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

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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

  1. SAT Math Full Practice Test, Beginner Level 91 min
  2. SAT Math Full Practice Test, Intermediate Level 112 min
  3. SAT Math Full Practice Test, Advanced Level 116 min
  4. SAT Math Tips and Strategies, 24 Explained Examples 73 min

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.

  1. Essential Skills

    All 6 pairs on YouTube
    Open the Essential Skills unit page

    Numbers and Proportional Reasoning

    1. Theory part 1Practice part 2

      fraction, numerator, denominator, negative number, order of operations and parentheses

    2. Theory part 3Practice part 4

      ratio, proportion, equivalent ratio, unit rate and direct proportion

      Builds on Fractions, Signs and Order of Operations.

    3. 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.

    4. 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

    1. Theory part 9Practice part 10

      variable, constant, coefficient, term, factor, expression, equation and substitution

      Builds on Fractions, Signs and Order of Operations.

    2. 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.

  2. Algebra

    All 13 pairs on YouTube
    Open the Algebra unit page

    Linear Equations

    1. 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.

    2. Theory part 15Practice part 16

      formula, subject of a formula, parameter, inverse operation, nonzero denominator and exceptional parameter case

      Builds on Solving Linear Equations.

    3. 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

    1. 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.

    2. 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.

    3. 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.

    4. 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.

    5. 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

    1. 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.

    2. 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.

    3. 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

    1. 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.

    2. 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.

  3. Advanced Math

    All 18 pairs on YouTube
    Open the Advanced Math unit page

    Powers and Expressions

    1. 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.

    2. Theory part 41Practice part 42

      principal square root, radical, rational exponent, cube root and absolute value

      Builds on Rearranging Formulas and Exponent Rules.

    3. 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.

    4. 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

    1. 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.

    2. 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.

    3. 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.

    4. 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.

    5. 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

    1. 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.

    2. 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.

    3. 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.

    4. 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.

    5. 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.

    6. 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.

    7. 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.

    8. 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.

    9. 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.

  4. Problem-Solving and Data Analysis

    All 9 pairs on YouTube
    Open the Problem-Solving and Data Analysis unit page

    Data and Probability

    1. 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.

    2. 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.

    3. 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.

    4. 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.

    5. 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.

    6. Theory part 85Practice part 86

      conditional probability, given, restricted sample space, intersection and independence

      Builds on Probability and Two-Way Tables.

    Statistical Reasoning

    1. 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.

    2. 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.

    3. 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.

  5. Geometry and Trigonometry

    All 11 pairs on YouTube
    Open the Geometry and Trigonometry unit page

    Lines, Angles and Triangles

    1. Theory part 93Practice part 94

      vertical angles, supplementary angles, corresponding angles, alternate angles and triangle angle sum

      Builds on Solving Linear Equations.

    2. 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.

    3. 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

    1. 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.

    2. 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

    1. 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.

    2. 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.

    3. 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

    1. 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.

    2. 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.

    3. 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.

  6. Test Strategy

    All 2 pairs on YouTube