University of Pittsburgh at Johnstown
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Math Placement Exam - Sample Problems

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 1College AlgebraPre-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