What's next? Introduction Welcome! Click on this lesson to get started. Browse lessons Algebra Geometry Trigonometry Algebra II Calculus Statistics Learn about functions, graphs, lines, and polynomials. "Algebra" is the math for describing how different things are related. **SUBJECT** **COMPLETION** Log in to track progress Addition and subtraction [Number line](/content/learn/algebra/number-line/index.html) Locating integers and non-​integers on the number line | | | | --- | --- | | | Start lesson | | | Log in to review | [Addition](/content/learn/algebra/addition/index.html) Using the number line to add numbers | | | | --- | --- | | | Start lesson | | | Log in to review | [Subtraction](/content/learn/algebra/subtraction/index.html) Moving left on the number line | | | | --- | --- | | | Start lesson | | | Log in to review | [Adding negatives](/content/learn/algebra/adding-negatives/index.html) What happens when you add negative numbers? | | | | --- | --- | | | Start lesson | | | Log in to review | [Subtracting negatives](/content/learn/algebra/subtracting-negatives/index.html) Turns out it's addition! | | | | --- | --- | | | Start lesson | | | Log in to review | [Absolute value](/content/learn/algebra/absolute-value/index.html) The "size" of a number, or how far it is from zero | | | | --- | --- | | | Start lesson | | | Log in to review | [Number line distance](/content/learn/algebra/distance-1d/index.html) Ways to find the distance between any two numbers | | | | --- | --- | | | Start lesson | | | Log in to review | Multiplication and division [Multiplication](/content/learn/algebra/multiplication/index.html) Multiplying positive numbers, in any order | | | | --- | --- | | | Start lesson | | | Log in to review | [Multiplying by 1 and 0](/content/learn/algebra/multiplicative-identities/index.html) Discover what happens when you multiply by 1 and 0 | | | | --- | --- | | | Start lesson | | | Log in to review | [Division](/content/learn/algebra/division/index.html) Dividing positive numbers, and ways to think about it | | | | --- | --- | | | Start lesson | | | Log in to review | [Dividing by 0](/content/learn/algebra/divide-by-zero/index.html) An operation you just can't perform... | | | | --- | --- | | | Start lesson | | | Log in to review | [Order of operations](/content/learn/algebra/pmdas/index.html) Is there more than one way to evaluate an expression? | | | | --- | --- | | | Start lesson | | | Log in to review | [Distributive law](/content/learn/algebra/distributive-law/index.html) Getting rid of parentheses when you add and multiply | | | | --- | --- | | | Start lesson | | | Log in to review | [Multiplying negatives](/content/learn/algebra/multiplying-negatives/index.html) What happens when you multiply negatives together? | | | | --- | --- | | | Start lesson | | | Log in to review | [Dividing negatives](/content/learn/algebra/dividing-negatives/index.html) What happens when you divide negative numbers? | | | | --- | --- | | | Start lesson | | | Log in to review | [Distributing negatives](/content/learn/algebra/distribute-negative/index.html) Distributing a negative flips the signs | | | | --- | --- | | | Start lesson | | | Log in to review | [\[Brackets\] and {braces}](/content/learn/algebra/brackets/index.html) What to do when you have too many parentheses! | | | | --- | --- | | | Start lesson | | | Log in to review | [Finding the average](/content/learn/algebra/average/index.html) Discover how to find the "average" of numbers | | | | --- | --- | | | Start lesson | | | Log in to review | Factoring [Factors](/content/learn/algebra/factors/index.html) Dividing by a factor always gives you a whole number | | | | --- | --- | | | Start lesson | | | Log in to review | [Prime numbers](/content/learn/algebra/primes/index.html) Their only factors are 1 and themselves | | | | --- | --- | | | Start lesson | | | Log in to review | [Factoring out](/content/learn/algebra/factor-out/index.html) Pulling out common factors using the distributive law | | | | --- | --- | | | Start lesson | | | Log in to review | [Factoring out negatives](/content/learn/algebra/factor-out-negative/index.html) Flip the signs when you factor out negative numbers | | | | --- | --- | | | Start lesson | | | Log in to review | [Greatest common factor](/content/learn/algebra/greatest-common-factor/index.html) The biggest factor that numbers have in common | | | | --- | --- | | | Start lesson | | | Log in to review | [Relatively prime](/content/learn/algebra/relatively-prime/index.html) When two numbers have no common factors | | | | --- | --- | | | Start lesson | | | Log in to review | [Euclid's algorithm](/content/learn/algebra/euclids-algorithm/index.html) A 2000-​year-​old way to calculate the GCF | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Multiples](/content/learn/algebra/multiples/index.html) What you get when you multiply numbers by integers | | | | --- | --- | | | Start lesson | | | Log in to review | [Least common multiple](/content/learn/algebra/least-common-multiple/index.html) The smallest multiple numbers have in common | | | | --- | --- | | | Start lesson | | | Log in to review | Fractions [Intro to fractions](/content/learn/algebra/fractions/index.html) Draw and compare fractions, and convert to decimals | | | | --- | --- | | | Start lesson | | | Log in to review | [Multiplying fractions](/content/learn/algebra/multiplying-fractions/index.html) What's 1/2 times 3/5? Learn the trick in this lesson! | | | | --- | --- | | | Start lesson | | | Log in to review | [Comparing fractions](/content/learn/algebra/comparing-fractions/index.html) How to tell when fractions are equal or which is bigger | | | | --- | --- | | | Start lesson | | | Log in to review | [Cancellation](/content/learn/algebra/cancellation/index.html) Simplifying fractions by removing common factors | | | | --- | --- | | | Start lesson | | | Log in to review | [Adding fractions](/content/learn/algebra/adding-fractions/index.html) Add and subtract fractions using common denominators | | | | --- | --- | | | Start