Algebra I
Where most people decide they are bad at math. Balance scales, factoring as rectangle area, and parabolas you can watch move.
17 units · 95 topics · 430 questions
What a variable actually stands for, the order operations must happen in, and the two moves that make every later unit possible.
What a Variable Actually Represents · Order of Operations · Evaluating Algebraic Expressions · Combining Like Terms · +1 more
Solving an equation is keeping a scale balanced -- every move you make to one side you make to the other, until x stands alone.
What It Means to Solve an Equation · One-Step Equations · Two-Step Equations · Equations with Variables on Both Sides · +2 more
A coordinate plane turns an equation into a picture -- every point on the line is a solution, and the line's steepness is its slope.
The Coordinate Plane and Plotting Points · What the Graph of an Equation Actually Means · Graphing a Line by Plotting Points · x- and y-Intercepts · +2 more
The same line written three different ways -- slope-intercept, point-slope, and standard form -- plus what makes two lines parallel or perpendicular.
Slope-Intercept Form · Point-Slope Form · Standard Form of a Linear Equation · Converting Between Forms · +3 more
Two lines drawn on the same plane -- their intersection point is the one pair of numbers that satisfies both equations at once.
What a System's Solution Means · Solving Systems by Graphing · Solving Systems by Substitution · Solving Systems by Elimination · +2 more
An inequality keeps a whole range of numbers true at once, drawn as a ray or a shaded region instead of a single point.
Solving One-Variable Inequalities · Why You Flip the Inequality Sign · Compound Inequalities · Graphing Two-Variable Inequalities · +2 more
A function is a rule with exactly one output for every input -- the same idea whether it's written as a table, a graph, or f(x).
What Makes a Relation a Function · Function Notation · Evaluating Functions · Domain and Range · +2 more
A sequence is a function whose inputs are the counting numbers -- arithmetic sequences add the same amount each step, geometric ones multiply.
Arithmetic Sequences · Writing Rules for Arithmetic Sequences · Geometric Sequences · Writing Rules for Geometric Sequences
Absolute value measures distance from zero, which is why its equations split into two cases and its graph folds into a V.
What Absolute Value Actually Measures · Solving Absolute Value Equations · Graphing Absolute Value Functions · Piecewise Functions · +1 more
The exponent rules turn repeated multiplication into fast arithmetic, and radicals are just exponents written the other way around.
Exponent Rules: Product and Quotient · Power of a Power and Power of a Product · Zero and Negative Exponents · Simplifying Radical Expressions · +2 more
Exponential functions multiply by the same factor every step, which is why they eventually blow past any straight line no matter its slope.
Exponential versus Linear Growth · Writing Exponential Growth Functions · Writing Exponential Decay Functions · Compound Interest · +1 more
A polynomial is a sum of terms built from whole-number powers of x -- adding, subtracting, and multiplying them all follow rules you already know.
What a Polynomial Is · Adding and Subtracting Polynomials · Multiplying a Monomial by a Polynomial · Multiplying Two Binomials · +1 more
Factoring runs multiplication backward -- you're rebuilding the rectangle whose area is a given expression, one dimension at a time.
Factoring Out the Greatest Common Factor · Factoring Trinomials with Leading Coefficient 1 · Factoring Trinomials with a Leading Coefficient · Factoring a Difference of Squares · +2 more
Every quadratic graphs as a parabola -- its vertex, its width, and which way it opens all come straight from the coefficients.
The Shape of a Parabola · The Vertex and Axis of Symmetry · Transformations of Quadratic Functions · Graphing from Vertex Form · +2 more
The same quadratic equation can be solved four ways -- factoring, square roots, completing the square, or the quadratic formula -- and they agree.
Solving Quadratics by Factoring · Solving Quadratics by Taking Square Roots · Completing the Square · The Quadratic Formula · +2 more
Not every number can be written as a fraction -- irrational numbers fill in the gaps the rationals leave behind on the number line.
Classifying the Real Number System · Why Some Square Roots Never Terminate or Repeat · Approximating and Comparing Irrational Numbers · Operations on Rational and Irrational Numbers
A single number can summarize a whole data set's center or spread, and a scatter plot turns two related variables into one visible trend.
Measures of Center · Measures of Spread · Box Plots · Scatter Plots and Correlation · +2 more