The mathematics skills test focuses
on material from MATH 110 (College Algebra), but also covers
material from MATH 111 (Trigonometry) and MATH 124 (Calculus).
MATH 110 Study Guide (College Algebra)
- 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
- Given f(x) = x² – 2x – 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 = x² – 5x + 2
- Find all real roots for: y = –2x³ + x² + 2x – 1
- Write a possible equation for each graph:
(click images to enlarge)
- Divide, using long division, (2x² + 2x – 3) / (x – 2)
- Consider f(x) = x³ – 2x² – 13x – 10
- Is (x – 2) a factor?
- Is 5 a zero?
- Find any y-intercepts.
- Let f(x) = 2x – 3 and g(x) = x² – 9. Find:
- (f + g)(3)
- (f o g)(4)
- 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.
MATH 111 Study Guide (Trigonometry)
- 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
MATH 124 Study Guide (Calculus)
- Basic differentiation: power rule, chain rule, product rule, and quotient rule
- Basic integration: method of substitution