- 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

- Simplify an expression or solve an equation
using basic properties of exponentials and logarithms
(including e
- 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.]

- Find the derivative of any of the following functions:
- 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)

- Find the antiderivative (indefinite integral) of any of the
following functions:

- 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.

Maintained by Scott R. Fulton

Last modified:
Thu May 25 16:13:14 EDT 2006