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# Mathematics Placement Test Readiness Guide

The mathematics placement tests are used in conjunction with a student's academic transcript to place incoming students into an appropriate level math class (Algebra 1, Geometry, Algebra 2, Precalculus and Calculus).
The tests and the content covered by them are outlined below. Additionally, links to free Khan Academy instructional videos and practice problems have been provided if a student needs to review a particular topic. Another site with just free mathematics instruction videos that students can access is PatrickJMT.

Some key mathematic facts and procedures should be memorized prior to enrolling in a subsequent math class. The following Memorization Guides summarize the mathematics content that should be memorized by the end of a given course. Looking at these guides prior to your student's placement test will aide your student in achieving a better score. Additionally, knowing this information will allow your student to advance to the subsequent math course with a solid foundation.

### List of 6 items.

• #### Math Memorization Guides

The algebra readiness test evaluates a student’s knowledge in the following content areas. Link(s) have been provided after each content area to assist a student in review if needed.  After following a link, use the content area description to select the appropriate Khan Academy video and practice resources.

The Number System: Students should understand numbers and the different representations that they can take: decimals, fractions, mixed numbers, radicals (square roots), and scientific notation.  Students should be able to classify numbers as natural, whole, integer, rational, irrational, or real.

Number Operations: Students should be able to add, subtract, multiply, and divide numbers in their various forms. Students should understand order of operations.

Expressions and Equations: Students should be able to write expressions and equations to model verbal statements.  Students should be able to rewrite expressions in equivalent forms (includes combining like terms, rules for exponents, and simplifying expressions). Students should be able to solve linear equations in one variable.

Functions: Students should understand function inputs and outputs.  Students should understand rates of change (slopes) for linear functions and equations. Students should be able to identify if a function is linear from an equation or from a graph.  Students should be able to write linear functions.

Geometry: Students should be able to find area and volume of basic geometric shapes.  Students should be comfortable working with right triangles and the Pythagorean Theorem. Students should be familiar with geometric transformations in a coordinate plane.  Students should be comfortable working with similar shapes.  Students should be able to perform geometric reasoning.

Statistics and Probability: Students should be able to calculate simple probabilities.  Students should understand data presented in frequency tables. Students should understand and determine the mean, median, mode, and range of data distributions.  Students should be able to estimate a line of best fit for a scatterplot.

The geometry readiness test evaluates a student’s algebra knowledge in the following content areas. A link has been provided after each content area to assist a student in review if needed.  After following the link, use the content area description to select the appropriate Khan Academy video and practice resources.

Equivalent Expressions: Students should be able to rewrite expressions in different forms using the properties of exponents and radicals.  Students should understand the distributive property and FOIL and be able to use these to expand expressions.  Students should be able to factor polynomial (specifically quadratic) expressions.

Linear Functions and Equations: Students should be able to write linear equations from tabular data or given a point and information about slope.  Students should understand parallel and perpendicular slope relationships. Students should understand the representation of variables in context.

Nonlinear Functions and Equations: Students should be able to solve quadratic equations by factoring and with the quadratic formula.  Students should be able to solve simple rational equations (two equivalent proportions).  Students should understand the difference between linear and exponential growth and decay and be able to model linear and/or exponential growth and decay in context.

Graphical Understanding (Linear): Students should understand the graphs of linear equations/functions including ones with context.  Students should understand how changes to the slope and/or y-intercept affect the graph of a linear function.  Students should be able to write the equation of a linear function seen in a graph.

Graphical Understanding (Nonlinear): Students should understand the connection between quadratic functions and their graphs.  Students should be able to find the domain, range, and vertex of a quadratic function. Students should understand how quadratic functions (parabolas) can be transformed.  Students should be able to determine the domain and range of an exponential function.  Students should understand nonlinear functions and their graphs in context.

Systems of Equations: Students should be able to write systems of linear equations to solve problems with context.  Students should be able to use both substitution and elimination to solve systems of linear equations.  Students should be able to use substitution to solve a system of equations containing a linear equation and a simple quadratic equation.

Inequalities and Systems of Inequalities: Students should be able to write linear inequalities that model a context or represent a graph.  Students should be able to graph one-variable linear inequalities on a number line. Students should be able to graph two-variable linear inequalities in a coordinate plane.  Students should be able to solve inequalities.  Students should be able to identify solutions to a simple absolute value inequality.

