The practice exercises below were written to allow you to do well on the ACCUPLACER Mathematics Placement Test for potential placement into Math 127, Math 132, or Math 181.  The indented links show detailed solutions and explanations of the concepts to the problems presented. 

PLEASE READ THE FOLLOWING CAREFULLY: 

NOTE: 

Many of the following concepts are taught in both Math 124 - College Algebra and in Math 126 - Precalculus 1.  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 theorythe 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 !

Math 124/126 - College Algebra/Precalculus 1 Concepts.  Know them well and potentially place into Math 127 or Math 132.

1.    Circles and Semi-Circles - Problems and Solutions

Detailed Solutions and Concepts - Circles and Semi-Circles

2.    Graphical Representation of Linear Equations in Two Variables - Problems and Solutions

Detailed Solutions and Concepts - Graphical Representation of Linear Equations in Two Variables

3.    Algebraic Representation of Linear Equations in Two Variables - Problems and Solutions

Detailed Solutions and Concepts - Algebraic Representation of Linear Equations in Two Variables

4.    Introduction to Functions - Problems and Solutions

Detailed Solutions and Concepts - Introduction to Functions

5.    Graphs of Common Functions - Problems and Solutions

Detailed Solutions and Concepts - Graphs of some Common Functions

6.    Piecewise-Defined Functions - Problems and Solutions

Detailed Solutions and Concepts - Piecewise-Defined Functions

7.    Combining Functions - Problems and Solutions

Detailed Solutions and Concepts - Combining Functions

8.    Quadratic Functions - Problems and Solutions

Detailed Solutions and Concepts - Quadratic Functions

9.    Polynomial Functions - Problems and Solutions

Detailed Solutions and Concepts - Polynomial Function

10.  Rational Functions - Problems and Solutions

Detailed Solutions and Concepts - Rational Functions

11.  Inverse Algebraic Functions - Problems and Solutions

Detailed Solutions and Concepts - Inverse Algebraic Functions

12.  Systems of Non-Linear Equations - Problems and Solutions

Detailed Solutions and Concepts - Systems of Non-Linear Equations

13.  Polynomial and Rational Inequalities - Problems and Solutions

Detailed Solutions and Concepts - Polynomial and Rational Inequalities

14.  Introduction to Exponential and Logarithmic Equations - Problems and Solutions

Detailed Solutions and Concepts - Introduction to Exponential and Logarithmic Equations

15.  Logarithm Rules and Basic Properties - Problems and Solutions

Detailed Solutions and Concepts - Logarithm Rules and Basic Properties

16.  Solving Exponential Equations - Problems and Solutions

Detailed Solutions and Concepts - Solving Exponential Equations

17.  Solving Logarithmic Equations - Problems and Solutions

Detailed Solutions and Concepts - Solving Logarithmic Equations

18.  Exponential Functions - Problems and Solutions

Detailed Solutions and Concepts - Exponential Function

19.  Logarithmic Functions - Problems and Solutions

Detailed Solutions and Concepts - Logarithmic Functions

20.  Matrices and Determinants - Problems and Solutions

Detailed Solutions and Concepts - Matrices and Determinants

21.  Sequences and Series - Problems and Solutions

Detailed Solutions and Concepts - Sequences and Series

 

Math 127 - Precalculus 2 (Trigonometry) Concepts.  Know them AND the above concepts well and potentially place into Math 181.

22.  Angles - Problems and Solutions

Detailed Solutions and Concepts - Angles

23.  The Six Trigonometric Ratios - Problems and Solutions

Detailed Solutions and Concepts - The Six Trigonometric Ratios

24.  Graphs of Sine and Cosine Functions - Problems and Solutions

Detailed Solutions and Concepts - Graphs of Sine and Cosine Functions

25.  Graphs of Tangent, Cotangent, Secant, and Cosecant Functions

Detailed Solutions and Concepts - Graphs of Tangent, Cotangent, Secant, and Cosecant Functions

26.  Inverse Trigonometric Functions - Problems and Solutions

Detailed Solutions and Concepts - Inverse Trigonometric Functions

27.  Solving Trigonometric Equations - Part 1 - Problems and Solutions

Detailed Solutions and Concepts - Solving Trigonometric Equations - Part 1

28.  Solving Trigonometric Equations - Part 2 - Problems and Solutions

Detailed Solutions and Concepts - Solving Trigonometric Equations - Part 2

29.  An Introduction to Conic Sections - Problems and Solutions

Detailed Solutions and Concepts - An Introduction to Conic Sections

30.  Right Triangle Trigonometry - Problems and Solutions

Detailed Solutions and Concepts - Right Triangle Trigonometry

31.  Verifying Trigonometric Identities - Problems and Solutions

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.