Math 119 - PreCalculus

 Final  Exam Information

Three hour, cumulative exam, self-scheduled in the finals week (December 14-December 19)

See http://www.randolphcollege.edu/x13440.xml for procedures about self-scheduled exams.

The final exam is cumulative with about 60% from the material covered after the third exam (from section 4.7 to section 6.5) and 40% from earlier material .

Topics

Numbers

•     The number line

•     Absolute values

•     Solving inequalities and sketching them on the real line

•     Coordinate plane

Functions

•     Domain/Range of a function

•     Linear Functions (lines)

•     Quadratic functions (parabolas- vertex of a parabola, zeros of a parabola, quadratic formula)

•     Absolute value function, greatest integer function

•     Polynomial functions (end behavior of a polynomial, rational zeros of a polynomial)

•     Rational functions

•     Functions involving radicals

•     Trigonometric functions

  •         The unit circle and sine and cosine of basic angles (0, 30,45,60, and 90 degrees)

  •          Other trigonometric functions and their relation to sine and cosine

  •         Period and amplitude of a trigonometric function

  •         Trigonometric identities (Pythagorean identities, sum and difference formulas, double-angle formulas)

  •         Right-triangle trigonometry, law of sines, law of cosines

  •         Inverse trigonometric functions

  •         Solving trigonometric equations

•     Exponential functions      

•     Logarithm functions

•     Composition of functions

Graphs of functions

•     Basic graphs

  • x^2, x^(1/2), x^(1/3), x^(m/n), sin(x), cos(x), tan(x), cot(x), sec(x), a^x, e^x, log(x), ln(x)
     

•     Graphs of  circles, ellipses, parabolas, hyperbolas

•     Using basic graphs to obtain graphs of more complicated functions
          Shift up/down, left/right, stretch (elongate), compress (shrink) horizontally/ vertically, flip over the x-axis, over the y-axis

•     Graph of a reciprocal function

•     Graph of a rational function

•     Graphs of inverse functions (mirror image about the line y=x)

•     Graphs of absolute value functions and step functions (the greatest integer function)

•     Sketching the graph of a function

  •         Finding the domain

  •         Finding the x,y intercepts

  •         Finding the vertical, horizontal asymptotes

  •         Making a sign chart for the function

  •         Putting all the information together

Applications of functions

•     Problems involving scenarios from real life - finding the maximum, minimum, problems involving trigonometric functions, problems about compound interest

Practice Problems

Solving ONLY these problems is NOT sufficient to do well in the exam!  You  should also go over class notes, examples in class, previous quizzes, exams, and  homework problems.  Pay extra attention to the problems that you had difficulty solving. Learn and understand how to solve them.

Textbook: PreCalculus by Faires and DeFranze, 4th Edition

• Review Exercises for Chapter 1 page 74 #1,3,5,7,9,11,13,15,17,19,21,23,25,31,33,35,43,44,45,47,49,51,53,55,57,59,61,63,65,67,71,73,75,76,78,80,81,83
   
• Chapter Test on page 79

CHAPTER 2

• Review Exercises for Chapter 2 page 118  #1,3,5,7,9,13,15,17,19,21,23,25,27,29,31,33,34,35,37,39,40,42,43

• Chapter Test on page 122

CHAPTER 3

• Review Exercises for Chapter 3 page 178  #1,3,5,7,9,11,17,19,21,23,29,31,35,37,39,45,65,67,69,71

• Chapter Test on page 183

CHAPTER 4

• Review Exercises for Chapter 4 page 265   #1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,34,35,37,39,40,42,43

• Chapter Test on page 269

CHAPTER 5

• Review Exercises for Chapter 5 page 304   #1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,47,49,51,53,

• Chapter Test on page 306

CHAPTER 6

• Review Exercises for Chapter 6 page 359 #13,15,17,19,21,35,36,40

If you finish the odd problems and want to practice more, you can  work on the even-numbered problems.