lesson | | | Log in to review | [Dividing fractions](/content/learn/algebra/dividing-fractions/index.html) Dividing by a fraction is really multiplying by its reciprocal! | | | | --- | --- | | | Start lesson | | | Log in to review | [Reciprocals](/content/learn/algebra/reciprocal/index.html) A number's multiplicative inverse is 1 over the number | | | | --- | --- | | | Start lesson | | | Log in to review | [Mixed fractions](/content/learn/algebra/mixed-numbers/index.html) Switching between mixed and improper fractions | | | | --- | --- | | | Start lesson | | | Log in to review | [Distributing division](/content/learn/algebra/distribute-division/index.html) The distributive law works for multiplying, but also dividing | | | | --- | --- | | | Start lesson | | | Log in to review | [When 'of' means multiply](/content/learn/algebra/multiply-of/index.html) Evaluating fractions of numbers (like 5/7 of 210) | | | | --- | --- | | | Start lesson | | | Log in to review | Powers and roots [Squaring a number](/content/learn/algebra/squares/index.html) Multiplying a number by itself | | | | --- | --- | | | Start lesson | | | Log in to review | [Raising to powers](/content/learn/algebra/higher-powers/index.html) Squaring, cubing, raising to the fourth, and so on... | | | | --- | --- | | | Start lesson | | | Log in to review | [Square roots](/content/learn/algebra/integer-roots/index.html) Work backwards to find the number that was squared | | | | --- | --- | | | Start lesson | | | Log in to review | [Roots of non-squares](/content/learn/algebra/noninteger-roots/index.html) How to find the roots of numbers that are NOT square | | | | --- | --- | | | Start lesson | | | Log in to review | [Square roots of negatives](/content/learn/algebra/negative-roots/index.html) Do negative numbers even have square roots? | | | | --- | --- | | | Start lesson | | | Log in to review | [Cube roots and beyond](/content/learn/algebra/higher-roots/index.html) Cube roots, fourth roots, fifth roots, and so on... | | | | --- | --- | | | Start lesson | | | Log in to review | [PEMDAS](/content/learn/algebra/pemdas/index.html) Order of operations, now with exponents! | | | | --- | --- | | | Start lesson | | | Log in to review | Rules for powers [Multiplying powers](/content/learn/algebra/multiplying-powers/index.html) A rule for multiplying one power by another | | | | --- | --- | | | Start lesson | | | Log in to review | [Dividing powers](/content/learn/algebra/dividing-powers/index.html) A rule for dividing one power by another | | | | --- | --- | | | Start lesson | | | Log in to review | [Raising powers to powers](/content/learn/algebra/combining-powers/index.html) A rule for raising one power to another | | | | --- | --- | | | Start lesson | | | Log in to review | [Distributing powers](/content/learn/algebra/distribute-powers/index.html) It works for multiplication and division, but that's it! | | | | --- | --- | | | Start lesson | | | Log in to review | [Raising to the zero](/content/learn/algebra/zero-power/index.html) What happens when you raise a number to the zero? | | | | --- | --- | | | Start lesson | | | Log in to review | [Negative powers](/content/learn/algebra/negative-powers/index.html) What does it mean to raise to a NEGATIVE exponent? | | | | --- | --- | | | Start lesson | | | Log in to review | [Roots as powers](/content/learn/algebra/root-powers/index.html) Taking a root is really the same as raising to a power | | | | --- | --- | | | Start lesson | | | Log in to review | [Fractional powers](/content/learn/algebra/fractional-powers/index.html) What does it mean to raise to the 2/3 power? | | | | --- | --- | | | Start lesson | | | Log in to review | [Distributing roots](/content/learn/algebra/splitting-roots/index.html) Roots are also exponents, so the same rules apply! | | | | --- | --- | | | Start lesson | | | Log in to review | [Simplifying roots](/content/learn/algebra/simplifying-roots/index.html) Getting smaller numbers under the root | | | | --- | --- | | | Start lesson | | | Log in to review | Solving equations [Solving for unknowns](/content/learn/algebra/number-line-solve/index.html) Solve for unknown values using the number line | | | | --- | --- | | | Start lesson | | | Log in to review | [Algebraic expressions](/content/learn/algebra/evaluate/index.html) Learn how to evaluate expressions with variables | | | | --- | --- | | | Start lesson | | | Log in to review | [Solving by adding](/content/learn/algebra/unitary-solve/index.html) Adding or subtracting on both sides of equations | | | | --- | --- | | | Start lesson | | | Log in to review | [Solving by multiplying](/content/learn/algebra/coefficient-solve/index.html) Multiplying or dividing on both sides of equations | | | | --- | --- | | | Start lesson | | | Log in to review | [Cross multiplication](/content/learn/algebra/cross-multiplication/index.html) A quick way to solve equations with fractions | | | | --- | --- | | | Start lesson | | | Log in to review | [Coefficients](/content/learn/algebra/coefficients/index.html) Numbers in front of variables | | | | --- | --- | | | Start lesson | | | Log in to review | [Combining like terms](/content/learn/algebra/simplify/index.html) Adding/subtracting terms with matching variables | | | | --- | --- | | | Start lesson | | | Log in to review | [Multi-step equations](/content/learn/algebra/linear-solve/index.html) Sometimes it takes more than one step to solve! | | | | --- | --- | | | Start lesson | | | Log in to review | [Multivariable equations](/content/learn/algebra/linear-multivariable/index.html) Solving equations when they have more than one variable | | | | --- | --- | | | Start lesson | | | Log in to review | [Unsolvable equations](/content/learn/algebra/no-solution/index.html) Some equations have no solutions, others have plenty! | | | | --- | --- | | | Start lesson | | | Log in to review | Inequalities and simultaneous equations [Inequalities](/content/learn/algebra/inequality-1d/index.html) Plotting inequalities on the number line | | | | --- | --- | | | Start