Skills Test Study Guide

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