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Expectations of students in science and engineering calculus

The following list of abilities reflects the basic precalculus skills important for success in our calculus sequence. In addition to these is the ability to read carefully and interpret what has been read in the context of solving a problem. The student should be able to demonstrate these skills without a calculator.

In many problems done in a calculus course, often more of the actual work has its basis in precalculus rather than in calculus.

  1. Be able to graph quadratic functions, ellipses, circles, and hyperbolas.
  2. Be able to manipulate algebraic expressions including using rules of exponents.
  3. Be able to complete the square of a quadratic expression and recognize when completion of the square is appropriate.
  4. Be able to determine the domain of a function.
  5. Understand the function concept including the composition of functions and be able to recognize the functions from which a given function is composed.
  6. Be able to determine the intersection of two lines or a line and a quadratic function.
  7. Be able to determine the equation of a line and understand when lines are parallel or perpendicular in terms of their slopes.
  8. Be able to solve linear inequalities and quadratic equations including equations which arise in novel circumstances.
  9. Be able to use properties of logarithmic functions to simplify expressions and solve equations.
  10. Be familiar with the graphs of logarithmic and exponential functions.
  11. Know the definitions of the trigonometric functions, be familiar with their graphs and periodicity, be able to evaluate trigonometric functions using standard triangles, and know basic trigonometric identities including the Law of Cosines.
  12. Know the Pythagorean Theorem and be able to apply it.
  13. Be able to recognize and use proportional relationships including those derived from similar triangles.
  14. Be able to use knowledge of basic plane and solid geometric figures to express relationships among them, e.g. when one is inscribed in another.