# Local Placement Exam Topics

## ﻿Algebra Placement Exam Summary

### Arithmetic

• Order of Operations
• Adding, subtracting, multiplying and dividing signed numbers
• Add and multiply fractions, simplify complex fractions
• Rationalize denominators (consisting of a single radical).

### Exponentials and Logarithms

• Integer exponents
• Properties of exponents (zero, negative powers)
• Converting between exponential and logarithmic equations.
• (Note: general properties of logarithms are not included)

### Elementary Algebra Topics

• Solve linear equations with decimal coefficients
• Combine linear terms using properties of numbers
• Simplify rational expressions involving variables
• Linear Inequalities
• Quadratic Equations (with real and complex number solutions)
• Quadratic Inequalities (demonstrating compound inequalities)

### Other Algebra Topics

• Factor difference of two squares
• Factor sum/difference of two cubes or higher powers.
• Absolute Values
• Absolute value inequalities
• Linear Systems of Equations: 2 equations, 2 unknowns

### Other Topics

• Graphs of linear equations
• Intercepts of graphs
• Evaluating Expressions at numerical values
• Evaluating Functions at numerical values and simple expressions.

## Taking the Exam

• The exam is scheduled for 40 minutes and has 32 problems.
• The exam is not pass/fail, simply a tool to determine an appropriate math course for which a student is prepared to succeed in.
• Tools for reviewing the topics above include any High School algebra text, Schaum's Outline of Intermediate Algebra, or the website www.sosmath.com

## ﻿Ready for Calculus Exam Summary

### Algebra

• Solving polynomial, rational equations.
• Simplifying expressions with rational exponents
• Solving logarithmic equations
• Factoring sums and differences of powers.
• Absolute value equations and inequalities.

### Coordinate geometry

• Intersections of lines.
• Coordinates of points from graphs of functions.
• Distance between points
• Slopes of lines

### Functions

• Domain and range
• Symmetry of graphs
• Graphs of specific types of functions (polynomial, exponential, etc)
• Composition of functions

### Verbal Problems

• Linear versus exponential growth
• Surface Area of rectangular boxes.
• Perimeter versus area.

### Trigonometry

• Values of sin(x), cos(x) at standard angles in the unit circle.
• Domains of the 6 trigonometric functions.
• Graphs of trigonometric functions.
• Simplifications of trigonometric expressions by ratios or the pythagorean identities.

## Taking the Exam

• A calculator is not allowed.
• The exam is scheduled for 30 minutes and has 25 problems.
• The exam is not pass/fail, simply a tool to determine an appropriate math course for which the student is prepared to succeed in.
• Tools for reviewing the topics above include any high school precalculus text, Schaum’s Outline of Precalculus, or the websites www.sosmath.com or Khan Academy.