Math Solutions Center

Prepare for math placement testing by exploring the math topics and skills covered in each unit below.

Unit Topics At-A-Glance

Units 0 – 2: Basic Operations on Whole Numbers, Integers, Decimals & Fractions; Basic Algebraic Expressions & Equations, Geometry, & Probability
Unit 3: Ratios, Proportions, Percentages
Unit 4: Lines
Unit 5: Exponents, Polynomials
Unit 6: Factoring Polynomials
Unit 7: Quadratic Equations, Relations & Functions
Unit 8: Rational Expressions, Equations
Unit 9: Radical Functions
Unit 10: Systems of Linear Equations
Unit 11: Inequalities in One and Two Variables, Systems of Linear Inequalities
Unit 12: Transformations of Graphs, Intro to Exponential & Logarithmic Functions

Units 0 – 2 Basic Operations on Whole Numbers, Integers, Decimals & Fractions; Basic Algebraic Expressions & Equations, Geometry, & Probability

• Perform operations with whole numbers and integers.
• Round numbers.
• Find opposite of numbers.
• Find absolute value of numbers.
• Identify prime and composite numbers.
• Find prime factors.
• Use the order of operations to evaluate numeric expressions.
• Calculate and rewrite numbers using exponents and scientific notation.
• Evaluate algebraic expressions.
• Simplify algebraic expressions.
• Use the distributive property.
• Use the identity and inverse properties.
• Identify terms, coefficients, and like terms of an algebraic expression.
• Introduction to fractions and mixed numbers.
• Multiply and divide fractions.
• Add and subtract fractions.
• Solve one-step equations.
• Solve equations using both the addition and the multiplication properties of equality.
• Find the mean, median, and mode.
• Estimate the probability of an event.
• Find the perimeter and area of common polygons.
• Make conversions involving American and Metric units of length.
• Write word statements as algebraic expressions.
• Translate word statements into expressions or equations.
• Identify a base and an exponent.
• Evaluate exponential expressions.
• Identify the base and exponent in exponential expressions.
• Evaluate algebraic expressions.
• Simplify algebraic expressions.
• Convert between percentages, decimals, and fractions.
• Solve equations using both the addition and the multiplication properties of equality.
• Solve linear equations involving non-simplified expressions.
• Solve linear equations involving grouping symbols.
• Solve linear equations containing decimals.
• Determine if a number is a solution to an equation.
• Solve problems involving geometry formulas.
• Evaluate a formula.

Unit 3: Ratios, Proportions, & Percentages

• Write two quantities as a ratio or a rate.
• Find a unit rate.
• Compare unit prices.
• Write proportions.
• Determine whether proportions are true or false.
• Solve proportions.
• Use proportions to solve applications.
• Find unknown lengths of sides in similar triangles.
• Solve applications involving similar triangles.
• Approximate square roots.
• Find square roots.
• Find cube roots.
• Use the Pythagorean Theorem.
• Solve applications using the Pythagorean Theorem.
• Translate word statements into percent equations.
• Solve percent equations.
• Solve problems by using a percent equation.
• Write percent problems as proportions.
• Solve percent problems using proportions.
• Solve applications involving percent.
• Compute simple interest.
• Compute compound interest.
• Solve percent problems involving discount, markups, and sales tax.
• Solve percent of change problems.
• Solve mixture problems.

Unit 4: Lines

• Solve linear equations by clearing fractions or decimals.
• Identify contradictions and identities.
• Read line graphs.
• Identify points in the rectangular coordinate system.
• Plot ordered pairs in the rectangular coordinate system.
• Create scatter plots.
• Determine if an ordered pair is a solution to an equation.
• Determine the unknown coordinate of an ordered pair solution.
• Graph linear equations by plotting points.
• Graph simple functions by plotting points.
• Find x- and y- intercepts.
• Graph linear equations using intercepts.
• Use linear equations to model data.
• Graph horizontal and vertical lines.
• Find the slope of a line given two points.
• Find the slope of horizontal and vertical lines.
• Graph a line using the slope and a point.
• Find and use the slopes of parallel and perpendicular lines.
• Use slope in applications.
• Determine the slope and y-intercept from a linear equation.
• Use the slope-intercept form to graph a linear equation.
• Write the equation of a line given its slope and y-intercept.
• Write the equation of a line given its slope and a point on the line.
• Write the equation of a line given two points.
• Determine the relationship between two lines.
• Use linear equations to solve applications.

