SAT Math
67 of 67 topics written so far. Greyed-out topics are coming soon.
Unit 1: Getting Started
Unit 2: Algebra
- 1Solving Linear Equations
Solving one-step to multi-step linear equations, including brackets, fractions and variables on both sides; writing equations from word problems; and checking solutions.
Draft - 2Rearranging Formulas
Isolating a variable in a formula, substituting values (including fractions and negatives), and solving for one variable when you know the others.
Draft - 3Representing Linear Relations
Showing one linear relation as a situation, a table, a graph and an equation; rate of change and initial value; direct and partial variation.
Draft - 4Equations of Lines
The slope formula, zero and undefined slopes, finding a line's equation from a graph, a table, a point and slope, or two points, and switching between y = mx + b, Ax + By + C = 0 and Ax + By = D.
Draft - 5Parallel and Perpendicular Lines
Parallel lines have equal slopes and perpendicular lines have negative reciprocal slopes. Testing pairs of lines and finding equations of parallel and perpendicular lines through a point.
Draft - 6Function Notation
Writing f(x), evaluating functions, and solving f(x) = a value — from equations, tables, and graphs.
Draft - 7Solving Linear Systems by Graphing
What a solution of a linear system is, solving by graphing, the three possible outcomes (one, none, or infinitely many solutions), predicting them from slopes and intercepts, and the limits of graphing.
Draft - 8Solving Linear Systems by Substitution
Solving a system of two linear equations exactly by isolating one variable and substituting it into the other equation, including systems with fractions and decimals.
Draft - 9Solving Linear Systems by Elimination
Adding or subtracting equations to eliminate a variable, multiplying one or both equations first, and recognizing systems with no solution or infinitely many solutions.
Draft - 10Applications of Linear Systems
Setting up and solving linear systems from word problems — break-even, investments with simple interest, mixtures, and rates with a current or wind — and checking that answers make sense.
Draft - 11Linear Inequalities
Solving one-variable linear inequalities, flipping the sign for negatives, number lines, compound inequalities, word problems, and a first look at two-variable inequalities.
Draft - 12Graphing Lines and Regions
Graphing x = k, y = k, x + y = k, x − y = k, ax + by = k (intercept method) and xy = k, then graphing the matching inequalities and reading points and regions in context.
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Unit 3: Advanced Math
- 1Exponent Laws
The product, quotient and power laws, what zero and negative exponents mean, and how the graph of y = 2^x compares with y = x².
Draft - 2Rational Exponents
What fractional exponents like 8^(2/3) mean, how to evaluate and simplify them, and how to rewrite powers in a different base.
Draft - 3Simplifying Radicals
Writing square roots in simplest form, and adding, subtracting, and multiplying radical expressions.
Draft - 4Adding, Subtracting, and Multiplying Polynomials
Combining like terms, subtracting carefully, and expanding products of polynomials — including the special products.
Draft - 5Common Factoring
Taking out the greatest common factor, factoring out a common binomial, and factoring four-term expressions by grouping.
Draft - 6Factoring Trinomials (x² + bx + c)
Factoring trinomials like x² + 7x + 12 by finding two numbers with the right product and sum, including all the sign cases and common factors.
Draft - 7Factoring Complex Trinomials (ax² + bx + c)
Factoring trinomials like 6x² − x − 12, where the coefficient of x² isn't 1, by decomposition and by inspection.
Draft - 8Factoring Special Cases
Difference of squares and perfect-square trinomials, expressions that take two steps to factor, and a strategy for choosing the right method.
Draft - 9Simplifying Rational Expressions
Factoring and cancelling to simplify rational expressions, and stating the restrictions on the variable.
Draft - 10Adding and Subtracting Rational Expressions
Finding the lowest common denominator, combining numerators carefully, and simplifying the result.
Draft - 11Solving Quadratic Equations by Factoring
Solving ax² + bx + c = 0 by rearranging, factoring, and using the zero product property, including double roots, checking roots, and connecting roots to x-intercepts.
Draft - 12Completing the Square
Rewriting a quadratic from standard form into vertex form, so you can read off its vertex and maximum or minimum.
Draft - 13The Quadratic Formula
Where the quadratic formula comes from, solving any quadratic equation with it (exact and decimal answers), choosing a solving method, and what a negative b² − 4ac means.
Draft - 14Zeros of Quadratics and the Discriminant
Finding the zeros of a quadratic function by factoring or the quadratic formula, and using the discriminant to count them.
Draft - 15Radical Equations
Solving equations with square roots and rational exponents — isolate, square, solve, and check for extraneous solutions — with pendulum and free-fall applications.
Draft - 16Solving Rational Equations
Solving equations with variables in the denominator by multiplying by the LCD, rejecting extraneous roots, and using them for work-rate, speed, and concentration problems.
Draft - 17Modulus Equations and Inequalities
Solving equations and inequalities with absolute values by cases, by squaring and graphically, and solving g(x) ≥ f(x) both graphically and analytically.
Draft - 18Linear–Quadratic Systems
Finding where a line meets a parabola, and using the discriminant to tell whether they cross twice, touch once, or miss.
Draft - 19Vertex Form and Transformations
Graphing y = a(x − h)² + k as a transformation of y = x², sketching by hand with the step pattern, and finding the equation of a parabola from its graph.