lesson | | | Log in to review | [Solving inequalities](/content/learn/algebra/inequality-1d-solve/index.html) Solving and plotting multi-​step inequalities | | | | --- | --- | | | Start lesson | | | Log in to review | [Negative inequalities](/content/learn/algebra/inequality-1d-negative/index.html) What happens when you multiply by a negative | | | | --- | --- | | | Start lesson | | | Log in to review | [2 equations, 2 unknowns](/content/learn/algebra/two-equations/index.html) Solve for both variables when you have two equations | | | | --- | --- | | | Start lesson | | | Log in to review | [2 equations, no solution](/content/learn/algebra/two-equations-singular/index.html) Sometimes two equations have no solutions, or many! | | | | --- | --- | | | Start lesson | | | Log in to review | Coordinates [The coordinate plane](/content/learn/algebra/cartesian/index.html) Plotting points and finding their coordinates | | | | --- | --- | | | Start lesson | | | Log in to review | [Quadrants](/content/learn/algebra/quadrants/index.html) The four quadrants, and the coordinates they contain | | | | --- | --- | | | Start lesson | | | Log in to review | [Finding a midpoint](/content/learn/algebra/midpoint/index.html) Given two points, which point is exactly halfway between? | | | | --- | --- | | | Start lesson | | | Log in to review | Slope [Slope (an introduction)](/content/learn/algebra/slope-intro/index.html) A number that tells you the steepness of a line | | | | --- | --- | | | Start lesson | | | Log in to review | [Slope formula](/content/learn/algebra/slope-formula/index.html) How to calculate the slope between any two points | | | | --- | --- | | | Start lesson | | | Log in to review | [Negative slopes](/content/learn/algebra/slope-negative/index.html) Discover what it means when slope is negative | | | | --- | --- | | | Start lesson | | | Log in to review | [Zero slope](/content/learn/algebra/slope-zero/index.html) What are the slopes of horizontal and vertical lines? | | | | --- | --- | | | Start lesson | | | Log in to review | [Find the slope of any line](/content/learn/algebra/slope-read/index.html) Two steps that will always give you the correct slope | | | | --- | --- | | | Start lesson | | | Log in to review | [Parallel slopes](/content/learn/algebra/slope-parallel/index.html) Explore why parallel lines have the same slope | | | | --- | --- | | | Start lesson | | | Log in to review | [Perpendicular slopes](/content/learn/algebra/slope-perpendicular/index.html) Discover how slopes of perpendicular lines relate | | | | --- | --- | | | Start lesson | | | Log in to review | Lines [Graphing an equation](/content/learn/algebra/first-line/index.html) Turn an equation into your very first graph! | | | | --- | --- | | | Start lesson | | | Log in to review | [Slope-intercept form](/content/learn/algebra/slope-intercept/index.html) Turning an equation into a line, and vice versa | | | | --- | --- | | | Start lesson | | | Log in to review | [Point-slope form](/content/learn/algebra/point-slope/index.html) A formula for when you know the slope and coordinates | | | | --- | --- | | | Start lesson | | | Log in to review | [Reading graphs](/content/learn/algebra/read-graph/index.html) Forget equations, let's just look at the graphs! | | | | --- | --- | | | Start lesson | | | Log in to review | [Intercepts](/content/learn/algebra/intercepts/index.html) Figuring out where lines cross the x-​ and y-​axes | | | | --- | --- | | | Start lesson | | | Log in to review | [Solving for intersections](/content/learn/algebra/intersection-solve/index.html) Given two lines, can you determine where they cross? | | | | --- | --- | | | Start lesson | | | Log in to review | [Graphing absolute value](/content/learn/algebra/absolute-graph/index.html) Exploring a graph that's not a line | | | | --- | --- | | | Start lesson | | | Log in to review | [Inequalities (2 variables)](/content/learn/algebra/inequality-2d/index.html) Simplify inequalities with two variables and test solutions | | | | --- | --- | | | Start lesson | | | Log in to review | [Graphing inequalities](/content/learn/algebra/inequality-2d-graph/index.html) Graph inequalities on the coordinate plane | | | | --- | --- | | | Start lesson | | | Log in to review | Polynomials [What are polynomials?](/content/learn/algebra/polynomials-intro/index.html) Learn about a common type of algebraic expression | | | | --- | --- | | | Start lesson | | | Log in to review | [Adding polynomials](/content/learn/algebra/polynomials-add/index.html) Computing sums and differences of polynomials | | | | --- | --- | | | Start lesson | | | Log in to review | [Multiplying monomials](/content/learn/algebra/monomials-multiply/index.html) Multiply and divide polynomials with one term | | | | --- | --- | | | Start lesson | | | Log in to review | [Multiplying binomials](/content/learn/algebra/binomials-multiply/index.html) Multiply binomials together using FOIL | | | | --- | --- | | | Start lesson | | | Log in to review | [Multiplying polynomials](/content/learn/algebra/polynomials-multiply/index.html) How to multiply polynomials with many terms | | | | --- | --- | | | Start lesson | | | Log in to review | [Difference of squares](/content/learn/algebra/difference-of-squares/index.html) A neat trick for simplifying certain binomials | | | | --- | --- | | | Start lesson | | | Log in to review | Quadratics [Quadratic equations](/content/learn/algebra/quadratic-equations/index.html) Sometimes, equations can have two solutions | | | | --- | --- | | | Start lesson | | | Log in to review | [Graphing a parabola](/content/learn/algebra/first-parabola/index.html) Plot points to draw your very first parabola | | | | --- | --- | | | Start lesson | | | Log in to review | [Graphing quadratics](/content/learn/algebra/quadratic-graph/index.html) Every quadratic graph boils down to these 3 numbers | | | | --- | --- | | | Start lesson | | | Log in to review | [Factoring quadratics](/content/learn/algebra/quadratic-factor/index.html) An extremely useful trick for solving