- Courses
- SAT Math
Mathematics
SAT Math
Preparation for the Math section of the digital SAT, from essential skills through algebra, advanced math, data analysis and geometry to test strategy.
- Introductory
- 59 lesson pairs
- Free
Nothing loads from YouTube until you press play.
About this course
This course prepares you for the Math section of the digital SAT. It starts with the essential skills that every question relies on, then follows the four content areas of the test, algebra, advanced math, problem solving and data analysis, and geometry and trigonometry.
All the video lessons are out. Every lesson has its own page with precise definitions, a worked example for each key term and a few exercises with answers, many of them written in the style of test questions, so you can read before or after each video.
The last unit covers the graphing calculator built into the test, for solving equations, finding intersections and checking models.
To put it all together, there are three full practice tests, at beginner, intermediate and advanced level, and a set of 24 tips with explained examples. Each has its own page with every question, its answer and explanation, and a link to the moment in the video where it is solved.
Full practice tests and strategies
Good to know first
- Arithmetic with fractions, decimals and negative numbers
- Basic algebra with one variable
- Basic geometry of angles, triangles and circles
Course outline
All 59 lesson pairs are on YouTube. Each pair is a theory video followed by a practice video, numbered as parts in the video titles. Open a unit to see its lessons, or follow a lesson for its definitions and examples.
Essential Skills
All 6 pairs on YouTubeOpen the Essential Skills unit pageNumbers and Proportional Reasoning
- Fractions, Signs and Order of OperationsOn YouTube
Theory part 1Practice part 2
fraction, numerator, denominator, negative number, order of operations and parentheses
- Ratios and ProportionsOn YouTube
Theory part 3Practice part 4
ratio, proportion, equivalent ratio, unit rate and direct proportion
Builds on Fractions, Signs and Order of Operations.
- Percentages and Percent ChangeOn YouTube
Theory part 5Practice part 6
percentage, percent change, original value, multiplier, reverse percentage and percentage point
Builds on Fractions, Signs and Order of Operations and Ratios and Proportions.
- Units, Rates and ConversionsOn YouTube
Theory part 7Practice part 8
unit, conversion factor, rate, dimensional analysis, squared unit and cubed unit
Builds on Fractions, Signs and Order of Operations and Ratios and Proportions.
Expressions and Word Problems
Theory part 9Practice part 10
variable, constant, coefficient, term, factor, expression, equation and substitution
Builds on Fractions, Signs and Order of Operations.
- Turning Word Problems into EquationsOn YouTube
Theory part 11Practice part 12
unknown quantity, relationship, constraint, equation model, at least, at most and per
Builds on Ratios and Proportions, Percentages and Percent Change, Units, Rates and Conversions and Expressions, Substitution and Mathematical Language.
Algebra
All 13 pairs on YouTubeOpen the Algebra unit pageLinear Equations
- Solving Linear EquationsOn YouTube
Theory part 13Practice part 14
linear equation, solution, equivalent equation, distributive property, inverse operation and requested expression
Builds on Fractions, Signs and Order of Operations and Expressions, Substitution and Mathematical Language.
- Rearranging FormulasOn YouTube
Theory part 15Practice part 16
formula, subject of a formula, parameter, inverse operation, nonzero denominator and exceptional parameter case
Builds on Solving Linear Equations.
Theory part 17Practice part 18
identity, contradiction, no solution, infinitely many solutions, coefficient, constant and parameter case
Builds on Solving Linear Equations.
Functions and Lines
- Coordinates, Functions and GraphsOn YouTube
Theory part 19Practice part 20
ordered pair, coordinate, input, output, function notation, table, graph, domain, reverse input and input expression
Builds on Expressions, Substitution and Mathematical Language.
- Slope and Rate of ChangeOn YouTube
Theory part 21Practice part 22
slope, rise, run, rate of change, horizontal line and vertical line
Builds on Units, Rates and Conversions and Coordinates, Functions and Graphs.
- Intercepts and Linear ModelsOn YouTube
Theory part 23Practice part 24
x-intercept, y-intercept, initial value, linear model and slope-intercept form
Builds on Solving Linear Equations, Coordinates, Functions and Graphs and Slope and Rate of Change.
- Writing the Equation of a LineOn YouTube
Theory part 25Practice part 26
point-slope form, slope-intercept form, standard form and two-point equation
Builds on Rearranging Formulas, Coordinates, Functions and Graphs, Slope and Rate of Change and Intercepts and Linear Models.
