# ACT Compass Test Prep made completely easy!

We've got you covered with our complete help for Compass math test including all five subject areas: Pre-algebra, Algebra, College Algebra, Geometry, and Trigonometry.

Our comprehensive lessons on compass test cover help on topics like Trigonometric identities, Linear equations, Exponents, Complex number, Logarithmic functions, Rational expressions, and so many more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest Compass math test problems. Then, strengthen your understanding with tons of Compass test practice.

All our lessons are taught by experienced math teachers. Let's finish your preparation in no time, and ACE that Compass test.

##### 1Numbers and Relations

##### 2Number Theory

##### 3Operations with Decimals

##### 4Number System and Radicals

##### 5Adding and Substracting Fractions

##### 6Multiplying and Dividing Fractions

##### 7Fractions, Decimals, and Percents

##### 8Introduction to Variables and Expressions

##### 9Introduction to Equations

##### 10Solving Linear Equations

##### 11Introduction to Relations and Functions

##### 12Linear Functions

- 12.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 12.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 12.3Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 12.4Slope intercept form: y = mx + b
- 12.5General form: Ax + By + C = 0
- 12.6Point-slope form: $y - y_1 = m (x - x_1)$
- 12.7Rate of change
- 12.8Graphing linear functions using table of values
- 12.9Graphing linear functions using x- and y-intercepts
- 12.10Graphing from slope-intercept form y=mx+b
- 12.11Graphing linear functions using a single point and slope
- 12.12Word problems of graphing linear functions
- 12.13Parallel and perpendicular lines in linear functions
- 12.14Applications of linear relations

- 12.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 13Linear Equations

- 13.1Introduction to linear equations
- 13.2Introduction to nonlinear equations
- 13.3Special case of linear equations: Horizontal lines
- 13.4Special case of linear equations: Vertical lines
- 13.5Parallel line equation
- 13.6Perpendicular line equation
- 13.7Combination of both parallel and perpendicular line equations
- 13.8Applications of linear equations

- 13.1Introduction to linear equations
##### 14Solving Systems of Linear Equations

- 14.1Determining number of solutions to linear equations
- 14.2Solving systems of linear equations by graphing
- 14.3Using elimination method to solve systems of equations
- 14.4Using substitution method to solve systems of equations
- 14.5Money related questions in linear equations
- 14.6Unknown number related questions in linear equations
- 14.7Distance and time related questions in linear equations
- 14.8Rectangular shape related questions in linear equations

- 14.1Determining number of solutions to linear equations
##### 15Exponents

- 15.1Product rule of exponents
- 15.2Quotient rule of exponents
- 15.3Power of a product rule
- 15.4Power of a quotient rule
- 15.5Power of a power rule
- 15.6Negative exponent rule
- 15.7Combining the exponent rules
- 15.8Scientific notation
- 15.9Convert between radicals and rational exponents
- 15.10Solving for exponents

- 15.1Product rule of exponents
##### 16Operations with Polynomials

##### 17Factoring Polynomial Expressions

- 17.1Common factors of polynomials
- 17.2Factoring polynomials by grouping
- 17.3Solving polynomials with the unknown "b" from $x^2 + bx + c$
- 17.4Solving polynomials with the unknown "c" from $x^2 + bx + c$
- 17.5Factoring polynomials: $x^2 + bx + c$
- 17.6Applications of polynomials: $x^2 + bx + c$
- 17.7Solving polynomials with the unknown "b" from $ax^2 + bx + c$
- 17.8Factoring polynomials: $ax^2 + bx + c$
- 17.9Factoring perfect square trinomials: $(a + b)^2 = a^2 + 2ab + b^2$ or $(a - b)^2 = a^2 - 2ab + b^2$
- 17.10Find the difference of squares: $(a - b)(a + b) = (a^2 - b^2)$
- 17.11Evaluating polynomials
- 17.12Using algebra tiles to factor polynomials
- 17.13Solving polynomial equations
- 17.14Word problems of polynomials

- 17.1Common factors of polynomials
##### 18Factoring Trinomials (Advanced)

##### 19Rational Expressions

- 19.1Simplifying rational expressions and restrictions
- 19.2Adding and subtracting rational expressions
- 19.3Multiplying rational expressions
- 19.4Dividing rational expressions
- 19.5Solving rational equations
- 19.6Applications of rational equations
- 19.7Simplifying complex fractions
- 19.8Partial fraction decomposition

- 19.1Simplifying rational expressions and restrictions
##### 20Reciprocal Functions

##### 21Radicals

##### 22Radicals (Advanced)

##### 23Ratios, Rates, and Proportions

##### 24Angles, Lines, and Transversals

##### 25Scale Factors and Similarity

##### 26Surface Area and Perimeter of Polygons

##### 27Circles

##### 28Statistics

##### 29Sequences and Series

##### 30Functions

- 30.1Function notation
- 30.2Operations with functions
- 30.3Adding functions
- 30.4Subtracting functions
- 30.5Multiplying functions
- 30.6Dividing functions
- 30.7Composite functions
- 30.8Inequalities of combined functions
- 30.9Inverse functions
- 30.10One to one functions
- 30.11Difference quotient: applications of functions

