The practice exercises below were written to allow you to do well on the Arithmetic portion of the ACCUPLACER Mathematics Placement Test and on the Math Diagnostic Tests for placement into Math 093 through Math 181. The indented links show detailed solutions and explanations of the concepts to the problems presented. Please read the document "Placement Cut-Off Scores" located on the Math Department Web site in the "Placement Info" column.
PLEASE READ THE FOLLOWING CAREFULLY:
- The questions on the Mathematics Placement Tests are multiple choice and will be presented to you on a computer screen. You will be given scratch paper by the Testing Center staff so that you can find the correct answer which you then have to mark on the computer screen!
- You are NOT allowed to use your own calculator. There is a calculator built into the ACCUPLACER testing software that will be displayed for certain questions. For the Diagnostic Tests you are not allowed to use a calculator at all. If you are caught using a calculator where not expressly allowed, you will be penalized.! See "Academic Dishonesty" policy.
- The placement tests are untimed. However, plan to be at the Testing Center for at least one (1) hour. Suggestion ... a longer stay and hard work will increase your chances of placing into your desired mathematics course.
NOTE:
Many of the following concepts are taught in both Math 124- College Algebra and in Math 126- Precalculus I. However, there is a huge difference in the approach. In Math 124, practical applications are the focal point. Some concepts are only introduced, not thoroughly investigated. In Math 126, a rigorous discussion of the algebra concepts necessary for Calculus is the focal point. In Math 126 more so than in Math 124, the emphasis shifts to theory—the precise statement of definitions and theorems and the logical processes by which those theorems are established.
Please understand that ONLY Math 126 is a prerequisite for Calculus, Math 181 !!!
1. Circles and Semi-Circles - Problems
and Solutions
(Math 124- College Algebra, Math 126- Pre-calculus Concept)
2. Graphical
Representation of Linear Equations in Two Variables - Problems and Solutions
(Math 096- Intermediate Algebra
, Math 124- College Algebra, Math 126- Precalculus I Concept)
Detailed Solutions and Concepts - Graphical Representation of Linear Equations in Two Variables
3. Algebraic
Representation of Linear Equations in Two Variables - Problems and Solutions
(Math 096- Intermediate Algebra
, Math 124- College Algebra, Math 126- Precalculus I Concept)
Detailed Solutions and Concepts - Algebraic Representation of Linear Equations in Two Variables
4. Introduction to Functions - Problems
and Solutions
(Math 096- Intermediate Algebra
, Math 124- College Algebra, Math 126- Precalculus I Concept)
5. Graphs of Common Functions - Problems
and Solutions
(Math 096- Intermediate Algebra
, Math 124- College Algebra, Math 126- Precalculus I Concept)
Detailed Solutions and Concepts - Graphs of some Common Functions
6. Piecewise-Defined Functions - Problems
and Solutions
(Math 124- College Algebra, Math 126- Pre-calculus Concept)
Detailed Solutions and Concepts - Piecewise-Defined Functions
7. Combining Functions - Problems and
Solutions
(Math 124- College Algebra, Math 126- Pre-calculus Concept)
8. Quadratic Functions - Problems and
Solutions
(Math 124- College Algebra, Math 126- Pre-calculus Concept)
9. Polynomial Functions - Problems and
Solutions
(Math 124- College Algebra, Math 126- Pre-calculus Concept)
10. Rational Functions - Problems and Solutions
(Math 124- College Algebra, Math 126- Pre-calculus Concept)
11. Inverse Algebraic Functions - Problems and
Solutions
(Math 124- College Algebra, Math 126- Pre-calculus Concept)
Detailed Solutions and Concepts - Inverse Algebraic Functions
12. Systems of Non-Linear Equations - Problems
and Solutions
(Math 124- College Algebra, Math 126- Pre-calculus Concept)
Detailed Solutions and Concepts - Systems of Non-Linear Equations
13. Polynomial and Rational Inequalities -
Problems and Solutions
(Math 124- College Algebra, Math 126- Pre-calculus Concept)
Detailed Solutions and Concepts - Polynomial and Rational Inequalities
14. Introduction to Exponential and Logarithmic
Equations - Problems and Solutions
(Math 124- College Algebra, Math 126- Pre-calculus Concept)
Detailed Solutions and Concepts - Introduction to Exponential and Logarithmic Equations
15. Logarithm Rules and Basic Properties -
Problems and Solutions
(Math 124- College Algebra, Math 126- Pre-calculus Concept)
Detailed Solutions and Concepts - Logarithm Rules and Basic Properties
16. Solving Exponential Equations - Problems
and Solutions
(Math 124- College Algebra, Math 126- Pre-calculus Concept)
Detailed Solutions and Concepts - Solving Exponential Equations
17. Solving Logarithmic Equations - Problems
and Solutions
(Math 124- College Algebra, Math 126- Pre-calculus Concept)
Detailed Solutions and Concepts - Solving Logarithmic Equations
18. Exponential Functions - Problems and
Solutions
(Math 124- College Algebra, Math 126- Pre-calculus Concept)
19. Logarithmic Functions - Problems and
Solutions
(Math 124- College Algebra, Math 126- Pre-calculus Concept)
20. Matrices and Determinants - Problems
and Solutions
(Math 124- College Algebra Concept)
21. Sequences and Series - Problems and
Solutions
(Math 124- College Algebra Concept)
22. Angles - Problems and Solutions
(Math 127- Pre-calculus II Concept)
23. The Six Trigonometric Ratios - Problems and
Solutions
(Math 127- Pre-calculus II Concept)
Detailed Solutions and Concepts - The Six Trigonometric Ratios
24. Graphs of Sine and Cosine Functions -
Problems and Solutions
(Math 127- Pre-calculus II Concept)
Detailed Solutions and Concepts - Graphs of Sine and Cosine Functions
25. Graphs of Tangent, Cotangent, Secant, and
Cosecant Functions
(Math 127- Pre-calculus II Concept)
Detailed Solutions and Concepts - Graphs of Tangent, Cotangent, Secant, and Cosecant Functions
26. Inverse Trigonometric Functions -
Problems and Solutions
(Math 127- Pre-calculus II Concept)
Detailed Solutions and Concepts - Inverse Trigonometric Functions
27. Solving Trigonometric Equations - Part 1 -
Problems and Solutions
(Math 127- Pre-calculus II Concept)
Detailed Solutions and Concepts - Solving Trigonometric Equations - Part 1
28. Solving Trigonometric Equations - Part 2 -
Problems and Solutions
(Math 127- Pre-calculus II Concept)
Detailed Solutions and Concepts - Solving Trigonometric Equations - Part 2
29. An Introduction to Conic Sections -
Problems and Solutions
(Math 127- Pre-calculus II Concept)
Detailed Solutions and Concepts - An Introduction to Conic Sections
30. Right Triangle Trigonometry - Problems and
Solutions
(Math 127- Pre-calculus II Concept)
Detailed Solutions and Concepts - Right Triangle Trigonometry
31. Verifying Trigonometric Identities -
Problems and Solutions
(Math 127- Pre-calculus II Concept)
Detailed Solutions and Concepts - Verifying Trigonometric Identities
The College Board, the designers of the ACCUPLACER test provides sample placement tests so that you can experience the "look and feel" of the actual test. You can find them at http://www.collegeboard.com/prod_downloads/student/testing/accuplacer/accuplacer-sample.pdf.