- Parallel and Perpendicular LinesOn YouTube
Theory part 27Practice part 28
parallel lines, perpendicular lines, negative reciprocal, vertical line and horizontal line
Builds on Slope and Rate of Change and Writing the Equation of a Line.
Linear Systems
Theory part 29Practice part 30
system of equations, simultaneous solution, intersection and substitution
Builds on Solving Linear Equations, Coordinates, Functions and Graphs and Writing the Equation of a Line.
- Systems of Equations by EliminationOn YouTube
Theory part 31Practice part 32
elimination, linear combination, equivalent system, substitution, solution check and target linear combination
Builds on Solving Linear Equations and Systems of Equations by Graphs and Substitution.
Theory part 33Practice part 34
consistent system, inconsistent system, coincident lines, parameter, number of solutions and parameter case
Builds on Equations with No or Infinitely Many Solutions, Writing the Equation of a Line and Systems of Equations by Elimination.
Linear Inequalities
- Solving Linear InequalitiesOn YouTube
Theory part 35Practice part 36
inequality, solution set, boundary, strict inequality, inclusive inequality, number line, compound inequality, intersection and union
Builds on Solving Linear Equations.
Theory part 37Practice part 38
boundary line, half-plane, feasible region, intersection, constraint and test point
Builds on Writing the Equation of a Line and Solving Linear Inequalities.
Advanced Math
All 18 pairs on YouTubeOpen the Advanced Math unit pagePowers and Expressions
- Exponent RulesOn YouTube
Theory part 39Practice part 40
power, base, exponent, product rule for powers, negative exponent and zero exponent
Builds on Fractions, Signs and Order of Operations and Expressions, Substitution and Mathematical Language.
- Radicals and Rational ExponentsOn YouTube
Theory part 41Practice part 42
principal square root, radical, rational exponent, cube root and absolute value
Builds on Rearranging Formulas and Exponent Rules.
- Expanding and Combining PolynomialsOn YouTube
Theory part 43Practice part 44
polynomial, degree, like terms, distributive property, product, equivalent expression and coefficient matching
Builds on Expressions, Substitution and Mathematical Language and Exponent Rules.
- Factoring and Recognizing StructureOn YouTube
Theory part 45Practice part 46
factor, greatest common factor, quadratic trinomial, difference of squares, perfect square, factoring by grouping and nested structure
Builds on Expanding and Combining Polynomials.
Quadratics
- Solving Quadratic Equations by FactoringOn YouTube
Theory part 47Practice part 48
quadratic equation, zero-product property, root, solution and factored form
Builds on Solving Linear Equations, Coordinates, Functions and Graphs and Factoring and Recognizing Structure.
- Completing the SquareOn YouTube
Theory part 49Practice part 50
completing the square, perfect-square trinomial, square-root method, vertex form and nonunit leading coefficient
Builds on Radicals and Rational Exponents, Expanding and Combining Polynomials and Solving Quadratic Equations by Factoring.
- Quadratic Formula and DiscriminantOn YouTube
Theory part 51Practice part 52
quadratic formula, discriminant, real root, repeated root and leading coefficient
Builds on Radicals and Rational Exponents and Completing the Square.
- Quadratic Graphs and Their FormsOn YouTube
Theory part 53Practice part 54
parabola, vertex, axis of symmetry, intercept, standard form, factored form and vertex form
Builds on Coordinates, Functions and Graphs, Solving Quadratic Equations by Factoring and Completing the Square.
Theory part 55Practice part 56
parameter, repeated root, discriminant condition, sum of roots, product of roots and parameter case
Builds on Solving Quadratic Equations by Factoring, Quadratic Formula and Discriminant and Quadratic Graphs and Their Forms.
Nonlinear Equations and Functions
- Polynomial Zeros and Graph FeaturesOn YouTube
Theory part 57Practice part 58
zero, factor, multiplicity, sign, intercept and polynomial graph
Builds on Coordinates, Functions and Graphs, Exponent Rules, Factoring and Recognizing Structure and Solving Quadratic Equations by Factoring.
- Rational Expressions and Excluded ValuesOn YouTube
Theory part 59Practice part 60
rational expression, denominator, excluded value, cancellation, equivalent expression, hole, shifted or scaled reciprocal, rational-expression operations and nonzero divisor
Builds on Factoring and Recognizing Structure and Solving Quadratic Equations by Factoring.