Draft - 20Factored Form of a Quadratic
Using y = a(x − r)(x − s) to find zeros, the axis of symmetry and the vertex, sketching from factored form, and finding an equation from its zeros.
Draft - 21Maximum and Minimum of a Quadratic
Finding the vertex of a quadratic by completing the square or averaging the zeros, and solving real-world optimization problems.
Draft - 22Exponential Functions
Graphs and key properties of y = a^x, and how to tell exponential, linear, and quadratic patterns apart.
Draft - 23Exponential Growth and Decay
Modelling populations, depreciation, half-life, and doubling with exponential functions, and solving real-world problems.
Draft - 24Polynomials in Factored Form
Reading zeros and their multiplicity from factored form, and sketching a polynomial from its intercepts, end behaviour, and sign intervals.
Draft - 25Combining Transformations
Graphing y = af(k(x − d)) + c by applying stretches, reflections, and translations in the right order.
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Unit 4: Problem-Solving and Data Analysis
- 1Ratios, Rates and Proportions
Ratios and equivalent ratios, unit rates and best buys, solving proportions, scale drawings and maps, and keeping track of units.
Draft - 2Measurement Conversions
Converting metric units of length, mass, capacity, area and volume, and converting between metric and imperial units with unit analysis.
Draft - 3Percent Problems
Finding a percent of a number, finding the whole, percent increase and decrease, HST and discounts, and why successive percents don't simply add.
Draft - 4Measures of Central Tendency
Mean, median, and mode; weighted means; estimating the mean from grouped data; the effect of outliers; and choosing the best measure.
Draft - 5Standard Deviation
Measuring spread with the range, variance, and standard deviation — population vs sample formulas, by hand and with technology.
Draft - 6Displaying One-Variable Data
Choosing the right graph for the data — bar and circle graphs, histograms, stem-and-leaf plots, and boxplots — and spotting graphs that mislead.
Draft - 7Quartiles and Percentiles
Quartiles, the interquartile range, the five-number summary, the 1.5 × IQR rule for outliers, boxplots, and percentiles.
Draft - 8Scatter Plots and Correlation
Independent and dependent variables, scatter plots, describing a relationship, the correlation coefficient r, and side-by-side boxplots.
Draft - 9Linear Regression
The line of best fit by least squares, interpreting slope and intercept, interpolation and extrapolation, residuals, and the effect of outliers.
Draft - 10Probability and Sample Spaces
Outcomes, sample spaces, and events; theoretical probability for equally likely outcomes; and probability distributions.
Draft - 11Contingency Tables
Two-way tables for two categorical variables — totals, relative frequencies, row and column percentages, and judging whether the variables are related.
Draft - 12Conditional Probability
The probability of B given A, from formulas, two-way tables, and tree diagrams — and why the order matters.
Draft - 13Sampling Methods
Populations and samples, random and non-random sampling methods, and organizing data in a spreadsheet.
Draft - 14Margin of Error
Interpreting poll results reported with a margin of error and confidence level, and how sample size, margin of error, and confidence level are related.
Draft - 15Survey and Experiment Design
Randomization, replication, and control in experiments; and writing fair, ethical surveys with clear questions.
Draft - 16Correlation and Causation
Why correlation doesn't prove cause and effect, the types of relationships between two variables, and how two-variable statistics get misused.
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Unit 5: Geometry and Trigonometry
- 1Surface Area of 3-D Objects
Using nets to find the surface area of prisms, cylinders, square-based pyramids and cones, including slant height and composite objects.
Draft - 2Volume of 3-D Objects
Volume of prisms, cylinders, pyramids and cones (and spheres), the one-third relationship, capacity in millilitres and litres, and composite objects.
Draft - 3Spheres, Cones, Pyramids and Composite Solids
Volume and surface area of spheres, hemispheres, right pyramids and right cones, and of solids built from them, with answers to 3 significant figures.
Draft - 4Triangle and Circle Properties
Angle relationships, parallel lines, triangle and circle properties, and how to use them to analyse and create designs.
Draft - 5Similar Triangles
Same shape, different size — matching angles, proportional sides, scale factors, and using similar triangles to measure things you can't reach.
Draft - 6The Pythagorean Theorem
The side-length relationship in right triangles — finding a hypotenuse or a leg, testing for right triangles, and solving real-life and composite-shape problems.
Draft - 7The Primary Trigonometric Ratios
Sine, cosine and tangent in right triangles — naming the sides, SOH CAH TOA, and finding missing sides and angles.
Draft - 8Right Triangle Problems
Angles of elevation and depression, clinometers, ladders, ramps, navigation, and problems with two right triangles.
Draft - 9Special Angles
Exact values of sine, cosine, and tangent for 0°, 30°, 45°, 60°, and 90°, from two special right triangles.
Draft - 10Radian Measure
What a radian is, converting between degrees and radians, arc length a = rθ, and angular velocity.
Draft - 11Arc Length and Sector Area
Arc length, sector area and sector perimeter with the angle in degrees or radians, and the area of a segment as a sector minus a triangle.
Draft - 12Circles Centred at the Origin
Developing the equation x² + y² = r² from the length formula, finding the radius, writing and sketching the equation, testing points, and working with diameters and chords.
Draft - 13Circle Equations
The standard form (x − h)² + (y − k)² = r², finding the centre and radius, writing equations from a centre and a point or a diameter, completing the square from general form, and tangent lines.
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