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100 concept guides

Mathematics

Mathematics on noobtopro is built around reasoning, not recall. Each concept below comes with a clear explanation, one fully worked example you can follow step by step, and self-check questions that probe whether you really understand the idea — the same way the platform grades you.

Test your mathematics reasoning

Elementary School

0–69

Foundations: the concrete ideas every later concept is built on.

Number & operations

Counting & cardinality Place value & the base-ten system Addition & subtraction Multiplication & division Properties of operations Factors & multiples Rounding & estimation

Fractions

Fractions: meaning & equivalence Comparing & ordering fractions Adding & subtracting fractions Multiplying fractions Decimals & decimal place value

Measurement & data

Measurement (length, mass, volume, time)Money Representing & interpreting data Area & perimeter Volume

Geometry

2D & 3D shapes Lines, angles & symmetry The coordinate plane (intro)

Algebraic thinking

Patterns & relationships

Middle School

70–139

Ratios, expressions, and the particle picture — the bridge to abstraction.

Ratios & proportional relationships

Ratios & unit rates Proportional relationships Percentages

The number system

Operations with rational numbers Negative numbers & the number line Absolute value Irrational numbers (intro)

Expressions & equations

Exponents Scientific notation Algebraic expressions One-variable equations & inequalities Linear equations in two variables Systems of linear equations

Functions

Functions (intro)Slope & rate of change

Geometry

Angle relationships Area, surface area & volume Scale drawings & similarity The Pythagorean theorem Transformations & congruence

Statistics & probability

Statistical distributions Measures of center & variability Probability (intro)

High School

140–209

Functions, mechanics, and stoichiometry — the core curriculum, reasoned out.

Number & quantity

Quantities & units The real & complex number systems Vectors (intro)Matrices (intro)

Algebra

Polynomial arithmetic Factoring & polynomial identities Quadratic functions & equations Rational expressions & equations Radical expressions & equations Systems of equations & inequalities

Functions

Exponential functions Logarithms & logarithmic functions Sequences & series Function notation & transformations Inverse functions

Trigonometry

Right-triangle trigonometry The unit circle & trigonometric functions Trigonometric identities & equations Graphs of trigonometric functions

Geometry

Congruence & geometric proof Similarity & transformations Circles & their properties Conic sections Coordinate (analytic) geometry Three-dimensional geometry & measurement

Statistics & probability

Probability rules & combinatorics Conditional probability Sampling & experimental design Descriptive statistics & distributions Inference & regression (intro)

Calculus readiness

Limits (intro to calculus)

University

210–279

Calculus, electromagnetism, and equilibrium — first-principles depth.

Single-variable calculus

Limits & continuity Derivatives & differentiation rules Applications of derivatives Integrals & the fundamental theorem of calculus Techniques of integration Applications of integration Infinite sequences & series Power & Taylor series Parametric & polar calculus

Multivariable calculus

Multivariable functions & partial derivatives Gradients & directional derivatives Multiple integrals Vector calculus (Green's, Stokes', divergence)

Linear algebra

Vectors & vector spaces Linear transformations & matrices Determinants Eigenvalues & eigenvectors Inner product spaces & orthogonality

Differential equations

First-order differential equations Higher-order & linear differential equations Systems of differential equations Laplace transforms

Probability & statistics

Probability theory Random variables & distributions Statistical inference & estimation

Other subjects

Physics Chemistry