- Solving Rational EquationsOn YouTube
Theory part 61Practice part 62
rational equation, common denominator, restriction, candidate solution and extraneous solution
Builds on Solving Linear Equations, Solving Quadratic Equations by Factoring and Rational Expressions and Excluded Values.
- Solving Radical EquationsOn YouTube
Theory part 63Practice part 64
radical equation, principal root, squaring, domain restriction and extraneous solution
Builds on Radicals and Rational Exponents, Solving Quadratic Equations by Factoring and Quadratic Formula and Discriminant.
- Absolute Value Equations and GraphsOn YouTube
Theory part 65Practice part 66
absolute value, distance, case split, vertex, piecewise interpretation and branch condition
Builds on Solving Linear Equations, Coordinates, Functions and Graphs and Solving Linear Inequalities.
- Systems with Lines and CurvesOn YouTube
Theory part 67Practice part 68
nonlinear system, intersection, simultaneous solution, substitution, tangent intersection and line and reciprocal intersection
Builds on Systems of Equations by Graphs and Substitution, Solving Quadratic Equations by Factoring, Quadratic Formula and Discriminant and Quadratic Graphs and Their Forms.
- Exponential Growth and DecayOn YouTube
Theory part 69Practice part 70
exponential model, initial value, growth factor, decay factor, percent rate, time interval, exponential equation, common base, unknown exponent, equivalent exponential form and time-unit conversion
Builds on Percentages and Percent Change, Coordinates, Functions and Graphs, Exponent Rules and Radicals and Rational Exponents.
Theory part 71Practice part 72
translation, reflection, vertical scale, horizontal scale, changed input, domain, quadratic transformation, exponential transformation, polynomial transformation and rational transformation
Builds on Coordinates, Functions and Graphs, Quadratic Graphs and Their Forms, Polynomial Zeros and Graph Features, Rational Expressions and Excluded Values, Absolute Value Equations and Graphs and Exponential Growth and Decay.
Theory part 73Practice part 74
constant difference, constant ratio, equal input intervals, linear model and exponential model
Builds on Coordinates, Functions and Graphs, Intercepts and Linear Models and Exponential Growth and Decay.
Problem-Solving and Data Analysis
All 9 pairs on YouTubeOpen the Problem-Solving and Data Analysis unit pageData and Probability
- Reading Data DisplaysOn YouTube
Theory part 75Practice part 76
frequency, dot plot, histogram, box plot, quartile, interquartile range, scale, grouped data and information limitation
Builds on Fractions, Signs and Order of Operations and Coordinates, Functions and Graphs.
- Mean, Median and Weighted AveragesOn YouTube
Theory part 77Practice part 78
mean, median, frequency, weighted mean, total and outlier
Builds on Fractions, Signs and Order of Operations, Ratios and Proportions and Reading Data Displays.
- Spread, Outliers and Standard DeviationOn YouTube
Theory part 79Practice part 80
range, spread, standard deviation, mean, outlier, shift, scale and shifted distribution
Builds on Reading Data Displays and Mean, Median and Weighted Averages.
- Scatterplots, Models and PredictionsOn YouTube
Theory part 81Practice part 82
scatterplot, association, line of best fit, residual, prediction, interpolation, extrapolation, quadratic model and exponential fit
Builds on Slope and Rate of Change, Intercepts and Linear Models, Quadratic Graphs and Their Forms, Exponential Growth and Decay and Reading Data Displays.
- Probability and Two-Way TablesOn YouTube
Theory part 83Practice part 84
sample space, event, probability, relative frequency, two-way table, complement, union and uniform area probability
Builds on Fractions, Signs and Order of Operations and Ratios and Proportions.
- Conditional ProbabilityOn YouTube
Theory part 85Practice part 86
conditional probability, given, restricted sample space, intersection and independence
Builds on Probability and Two-Way Tables.
Statistical Reasoning
- Samples, Populations and BiasOn YouTube
Theory part 87Practice part 88
population, sample, random sample, representative sample, selection bias and sample proportion
Builds on Ratios and Proportions, Mean, Median and Weighted Averages and Probability and Two-Way Tables.
Theory part 89Practice part 90
estimate, margin of error, percentage point, uncertainty interval, sample size and confidence level
Builds on Percentages and Percent Change and Samples, Populations and Bias.
Theory part 91Practice part 92
observational study, randomized experiment, random assignment, confounding, causal inference and generalization
Builds on Scatterplots, Models and Predictions, Samples, Populations and Bias and Margin of Error and Interpreting Estimates.
