# 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

≺ Quadratics

≺
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

**· 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 = a

^{x}and y = log

_{a}x (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.

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