Linear Expressions and Equations: Students should be able to evaluate linear expressions. Students should be able to solve linear equations and inequalities. Students should be able to write equations of lines through given points and with descriptions such as parallel and perpendicular. Students should understand the terminology about lines including slope and intercepts. Students should be able to graph points and inequalities on a number line. Students should be able to graph lines and linear inequalities on a coordinate plane. Students should be able to solve systems of equations by substitution and elimination. Students should understand direct variation. Students should understand the relationship between distance, rate and time. Students should be able to set up and solve linear algebraic equations from verbal descriptions.
Exponents and Radicals: Students should understand the rules for exponents and be able to use these rules to simplify expressions containing exponents. Students should be able to simplify expressions involving square roots. Students should understand how to work with numbers in scientific notation.
Polynomial Expressions and Equations: Students should be able to factor, expand and simplify polynomial expressions. Students should be able to solve quadratic equations by factoring and with the quadratic formula. Students should be able to graph quadratic equations on a coordinate plane.
Rational Expressions and Equations: Students should be able to graph rational numbers on a number line. Students should be able to evaluate rational expressions. Students should be able to simplify rational expressions. Students should be able to solve rational equations.
Geometry: Students should understand the angle relationships for triangles, quadrilaterals, circles and parallel and perpendicular lines. Students should be able to find perimeter and area for triangles, squares and rectangles. Students should be able to find circumference and area for circles. Students should be able to find the surface area of rectangular solids. Students should be able to find the volume of rectangular solids. Students should know the midpoint and distance formulas for points in a coordinate plane. Students should know the Pythagorean Theorem. Students should know the relationships in the special right triangles (30-60-90 and 45-45-90). Students should be able to recognize similar triangles and set up equivalent ratios of corresponding sides.

Linear Expressions and Equations: Students should be able to evaluate linear expressions. Students should be able to solve linear equations and inequalities. Students should be able to write equations of lines through given points and with descriptions such as parallel and perpendicular. Students should understand the terminology about lines including slope and intercepts. Students should be able to graph lines and linear inequalities on a coordinate plane. Students should understand direct variation. Students should be able to set up and solve linear algebraic equations from verbal descriptions.
Polynomial Expressions and Equations: Students should be able to evaluate polynomial functions. Students should be able to factor, expand and simplify polynomial expressions. Students should be able to divide polynomial expressions using both synthetic division and long division. Students should understand the process of completing the square for quadratic expressions. Students should be able to solve quadratic equations by factoring, completing the square and with the quadratic formula. Students should be able to find both real and imaginary solutions to quadratic functions. Students should be able to graph quadratic inequalities on a number line. Students should be able to graph quadratic functions on a coordinate plane. Students should be able to find intercepts for polynomial functions. Students should be able to analyze graphs of polynomial functions. Students should be comfortable working with quadratic functions modeling projectile motion.
Rational and Absolute Value Expressions and Equations: Students should be able to evaluate rational and absolute value expressions. Students should be able to simplify rational expressions. Students should be able to solve rational equations.
Exponents, Radicals and Logarithms: Students should understand the rules for exponents and be able to use these rules to simplify expressions containing exponents. Students should be able to simplify expressions involving square roots. Students should be able to solve equations with radicals and non-integer exponents. Students should be able to solve equations with variable exponents. Students should be able to evaluate logarithmic expressions. Students should understand the properties of logarithms. Students should be able to solve equations containing logarithms. Students should be able to graph exponential and logarithmic equations. Students should be able to write exponential equations given an exponential graph and two points on it.
Geometry and Right Triangle Trigonometry: Students should know the triangle inequality theorem. Students should be able to find perimeter and area for triangles, squares and rectangles. Students should be able to find circumference and area for circles. Students should be able to find the volume of rectangular solids. Students should know the Pythagorean Theorem. Students should be able to recognize similar triangles and set up equivalent ratios of corresponding sides. Students should understand right triangle trigonometry (SOH CAH TOA). Students should understand the equation of a circle.

Linear Equations, Inequalities, Absolute Value: Students should be able to evaluate linear and absolute value expressions. Students should be able to solve linear inequalities and inequalities that contain absolute value. Students should be able to write equations of lines given information about the line. Students should be able to solve systems of linear equations by substitution and elimination. Students should be able to set up and solve linear algebraic equations from verbal descriptions.
Polynomial Expressions and Equations: Students should be able to factor, expand and simplify polynomial expressions. Students should be able to divide polynomial expressions using both synthetic division and long division. Students should understand the process of completing the square for quadratic expressions. Students should be able to solve quadratic equations by factoring, completing the square and with the quadratic formula.
Functions: Students should be comfortable with function terminology. Students should be able to evaluate functions. Students should be able to combine functions including composition. Students should understand domain and range. Students should be able to understand changes to a function graphically.
Rational Expressions and Equations: Students should be able to evaluate rational expressions. Students should be able to simplify rational expressions.
Exponents and Radicals: Students should understand the rules for exponents and be able to use these rules to simplify expressions containing exponents. Students should be able to simplify expressions involving square roots.
Exponential and Logarithmic Functions: Students should be able to solve equations that contain variable exponents. Students should understand the properties of logarithms. Students should be able to simplify logarithmic expressions. Students should be able to solve logarithmic equations.
Trigonometry: Students should understand right triangle trigonometry (SOH CAH TOA). Students should understand the graphs of the trigonometric functions. Students should understand the trigonometric identities.
Geometry: Students should be able to find perimeter and area for triangles, squares, rectangles and trapezoids. Students should be able to find circumference and area for circles. Students should be able to find the surface area of rectangular solids. Students should understand how changes in linear, area and volume measurements affect each other. Students should know the Pythagorean Theorem. Students should be able to recognize similar triangles and set up equivalent ratios of corresponding sides.
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