Geometry and Trigonometry
All 11 pairs on YouTubeOpen the Geometry and Trigonometry unit pageLines, Angles and Triangles
- Angles, Parallel Lines and TrianglesOn YouTube
Theory part 93Practice part 94
vertical angles, supplementary angles, corresponding angles, alternate angles and triangle angle sum
Builds on Solving Linear Equations.
- Similar and Congruent TrianglesOn YouTube
Theory part 95Practice part 96
similarity, congruence, corresponding sides, corresponding angles, scale factor, AA, SSS, SAS and sufficient information
Builds on Ratios and Proportions and Angles, Parallel Lines and Triangles.
Theory part 97Practice part 98
right triangle, hypotenuse, Pythagorean theorem, 45-45-90 triangle and 30-60-90 triangle
Builds on Radicals and Rational Exponents, Angles, Parallel Lines and Triangles and Similar and Congruent Triangles.
Right Triangle Trigonometry and the Unit Circle
Theory part 99Practice part 100
sine, cosine, tangent, opposite, adjacent, hypotenuse, complementary angles and similarity and trigonometric ratios
Builds on Ratios and Proportions, Similar and Congruent Triangles and The Pythagorean Theorem and Special Right Triangles.
- Degrees, Radians and the Unit CircleOn YouTube
Theory part 101Practice part 102
degree, radian, unit circle, arc length, sine coordinate, cosine coordinate and quadrant
Builds on Coordinates, Functions and Graphs, Radicals and Rational Exponents, The Pythagorean Theorem and Special Right Triangles and Sine, Cosine and Tangent in Right Triangles.
Circles
- Circle Angles, Chords and TangentsOn YouTube
Theory part 103Practice part 104
radius, diameter, chord, tangent, central angle, inscribed angle and intercepted arc
Builds on Angles, Parallel Lines and Triangles, Similar and Congruent Triangles and The Pythagorean Theorem and Special Right Triangles.
- Arc Length and Sector AreaOn YouTube
Theory part 105Practice part 106
arc length, sector area, circumference, central angle, radians and fraction of a circle
Builds on Ratios and Proportions, Degrees, Radians and the Unit Circle and Circle Angles, Chords and Tangents.
- Circle Equations, Centers and RadiiOn YouTube
Theory part 107Practice part 108
circle equation, center, radius, distance formula, completing the square, diameter endpoints and normalized circle equation
Builds on Coordinates, Functions and Graphs, Completing the Square and The Pythagorean Theorem and Special Right Triangles.
Area, Volume and Scaling
- Area, Perimeter and Composite FiguresOn YouTube
Theory part 109Practice part 110
area, perimeter, perpendicular height, composite figure, subtraction of areas and units
Builds on Ratios and Proportions, Units, Rates and Conversions, Angles, Parallel Lines and Triangles and The Pythagorean Theorem and Special Right Triangles.
- Volume and Surface AreaOn YouTube
Theory part 111Practice part 112
volume, surface area, prism, cylinder, pyramid, cone, sphere, radius, height and net
Builds on Units, Rates and Conversions, The Pythagorean Theorem and Special Right Triangles, Arc Length and Sector Area and Area, Perimeter and Composite Figures.
- Scaling Lengths, Areas and VolumesOn YouTube
Theory part 113Practice part 114
scale factor, similar figures, square scale factor, cubic scale factor and units
Builds on Ratios and Proportions, Similar and Congruent Triangles, Area, Perimeter and Composite Figures and Volume and Surface Area.
Test Strategy
All 2 pairs on YouTubeOpen the Test Strategy unit pageUsing the Graphing Calculator
- Desmos for Equations and IntersectionsOn YouTube
Theory part 115Practice part 116
Desmos, graphing calculator, intersection, zero, viewport, exact answer and approximation
Builds on Coordinates, Functions and Graphs, Writing the Equation of a Line, Systems of Equations by Graphs and Substitution, Solving Quadratic Equations by Factoring and Systems with Lines and Curves.
Theory part 117Practice part 118
table, parameter, slider, model, regression, coefficient and test-mode calculator
Builds on Systems with One, No or Infinite Solutions, Quadratic Graphs and Their Forms, Quadratic Parameters and Root Relationships, Exponential Growth and Decay, Linear and Exponential Models from Tables, Scatterplots, Models and Predictions and Desmos for Equations and Intersections.