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)
• 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.

## 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