some equations | | | | --- | --- | | | Start lesson | | | Log in to review | [The quadratic formula](/content/learn/algebra/quadratic-formula-proof/index.html) A method for solving ANY quadratic equation! | | | | --- | --- | | | Start lesson | | | Log in to review | [Discriminants and roots](/content/learn/algebra/quadratic-formula-apply/index.html) A quick way to tell how many solutions a quadratic has | | | | --- | --- | | | Start lesson | | | Log in to review | The mathematics of lines, shapes, and angles. Essential stuff for describing the world around you. **SUBJECT** **COMPLETION** Log in to track progress Lines and angles [Lines, rays, & segments](/content/learn/geometry/lines-rays/index.html) Learn about lines, rays, and line segments | | | | --- | --- | | | Start lesson | | | Log in to review | [Angles and degrees](/content/learn/geometry/degrees/index.html) Learn what angles are, and how to measure them | | | | --- | --- | | | Start lesson | | | Log in to review | [Right, acute, and obtuse](/content/learn/geometry/angle-names/index.html) Learn the names for angles of all sizes | | | | --- | --- | | | Start lesson | | | Log in to review | [Parallel lines](/content/learn/geometry/parallel/index.html) Lines that never, ever cross | | | | --- | --- | | | Start lesson | | | Log in to review | [Perpendicular lines](/content/learn/geometry/perpendicular/index.html) Lines that cross, forming right angles | | | | --- | --- | | | Start lesson | | | Log in to review | [Naming angles](/content/learn/geometry/angle-labels/index.html) With these rules, you know which angle you mean | | | | --- | --- | | | Start lesson | | | Log in to review | [Perpendicular bisectors](/content/learn/geometry/perpendicular-bisector/index.html) The equidistant points also cut segments in two | | | | --- | --- | | | Start lesson | | | Log in to review | Related angles [Combining angles](/content/learn/geometry/adding-angles/index.html) Adding and subtracting adjacent angles | | | | --- | --- | | | Start lesson | | | Log in to review | [Complementary angles](/content/learn/geometry/complementary/index.html) Learn about complementary and supplementary angles | | | | --- | --- | | | Start lesson | | | Log in to review | [Coterminal angles](/content/learn/geometry/coterminal-angles/index.html) What about angles bigger than 360 degrees? | | | | --- | --- | | | Start lesson | | | Log in to review | [Vertical angles](/content/learn/geometry/vertical-angles/index.html) Angles on opposite sides of intersecting lines | | | | --- | --- | | | Start lesson | | | Log in to review | [Corresponding angles](/content/learn/geometry/corresponding-angles/index.html) Parallel lines form congruent angles in matching places | | | | --- | --- | | | Start lesson | | | Log in to review | [Alternate interior angles](/content/learn/geometry/alternate-interior-angles/index.html) Congruent angles INSIDE parallel lines | | | | --- | --- | | | Start lesson | | | Log in to review | [Alternate exterior angles](/content/learn/geometry/alternate-exterior-angles/index.html) Congruent angles OUTSIDE parallel lines | | | | --- | --- | | | Start lesson | | | Log in to review | Triangles [Polygons](/content/learn/geometry/polygons/index.html) A fancy name for shapes with straight sides | | | | --- | --- | | | Start lesson | | | Log in to review | [Congruence](/content/learn/geometry/congruence/index.html) When line segments, angles, or shapes are the same | | | | --- | --- | | | Start lesson | | | Log in to review | [Triangles](/content/learn/geometry/triangles/index.html) Introducing triangles and three different types of them | | | | --- | --- | | | Start lesson | | | Log in to review | [180 degrees in a triangle](/content/learn/geometry/triangle-180/index.html) See if it's really true, and then prove it! | | | | --- | --- | | | Start lesson | | | Log in to review | [Triangles by angle](/content/learn/geometry/triangle-angles/index.html) Learn about right, acute, and obtuse triangles | | | | --- | --- | | | Start lesson | | | Log in to review | [Altitudes](/content/learn/geometry/altitudes/index.html) Perpendicular line segments in triangles | | | | --- | --- | | | Start lesson | | | Log in to review | [Medians of triangles](/content/learn/geometry/triangle-median/index.html) Line segments connecting vertices and midpoints | | | | --- | --- | | | Start lesson | | | Log in to review | [Isosceles triangles](/content/learn/geometry/isosceles-angles/index.html) They have two equal sides, but what about their angles? | | | | --- | --- | | | Start lesson | | | Log in to review | [Triangle inequality](/content/learn/geometry/triangle-inequality/index.html) The rules a triangle's side lengths always follow | | | | --- | --- | | | Start lesson | | | Log in to review | [Big angles, longer sides](/content/learn/geometry/triangle-compare/index.html) In triangles, sides and their opposite angles are related! | | | | --- | --- | | | Start lesson | | | Log in to review | Triangle congruence and similarity [Similarity](/content/learn/geometry/similarity/index.html) When they have the same shape, but different sizes | | | | --- | --- | | | Start lesson | | | Log in to review | [Similar ratios](/content/learn/geometry/similar-ratios/index.html) Use similarity to find unknown side lengths! | | | | --- | --- | | | Start lesson | | | Log in to review | [SSS Postulate](/content/learn/geometry/triangles-sss/index.html) Using sides to see if triangles are congruent | | | | --- | --- | | | Start lesson | | | Log in to review | [SAS Postulate](/content/learn/geometry/triangles-sas/index.html) Congruence check using two sides and the angle between | | | | --- | --- | | | Start lesson | | | Log in to review | [ASA Postulate](/content/learn/geometry/triangles-asa/index.html) Congruence check using two angles and the side between | | | | --- | --- | | | Start lesson | | | Log in to review | [AAS Postulate](/content/learn/geometry/triangles-aas/index.html) The final congruence check for triangles | | | | --- | --- | | | Start lesson | | | Log