# ACCUPLACER Test Prep Help & Practice

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##### 1Numbers and Relations

##### 2Number Theory

##### 3Adding and Subtracting Integers

##### 4Multiplying and Dividing Integers

##### 5Operations with Decimals

##### 6Fractions, Decimals, and Percents

##### 7Adding and Subtracting Fractions

##### 8Multiplying and Dividing Fractions

##### 9Introduction to Variables and Expressions

##### 10Introduction to Equations

##### 11Solving Linear Equations

##### 12Ratios, Rates, and Proportions

##### 13Angles, Lines, and Transversals

##### 14Circles

##### 15Surface Area of 3D Shapes

##### 16Symmetry and Surface Area

##### 17Scale Factors and Similarity

##### 18Pythagorean Theorem

##### 19Statistics

##### 20Data and Graphs

##### 21Linear Inequalities

##### 22Introduction to Relations and Functions

##### 23Linear Functions

- 23.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 23.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 23.3Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 23.4Slope intercept form: y = mx + b
- 23.5General form: Ax + By + C = 0
- 23.6Point-slope form: $y - y_1 = m (x - x_1)$
- 23.7Rate of change
- 23.8Graphing linear functions using table of values
- 23.9Graphing linear functions using x- and y-intercepts
- 23.10Graphing from slope-intercept form y=mx+b
- 23.11Graphing linear functions using a single point and slope
- 23.12Word problems of graphing linear functions
- 23.13Parallel and perpendicular lines in linear functions
- 23.14Applications of linear relations

- 23.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 24Linear Equations

- 24.1Introduction to linear equations
- 24.2Introduction to nonlinear equations
- 24.3Special case of linear equations: Horizontal lines
- 24.4Special case of linear equations: Vertical lines
- 24.5Parallel line equation
- 24.6Perpendicular line equation
- 24.7Combination of both parallel and perpendicular line equations
- 24.8Applications of linear equations

- 24.1Introduction to linear equations
##### 25Solving Systems of Linear Equations

- 25.1Determining number of solutions to linear equations
- 25.2Solving systems of linear equations by graphing
- 25.3Using elimination method to solve systems of equations
- 25.4Using substitution method to solve systems of equations
- 25.5Money related questions in linear equations
- 25.6Unknown number related questions in linear equations
- 25.7Distance and time related questions in linear equations
- 25.8Rectangular shape related questions in linear equations

- 25.1Determining number of solutions to linear equations
##### 26Exponents

- 26.1Product rule of exponents
- 26.2Quotient rule of exponents
- 26.3Power of a product rule
- 26.4Power of a quotient rule
- 26.5Power of a power rule
- 26.6Negative exponent rule
- 26.7Combining the exponent rules
- 26.8Scientific notation
- 26.9Convert between radicals and rational exponents
- 26.10Solving for exponents

- 26.1Product rule of exponents
##### 27Operations with Polynomials

##### 28Factoring Polynomial Expressions

- 28.1Common factors of polynomials
- 28.2Factoring polynomials by grouping
- 28.3Solving polynomials with the unknown "b" from
*x^2 + bx + c* - 28.4Solving polynomials with the unknown "c" from
*x^2 + bx + c* - 28.5Factoring polynomials:
*x^2 + bx + c* - 28.6Applications of polynomials:
*x^2 + bx + c* - 28.7Solving polynomials with the unknown "b" from $ax^2 + bx + c$
- 28.8Factoring polynomials: $ax^2 + bx + c$
- 28.9Factoring perfect square trinomials:
*(a + b)^2 = a^2 + 2ab + b^2*or*(a - b)^2 = a^2 - 2ab + b^2* - 28.10Find the difference of squares:
*(a - b)(a + b) = (a^2 - b^2)* - 28.11Evaluating polynomials
- 28.12Using algebra tiles to factor polynomials
- 28.13Solving polynomial equations
- 28.14Word problems of polynomials

- 28.1Common factors of polynomials
##### 29Factoring Trinomials (Advanced)

##### 30Rational Expressions

- 30.1Simplifying rational expressions and restrictions
- 30.2Adding and subtracting rational expressions
- 30.3Multiplying rational expressions
- 30.4Dividing rational expressions
- 30.5Solving rational equations
- 30.6Applications of rational equations
- 30.7Simplifying complex fractions
- 30.8Partial fraction decomposition

- 30.1Simplifying rational expressions and restrictions
##### 31Reciprocal Functions

##### 32Radicals

##### 33Radicals (Advanced)

##### 34Quadratic Functions

- 34.1Introduction to quadratic functions
- 34.2Transformations of quadratic functions
- 34.3Quadratic function in general form:
*y = ax^2 + bx + c* - 34.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 34.5Completing the square
- 34.6Converting from general to vertex form by completing the square
- 34.7Shortcut: Vertex formula
- 34.8Graphing quadratic functions: General form VS. Vertex form
- 34.9Finding the quadratic functions for given parabolas
- 34.10Applications of quadratic functions

