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Search every subject world, from Preschool to Grade 12. The first five courses of every subject path are free.

44 courses

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Mathematics · Grade 10

Questions, Variables and Data

Learners begin the statistics elective by asking questions that data can answer. They identify individuals and variables, classify variables, summarize categorical data with frequencies and displays, analyze two-way tables with marginal, joint and conditional relative frequencies, judge whether two variables are associated, and consider the ethics of collecting and sharing data.

  • 4 lessons
  • About 130 min
  • Quiz: 11 questions
Free starter

Mathematics · Grade 10

Designing Studies and Sampling

Learners study where data come from. They compare sampling methods and see sampling variability in a simulation, identify sources of bias, distinguish observational studies from experiments, explain confounding, design experiments with control, random assignment, replication, blocking and blinding, and decide what conclusions a study's design allows.

  • 4 lessons
  • About 140 min
  • Quiz: 11 questions
Free starter

Mathematics · Grade 10

Exploring Distributions

Learners describe distributions of quantitative data: they choose displays, describe shape, center, spread and unusual values, compute and compare the mean, median, standard deviation and interquartile range, identify outliers with the 1.5 × IQR rule, standardize values with z-scores and percentiles, see how linear transformations change summaries, and use the empirical rule for normal distributions.

  • 4 lessons
  • About 140 min
  • Quiz: 11 questions
Free starter

Mathematics · Grade 10

Association and Regression

Learners study relationships between two quantitative variables. They describe scatterplots, interpret the correlation r and its properties, build the least-squares regression line from summary statistics, interpret slope, intercept and r² in context, use residuals and residual plots to judge fit, recognize outliers and influential points, avoid extrapolation, and separate correlation from causation. An optional honors lesson straightens curved data with logarithms.

  • 5 lessons
  • About 150 min
  • Quiz: 11 questions
Free starter

Mathematics · Grade 10

Probability and Random Variables

Learners build the probability tools that inference relies on: the addition and multiplication rules, conditional probability, independence and tree diagrams; discrete random variables with their means and standard deviations; binomial and geometric settings; and simulation as a way to estimate probabilities. An optional honors lesson reverses conditional probabilities with natural frequencies.

  • 5 lessons
  • About 150 min
  • Quiz: 11 questions
Free starter

Mathematics · Grade 10

Sampling Distributions

Learners treat a sample statistic as a random variable. Starting from a sampling simulation, they describe sampling variability, find the mean and standard deviation of the sampling distributions of a sample proportion and a sample mean, check when a normal model is appropriate, meet the Central Limit Theorem, and distinguish bias from variability in estimators.

  • 4 lessons
  • About 140 min
  • Quiz: 10 questions

Mathematics · Grade 10

Estimation and Confidence Intervals

Learners turn sampling distributions into estimates with honest uncertainty. They build confidence intervals for a proportion after checking conditions, interpret intervals and confidence levels correctly, see how confidence level and sample size change the margin of error, choose a sample size for a desired margin, and construct a t interval for a mean.

  • 4 lessons
  • About 145 min
  • Quiz: 11 questions

Mathematics · Grade 10

Tests of Statistical Claims

Learners test claims with data. They state hypotheses, see the logic of a significance test through simulation, carry out a one-proportion z test, interpret P-values and significance levels, weigh Type I and Type II errors and power, meet the one-sample t test and randomization tests for two groups, and distinguish statistical significance from practical importance.

  • 4 lessons
  • About 150 min
  • Quiz: 11 questions

Mathematics · Grade 10

Model Assumptions and Limitations

Learners study what can go wrong. They check the conditions behind intervals and tests and see what happens when they fail, diagnose regression models with residual plots and influential points, recognize the dangers of multiple comparisons and p-hacking, untangle Simpson's paradox, and practice communicating uncertainty and the limits of generalization honestly.

  • 4 lessons
  • About 140 min
  • Quiz: 10 questions

Mathematics · Grade 10

Communicate an Original Investigation

In this capstone, learners carry a statistical investigation from question to report using a fictional school sleep survey. They pose questions and plan data collection, choose and carry out descriptive and inferential methods (an interval, a test, a comparison of groups and a regression), critique conditions, bias and scope, and write a clear, honest report for a general audience, while retrieving key skills from the whole elective.

  • 4 lessons
  • About 160 min
  • Quiz: 11 questions

Mathematics · Grade 11

Functions, Domain and Algebraic Structure

Algebra II opens by sharpening the language of functions. Learners find domains and ranges in interval notation, including restrictions from denominators and square roots, analyze piecewise and absolute value functions, combine and compose functions (and find the domain of a composition), and use algebraic structure: testing whether functions are even or odd, decomposing composite functions, and computing average rates of change.

