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
COMPLETION
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Addition and subtraction
Multiplication and division
Multiplying by 1 and 0
Discover what happens when you multiply by 1 and 0
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Order of operations
Is there more than one way to evaluate an expression?
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Factoring
Factoring out negatives
Flip the signs when you factor out negative numbers
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Fractions
Multiplying fractions
What's 1/2 times 3/5? Learn the trick in this lesson!
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Comparing fractions
How to tell when fractions are equal or which is bigger
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Dividing fractions
Dividing by a fraction is really multiplying by its reciprocal!
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Distributing division
The distributive law works for multiplying, but also dividing
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When 'of' means multiply
Evaluating fractions of numbers (like 5/7 of 210)
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Powers and roots
Roots of non-squares
How to find the roots of numbers that are NOT square
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Cube roots and beyond
Cube roots, fourth roots, fifth roots, and so on...
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Rules for powers
Distributing powers
It works for multiplication and division, but that's it!
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Solving equations
Solving by multiplying
Multiplying or dividing on both sides of equations
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Multivariable equations
Solving equations when they have more than one variable
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Unsolvable equations
Some equations have no solutions, others have plenty!
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Inequalities and simultaneous equations
2 equations, 2 unknowns
Solve for both variables when you have two equations
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2 equations, no solution
Sometimes two equations have no solutions, or many!
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Coordinates
Finding a midpoint
Given two points, which point is exactly halfway between?
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Slope
Find the slope of any line
Two steps that will always give you the correct slope
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Lines
Solving for intersections
Given two lines, can you determine where they cross?
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Inequalities (2 variables)
Simplify inequalities with two variables and test solutions
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Polynomials
Quadratics
Factoring quadratics
An extremely useful trick for solving some equations
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Discriminants and roots
A quick way to tell how many solutions a quadratic has
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The mathematics of lines, shapes, and angles. Essential stuff for describing the world around you.
SUBJECT
COMPLETION
COMPLETION
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Lines and angles
Related angles
Corresponding angles
Parallel lines form congruent angles in matching places
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Triangles
Isosceles triangles
They have two equal sides, but what about their angles?
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Big angles, longer sides
In triangles, sides and their opposite angles are related!
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Triangle congruence and similarity
AA Postulate (Similarity)
Triangles are similar when they have matching angles
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SSA (ambiguous case)
Depending on the sides, you can have 0, 1, or 2 triangles!
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Polygons and quadrilaterals
Angles in polygons
Find a formula for the sum of the angles in any polygon
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Paralleogram diagonals
In parallelograms, diagonals always bisect each other
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Area of polygons
The Pythagorean theorem
Proving Heron's formula
You might know the formula, but where does it come from?
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Circles, ellipses, and their areas
Circumference and Pi
Find the distance around a circle (and then eat some pi)
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Angles in circles
Central angles and arcs
As you'll see, there are 360 degrees in every circle
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Inscribed angles
Discover how inscribed angles are related to central angles!
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Inscribing the diameter
Prove that inscribed angles drawn to diameters are right
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Lines in circles
Secant and tangent lines
Some lines cross circles twice, others touch them only once
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Circumscribed angles
Discover how angles between tangents are related to arcs
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Volume
Cavalieri's Principle (3D)
Instead of matching widths, you'll be matching areas!
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Surface area
Pyramid surface area
Find a pyramid's surface area using squares and triangles
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Cone surface area
Discover and use the formula for a cone's surface area!
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Internal diagonals
What's the distance between opposite corners of a cube?
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Transformations
Geometric optics
Rainbows explained
Use refraction to understand rainbows and their features
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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
COMPLETION
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Radians
Radians and degrees
How to switch back and forth between units for angles
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Lengths of circular arcs
A formula for arc length in terms of radius and angle
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Trig functions
Sides of right triangles
Your friendly hypotenuses, opposites, and adjacents
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Components (and cops)
Find legs of right triangles, and don't get pulled over!
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Special angles
30/60 degrees
Calculate the sine, cosine, and tangent of 30 and 60 degrees
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0/90 degrees
Calculate the sine, cosine, and tangent of 0 and 90 degrees
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The unit circle
Trig for larger angles
What's sin(250)? Use the unit circle to tackle bigger angles
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Trig for negative angles
Using the unit circle for trig with negative angles
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Trig for coterminals
How trig functions are related for coterminal angles
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Inverse trig functions
Trig identities
Triangle formulas
Triangulation
Real-world application of the law of sines to find distances
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Triangle area: SAS
Find a triangle's area using 2 sides and the angle between
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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
COMPLETION
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Real numbers
Imaginary and complex numbers
Working with imaginaries
Add, subtract, multiply, and divide imaginary numbers
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Functions
Describing functions
Make your own functions, and live to tell the tale
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Odd and even functions
Turns out functions can be "odd" and "even" too
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Exponents
Logarithms
Playing with functions
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
COMPLETION
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Limits
Limits to infinity
What happens to functions as x gets really, really big?
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Continuity (for real)
Dive deeper into continuity, using one-sided limits
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Splitting limits
Tricks for simplifying limits (and when they don't work!)
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Derivatives
Integrals
Series
The math of data collection and analysis. Very useful for finding trends and making predictions!
SUBJECT
COMPLETION
COMPLETION
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Sensitivity analysis
Sensitivity and specificity
Quantifying whether tests for diseases are any good
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Cutoffs and ROCs
Sensitivity vs. specifity, cutoff selection, and ROC curves
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Distributions
Regression analysis
Hypothesis testing
