# ACT Compass Test Prep Help & Practice!

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##### 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 / a^y) = a^(x-y)
- 31.3Exponents: Power rule
*(a^x)^y = a^(x * 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
##### 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