  • 4 lessons
  • About 125 min
  • Quiz: 11 questions
Free starter

Mathematics · Grade 11

Functions and Rates of Change

Learners open the calculus elective by studying how fast quantities change. They compute average rates of change with units, estimate instantaneous rates from tables and graphs using local linearity, connect position and velocity, approximate with tangent lines, and simplify difference quotients in preparation for the formal definition of the derivative.

  • 4 lessons
  • About 135 min
  • Quiz: 11 questions
Free starter

Mathematics · Grade 11

Limits and Continuity

Learners make 'approaching' precise. They estimate limits from tables and graphs, compare one-sided limits, evaluate limits with limit laws, factoring and rationalizing, analyze limits involving infinity, test continuity with three conditions, classify discontinuities, and use the Intermediate Value Theorem. An optional honors lesson introduces the squeeze theorem and the limit of sin x / x.

  • 5 lessons
  • About 150 min
  • Quiz: 12 questions
Free starter

Mathematics · Grade 11

Linear and Quadratic Models Revisited

Learners return to linear and quadratic models with Algebra II tools: piecewise-linear pricing, interpreting technology-produced lines of fit, vertex form by completing the square for maximum and minimum problems, linear–quadratic systems, and quadratic inequalities solved with sign analysis. An optional honors lesson fits a quadratic through three points with a system of three equations.

  • 5 lessons
  • About 130 min
  • Quiz: 11 questions
Free starter

Mathematics · Grade 11

Polynomial Functions and Equations

Learners connect a polynomial's degree, leading coefficient, zeros and multiplicities to the shape of its graph, divide polynomials by long and synthetic division, and use the remainder and factor theorems. They find rational zeros with the rational root theorem to solve polynomial equations, and prove polynomial identities, including one that generates Pythagorean triples.

  • 4 lessons
  • About 130 min
  • Quiz: 11 questions
Free starter

Mathematics · Grade 11

Derivative Meaning and Rules

Learners define the derivative as a limit of difference quotients, interpret it with units, connect the graphs of f and f′, and learn where derivatives fail to exist. They then derive and apply the power, sum, product and quotient rules, use the derivatives of sine, cosine, the exponential and the natural logarithm, apply the chain rule, and write tangent lines.

  • 5 lessons
  • About 155 min
  • Quiz: 12 questions
Free starter

Mathematics · Grade 11

Rational Expressions and Functions

Learners treat rational expressions like fractions with variables: they simplify, multiply, divide, add and subtract them while tracking domain restrictions, solve rational equations and detect extraneous solutions, analyze rational functions (vertical and horizontal asymptotes, holes, transformations of 1/x), and model inverse variation, combined work rates and average cost.

  • 4 lessons
  • About 130 min
  • Quiz: 11 questions
Free starter

Mathematics · Grade 11

Implicit and Related-Rate Reasoning

Learners differentiate equations that do not give y explicitly, derive the derivatives of inverse functions such as ln x, arcsin x and arctan x, solve related-rate problems about sliding ladders, spreading ripples, filling tanks and lengthening shadows, and use local linear approximation and differentials to estimate values and measurement errors.

  • 4 lessons
  • About 145 min
  • Quiz: 11 questions
Free starter

Mathematics · Grade 11

Radicals and Rational Exponents

Learners extend the exponent laws to rational exponents and see why a^1/n^ must mean the nth root. They simplify and combine radicals, rationalize denominators, solve radical equations while checking for extraneous solutions, and analyze square root and cube root functions and models such as a pendulum's period.

  • 4 lessons
  • About 120 min
  • Quiz: 12 questions
Free starter

Mathematics · Grade 11

Applications and Optimization

Learners use derivatives to analyze and optimize. They find critical points, classify extrema with the first- and second-derivative tests, study concavity and inflection points, locate absolute extrema on closed intervals, solve optimization problems such as designing a box or a fence, apply the Mean Value Theorem, and decide when a moving object speeds up or slows down. An optional honors lesson introduces L'Hôpital's rule.

  • 5 lessons
  • About 160 min
  • Quiz: 12 questions
Free starter

Mathematics · Grade 11

Accumulation and Definite Integrals

Learners discover that the area under a rate graph is the accumulated change in a quantity, approximate that accumulation with Riemann and trapezoid sums, and then define the definite integral as the limit of those sums. They evaluate integrals with geometry, properties and a symbolic rule derived from sums, build accumulation functions, and learn to say exactly when each rule or estimate applies.