in to review | [AA Postulate (Similarity)](/content/learn/geometry/triangles-aa/index.html) Triangles are similar when they have matching angles | | | | --- | --- | | | Start lesson | | | Log in to review | [SSA (ambiguous case)](/content/learn/geometry/triangles-ssa/index.html) Depending on the sides, you can have 0, 1, or 2 triangles! | | | | --- | --- | | | Start lesson | | | Log in to review | Polygons and quadrilaterals [Quadrilaterals](/content/learn/geometry/quads/index.html) Learn about rectangles, rhombi, and more! | | | | --- | --- | | | Start lesson | | | Log in to review | [Regular polygons](/content/learn/geometry/regular-polygons/index.html) Polygons with equal sides and angles | | | | --- | --- | | | Start lesson | | | Log in to review | [Perimeter](/content/learn/geometry/perimeter/index.html) Tricks for finding the distance around a shape | | | | --- | --- | | | Start lesson | | | Log in to review | [Angles in polygons](/content/learn/geometry/polygon-180/index.html) Find a formula for the sum of the angles in any polygon | | | | --- | --- | | | Start lesson | | | Log in to review | [Parallelogram angles](/content/learn/geometry/parallelogram-angles/index.html) Opposite angles are congruent in parallelograms | | | | --- | --- | | | Start lesson | | | Log in to review | [Parallelogram sides](/content/learn/geometry/parallelogram-sides/index.html) Opposite sides are congruent in parallelograms | | | | --- | --- | | | Start lesson | | | Log in to review | [Paralleogram diagonals](/content/learn/geometry/parallelogram-diagonals/index.html) In parallelograms, diagonals always bisect each other | | | | --- | --- | | | Start lesson | | | Log in to review | [Rectangle diagonals](/content/learn/geometry/rectangle-diagonals/index.html) Rectangles always have two congruent diagonals | | | | --- | --- | | | Start lesson | | | Log in to review | [Rhombus diagonals](/content/learn/geometry/rhombus-diagonals/index.html) In rhombi, the diagonals are always perpendicular | | | | --- | --- | | | Start lesson | | | Log in to review | [Trapezoid angles](/content/learn/geometry/trapezoid-angles/index.html) Supplementary pairs of angles in trapezoids | | | | --- | --- | | | Start lesson | | | Log in to review | Area of polygons [Intro to area](/content/learn/geometry/area/index.html) Measuring how much space is inside a shape | | | | --- | --- | | | Start lesson | | | Log in to review | [Rectangle area](/content/learn/geometry/rectangle-area/index.html) Discover the formula for the area of a rectangle | | | | --- | --- | | | Start lesson | | | Log in to review | [Parallelogram area](/content/learn/geometry/parallelogram-area/index.html) Discover the formula for the area of a parallelogram | | | | --- | --- | | | Start lesson | | | Log in to review | [Triangle area](/content/learn/geometry/triangle-area/index.html) Discover a formula for the area of any triangle | | | | --- | --- | | | Start lesson | | | Log in to review | [Trapezoid area](/content/learn/geometry/trapezoid-area/index.html) Discover the formula for the area of a trapezoid | | | | --- | --- | | | Start lesson | | | Log in to review | [Rhombus area](/content/learn/geometry/rhombus-area/index.html) Find a rhombus' area using its diagonals | | | | --- | --- | | | Start lesson | | | Log in to review | The Pythagorean theorem [Pythagorean theorem](/content/learn/geometry/pythagorean-theorem/index.html) How the sides of right triangles are related | | | | --- | --- | | | Start lesson | | | Log in to review | [Pythagorean triples](/content/learn/geometry/pythagorean-triples/index.html) When whole numbers are the sides of right triangles | | | | --- | --- | | | Start lesson | | | Log in to review | [Generating triples](/content/learn/geometry/pythagorean-triples-generate/index.html) Ways to write out every last Pythagorean triple | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Distance formula](/content/learn/geometry/distance-formula/index.html) Find the distance between any two points | | | | --- | --- | | | Start lesson | | | Log in to review | [Equilateral area](/content/learn/geometry/equilateral-area/index.html) Finding the area of equilateral and isosceles triangles | | | | --- | --- | | | Start lesson | | | Log in to review | [Heron's formula](/content/learn/geometry/herons-formula/index.html) Another way to find the area of a triangle | | | | --- | --- | | | Start lesson | | | Log in to review | [Proving Heron's formula](/content/learn/geometry/herons-formula-proof/index.html) You might know the formula, but where does it come from? | | | | --- | --- | | | Start lesson | | | Reviews coming soon | Circles, ellipses, and their areas [Circles](/content/learn/geometry/circles/index.html) An intro to circles, radii, diameters, and chords | | | | --- | --- | | | Start lesson | | | Log in to review | [Circumference and Pi](/content/learn/geometry/circumference/index.html) Find the distance around a circle (and then eat some pi) | | | | --- | --- | | | Start lesson | | | Log in to review | [Size of the Earth](/content/learn/geometry/earth-size/index.html) Use shadows to measure the Earth's circumference! | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Ellipses](/content/learn/geometry/ellipse/index.html) What you get when you "stretch" a circle | | | | --- | --- | | | Start lesson | | | Log in to review | [Area of a circle](/content/learn/geometry/circle-area/index.html) Using circumference to find a circle's area | | | | --- | --- | | | Start lesson | | | Log in to review | [Cavalieri's principle](/content/learn/geometry/cavalieri-2d/index.html) Comparing shapes to find areas of the unusual ones | | | | --- | --- | | | Start lesson | | | Log in to review | [Ellipse area](/content/learn/geometry/ellipse-area/index.html) Calculate how many people can fit on the Ellipse in DC | | | | --- | --- | | | Start lesson | | | Log in to review | [Areas of complex shapes](/content/learn/geometry/combining-areas/index.html) Add and subtract the ares of simpler shapes! | | | | --- | --- | | | Start lesson | | | Log in to review | Angles in circles [Central angles and arcs](/content/learn/geometry/central-angle/index.html) As you'll see, there are 360 degrees in every circle | | | | --- | --- | | | Start lesson | | | Log in to review | [Inscribed angles](/content/learn/geometry/inscribed-angle/index.html) Discover how inscribed angles are related to central angles! | | | | --- | --- | | | Start lesson | | | Log in to review | [Inscribing the diameter](/content/learn/geometry/inscribed-diameter/index.html) Prove that inscribed angles drawn to diameters are right | | | | --- | --- | | | Start lesson | | | Log in to review | [Arc length](/content/learn/geometry/arc-degrees/index.html) Finding a formula for the length of any arc | | | | --- | --- | | | Start lesson | | | Log in to review | [Sector area](/content/learn/geometry/sector-degrees/index.html) How to find the area of any slice of a circle | | | | --- | --- | | | Start lesson | | | Log in to review | Lines in circles [Secant and tangent lines](/content/learn/geometry/circle-lines/index.html) Some lines cross circles twice, others touch them only once | | | | --- | --- | | | Start lesson | | | Log in to review | [Congruent tangents](/content/learn/geometry/congruent-tangents/index.html) Prove that tangents from the same point are congruent | | | | --- | --- | | | Start lesson | | | Log in to review | [Circumscribed angles](/content/learn/geometry/circumscribed-angle/index.html) Discover how angles between tangents are related to arcs | | | | --- | --- | | | Start lesson | | | Log in to review | [Parallel chords](/content/learn/geometry/parallel-chords/index.html) Prove that the arcs between them are always congruent | | | | --- | --- | | | Start lesson | | | Log in to review | [Intersecting chords](/content/learn/geometry/chord-product/index.html) Discover a rule for how intersecting chords relate | | | | --- | --- | | | Start lesson | | | Log in to review | [Cyclic quadrilaterals](/content/learn/geometry/cyclic-quad/index.html) See how their opposite angles are related! | | | | --- | --- | | | Start lesson | | | Log in to review | [Intersecting secants](/content/learn/geometry/secant-product/index.html) Like chords, intersecting secants are also related! | | | | --- | --- | | | Start lesson | | | Log in to review | [Inscribed circles](/content/learn/geometry/inscribed-circle/index.html) Calculate the radius of any inscribed circle | | | | --- | --- | | | Start lesson | | | Log in to review | Volume [Intro to solids](/content/learn/geometry/shapes-3d/index.html) Learn the names and features of 3D shapes | | | | --- | --- | | | Start lesson | | | Log in to review | [Rectangular prisms](/content/learn/geometry/prism-volume/index.html) Discover how to find the volume of any box! | | | | --- | --- | | | Start lesson | | | Log in to review | [Prism volume](/content/learn/geometry/other-prism-volume/index.html) Find the volume of prisms and cylinders | | | | --- | --- | | | Start lesson | | | Log in to review | [Cavalieri's Principle (3D)](/content/learn/geometry/cavalieri-3d/index.html) Instead of matching widths, you'll be matching areas! | | | | --- | --- | | | Start lesson | | | Log in to review | [Pyramid volume](/content/learn/geometry/pyramid-volume/index.html) Starting with a cube, discover the pyramid volume formula | | | | --- | --- | | | Start lesson | | | Log in to review | [Cone volume](/content/learn/geometry/cone-volume/index.html) Find the volume of any cone, and learn about slant height | | | | --- | --- | | | Start lesson | | | Log in to review | [Sphere volume](/content/learn/geometry/sphere-volume/index.html) Use Cavalieri's principle to find the volume of a sphere | | | | --- | --- | | | Start lesson | | | Log in to review | Surface area [Prism surface area](/content/learn/geometry/prism-surface/index.html) Learn why ice is commonly shaped into cubes | | | | --- | --- | | | Start lesson | | | Log in to review | [Pyramid surface area](/content/learn/geometry/pyramid-surface/index.html) Find a pyramid's surface area using squares and triangles | | | | --- | --- | | | Start lesson | | | Log in to review | [Cylinder surface area](/content/learn/geometry/cylinder-surface/index.html) Unroll any cylinder to find its surface area! | | | | --- | --- | | | Start lesson | | | Log in to review | [Cone surface area](/content/learn/geometry/cone-surface/index.html) Discover and use the formula for a cone's surface area! | | | | --- | --- | | | Start lesson | | | Log in to review | [Sphere surface area](/content/learn/geometry/sphere-surface/index.html) Find the the total area of a sphere's curved surface | | | | --- | --- | | | Start lesson | | | Log in to review | [Internal diagonals](/content/learn/geometry/internal-diagonal/index.html) What's the distance between opposite corners of a cube? | | | | --- | --- | | | Start lesson | | | Log in to review | Transformations [Translation](/content/learn/geometry/translation/index.html) Moving points and shapes in the coordinate plane | | | | --- | --- | | | Start lesson | | | Log in to review | [Rotation](/content/learn/geometry/rotation/index.html) Rotating points and shapes around the origin | | | | --- | --- | | | Start lesson | | | Log in to review | [Reflection](/content/learn/geometry/reflection/index.html) Flipping across different axes (and the origin) | | | | --- | --- | | | Start lesson | | | Log in to review | [Dilation](/content/learn/geometry/stretch/index.html) Stretching shapes in one or two directions | | | | --- | --- | | | Start lesson | | | Log in to review | [Preserving congruence](/content/learn/geometry/preserving-congruence/index.html) See which transformations keep things congruent | | | | --- | --- | | | Start lesson | | | Log in to review | [Symmetry](/content/learn/geometry/symmetry/index.html) When reflection or rotation doesn't change anything | | | | --- | --- | | | Start lesson | | | Log in to review | Geometric optics [Why light bends](/content/learn/geometry/refraction/index.html) Using Fermat's principle to understand