Master SAT Math

Place values

Comparing and ordering numbers

Rounding numbers

Introduction to integer addition

Adding integers

Introduction to integer subtraction

Subtracting integers

Application of integer operations

Understanding integer multiplication

Multiplying integers

Understanding integer division

Dividing integers

Applications of integer operations

Divisibility Rules

Determining Common Factors

Determining Common Multiples

Introduction to exponents

Using models to add and subtract fractions

Adding fractions with like denominators

Subtracting fractions with like denominators

Adding and subtracting fractions with unlike denominators

Adding and subtracting mixed numbers

Multiplying fractions and whole numbers

Dividing fractions with whole numbers

Multiplying proper fractions

Multiplying improper fractions and mixed numbers

Dividing fractions and mixed numbers

Applications of fraction operations

Adding and subtracting decimals

Multiplying decimals

Dividing decimals

Order of operations (BEDMAS)

Representing percents

Percent of a number

Converting among decimals, fractions, and percents

Applications of percents

Taxes, discounts, tips and more

Ratios

Rates

Proportions

Evaluating algebraic expressions

Solving linear equations using multiplication and division

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Solving literal equations

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Solving multi-step linear inequalities

Compound inequalities

Graphing linear inequalities in two variables

Metric systems

Imperial systems

Conversions between metric and imperial systems

Conversions involve squares and cubic

Understanding the number systems

Prime factorization

Greatest Common Factors (GCF)

Least Common Multiple (LCM)

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Operations with radicals

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals

Multiplying radicals

Solving radical equations

Exponents: Product rule (a^x)(a^y) = a^(x+y)

Exponents: Division rule (a^x / a^y) = a^(x-y)

Exponents: Power rule (a^x)^y = a^(x * y)

Exponents: Negative exponents

Exponents: Zero exponent: a^0 = 1

Exponents: Rational exponents

Scientific notation

Convert between radicals and rational exponents

Solving for exponents

Solving exponential equations using exponent rules

What is a polynomial?

Polynomial components

Multiplying monomial by monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$

Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Point-slope form: $y - y_1 = m (x - x_1)$

Rate of change

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Parallel and perpendicular lines in linear functions

Applications of linear relations

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Using elimination method to solve systems of linear equations

Using substitution method to solve systems of linear equations

System of linear-quadratic equations

Factor by taking out the greatest common factor

Factor by grouping

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring difference of cubes

Factoring sum of cubes

Introduction to quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Quadratic function in vertex form: y = a(x-p)^2 + q

Completing the square

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

Solving quadratic inequalities

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Multiplying rational expressions

Dividing rational expressions

Solving rational equations

Applications of rational equations

Simplifying complex fractions

Partial fraction decomposition

Function notation

Operations with functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Composite functions

Inequalities of combined functions

Inverse functions

One to one functions

Difference quotient: applications of functions

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Combining transformations of functions

Even and odd functions

What is a polynomial function?

Polynomial long division

Polynomial synthetic division

Remainder theorem

Factor theorem

Rational zero theorem

Characteristics of polynomial graphs

Multiplicities of polynomials

Imaginary zeros of polynomials

Descartes' rule of signs

Direct variation

Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )

Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )

Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )

Combination of SohCahToa questions

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Other word problems relating angles in trigonometry

Standard angles

Coterminal angles

Reference angles

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

Unit circle

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

Law of sines

Law of cosines

Applications of the sine law and cosine law

Introduction to imaginary numbers

Adding and subtracting complex numbers

Complex conjugates

Multiplying and dividing complex numbers

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Circle and circumference

Angles in a circle

Arcs of a circle

Areas and sectors of circles

Conics - Circle

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Median and mode

Mean

Range and outliers

Application of averages

Reading and drawing bar graphs

Reading and drawing histograms

Reading and drawing line graphs

Box-and-whisker plots and scatter plots

Stem-and-leaf plots

Reading and drawing Venn diagrams

Determining probabilities using tree diagrams and tables

Probability of independent events

Probability with Venn diagrams