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ACT Compass Test Prep Topics

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

Linear Equations

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Applications of linear equations

Solving Systems of Linear Equations

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Using elimination method to solve systems of equations

Using substitution method to solve systems of equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Exponents

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Solving for exponents

Operations with Polynomials

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

Factoring Polynomial Expressions

Common factors of polynomials

Factoring polynomials by grouping

Solving polynomials with the unknown "b" from x^2 + bx + c

Solving polynomials with the unknown "c" from x^2 + bx + c

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

Solving polynomials with the unknown "b" from

ax^2 + bx + c

Factoring polynomials:

ax^2 + bx + c

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Evaluating polynomials

Using algebra tiles to factor polynomials

Solving polynomial equations

Word problems of polynomials

Factoring Trinomials (Advanced)

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

Rational Expressions

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

Reciprocal Functions

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

Radicals

Square and square roots

Cubic and cube roots

Evaluating and simplifying radicals

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding and subtracting radicals

Multiplying and dividing radicals

Rationalize the denominator

Radicals (Advanced)

Operations with radicals

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals

Multiplying radicals

Solving radical equations

Ratios, Rates, and Proportions

Ratios

Rates

Proportions

Angles, Lines, and Transversals

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Scale Factors and Similarity

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Surface Area and Perimeter of Polygons

Classifying Triangles

Circles

Circles and circumference

Arcs of a circle

Areas and sectors of circles

Angles in a circle

Chord properties in circles

Tangent properties in circles

Central and inscribed angles in circles

Equation of a circle

Statistics

Median and mode

Mean

Range and outliers

Application of averages

Sequences and Series

Infinite geometric series

Sigma notation

Arithmetic mean vs. Geometric mean

Functions

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

Exponential Functions

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

Solving exponential equations using exponent rules

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Logarithmic Functions

What is a logarithm?

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

Converting from exponential form to logarithmic form

Solving exponential equations with logarithms

Product rule of logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

Solving logarithmic equations

Graphing logarithmic functions

Finding a logarithmic function given its graph

Applications of Exponential and Logarithmic Functions

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

Finance: Compound interest

Continuous growth and decay

Logarithmic scale: Richter scale (earthquake)

Logarithmic scale: pH scale

Logarithmic scale: dB scale

Finance: Future value and present value

Right Triangle Trigonometry

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

Laws of sines and cosines

Law of sines

Law of cosines

Applications of the sine law and cosine law

Bearings

Introduction to bearings

Bearings and direction word problems

Angle of elevation and depression

Trigonometric Ratios and Angle Measure

Angle in standard position

Coterminal angles

Reference angle

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

Graphs of Trigonometric Functions

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Cotangent graph: y = cot x

Secant graph: y = sec x

Cosecant graph: y = csc x

Graphing transformations of trigonometric functions

Determining trigonometric functions given their graphs

Trigonometric Identities

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Cofunction identities

Double-angle identities

Solving Trigonometric Equations

Solving first degree trigonometric equations

Determining non-permissible values for trig expressions

Solving second degree trigonometric equations

Solving trigonometric equations involving multiple angles

Solving trigonometric equations using pythagorean identities

Solving trigonometric equations using sum and difference identities

Solving trigonometric equations using double-angle identities

Imaginary and Complex Numbers

Introduction to imaginary numbers

Complex numbers and complex planes

Adding and subtracting complex numbers

Complex conjugates

Multiplying and dividing complex numbers

Distance and midpoint of complex numbers

Angle and absolute value of complex numbers

Polar form of complex numbers

Operations on complex numbers in polar form

Introduction to Matrices

Notation of matrices

Adding and subtracting matrices

Scalar multiplication

Matrix multiplication

The three types of matrix row operations

Representing a linear system as a matrix

Solving a linear system with matrices using Gaussian elimination

Properties of Matrices

Zero matrix

Identity matrix

Properties of matrix addition

Properties of scalar multiplication

Determinants and Inverses of Matrices

The determinant of a 2 x 2 matrix

The determinant of a 3 x 3 matrix (General & Shortcut Method)

The inverse of a 2 x 2 matrix

The inverse of 3 x 3 matrices with matrix row operations

The inverse of 3 x 3 matrix with determinants and adjugate

2 x 2 invertible matrix

Solving linear systems using Cramer's Rule

Solving linear systems using 2 x 2 inverse matrices

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