refraction | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Rainbows explained](/content/learn/geometry/rainbow/index.html) Use refraction to understand rainbows and their features | | | | --- | --- | | | Start lesson | | | Reviews coming soon | Trigonometry helps you understand any topic that involves distances, angles, or waves. The trig functions (sin, cos, and tan) show up all over science and engineering. **SUBJECT** **COMPLETION** Log in to track progress Radians [What's a "radian"?](/content/learn/trigonometry/radians/index.html) Discover another way to measure angles. | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Radians and degrees](/content/learn/trigonometry/radians-conversion/index.html) How to switch back and forth between units for angles | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Lengths of circular arcs](/content/learn/trigonometry/arc-radian/index.html) A formula for arc length in terms of radius and angle | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Sectors](/content/learn/trigonometry/sector-area/index.html) Learn what a sector is, and a formula for finding its area | | | | --- | --- | | | Start lesson | | | Reviews coming soon | Trig functions [Sides of right triangles](/content/learn/trigonometry/side-names/index.html) Your friendly hypotenuses, opposites, and adjacents | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Sine](/content/learn/trigonometry/sine/index.html) Your very first trig function | | | | --- | --- | | | Start lesson | | | Log in to review | [Cosine](/content/learn/trigonometry/cosine/index.html) Along with sine, cosine is a fundamental trig function | | | | --- | --- | | | Start lesson | | | Log in to review | [Tangent](/content/learn/trigonometry/tangent/index.html) Another important trig function (like sine and cosine) | | | | --- | --- | | | Start lesson | | | Log in to review | [Components (and cops)](/content/learn/trigonometry/components/index.html) Find legs of right triangles, and don't get pulled over! | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Sec, Csc, and Cot](/content/learn/trigonometry/secant/index.html) Secant and friends (three more trig functions) | | | | --- | --- | | | Start lesson | | | Reviews coming soon | Special angles [45 degrees](/content/learn/trigonometry/trig-45/index.html) Calculate the sine, cosine, and tangent of 45 degrees | | | | --- | --- | | | Start lesson | | | Log in to review | [30/60 degrees](/content/learn/trigonometry/trig-30/index.html) Calculate the sine, cosine, and tangent of 30 and 60 degrees | | | | --- | --- | | | Start lesson | | | Log in to review | [0/90 degrees](/content/learn/trigonometry/trig-90/index.html) Calculate the sine, cosine, and tangent of 0 and 90 degrees | | | | --- | --- | | | Start lesson | | | Reviews coming soon | The unit circle [Trig for larger angles](/content/learn/trigonometry/larger-angles/index.html) What's sin(250)? Use the unit circle to tackle bigger angles | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Trig for negative angles](/content/learn/trigonometry/negative-angles/index.html) Using the unit circle for trig with negative angles | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Trig for coterminals](/content/learn/trigonometry/coterminal-trig/index.html) How trig functions are related for coterminal angles | | | | --- | --- | | | Start lesson | | | Reviews coming soon | Inverse trig functions [Inverse sine](/content/learn/trigonometry/inverse-sin/index.html) A function that takes you from side ratios to angles | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Inverse cosine](/content/learn/trigonometry/inverse-cos/index.html) Another inverse trig function | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Inverse tangent](/content/learn/trigonometry/inverse-tan/index.html) And one last inverse trig function! | | | | --- | --- | | | Start lesson | | | Reviews coming soon | Trig identities [Trig identities](/content/learn/trigonometry/trig-identities-intro/index.html) The tools for simplifying trig expressions | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Addition identities](/content/learn/trigonometry/trig-identities-addition/index.html) Simplify trig functions of sums | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Negative angle identities](/content/learn/trigonometry/trig-identities-negative/index.html) Simplify trig functions of negative angles | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Subtraction identities](/content/learn/trigonometry/trig-identities-difference/index.html) Simplify trig functions of differences | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Double angle identities](/content/learn/trigonometry/trig-identities-double/index.html) Trig functions of twice an angle | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Triple angle identities](/content/learn/trigonometry/trig-identities-triple/index.html) Trig functions of three times an angle | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Pythagorean identities](/content/learn/trigonometry/trig-identities-pythagorean/index.html) Relating squares of trig functions | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Half angle identities](/content/learn/trigonometry/trig-identities-half/index.html) Trig functions of half an angle | | | | --- | --- | | | Start lesson | | | Reviews coming soon | Triangle formulas [Law of sines](/content/learn/trigonometry/law-of-sines/index.html) Relating angles and opposite sides for any triangle | | | | --- | --- | | | Start lesson | | | Log in to review | [Triangulation](/content/learn/trigonometry/triangulation/index.html) Real-​world application of the law of sines to find distances | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Law of cosines](/content/learn/trigonometry/law-of-cosines/index.html) Relating three sides and an angle for any triangle | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Triangle area: SAS](/content/learn/trigonometry/triangle-area-sas/index.html) Find a triangle's area using 2 sides