The mathematics skills test focuses on material from MATH 110 (College Algebra), but also covers material from MATH 111 (Trigonometry) and MATH 124 (Calculus).

- Know formulas for midpoint, distance, slope
- Write the question for the line described by:
- Slope is 4,
*y*-intercept at (0, 5) - Passes through the points (4, –3) and (5, –7)
- Slope is undefined and goes through (–5, 2)
- General equation for a vertical and horizontal line
- Parallel and perpendicular lines

- Slope is 4,
- Given
*f*(*x*) =*x*² – 2*x*– 35, find:- All intercepts
- Standard form
- Determine if this function is odd, even or neither
- Find
*f*(3),*f*(*x*+ 8),*f*(0). What is*f*(0) also called? - Sketch a graph of this function labeling all important points such as the intercepts and max and/or min.

- Know how to determine if something is a function and if it has an inverse.
- Know how to evaluate step functions.
- Given only the graph of a function find:
- The domain and range
- Where the graph is increasing and decreasing (answers should be in interval notation)

- Know the basic graphs for:
- 1st, 2nd, and 3rd degree polynomials
- absolute value and square root functions
- explain how transformations change the graph

- Using a graphing calculator, find the intersection of the two following functions in the 2nd quadrant:
*y*= 4 + log(–*x*+ 5)*y*=*x*² – 5*x*+ 2

- Find all real roots for:
*y*= –2*x*³ +*x*² + 2*x*– 1 - Write a possible equation for each graph:

(click images to enlarge) - Divide, using long division, (2
*x*² + 2*x*– 3) / (*x*– 2) - Consider
*f*(*x*) =*x*³ – 2*x*² – 13*x*– 10- Is (
*x*– 2) a factor? - Is 5 a zero?
- Find any
*y*-intercepts.

- Is (
- Let
*f*(*x*) = 2*x*– 3 and*g*(*x*) =*x*² – 9. Find:- (
*f*+*g*)(3) - (
*f*o*g*)(4) *f*^{–1}(*x*)

- (
- Know equations for continuous and compound interest.
- Know basic equations and graphs for exponential and logarithmic functions.
- Know how to evaluate exponents and logarithms with a calculator and know what rounding to
*n*decimal places means. - Know how to find domain, range, intercepts, and asymptotes for rational functions.
- Know how to simplify and solve logarithmic and exponential expressions and equations.

- Know the six trig ratios
- Know how to convert from radian to degrees and back
- Know basic graphs of trig functions including: amplitude, period, phase shift
- Know how to read off information from a right triangle and the unit circle
- Know how to find other angles with the same cosine or sine as the angle given to you

- Basic differentiation: power rule, chain rule, product rule, and quotient rule
- Basic integration: method of substitution