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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
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Mathematics · Grade 10

Geometric Reasoning and Definitions

The opening course of geometry builds the language and logic of proof. Learners work with undefined terms and precise definitions, analyze conditional statements and their converses, inverses and contrapositives, contrast inductive conjectures with deductive arguments, apply the segment and angle addition postulates, and write their first two-column and paragraph proofs, including the vertical angles theorem.

  • 4 lessons
  • About 120 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

Constructions and Transformations

Learners carry out classical compass-and-straightedge constructions as precise procedures and explain why they work, then describe rigid motions (translations, reflections and rotations) exactly with coordinate rules. They compose transformations, find sequences that map one figure onto another, and use rotations and reflections to describe the symmetry of polygons.

  • 4 lessons
  • About 120 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

Congruence and Rigid Motion

Learners define congruence through rigid motions, read congruence statements to find corresponding parts, and justify the triangle congruence criteria SSS, SAS, ASA, AAS and HL, including counterexamples showing why SSA and AAA fail. They plan and write two-column proofs of triangle congruence and then use congruent triangles (CPCTC) to prove further facts, such as the perpendicular bisector theorem.

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

Mathematics · Grade 10

Triangle Properties and Proof

Learners prove the triangle angle-sum and exterior angle theorems, the isosceles triangle theorem and its converse, and use the triangle inequality and the midsegment theorem. They then meet the four classical points of concurrency (circumcenter, incenter, centroid and orthocenter), prove why the circumcenter is equidistant from the vertices, and apply the centroid's 2 : 1 property.

  • 4 lessons
  • About 125 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

Parallel Lines and Coordinate Reasoning

Learners prove the angle relationships formed when a transversal crosses parallel lines and use their converses to prove lines parallel. They connect parallel and perpendicular lines to slopes, write equations of such lines, use the distance and midpoint formulas, partition segments in a given ratio, and write coordinate proofs that classify triangles and quadrilaterals.

  • 4 lessons
  • About 125 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

Similarity and Scale

Learners study dilations and their properties, define similarity with similarity transformations, and use the AA, SAS and SSS similarity criteria to find unknown lengths, including indirect measurement with shadows. They prove the triangle proportionality (side-splitter) theorem and the Pythagorean theorem with similar triangles, and apply scale factors to maps, models, areas and volumes. An optional honors lesson develops geometric means in right triangles.

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

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

Right Triangles and Trigonometric Ratios

Learners use the Pythagorean theorem and its converse to find lengths and classify triangles, and learn the 45°–45°–90° and 30°–60°–90° relationships. They see sine, cosine and tangent as ratios that similar right triangles share, use them and their inverses to find sides and angles, connect sine and cosine of complementary angles, and solve angle-of-elevation and depression problems. An optional honors lesson introduces the Law of Sines, the Law of Cosines and the area formula ½ab sin C.

  • 5 lessons
  • About 135 min
  • Quiz: 11 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

Quadrilaterals and Polygons

Learners prove the properties of parallelograms with congruent triangles, learn several ways to prove that a quadrilateral is a parallelogram, and distinguish rectangles, rhombuses and squares by their diagonals. They study trapezoids and kites, organize quadrilaterals in a hierarchy, and derive and apply the interior and exterior angle sums of polygons.

  • 4 lessons
  • About 125 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

Circles, Arcs and Angles

Learners relate central angles, arcs and inscribed angles and prove the inscribed angle theorem, including the right angle in a semicircle and the supplementary opposite angles of a cyclic quadrilateral. They use tangent and chord properties, compute arc lengths and sector areas, meet radian measure as arc length divided by radius, and write and analyze equations of circles on the coordinate plane.

  • 4 lessons
  • About 130 min
  • Quiz: 11 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 10

Area, Surface Area and Volume

Learners justify area formulas by cutting and rearranging, including an informal limit argument for the area of a circle, and explain volume formulas with Cavalieri's principle and the one-third relationship between pyramids and prisms. They compute surface areas from nets, identify cross-sections and solids of revolution, and apply density and scale factors in modeling problems. An optional honors lesson shows three pyramids filling a cube.

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

Mathematics · Grade 10

Geometric Modeling and Constraints

Learners use geometry to model and design real objects: they represent irregular objects with simple shapes and state their assumptions, explore designs numerically to find the best option under a constraint (the largest pen, the biggest open box), check whether designs satisfy limits on slope, clearance and capacity, and reason about measurement precision before communicating a recommendation.

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

Mathematics · Grade 10

A Proof and Design Portfolio

The geometry capstone. Learners choose among two-column, paragraph, coordinate and transformation proofs for the same theorem, critique and repair flawed proofs, and complete a design brief for a fictional community-garden pavilion that draws on area, volume, similarity and trigonometry. They finish by assembling portfolio pieces: a polished proof and a design report written for a non-specialist audience.

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

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

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

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

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

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

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

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

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

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

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