and the angle between | | | | --- | --- | | | Start lesson | | | Reviews coming soon | Take the next step in Algebra! Here we'll introduce the most common functions you're likely to see, and different ways to describe functions. **SUBJECT** **COMPLETION** Log in to track progress Real numbers [Integers](/content/learn/precalculus/integers/index.html) Whole numbers, positives, and negatives | | | | --- | --- | | | Start lesson | | | Log in to review | [Rationals](/content/learn/precalculus/rationals/index.html) Numbers that are quotients of integers | | | | --- | --- | | | Start lesson | | | Log in to review | [Irrationals](/content/learn/precalculus/irrationals/index.html) Numbers that are NOT quotients of integers | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Real numbers](/content/learn/precalculus/reals/index.html) All the rationals and the irrationals | | | | --- | --- | | | Start lesson | | | Reviews coming soon | Imaginary and complex numbers [Imaginary numbers](/content/learn/precalculus/imaginary/index.html) Their squares are negative! | | | | --- | --- | | | Start lesson | | | Log in to review | [Working with imaginaries](/content/learn/precalculus/imaginary-operations/index.html) Add, subtract, multiply, and divide imaginary numbers | | | | --- | --- | | | Start lesson | | | Log in to review | [Complex numbers](/content/learn/precalculus/complex-numbers/index.html) Combining the real and the imaginary | | | | --- | --- | | | Start lesson | | | Log in to review | [The complex plane](/content/learn/precalculus/complex-plane/index.html) A way to graph complex numbers | | | | --- | --- | | | Start lesson | | | Log in to review | [Powers of _i_](/content/learn/precalculus/powers-of-i/index.html) Raising _i_ to positive and negative integer powers | | | | --- | --- | | | Start lesson | | | Reviews coming soon | Functions [Relations](/content/learn/precalculus/relations/index.html) Sets of (x,y) coordinates | | | | --- | --- | | | Start lesson | | | Log in to review | [Functions](/content/learn/precalculus/functions/index.html) Relations where each input gives exactly one output | | | | --- | --- | | | Start lesson | | | Log in to review | [Functional notation](/content/learn/precalculus/functional-notation/index.html) Explore what f(x) means, and evaluate functions | | | | --- | --- | | | Start lesson | | | Log in to review | [Continuity and smoothness](/content/learn/precalculus/continuity/index.html) Some functions end and others keep going | | | | --- | --- | | | Start lesson | | | Log in to review | [Describing functions](/content/learn/precalculus/describing-functions/index.html) Make your own functions, and live to tell the tale | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Concavity](/content/learn/precalculus/concavity/index.html) Math-​talk for "curvy" | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Odd and even functions](/content/learn/precalculus/odd-even/index.html) Turns out functions can be "odd" and "even" too | | | | --- | --- | | | Start lesson | | | Reviews coming soon | Exponents Logarithms Playing with functions [Piecewise functions](/content/learn/precalculus/piecewise/index.html) Franken-​functions. They're alive! | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Compositions](/content/learn/precalculus/compositions/index.html) Functions of functions | | | | --- | --- | | | Start lesson | | | Reviews coming soon | Conic sections Rational functions Polar functions The mathematics of change. And it'll use just about every branch of math you've learned before it. **SUBJECT** **COMPLETION** Log in to track progress Limits [Limits to infinity](/content/learn/calculus/horizontal-asymptotes/index.html) What happens to functions as _x_ gets really, really big? | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Vertical limits](/content/learn/calculus/vertical-asymptotes/index.html) Sometimes _y_ goes off to infinity | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Finite limits](/content/learn/calculus/finite-limits/index.html) Limits when both _x_ and _y_ stay finite | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [One-sided limits](/content/learn/calculus/one-sided-limits/index.html) Limits that come from only the left or right side | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Continuity (for real)](/content/learn/calculus/discontinuities/index.html) Dive deeper into continuity, using one-​sided limits | | | | --- | --- | | | Start lesson | | | Reviews coming soon | [Splitting limits](/content/learn/calculus/limit-rules/index.html) Tricks for simplifying limits (and when they don't work!) | | | | --- | --- | | | Start lesson | | | Reviews coming soon | Derivatives [Tangent lines](/content/learn/calculus/tangent-lines/index.html) Finding the "slope" of a curve | | | | --- | --- | | | Start lesson | | | Log in to review | [Drawing derivatives](/content/learn/calculus/drawing-derivatives/index.html) Learn what a derivative is, and draw your own | | | | --- | --- | | | Start lesson | | | Reviews coming soon | Integrals Series The math of data collection and analysis. Very useful for finding trends and making predictions! **SUBJECT** **COMPLETION** Log in to track progress Sensitivity analysis [Sensitivity and specificity](/content/learn/statistics/sensitivity/index.html) Quantifying whether tests for diseases are any good | | | | --- | --- | | | Start lesson | | | Log in to review | [Predictive value](/content/learn/statistics/predictive-value/index.html) If you test positive/negative, what are your chances? | | | | --- | --- | | | Start lesson | | | Log in to review | [Cutoffs and ROCs](/content/learn/statistics/test-cutoff/index.html) Sensitivity vs. specifity, cutoff selection, and ROC curves | | | | --- | --- | | | Start lesson | | | Log in to review | [Prevalence](/content/learn/statistics/prevalence/index.html) How rare a disease is, and how it affects PPV and NPV | | | | --- | --- | | | Start lesson | | | Log in to review | Distributions Regression analysis Hypothesis testing * * *