University of Pittsburgh at Johnstown
Math Placement Exam - Sample Problems
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Exam questions are selected from topics in three Pitt-Johnstown courses: Math 0001 Algebra 1, Math 0002 College Algebra, and Math 0004 Pre-Calculus. The specific topics are listed in the table below. To see sample problems (in PDF format), click on the Problem Set Link. (Note: The sample problems are not multiple choice. Answers for all problems and complete solutions for the odd problems are included.)
Algebra 1
College Algebra
Pre-Calculus
Problem Set 1
Arithmetic of signed numbers
Whole number exponents
Simplifying expressions
Order of operations
Problem Set 8
Review and extension of topics in Algebra 1
Problem Set 14
Review and extension of topics in Algebra 1 and College Algebra
Problem Set 2
Factoring polynomials
Problem Set 9
Solving radical equations
Solving quadratic in form equations
Problem Set 15
Operations with complex numbers
Polynomial long division
Zeros of polynomials
Graphing rational functions
Problem Set 3
Simplifying rational expressions
Arithmetic of rational expressions
Problem Set 10
Distance and Midpoint formulas
X and Y intercepts
Linear equations in 2 variables
Quadratic equations in 2 variables
Symmetry
Translations
Circles
Problem Set 16
Solving absolute value, polynomial and rational inequalities
Problem Set 4
Solving first degree equations
Solving first degree inequalities
Solving quadratic equations & quadratic formula
Solving linear absolute value equations
Problem Set 11
Functions
Function notation
Arithmetic of functions
Composition of functions
The difference quotient
Inverse functions
Multipart or Piecewise defined functions
Problem Set 17
Radian vs. Degree measure
Trig functions and special angles
Trig identities and inverse functions
Solving Trig equations
Graphs of Trig functions
Problem Set 5
Radical notation and rational exponents
Simplification of radical expressions
Problem Set 12
Exponential functions
Logarithmic functions
Rules of Logarithms
Solving exponential and logarithmic equations
Problem Set 6
Solving word problems
Problem Set 13
System of equations
Word Problems
Problem Set 7
Introduction to the Cartesian Coordinate System
Graphs of 2-variable equations
Last Reviewed: December 18, 2007
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