Mathematics
Build fluency in algebra, geometry, trigonometry, calculus, and statistics — the quantitative foundation for science, engineering, and everyday problem-solving.
Popular Topics
Linear Equations
A linear equation is an algebraic equation where each term has an exponent of 1, and its graph is always a straight line.
Quadratic Equations
Solve quadratics using factoring, completing the square, and the quadratic formula.
Multiplication Tables, Squares & Cubes
Interactive multiplication tables for numbers 1–25, with memory tricks for faster mental recall.
1Algebra
Linear Equations
A linear equation is an algebraic equation where each term has an exponent of 1, and its graph is always a straight line.
Quadratic Equations
Solve quadratics using factoring, completing the square, and the quadratic formula.
Systems of Equations
Solve systems of two or more equations using substitution, elimination, or graphing.
Polynomials
Add, subtract, multiply, divide, and factor polynomial expressions.
Rational Expressions
Simplify, add, subtract, multiply, and divide expressions involving polynomial fractions.
Exponents & Logarithms
Apply exponent rules and understand logarithms as the inverse of exponentiation.
Inequalities
Solve and graph linear and quadratic inequalities on a number line and coordinate plane.
Functions & Graphs
Understand domain, range, function notation, and transformations of common function families.
Sequences & Series
Analyze arithmetic and geometric sequences and compute finite and infinite series.
Absolute Value
Solve equations and inequalities involving absolute value by considering positive and negative cases.
Multiplication Tables, Squares & Cubes
Interactive multiplication tables for numbers 1–25, with memory tricks for faster mental recall.
2Geometry
Points, Lines & Planes
Understand the foundational undefined terms and postulates of Euclidean geometry.
Angles & Triangles
Classify angles and triangles, and apply the triangle angle-sum theorem (180°).
Congruence & Similarity
Prove triangles congruent (SSS, SAS, ASA, AAS) or similar (AA, SAS~, SSS~) and use proportions.
Circles
Explore circle properties including arcs, chords, tangent lines, and inscribed angles.
Area & Perimeter
Calculate area and perimeter for triangles, quadrilaterals, circles, and composite figures.
Surface Area & Volume
Compute surface area and volume of prisms, cylinders, pyramids, cones, and spheres.
Coordinate Geometry
Apply algebra to geometry using the coordinate plane — distance, midpoint, and slope formulas.
Transformations
Perform and describe translations, reflections, rotations, and dilations on the coordinate plane.
Pythagorean Theorem
Use a² + b² = c² to find missing sides in right triangles and verify right angles.
Geometric Proofs
Construct two-column and paragraph proofs using definitions, postulates, and theorems.
3Trigonometry
Right Triangle Trigonometry
Define sine, cosine, and tangent as ratios of sides in a right triangle (SOH-CAH-TOA).
The Unit Circle
Extend trig functions to all angles using the unit circle (radius = 1 centered at the origin).
Trigonometric Graphs
Graph sine, cosine, and tangent functions and identify amplitude, period, and phase shift.
Trigonometric Identities
Prove and apply fundamental identities like sin²θ + cos²θ = 1 and double-angle formulas.
Law of Sines
Solve non-right triangles using a/sinA = b/sinB = c/sinC, including the ambiguous case.
Law of Cosines
Solve non-right triangles using c² = a² + b² − 2ab·cos(C) for SAS and SSS cases.
Inverse Trigonometric Functions
Use arcsin, arccos, and arctan to find angles from known trig ratios, with restricted domains.
Solving Trigonometric Equations
Find all solutions to trigonometric equations using identities, inverse functions, and periodicity.
Polar Coordinates
Represent points and curves using distance r and angle θ instead of Cartesian x, y.
Complex Numbers & Trig Form
Express complex numbers in trigonometric (polar) form r(cosθ + i·sinθ) and apply De Moivre's theorem.
4Calculus AP
Limits & Continuity
Understand the concept of a limit and determine where functions are continuous or discontinuous.
Definition of the Derivative
Define the derivative as the limit of the difference quotient, representing instantaneous rate of change.
Differentiation Rules
Apply power, product, quotient, and chain rules to differentiate functions efficiently.
Applications of Derivatives
Use derivatives to find extrema, sketch curves, and solve optimization problems.
Related Rates
Differentiate equations with respect to time to find how changing quantities are connected.
Definite Integrals
Compute the signed area under a curve using Riemann sums and definite integral notation.
Fundamental Theorem of Calculus
Connect differentiation and integration: the FTC shows they are inverse operations.
Integration Techniques
Evaluate integrals using u-substitution, integration by parts, and partial fractions.
Applications of Integrals
Use integrals to compute areas between curves, volumes of revolution, and accumulated quantities.
Differential Equations (Intro)
Solve basic separable differential equations and model exponential growth and decay.
5Statistics
Descriptive Statistics
Summarize data using measures of center (mean, median, mode) and spread (range, standard deviation).
Probability Basics
Calculate probabilities of simple and compound events using counting, addition, and multiplication rules.
Conditional Probability
Find the probability of an event given that another event has occurred, using P(A|B) = P(A∩B)/P(B).
Discrete Random Variables
Define probability distributions for discrete variables and compute expected value and variance.
Normal Distribution
Model continuous data with the bell curve and use z-scores to find probabilities.
Sampling Distributions
Understand how sample statistics vary from sample to sample and apply the Central Limit Theorem.
Confidence Intervals
Estimate a population parameter with a range of plausible values and a stated confidence level.
Hypothesis Testing
Test claims about population parameters using null/alternative hypotheses, test statistics, and p-values.
Chi-Square Tests
Test whether observed categorical data differs significantly from expected distributions.
Regression & Correlation
Model the relationship between two quantitative variables with a line of best fit and measure its strength with r.