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

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

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

· 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

· 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
· 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

· Quadratic
≺ 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

· 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.

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