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PreCalculus Exam 2: Practice Problems and Topics Review, Exams of Pre-Calculus

Western Michigan University (WMU)Pre-Calculus

A summary of the topics covered in a precalculus exam, along with practice problems. The topics include polynomials, rational functions, exponential and logarithmic functions, trigonometric functions, and exponential growth and decay. Students are encouraged to use this document to prepare for the exam by solving the practice problems and reviewing the concepts covered.

Typology: Exams

Pre 2010

Uploaded on 07/23/2009

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Math 1180: PreCalculus
Practice for Exam #2
Here is some information which you may find helpful as you prepare for Exam
2. The first is a brief, and incomplete, summary of the topics on the exam, the
second is a bunch of problems.
Brief List of Topics. This list is not complete, but it should be a
valuable overview of the stuff we have covered since the last exam.
Ch. 3 Polynomials and Rational Functions (all of it)
(a) basic terminology of polynomials
(b) the algebra of polynomials, including long division
(c) real, complex and rational zeros of polynomials, including the Fun-
damental Theorem of Algebra
(d) the connection between the zeros of polynomials and factorization of
polynomials
(e) the end behavior of polynomials
(f) the zeros and domain of rational functions
(g) the graph of rational functions, including horizontal, vertical, and
slant asymptotes
Ch. 4 Exponential and Logarithm Functions (all of it)
(a) basic terminology of exponential and logarithmic functions
(b) conversion between exponential and logarithmic equations
(c) algebra of exponentials and logarithms, including solving exponential
and logarithmic equations
(d) applications of exponentials and logarithms, such as compound in-
terest, radioactive decay, population growth, etc.
Ch. 5 Trigonometric Functions (Sections 5.1 – 5.5)
(a) measuring angles
(b) definition of trigonometric functions in terms of triangles and in terms
of circles
(c) the trigonometric function values at special angles such as π
6,π
4,π
3,π
2,
etc.
(d) the graphs of trigonometric functions
(e) basic terminology of periodic functions
pf3
pf4

Partial preview of the text

Download PreCalculus Exam 2: Practice Problems and Topics Review and more Exams Pre-Calculus in PDF only on Docsity!

Math 1180: PreCalculus

Practice for Exam

Here is some information which you may find helpful as you prepare for Exam

  1. The first is a brief, and incomplete, summary of the topics on the exam, the second is a bunch of problems.

Brief List of Topics. This list is not complete, but it should be a

valuable overview of the stuff we have covered since the last exam.

Ch. 3 Polynomials and Rational Functions (all of it)

(a) basic terminology of polynomials (b) the algebra of polynomials, including long division (c) real, complex and rational zeros of polynomials, including the Fun- damental Theorem of Algebra (d) the connection between the zeros of polynomials and factorization of polynomials (e) the end behavior of polynomials (f) the zeros and domain of rational functions (g) the graph of rational functions, including horizontal, vertical, and slant asymptotes

Ch. 4 Exponential and Logarithm Functions (all of it)

(a) basic terminology of exponential and logarithmic functions (b) conversion between exponential and logarithmic equations (c) algebra of exponentials and logarithms, including solving exponential and logarithmic equations (d) applications of exponentials and logarithms, such as compound in- terest, radioactive decay, population growth, etc.

Ch. 5 Trigonometric Functions (Sections 5.1 – 5.5)

(a) measuring angles (b) definition of trigonometric functions in terms of triangles and in terms of circles (c) the trigonometric function values at special angles such as π 6 , π 4 , π 3 , π 2 , etc. (d) the graphs of trigonometric functions (e) basic terminology of periodic functions

Practice Problems These are a bunch of problems to help you see

what I have in mind for the exam. Some of these problems are a little more complicated than the exam problems; also, many of the exam problems will be multiple choice. But if you can solve all of these, you should be in good shape for the exam.

  1. The polynomial p(x) = 2 x^3 − 7 x^2 − 24 x + 45 has only rational roots. Factor it into three linear factors. Use your factorization to give a rough graph of p(x).
  2. The polynomial q(x) = x^3 + 5 x^2 + 8 x + 6 has one rational root. Factor it into three linear factors.
  3. Here is part of the graph of g(x)

O

expand x

2

C 2 $ x C 2 $ x C 3 ;

x

3

C 5 x

2

C 8 x C 6

latex % ;

2 x x $ 5 x C 6 x x $ 5 $ 3 $ x $ 5 x $ 9 $ x $ 5

collect % , x ;

latex % ;

{x}^{3}+5,{x}^{2}+8,x+

2 x C 6 x x $ 5 $ 3 $ x $ 5 x $ 9 $ x $ 5

plot x $ 1 $ x C 1 $ x $ 2 $ x $ 100 , x =$1.2 ..2.

    1. 0 0. 0 0. 5 1. 0 1. 5

40

    1. 5

120

  • 120

80

0

  • 40
  • 80
  • 160
  • 200
  • 240

x

  1. 0 2. 5

I know that g is a polynomial function of degree 4. Explain why the graph of g must cross the x-axis at one more place. Could it possibly cross the x-axis at more than one place not shown here? Explain why, or why not. How many turning points does g(x) have?

  1. Divide x^4 − 4 x^3 + x − 1 into x^7 + x^5 + x^3 + x.
  1. If xx^ = 2y^ , then solve for y in terms of x.
  2. If a bank offers an interest rate of 7%, them how long does it take for $ to grow to $250?
  3. Carbon 14 decays with a half life of about 5760 years. If you have a sample of carbon which has only 10% of the amount of in fresh carbon. How old is your sample?
  4. If angle θ has radian measure 360, then what is its degree measure? What is the reference angle for θ? Is cos(θ) positive or negative? Is sin(θ) positive or negative?
  5. A certain right triangle has hypotenuse of 11 and one of the angles is π 5. Determine the lengths of the sides, and the measures of all the angles.
  6. What is the period of the function h(x) = cos(3x) + 2? What is the amplitude? Sketch the graph of a single period.
  7. A bike is travelling at 20 feet per second. The tires have radius 26 inches. What is their angular velocity?
  8. A circular pie has radius 8 inches. A piece is cut from the pie with angle measuring 23 radians. What is the area of the slice?
  9. If cos(θ) = 35 , then what might sin(θ) be? Can you say for sure what sin(θ) is, based on this information?