  • 5 lessons
  • About 150 min
  • Quiz: 12 questions

Mathematics · Grade 11

Complex Numbers and Quadratic Reasoning

Learners meet the imaginary unit i, do arithmetic with complex numbers (including powers of i, conjugates and division), and plot complex numbers in the complex plane. They solve every quadratic equation, including those with complex solutions, derive the quadratic formula by completing the square, and use the Fundamental Theorem of Algebra and conjugate pairs to count and find polynomial zeros. An optional honors lesson explains why complex zeros of real polynomials come in pairs.

  • 5 lessons
  • About 130 min
  • Quiz: 11 questions

Mathematics · Grade 11

Exponential and Logarithmic Functions

Learners extend exponential models to the base e and continuous compounding, define the logarithm as the inverse of exponentiation, derive the product, quotient and power properties from the exponent laws, and use logarithms (including change of base) to solve exponential equations for doubling times, half-lives and growth rates.

  • 4 lessons
  • About 130 min
  • Quiz: 11 questions

Mathematics · Grade 11

The Fundamental Theorem of Calculus

Learners connect the two halves of calculus. Building on accumulation functions, they see why the derivative of an accumulated amount is the rate (Fundamental Theorem, part 1), find antiderivatives, evaluate definite integrals exactly with antiderivatives (part 2), and use the net change theorem and average value in context. An optional honors lesson handles variable upper limits with the chain rule.

  • 5 lessons
  • About 155 min
  • Quiz: 12 questions

Mathematics · Grade 11

Integral Techniques and Applications

Learners widen their integration toolkit with substitution, then use integrals to measure: areas between curves, volumes of solids built from disks, washers and known cross-sections, and positions recovered from velocity and acceleration. An optional honors lesson introduces integration by parts.

  • 5 lessons
  • About 155 min
  • Quiz: 12 questions

Mathematics · Grade 11

Function Transformations and Inverses

Learners describe how shifts, stretches, compressions and reflections change a function's equation, graph and key points, and write transformed equations from descriptions. They then find inverse functions algebraically, verify them by composition, relate their graphs by reflection in y = x, test invertibility with the horizontal line test, and restrict domains so that quadratics have inverses.

  • 4 lessons
  • About 125 min
  • Quiz: 11 questions

Mathematics · Grade 11

Sequences and Series

Learners write arithmetic and geometric sequences explicitly and recursively, use sigma notation, and prove the arithmetic series formula by pairing and the geometric series formula by multiplying and subtracting. They apply finite geometric series to savings plans and decide when an infinite geometric series has a sum, using it for repeating decimals and a bouncing ball.

  • 4 lessons
  • About 125 min
  • Quiz: 11 questions

Mathematics · Grade 11

Differential Equations and Models

Learners read equations about rates of change as models. They verify solutions, sketch and interpret slope fields, approximate solutions with Euler's method, solve separable equations with initial conditions, and model exponential growth and decay, Newton's law of cooling and logistic growth, including equilibrium and long-run behavior.

  • 4 lessons
  • About 150 min
  • Quiz: 12 questions

Mathematics · Grade 11

A Calculus Investigation

In this capstone, learners investigate a fictional reservoir during a twelve-hour storm. Using inflow and outflow rates, they build an accumulation model, find when the water volume rises, falls and reaches its extremes, approximate integrals from data and judge their accuracy, connect volume and depth with related rates, extend the model with a differential equation, and write a complete, justified report.

  • 4 lessons
  • About 160 min
  • Quiz: 12 questions

Mathematics · Grade 11

Trigonometric Functions and Periodic Models

Learners extend trigonometry from right triangles to all angles. They measure angles in radians, use the unit circle to evaluate sine, cosine and tangent of any angle, prove the Pythagorean identity sin^2^θ + cos^2^θ = 1, graph sinusoidal functions with amplitude, period, midline and phase shift, and model Ferris wheels, tides and daylight hours with invented but realistic data.

  • 4 lessons
  • About 135 min
  • Quiz: 11 questions

Mathematics · Grade 11

Probability, Data and Statistical Reasoning

Learners build sample spaces and use the addition and multiplication rules, compute conditional probabilities from two-way tables and test for independence, use normal distributions, the empirical rule and z-scores to estimate proportions and compare values, and distinguish surveys, observational studies and experiments while judging sample estimates with simulation and margins of error.

  • 4 lessons
  • About 130 min
  • Quiz: 11 questions

Mathematics · Grade 11

A Multi-Model Investigation

The Algebra II capstone. Working with invented monitoring data from a fictional lake, learners decide which function family fits each data set (linear, quadratic, exponential, logarithmic or periodic), build models from key features and from transformed data, compare competing models with residuals and context, and write an investigation report that states its assumptions and limits.

  • 4 lessons
  • About 145 min
  • Quiz: 10 questions

Mathematics · Grade 12

Advanced Functions and Modeling Readiness

Precalculus opens with building functions from situations: writing explicit formulas from geometry and business contexts, describing processes recursively, composing and inverting functions to answer chained and reverse questions, and analyzing how a model behaves on intervals with average rates of change, extreme values and domain limits. Learners finish by choosing and defending a model family for a purpose.

