All courses
- Applications of Derivatives
Related rates, optimization, curve sketching, and the mean value theorem.
- Applications of Integrals
Area between curves, volumes of revolution, average value, and accumulation problems.
- Area & Volume
Area of polygons and circles, and surface area and volume of prisms, cylinders, pyramids, cones and spheres.
- Circles
Arcs, chords, tangents and inscribed angles, arc length and sector area, and the equation of a circle.
- Complex Numbers
The imaginary unit, arithmetic with complex numbers, and complex solutions to quadratic equations.
- Conic Sections
Parabolas, circles, ellipses and hyperbolas: their equations, graphs and key features.
- Counting & Probability
Counting principles, permutations and combinations, and the rules of probability, including conditional probability.
- Derivatives
The derivative as a rate of change and slope, and the power, product, quotient and chain rules.
- Describing Data
Displaying data with dot plots, histograms and box plots, and summarizing it with center, spread and shape.
- Differential Equations
Slope fields, separable differential equations, and exponential and logistic growth models.
- Exponential Functions
Exponential growth and decay, compound interest, the number e, and graphs of exponential functions.
- Exponents & Radicals
Exponent rules, zero and negative exponents, scientific notation, and simplifying square roots and other radicals.
- Functions & Transformations
Function notation, domain and range, and how shifting, stretching and reflecting a graph changes its equation.
- Graphs of Trig Functions
Graph sine, cosine and tangent; amplitude, period and phase shift; and inverse trig functions.
- Hypothesis Testing
Significance tests for proportions and means: hypotheses, p-values, and errors in drawing conclusions.
- Integrals & the Fundamental Theorem
Riemann sums, definite and indefinite integrals, u-substitution, and the fundamental theorem of calculus.
- Integration Techniques
Integration by parts, partial fractions, trigonometric integrals, and improper integrals.
- Laws of Sines & Cosines
Solve any triangle, not just right triangles, and find the area of a triangle from two sides and an angle.
- Limits & Continuity
What a limit is, how to evaluate one, limits at infinity, and what it means for a function to be continuous.
- Linear Equations & Inequalities
Solve one-variable equations and inequalities, including multi-step and absolute value problems, and turn word problems into equations.
- Linear Functions & Graphs
Slope, intercepts, and the forms of a line. Graph linear relationships and write equations from graphs, tables and words.
- Lines, Angles & Constructions
Points, lines and planes, angle relationships, parallel lines cut by a transversal, and compass-and-straightedge constructions.
- Logarithms
Logarithms as inverses of exponentials, the laws of logarithms, and solving exponential and logarithmic equations.
- Logic & Proof
Conditional statements, deductive reasoning, and writing two-column and paragraph proofs.
- Matrices
Matrix operations, determinants and inverses, and solving systems of equations with matrices.
- Polar & Parametric Equations
Polar coordinates and graphs, parametric equations, and the polar form of complex numbers.
- Polynomial Functions
Polynomial division, the remainder and factor theorems, finding zeros, and end behavior of polynomial graphs.
- Polynomials & Factoring
Add, subtract and multiply polynomials, then factor them: common factors, trinomials, difference of squares and grouping.
- Quadratic Functions & Equations
Graph parabolas and solve quadratics by factoring, completing the square and the quadratic formula.
- Radical Functions & Equations
Rational exponents, graphs of square-root and cube-root functions, and solving radical equations (and spotting extraneous solutions).
- Random Variables & Distributions
Expected value and spread of random variables, and the binomial and normal distributions.
- Rational Functions
Simplify and operate on rational expressions, solve rational equations, and graph functions with asymptotes and holes.
- Right Triangle Trigonometry
Sine, cosine and tangent as ratios in right triangles, and using them to find missing sides and angles.
- Sampling & Confidence Intervals
Sampling distributions, the central limit theorem, and estimating a population value with a confidence interval.
- Scatterplots & Regression
Correlation, lines of best fit, residuals, and when a linear model is (and isn't) appropriate.
- Sequences & Series
Arithmetic and geometric sequences, sigma notation, and finite and infinite geometric series.
- Similarity & the Pythagorean Theorem
Similar figures, scale factors and proportions, and the Pythagorean theorem and its converse.
- Systems of Equations
Solve two equations at once by graphing, substitution and elimination, and model problems with systems of inequalities.
- The Unit Circle & Radians
Radian measure, the unit circle, and the trigonometric functions of any angle.
- Transformations & Coordinate Geometry
Translations, reflections, rotations and dilations, and proving geometric facts with coordinates.
- Triangle Congruence
Prove triangles congruent with SSS, SAS, ASA, AAS and HL, and use congruence to prove properties of triangles and quadrilaterals.
- Trig Identities & Equations
Pythagorean, sum and difference, and double-angle identities, and solving trigonometric equations.
- Vectors
Vectors in the plane: components, magnitude and direction, addition, scalar multiplication and the dot product.