- 34.1Introduction to quadratic functions
##### 35Quadratic Equations and Inequalities

##### 36Right Triangle Trigonometry

- 36.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
- 36.2Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )
- 36.3Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )
- 36.4Combination of SohCahToa questions
- 36.5Solving expressions using 45-45-90 special right triangles
- 36.6Solving expressions using 30-60-90 special right triangles
- 36.7Word problems relating ladder in trigonometry
- 36.8Word problems relating guy wire in trigonometry
- 36.9Other word problems relating angles in trigonometry

- 36.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
##### 37Laws of sines and cosines

##### 38Bearings

##### 39Sequences and Series

##### 40Functions

- 40.1Function notation
- 40.2Operations with functions
- 40.3Adding functions
- 40.4Subtracting functions
- 40.5Multiplying functions
- 40.6Dividing functions
- 40.7Composite functions
- 40.8Inequalities of combined functions
- 40.9Inverse functions
- 40.10One to one functions
- 40.11Difference quotient: applications of functions

- 40.1Function notation
##### 41Exponential Functions

- 41.1Exponents: Product rule
*(a^x)(a^y) = a^(x+y)* - 41.2Exponents: Division rule (a^x / a^y) = a^(x-y)
- 41.3Exponents: Power rule
*(a^x)^y = a^(x * y)* - 41.4Exponents: Negative exponents
- 41.5Exponents: Zero exponent:
*a^0 = 1* - 41.6Exponents: Rational exponents
- 41.7Solving exponential equations using exponent rules
- 41.8Graphing exponential functions
- 41.9Graphing transformations of exponential functions
- 41.10Finding an exponential function given its graph

- 41.1Exponents: Product rule
##### 42Logarithmic Functions

- 42.1What is a logarithm?
- 42.2Converting from logarithmic form to exponential form
- 42.3Evaluating logarithms without a calculator
- 42.4Common logarithms
- 42.5Natural log: ln
- 42.6Evaluating logarithms using change-of-base formula
- 42.7Converting from exponential form to logarithmic form
- 42.8Solving exponential equations with logarithms
- 42.9Product rule of logarithms
- 42.10Quotient rule of logarithms
- 42.11Combining product rule and quotient rule in logarithms
- 42.12Evaluating logarithms using logarithm rules
- 42.13Solving logarithmic equations
- 42.14Graphing logarithmic functions
- 42.15Finding a logarithmic function given its graph

- 42.1What is a logarithm?
##### 43Applications of Exponential and Logarithmic Functions

- 43.1Exponential growth and decay by a factor
- 43.2Exponential decay: Half-life
- 43.3Exponential growth and decay by percentage
- 43.4Finance: Compound interest
- 43.5Continuous growth and decay
- 43.6Logarithmic scale: Richter scale (earthquake)
- 43.7Logarithmic scale: pH scale
- 43.8Logarithmic scale: dB scale
- 43.9Finance: Future value and present value

- 43.1Exponential growth and decay by a factor
##### 44Graphs of Trigonometric Functions

##### 45Trigonometric Identities

##### 46Solving Trigonometric Equations

- 46.1Solving first degree trigonometric equations
- 46.2Determining non-permissible values for trig expressions
- 46.3Solving second degree trigonometric equations
- 46.4Solving trigonometric equations involving multiple angles
- 46.5Solving trigonometric equations using pythagorean identities
- 46.6Solving trigonometric equations using sum and difference identities
- 46.7Solving trigonometric equations using double-angle identities

- 46.1Solving first degree trigonometric equations
##### 47Permutations and Combinations

##### 48Conics

##### 49Imaginary and Complex Numbers

- 49.1Introduction to imaginary numbers
- 49.2Complex numbers and complex planes
- 49.3Adding and subtracting complex numbers
- 49.4Complex conjugates
- 49.5Multiplying and dividing complex numbers
- 49.6Distance and midpoint of complex numbers
- 49.7Angle and absolute value of complex numbers
- 49.8Polar form of complex numbers
- 49.9Operations on complex numbers in polar form

- 49.1Introduction to imaginary numbers
##### 50Introduction to Matrices

##### 51Determinants and Inverses of Matrices

- 51.1The determinant of a 2 x 2 matrix
- 51.2The determinant of a 3 x 3 matrix (General & Shortcut Method)
- 51.3The inverse of a 2 x 2 matrix
- 51.4The inverse of 3 x 3 matrices with matrix row operations
- 51.5The inverse of 3 x 3 matrix with determinants and adjugate
- 51.62 x 2 invertible matrix
- 51.7Solving linear systems using Cramer's Rule
- 51.8Solving linear systems using 2 x 2 inverse matrices

- 51.1The determinant of a 2 x 2 matrix