  • 4 lessons
  • About 125 min
  • Quiz: 10 questions
Free starter

Mathematics · Grade 12

Polynomial and Rational Function Analysis

Learners analyze polynomial and rational functions as a precalculus student should: complete factorization over the complex numbers, end behavior and turning points, sign charts for polynomial inequalities, a full analysis of rational graphs including holes and slant asymptotes, and rational inequalities in context, such as keeping an average cost below a target.

  • 4 lessons
  • About 130 min
  • Quiz: 11 questions
Free starter

Mathematics · Grade 12

Exponential and Logarithmic Models

Learners use exponential and logarithmic functions as modeling tools: cooling toward room temperature, logistic growth with a carrying capacity, straightening exponential data with a semi-log plot, and logarithmic scales such as pH and decibels. Throughout, they compare models and explain which assumptions each one makes.

  • 4 lessons
  • About 130 min
  • Quiz: 10 questions
Free starter

Mathematics · Grade 12

Trigonometric Functions and Identities

Learners extend trigonometry to all six functions on the unit circle, define inverse trigonometric functions on restricted domains, verify identities with chains of justified steps, disprove false identities with counterexamples, and derive and use the sum, difference and double-angle formulas.

  • 4 lessons
  • About 135 min
  • Quiz: 11 questions
Free starter

Mathematics · Grade 12

Trigonometric Equations and Applications

Learners solve trigonometric equations on an interval and in general form, then apply trigonometry to triangles that are not right triangles: the Law of Sines with its ambiguous case, the Law of Cosines, the area formula ½ab sin C, navigation with bearings, and periodic motion modeled by sine and cosine.

  • 4 lessons
  • About 135 min
  • Quiz: 11 questions
Free starter

Mathematics · Grade 12

Vectors and Parametric Representations

Learners represent quantities with both size and direction as vectors, combine them, use the dot product to measure angles and work, solve navigation and force problems, and describe motion with parametric equations such as the path of a launched ball. An optional honors lesson introduces polar coordinates.

  • 5 lessons
  • About 145 min
  • Quiz: 11 questions

Mathematics · Grade 12

Conic Sections and Coordinate Models

Learners study circles, parabolas, ellipses and hyperbolas as sets of points defined by distances. They complete the square to find centers, derive the equation of a parabola from its focus and directrix, read foci and eccentricity from equations, classify conics from general equations, and use reflective properties in designs such as dishes, reflectors and orbits.

  • 4 lessons
  • About 135 min
  • Quiz: 11 questions

Mathematics · Grade 12

Sequences, Series and Mathematical Reasoning

Learners prove statements about all natural numbers with mathematical induction, manipulate sigma notation, decide when an infinite geometric series converges and find its sum, expand powers with the binomial theorem and Pascal's triangle, and investigate the long-run behavior of sequences, including recursive ones.

  • 4 lessons
  • About 140 min
  • Quiz: 11 questions

Mathematics · Grade 12

Probability and Statistical Model Critique

Learners count outcomes with permutations and combinations, use expected value to compare decisions such as buying a warranty or guessing on a test, model repeated trials with the binomial distribution, and critique statistical claims: biased samples, misleading graphs, overfitted models and confusing conditional probabilities.

  • 4 lessons
  • About 135 min
  • Quiz: 11 questions

Mathematics · Grade 12

Rates of Change and Limits Readiness

Learners prepare for calculus by moving from average to instantaneous rates of change: secant slopes that approach a tangent slope, difference quotients simplified with algebra, limits read from tables, graphs and formulas, informal continuity, and limits at infinity that describe end behavior.

  • 4 lessons
  • About 135 min
  • Quiz: 11 questions

Mathematics · Grade 12

Choose a Calculus, Statistics or Modeling Extension

Learners meet three directions that mathematics takes after precalculus: calculus (finding accumulated change from a rate), statistics (estimating with uncertainty from random samples), and mathematical modeling (optimizing a decision under constraints). Every learner works through all three short extensions, decides which tool fits which question, and goes deeper in the one they choose.

  • 4 lessons
  • About 140 min
  • Quiz: 11 questions

Mathematics · Grade 12

A Quantitative Capstone and Explanation

In this capstone, learners carry a quantitative question from start to finish: they make a vague question precise, choose and justify a model or method, compute and check results, test how sensitive conclusions are to assumptions, and explain the findings honestly to a non-specialist audience. The quiz also retrieves key skills from across the year.

  • 4 lessons
  • About 150 min
  • Quiz: 11 questions