Unit 5: Exponents & Polynomials

• Simplify exponential expressions using the product rule or the quotient rule.
• Use the zero-power rule.
• Use the power-to-power rule.
• Use the product-to-power rule.
• Use the quotient-to-power rule.
• Simplify exponential expressions using a combination of rules.
• Use the negative power rule.
• Simplify expressions containing negative exponents using a combination of rules.
• Classify polynomials as monomial, binomial, or trinomial.
• Determine the degree and coefficient of a monomial.
• Determine the degree and leading coefficient of a polynomial.
• Evaluate a polynomial for a given value.
• Simplify polynomials by combining like terms.
• Add polynomials.
• Find the opposite of a polynomial.
• Subtract polynomials.
• Multiply monomials.
• Multiply a polynomial by a monomial.
• Multiply two binomials.
• Multiply two or more polynomials.
• Square a binomial sum.
• Square a binomial difference.
• Multiply the sum and difference of two terms.
• Determine the degree of a polynomial in several variables.
• Evaluate polynomials in several variables.
• Add or subtract polynomials in several variables.
• Multiply polynomials in several variables.

Unit 6: Factoring Polynomials

• Find the greatest common factor of a group of integers.
• Find the greatest common factor of a group of monomials.
• Factor out the greatest common factor from a polynomial.
• Factor by grouping.
• Factor trinomials of the form x² + bx + c.
• Factor trinomials of the form x² + bxy + cy².
• Factor trinomials of the form ax² + bx + c.
• Factor trinomials of the form ax² + bxy + cy².
• Factor trinomials of the form ax² + bx + c after factoring out the GCF.
• Factor trinomials of the form ax² + bx + c using the ac method.
• Factor the difference of two squares.
• Factor perfect square trinomials.
• Factor the sum or difference of two cubes.
• Factor polynomials completely.

Unit 7: Quadratic Equations & Relations & Functions

• Solve quadratic equations by factoring.
• Solve polynomial equations by factoring.
• Solve quadratic equations using the square root property.
• Use the discriminant to determine the number of and type of solutions to a quadratic function.
• Solve quadratic equations using the quadratic formula.
• Solve application problems involving geometric figures.
• Solve application problems using the Pythagorean Theorem.
• Solve application problems involving quadratic models.
• Solve applications involving unknown numbers.
• Solve applications involving projectile motion.
• Solve applications involving geometric formulas.
• Solve applications involving distance, rate, and time.
• Solve applications involving work.
• Find the distance between two points.
• Find the midpoint of a line segment.
• Write the standard form of an equation of a circle.
• Sketch the graph of a circle given in standard form.
• Find the domain and range of a relation.
• Determine if relations are functions.
• Identify a function with the vertical line test.
• Express equations of functions using function notation.
• Evaluate functions.
• Find the domain of a polynomial or rational function.
• Find the sum, difference, and product of functions.
• Interpret graphs of functions.
• Solve application problems involving functions.

Unit 8: Rational Expressions & Equations

• Evaluate rational expressions.
• Find restricted values for rational expressions.
• Simplify rational expressions.
• Divide monomials.
• Divide a polynomial by a monomial.
• Multiply and divide rational expressions.
• Find the least common denominator of rational expressions.
• Write equivalent rational expressions.
• Add and subtract rational expressions with common denominators.
• Add and subtract rational expressions with unlike denominators.
• Simplify complex fractions.
• Simplify complex rational expressions by first simplifying the numerator and denominator.
• Simplify complex rational expressions by multiplying by a common denominator.
• Identify rational equations.
• Solve rational equations.
• Identify and solve proportions.
• Solve a formula containing rational expressions for a given variable.
• Use proportions to solve problems.
• Use formulas containing rational expressions to solve problems.
• Solve uniform motion problems involving rational equations.
• Solve problems involving rate of work.

