NKU offers a free online textbook, Transition to College Mathematics, which closely aligns with KYOTE college readiness placement exams and standards.
Preface
Chapter 1: Foundations of Algebra
Chapter 2: Basic Geometry
Chapter 3: Exponents
Chapter 4: Polynomials
Chapter 5: Rational Expressions
Chapter 6: Linear Equations & Inequalities
Chapter 7: Lines
Chapter 8: Quadratic Equations & Functions
Chapter 9: Systems of Linear Equations
Chapter 10: Additional Topics
Appendix 1. KYOTE Placement Exam Standards
Appendix 2. College Readiness Indicators and Learning Outcomes
The Kentucky Online Testing (KYOTE) system offers free online placement tests in math, reading, and writing to assess college readiness. These exams are approved by Kentucky’s Council on Postsecondary Education (CPE) and Department of Education for academic and transition readiness.
Visit CPE's College Readiness Indicators webpage for all exams accepted by the Council, and their corresponding benchmarks.
CR 1. Evaluate numerical expressions involving signed numbers, positive integer exponents, order of operations and parentheses.
CR 2. Evaluate algebraic expressions at specified values of their variables using signed numbers, positive integer exponents, order of operations and parentheses.
CR 3. Perform arithmetic calculations involving fractions, decimals and percents.
CR 4. Order fractions and decimals on a number line.
CR 5. Solve applied arithmetic problems using appropriate units, including problems involving percentage increase and decrease, rates and proportions.
CR 6. Solve simple geometry problems involving properties of rectangles and triangles.
CR 7. Solve simple coordinate geometry problems.
CR 8. Add and subtract polynomials.
CR 9. Multiply polynomials.
CR 10. Simplify algebraic expressions involving positive and negative integer exponents, and square roots.
CR 11. Factor a polynomial in one or more variables by factoring out its greatest common factor; factor a quadratic polynomial.
CR 12. Add, subtract and multiply simple rational expressions.
CR 13. Simplify a rational expression.
CR 14. Solve a linear equation.
CR 15. Solve a multivariable equation for one of its variables.
CR 16. Use a linear equation to solve a simple word problem.
CR 17. Solve a linear inequality.
CR 18. Find the slope of a line given two points on the line or its equation; find the equation of a line given two points on the line, or a point on the line and the slope of the line.
CR 19. Graph a line given its equation; find the equation of a line given its graph.
CR 20. Solve a quadratic equation by factoring or by using the quadratic formula.
CR 21. Solve a system of two linear equations in two variables.
CA 1. Evaluate algebraic expressions at specified values of their variables using signed numbers, rational exponents, order of operations and parentheses.
CA 2. Add, subtract and multiply polynomials.
CA 3. Simplify algebraic expressions involving integer exponents.
CA 4. Simplify algebraic expressions involving square roots and cube roots.
CA 5. Factor a polynomial in one or more variables by factoring out its greatest common factor. Factor a trinomial. Factor the difference of squares.
CA 6. Add, subtract, multiply and divide rational expressions.
CA 7. Simplify a rational expression.
CA 8. Solve a linear equation.
CA 9. Solve a multivariable equation for one of its variables.
CA 10. Solve a linear inequality in one variable.
CA 11. Solve a quadratic equation.
CA 12. Solve an equation involving a radical, a rational or an absolute value expression.
CA 13. Solve a system of two linear equations in two variables.
CA 14. Solve problems that can be modeled using a linear or quadratic equation or expression.
CA 15. Solve geometry problems using the Pythagorean theorem and the properties of similar triangles.
CA 16. Understand and apply the relationship between the properties of a graph of a line and its equation.
CA 17. Find the intercepts and the graph of a parabola given its equation. Find an equation of a parabola given its graph.
CA 18. Evaluate a function at a number in its domain. Find the domain of a rational function or the square root of a linear function.
| Chapter Exercises | KYOTE Standards |
|---|---|
| 1.1 Signed Numbers, Exponents, and Order of Operations | CR 1, CR 2; CA 1 |
| 1.2 Prime Numbers, GCF, and LCM | Foundational Content |
| 1.3 Fractions | CR 2, CR 3; CA 1 |
| 1.4 Decimals and Percentages | CR 3 |
| 1.5 Number Line and Absolute Value | CR 4 |
| 1.6 Applications Using Units, Rates and Proportions | CR 5 |
| 2.1 Properties of Simple Geometric Figures | CR 6 |
| 2.2 Coordinate Geometry | CR 7 |
| 2.3 Pythagorean Theorem and Similar Triangles | CA 15 |
| 3.1 Integer Exponents | CR 10; CA 1, CA 3 |
| 3.2 Square Roots | CR 10; CA 1, CA 4 |
| 3.3 Roots and Rational Exponents | CA 1, CA 4 |
| 4.1 Add and Subtract Polynomials | CR 8; CA 2 |
| 4.2 Multiply Polynomials | CR 9; CA 2 |
| 4.3 Factor Polynomials | CR 11; CA 5 |
| 5.1 Simplify Rational Expressions | CR 13; CA 7 |
| 5.2 Multiply and Divide Rational Expressions | CR 12; CA 6 |
| 5.3 Add and Subtract Rational Expressions | CR 12; CA 6 |
| 6.1 Solve Linear Equations in One Variable | CR 14; CA 8 |
| 6.2 Solve Multivariable Linear Equations for One of Their Variables | CR 15; CA 9 |
| 6.3 Applications of Linear Equations | CR 16; CA 14 |
| 6.4 Solve Linear Inequalities in One Variable | CR 17; CA 10 |
| 7.1 Slopes and Graphs of Lines | CR 18; CA 16 |
| 7.2 Equations and Graphs of Lines | CR 18, CR 19; CA 16 |
| 7.3 Parallel and Perpendicular Lines | CA 16 |
| 8.1 Solve Quadratic Equations | CR 20; CA 11 |
| 8.2 Completing the Square | CA 11, CA 17 |
| 8.3 Graph Quadratic Function | CA 17 |
| 8.4 Applications of Quadratic Equations | CA 14 |
| 9.1 Solve Systems of Linear Equations by Graphing | CR 21; CA 13 |
| 9.2 Solve Systems of Linear Equations Analytically | CR 21; CA 13 |
| 10.1 Functions | CA 18 |
| 10.2 Solve Rational, Radical and Absolute Value Equations | CA 12 |
Department of Mathematics & Statistics
Mathematics-Education-Psychology Center, Room 401
(859) 572-5377 | math@nku.edu
