approximation. This is the fastest-scoring part of the test.
4 lessons · 4 h 40 min of study · ≈15% of the test
Unit 2
Integration techniques, the fundamental theorem, geometric and physical applications of the integral, and convergence and manipulation of infinite, power and Taylor series.
4 lessons · 5 h 25 min of study · ≈16% of the test
Unit 3
Vectors and geometry in space, partial derivatives and gradients, optimization in several variables, multiple integrals and the theorems of vector calculus.
5 lessons · 5 h 55 min of study · ≈15% of the test
Unit 4
The ordinary differential equations included in ETS’s calculus outline: first-order methods and models, linear equations with constant coefficients and linear systems.
2 lessons · 2 h 20 min of study · ≈5% of the test
Unit 5
High-school algebraic technique and the linear algebra of a first university course: matrices and systems, vector spaces and linear maps, and eigenvalues. Linear algebra is the largest non-calculus block on the test.
4 lessons · 5 h 5 min of study · ≈14% of the test
Unit 6
Elementary group theory, rings and fields, and number theory at the level of a first undergraduate course: the conceptual core of the algebra 25%.
4 lessons · 4 h 55 min of study · ≈12% of the test
Unit 7
Rigorous treatment of sequences, series, continuity, differentiability and integrability; the topology of the real line and Euclidean space; and point-set topology. Questions here are usually conceptual: which statements must be true, and which counterexample breaks the others.
4 lessons · 4 h 45 min of study · ≈10% of the test
Unit 8
Logic and set theory, combinatorics, graph theory and algorithms, as listed in ETS’s additional topics.
3 lessons · 3 h of study · ≈7% of the test
Unit 9
The remaining additional topics in ETS’s outline. Complex variables and probability appear most often; geometry and numerical analysis supply the occasional quick point.
4 lessons · 4 h 15 min of study · ≈8% of the test
Unit 10
Converting knowledge into points across 66 questions in 170 minutes without a calculator.
1 lesson · 45 min of study · ≈1% of the test
Start here
Calculus I: limits, derivatives and their applications · Lesson 1 of 4
The precalculus toolkit the test assumes: elementary functions and their graphs, trigonometric identities and exact values, conic sections and polar coordinates.
1 h of study≈3% of the test
Start the first lessonSign in to keep your place and see your mastery on every topic.
Every lesson is free to read. With an account, finished lessons are ticked off, quick checks feed your mastery, and flashcards come back for review.
Strategy, scoring and test day, beyond the syllabus.
Learn, then practise
Each lesson ends with three quick questions. For more, practice adapts to the topics you’re weakest on.
Open practice