Math Placement Exam
Topics


PART I: High School Algebra

  1. arithmetic, including working with fractions
  2. ratio, proportion, and percentages
  3. manipulation of algebraic expressions
  4. factoring algebraic expressions
  5. solving linear equations
  6. solving linear inequalities
  7. lines and graphs
  8. simultaneously solving two equations in two unknowns
  9. working with quadratic equations
  10. working with higher degree equations
  11. working with exponents and radicals
  12. word problems

PART II: Precalculus

  1. working with rational exponents
  2. understanding the idea of a function
  3. working with graphs of functions
  4. working with quadratic functions
  5. working with exponential functions
  6. working with logarithmic functions
  7. understanding how to compose functions
  8. working with absolute value
  9. understanding trigonometric values, especially radians
  10. working with trigonometric identities

PART III: Calculus

Section III(a)

  1. understanding limits
  2. finding the equation of a tangent to a curve
  3. differentiating with the chain rule
  4. doing implicit differentiation
  5. finding where a function is increasing or decreasing
  6. finding the maxima and/or minima of polynomials
  7. finding the maxima and/or minima of other functions
  8. graphing rational functions
  9. finding the derivatives of trigonometric functions
  10. finding the derivatives of exponential functions
  11. finding the derivatives of logarithmic functions

Section III(b)

  1. finding the derivative of definite integrals
  2. finding the integrals of derivatives (that is, computing anti-derivatives and using the Fundamental Theorem of Calculus)
  3. evaluating definite integrals
  4. evaluating indefinite integrals
  5. working with integrals as an area under a graph
  6. finding the area of regions bounded by straight lines
  7. finding the area of regions bounded by other graphs

Section III(c)

  1. finding the integrals of trigonometric functions
  2. finding the integrals of exponential and logarithmic functions
  3. finding volumes by slicing
  4. understanding rectilinear motion
  5. understanding work
  6. being able to integrate by parts
  7. being able to integrate using substitutions

Section III(d)

  1. computing improper integrals
  2. using l'Hôpital's rules
  3. finding the sums of particular power series
  4. working with Taylor series
  5. finding the sum of an infinite series
  6. working with complex numbers
  7. solving differential equations of the form dy/dt=ky
  8. solving initial-value problems
  9. solving separable differential equations


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