- 30.1Function notation
##### 31Exponential Functions

- 31.1Exponents: Product rule $(a^x)(a^y)=a^{(x+y)}$
- 31.2Exponents: Division rule ${a^x \over a^y}=a^{(x-y)}$
- 31.3Exponents: Power rule $(a^x)^y = a^{(x\cdot y)}$
- 31.4Exponents: Negative exponents
- 31.5Exponents: Zero exponent: $a^0 = 1$
- 31.6Exponents: Rational exponents
- 31.7Solving exponential equations using exponent rules
- 31.8Graphing exponential functions
- 31.9Graphing transformations of exponential functions
- 31.10Finding an exponential function given its graph

- 31.1Exponents: Product rule $(a^x)(a^y)=a^{(x+y)}$
##### 32Logarithmic Functions

- 32.1What is a logarithm?
- 32.2Converting from logarithmic form to exponential form
- 32.3Evaluating logarithms without a calculator
- 32.4Common logarithms
- 32.5Natural log: ln
- 32.6Evaluating logarithms using change-of-base formula
- 32.7Converting from exponential form to logarithmic form
- 32.8Solving exponential equations with logarithms
- 32.9Product rule of logarithms
- 32.10Quotient rule of logarithms
- 32.11Combining product rule and quotient rule in logarithms
- 32.12Evaluating logarithms using logarithm rules
- 32.13Solving logarithmic equations
- 32.14Graphing logarithmic functions
- 32.15Finding a logarithmic function given its graph

- 32.1What is a logarithm?
##### 33Applications of Exponential and Logarithmic Functions

- 33.1Exponential growth and decay by a factor
- 33.2Exponential decay: Half-life
- 33.3Exponential growth and decay by percentage
- 33.4Finance: Compound interest
- 33.5Continuous growth and decay
- 33.6Logarithmic scale: Richter scale (earthquake)
- 33.7Logarithmic scale: pH scale
- 33.8Logarithmic scale: dB scale
- 33.9Finance: Future value and present value

- 33.1Exponential growth and decay by a factor
##### 34Right Triangle Trigonometry

- 34.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
- 34.2Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )
- 34.3Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )
- 34.4Combination of SohCahToa questions
- 34.5Solving expressions using 45-45-90 special right triangles
- 34.6Solving expressions using 30-60-90 special right triangles
- 34.7Word problems relating ladder in trigonometry
- 34.8Word problems relating guy wire in trigonometry
- 34.9Other word problems relating angles in trigonometry

- 34.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
##### 35Laws of sines and cosines

##### 36Bearings

##### 37Trigonometric Ratios and Angle Measure

- 37.1Angle in standard position
- 37.2Coterminal angles
- 37.3Reference angle
- 37.4Find the exact value of trigonometric ratios
- 37.5ASTC rule in trigonometry (
**A**ll**S**tudents**T**ake**C**alculus) - 37.6Unit circle
- 37.7Converting between degrees and radians
- 37.8Trigonometric ratios of angles in radians
- 37.9Radian measure and arc length

- 37.1Angle in standard position
##### 38Graphs of Trigonometric Functions

##### 39Trigonometric Identities

##### 40Solving Trigonometric Equations

- 40.1Solving first degree trigonometric equations
- 40.2Determining non-permissible values for trig expressions
- 40.3Solving second degree trigonometric equations
- 40.4Solving trigonometric equations involving multiple angles
- 40.5Solving trigonometric equations using pythagorean identities
- 40.6Solving trigonometric equations using sum and difference identities
- 40.7Solving trigonometric equations using double-angle identities

- 40.1Solving first degree trigonometric equations
##### 41Imaginary and Complex Numbers

- 41.1Introduction to imaginary numbers
- 41.2Complex numbers and complex planes
- 41.3Adding and subtracting complex numbers
- 41.4Complex conjugates
- 41.5Multiplying and dividing complex numbers
- 41.6Distance and midpoint of complex numbers
- 41.7Angle and absolute value of complex numbers
- 41.8Polar form of complex numbers
- 41.9Operations on complex numbers in polar form

- 41.1Introduction to imaginary numbers
##### 42Introduction to Matrices

##### 43Properties of Matrices

##### 44Determinants and Inverses of Matrices

- 44.1The determinant of a 2 x 2 matrix
- 44.2The determinant of a 3 x 3 matrix (General & Shortcut Method)
- 44.3The inverse of a 2 x 2 matrix
- 44.4The inverse of 3 x 3 matrices with matrix row operations
- 44.5The inverse of 3 x 3 matrix with determinants and adjugate
- 44.62 x 2 invertible matrix
- 44.7Solving linear systems using Cramer's Rule
- 44.8Solving linear systems using 2 x 2 inverse matrices

- 44.1The determinant of a 2 x 2 matrix