Unit 9: Radical Functions

• Find square roots of perfect squares.
• Approximate square roots.
• Simplify radical expressions of the form \(\sqrt{a^2}\).
• Find cube roots.
• Find and approximate n^th roots.
• Evaluate radical functions.
• Use the definition for rational exponents of the form \(a^{\tfrac{1}{n}}\).
• Use the definition for rational exponents of the form \(a^{\tfrac{n}{m}}\).
• Simplify exponential expressions involving rational exponents.
• Use rational exponents to simplify radical expressions.
• Simplify radical expressions using the product rule.
• Simplify radical expressions using the quotient rule.
• Add and subtract radical expressions.
• Multiply radical expressions.
• Rationalize denominators of radical expressions.
• Solve equations involving one radical expression.
• Solve equations involving two radical expressions.
• Use radical equations and models to solve application problems.
• Simplify powers of i.
• Simplify radicals with negative radicands.
• Add and subtract complex numbers.
• Multiply and divide complex numbers.

Unit 10: Systems of Linear Equations

• Determine if an ordered pair is a solution to a system of linear equations in two variables.
• Determine the number of solutions to a system without graphing.
• Solve systems of linear equations by graphing.
• Solve systems of linear equations by substitution.
• Solve special systems by substitution.
• Solve systems of linear equations by elimination.
• Solve special systems by elimination.
• Solve related quantity applications using systems of equations.
• Solve geometry applications using systems of equations.
• Solve uniform motion applications using systems of equations.
• Solve mixture applications using systems of equations.

Unit 11: Inequalities in One & Two Variables, Systems of Linear Inequalities

• Write the solution set of an inequality in set-builder notation.
• Graph the solution set of an inequality on a number line.
• Use interval notation to express the solution set of an inequality.
• Solve linear inequalities in one variable.
• Solve three-part inequalities.
• Use linear inequalities to solve application problems.
• Find the union and intersection of two sets.
• Solve compound linear inequalities in one variable.
• Solve absolute value equations and inequalities.
• Determine if an ordered pair is a solution to a linear inequality in two variables.
• Graph a linear inequality in two variables.
• Solve applications involving linear inequalities in two variables.
• Determine if an ordered pair is a solution to a system of linear inequalities in two variables.
• Graph systems of linear inequalities.
• Solve applications involving systems of linear inequalities.
• Solve polynomial inequalities.
• Solve rational inequalities.

Unit 12: Transformations of Graphs & Intro to Exponential & Logarithm Functions

• Identify the characteristics of a quadratic function from its graph.
• Graph quadratic functions by using translations.
• Graph quadratic functions of the form f(x) = a(x – h)² + k.
• Find the vertex of a quadratic function by using the vertex formula.
• Maximize quadratic functions to solve application problems.
• Minimize quadratic functions to solve application problems.
• Evaluate radical functions.
• Find the domain of a radical function.
• Graph functions that contain square roots or cube roots.
• Use vertical shifts to graph functions.
• Use horizontal shifts to graph functions.
• Use reflections to graph functions.
• Use combinations of transformations to graph functions.
• Form and evaluate composite functions.
• Determine if a function is one-to-one using the horizontal line test.
• Find the inverse of a one-to-one function.
• Use the characteristics of exponential functions.
• Sketch the graphs of exponential functions using transformations.
• Solve exponential equations by relating the bases.
• Solve applications of exponential functions.
• Use the characteristics of the natural exponential function.
• Sketch the graphs of natural exponential functions using transformations.
• Solve natural exponential equations by relating the bases.
• Solve applications of the natural exponential function.
• Change from exponential to logarithmic form and vice versa.
• Evaluate logarithmic expressions.
• Use the properties of logarithms.
• Use the common and natural logarithms.
• Use the characteristics of logarithmic functions.