Calculus ABCs for MA132 (Calculus II)

Revised 23 October 2002

Test Content:

Algebra, Trigonometry, and Geometry (25%):
- Find the equation of a given line (in slope-intercept or point-slope form)
- Evaluate arcsin, arccos, and arctan at arguments corresponding to integer multiples of pi/6 and pi/4 (in radians)
- Rewrite a quadratic polynomial by completing the square
- All other such ABCs questions as for MA131
Exponentials and Logarithmic Functions (15%):
- Simplify an expression or solve an equation using basic properties of exponentials and logarithms (including e^x and ln(x))
- Sketch a graph of e^x, e^-x, or ln(x) (with asymptote, intercept, and one other point labeled)
- All other such ABCs questions as for MA131
Derivatives (35%):
- Find the derivative of any of the following functions:
  - powers, roots, and polynomials
  - trig functions [sin(x), cos(x), and tan(x)]
  - exponentials [e^x]
  - logarithms [ln(x)]
  - any these functions evaluated at (ax+b), where a and b are constants [for example, sin(2x-7)]
  - any linear combination of these (i.e., multiplied by constants and added)
- Find the derivative of any combination of the above functions using one or two applications of the product, quotient, and/or chain rules [for example: tan(3x^2-4), ln(x*sin(x)), etc.]
Basic Integrals (25%):
- Find the antiderivative (indefinite integral) of any of the following functions:
  - powers, roots, and polynomials
  - trig functions [sin(x) and cos(x)]
  - exponentials [e^x]
  - any these functions evaluated at (ax+b), where a and b are constants [for example, 1/(3x+4)]
  - any linear combination of these (i.e., multiplied by constants and added)
- Evaluate integrals by substitution (where a single substitution u = f(x) transforms the integrand to one on the list above)
- Evaluate definite integrals using the Fundamental Theorem of Calculus (where the antiderivative is either given or on the above list)

Notes:

Each test will consist of twenty questions, to be graded right/wrong (for details, see the Instructions for Grading).
All questions count equally, so you must get at least 18 out of 20 answers completely correct to pass the test.
For derivatives, both the prime notation [f'(x)] and the Leibniz notation [dy/dx] will be used.
In addition to the traditional variables x and y, different symbols for variables (for example, s, t, w, theta, ...) will be used.

Resources and Links:

Maintained by Scott R. Fulton
Last modified: Thu May 25 16:13:14 EDT 2006