 List of Topics for MATH 123 Gateway Exam

Students who want to be successful in MATH 123 Calculus I at South Dakota State University
should have a good understanding of the following topics. In order to determine a student’s
knowledge base, a Gateway Exam covering these topics will be given on the second day of class
each semester beginning in Fall 2007. NO CALCULATORS will be allowed on the Gateway
Exam.

General Knowledge
· Know laws of exponents
· Understand negative exponents
· Be able to work with fractional exponents and convert from radicals to fractional exponents
· Be able to add, subtract, multiply , divide, and simplify algebraic expressions
· Know the definition of absolute value and be able to apply it
· Expand binomials, such as (a + b)2 , (a + b)3 , etc.
· Know how to factor

≺ Using a common factor
≺ Special cases such as the difference of squares , difference of cubes , sum of
cubes

· Graphing—know how to graph the basic functions, such as ≺ Using the basic graphs, be able to translate horizontally and vertically,
reflect, stretch, and compress
· Know formulas for area and perimeter(triangle, rectangle, circle ) , volume and surface area
(cylinder, rectangular solid, sphere)
· Know the formula for the distance between two points

Functions
· Know how to find domain and range.
· Be able to evaluate a function at a specific x-value, f (a), f (2a), etc.
· Understand the relationship between a function and its inverse both algebraically and
graphically
· Be able to do composition of functions
· Be able to evaluate and simplify the difference quotient · Linear
≺ Find the slope of a line between two points
≺ Know both the point- slope form of a line and the slope -intercept form
≺ Write a linear equation given two points or a point and slope
≺ Be able to recognize the equation of a linear function
≺ Be able to solve linear equations and inequalities
≺ Be able to solve absolute value equations and inequalities

≺ Be able to use the quadratic formula
≺ Be able to solve a quadratic equation and understand the meaning of the
solution(s) (i.e. x-intercept(s))
≺ Be able to solve a quadratic inequality using test points

· Exponential and Logarithmic
≺ Know graphs of y = ax and y = logax (particularly when the base is e)
≺ Know exponent and logarithmic properties
≺ Understand the inverse relationship between exponentials and logarithms
≺ Be able to solve equations involving exponents and logarithms

· Rational
≺ Be able to find vertical asymptotes
≺ Be able to add, subtract, multiply, and divide rational functions, including
long division of polynomials
≺ Be able to simplify by rationalizing with a conjugate
≺ Be able to solve rational equations and inequalities
≺ Be able to factor a common factor out of a rational expression, particularly
when there is a negative fractional exponent

Trigonometry
· Know the unit circle—particularly the sine, cosine, and tangent of and .
· Know the graphs of sine, cosine, and tangent, and their domains and ranges; also, be able to
translate, stretch, compress, and reflect these graphs
· Be able to define the six trigonometric functions using a right triangle
· Be able to define the six trigonometric functions using sine and cosine
· Know basic trig identities, such as the Pythagorean identities, even-odd identities, and the
addition and subtraction formulas for sine and cosine
· Be able to solve trigonometric equations
· Understand the functions sin-1 x, cos-1 x, and tan-1 x ; know their domains and ranges and be
able to evaluate these functions at a specific x, i.e. Prev Next