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.
Integers: Students should be able to add, subtract, multiply and divide integers. Students should be comfortable with order of operations and understand prime factorization.
Decimals and Percentages: Students should be able to add, subtract, multiply and divide decimal numbers. Students should be able to round numbers and be comfortable with estimation. Students need to be comfortable working with problems that contain percentages.
Fractions and Mixed Numbers: Students should be able to add, subtract, multiply and divide fractions and mixed numbers. Students should be able to compare fractions and place them on a number line. Students should be able to convert fractions to decimals.
Basic Algebra Concepts: Students should be able simplify and evaluate variable expressions. Students should be able to write variable expressions and equations from a written variable description. Students should be able to solve the simplest algebra equations.
Mathematical Reasoning, Probability, and Basic Statistics: Students should be able to analyze data given in graphs and charts. Students should understand basic probability. Students should understand the statistical concepts of mean and median.
Coordinate Geometry and Basic Geometry: Students should be able to graph points in a Cartesian coordinate plane. Students should be able to find area and perimeter of squares, rectangles and triangles. Students should be able to use the Pythagorean Theorem to find missing sides in right triangles. Students should be able to find the volume of a box. Students should be able to use geometric ratios to solve problems.
Linear Expressions and Equations: Students should be able to simplify expressions by combining like terms. Students should be able to solve linear equations. Students should be able to solve systems of linear equations. Students should be able to solve linear inequalities. Students should be familiar with direct variation.
Exponents and Radicals: Students should be able to simplify expressions with exponents. Students should be able to simplify expressions with square roots.
Quadratic Expressions and Equations: Students should be able to expand and factor quadratic expressions. Students should be able to solve quadratic equations.
Rational Expressions and Equations: Students should be able to evaluate and simplify rational expressions. Students should be able to solve rational equations.
Graphical Representation: Students should be able to graph rational numbers and inequalities on a number line. Students should be able to graph linear and quadratic equations and inequalities on a coordinate plane. Students should be comfortable working with lines in slope-intercept format. Students should be able to perform graphical analysis.
Geometry - Area and Perimeter: Students should be able to find area and perimeter for triangles, squares, rectangles, parallelograms, and simple polygons. Students should be able to find area and circumference for circles.
Geometry - Other: Students should understand basic coordinate geometry (placing geometric shapes on a coordinate plane). Students should understand informal logic statements. Students should understand basic geometric angle relationships (the angles in a triangle add to 180 degrees, complementary angles add to 90 degrees, supplementary angles add to 180 degrees, and perpendicular angles measure 90 degrees). Students should understand the Pythagorean Theorem. Students should be able to compute volumes of boxes.
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.