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Sample Final Exam for College Algebra - Fall 2007 | MATH 143, Exams of Algebra

Material Type: Exam; Class: COLLEGE ALGEBRA; Subject: Mathematics; University: Idaho State University; Term: Fall 2007;

Typology: Exams

Pre 2010

Uploaded on 09/02/2009

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Math 143: College Algebra Name:
Sample Final Exam Instructor:
Fall 2007 Section:
You are allowed to use a couple of 3 ร—5 cards of notes. Calculators are allowed.
Part I consists of 10 multiple choice questions worth 5 points each. Record your answers by
placing an Xthrough one letter for each problem on this answer sheet.
Part II consists of 10 partial credit problems worth a total of 100 points. Show all your work
on the page on which the question appears.
Do not remove this answer page โ€“ you need to return the whole exam. You are allowed two
hours to do the exam. You may leave earlier if you are finished.
Answer Sheet
1. a b c d e
2. a b c d e
3. a b c d e
4. a b c d e
5. a b c d e
6. a b c d e
7. a b c d e
8. a b c d e
9. a b c d e
10. a b c d e
For Grading Use Only
1โ€“10 11 12 13 14 15
16 17 18 19 20 Total
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Download Sample Final Exam for College Algebra - Fall 2007 | MATH 143 and more Exams Algebra in PDF only on Docsity!

Math 143: College Algebra Name:

Sample Final Exam Instructor:

Fall 2007 Section:

You are allowed to use a couple of 3 ร— 5 cards of notes. Calculators are allowed.

Part I consists of 10 multiple choice questions worth 5 points each. Record your answers by placing an X through one letter for each problem on this answer sheet.

Part II consists of 10 partial credit problems worth a total of 100 points. Show all your work on the page on which the question appears.

Do not remove this answer page โ€“ you need to return the whole exam. You are allowed two hours to do the exam. You may leave earlier if you are finished.

Answer Sheet

  1. a b c d e
  2. a b c d e
  3. a b c d e
  4. a b c d e
  5. a b c d e
    1. a b c d e
    2. a b c d e
    3. a b c d e
    4. a b c d e
  6. a b c d e

For Grading Use Only

1โ€“10 11 12 13 14 15

16 17 18 19 20 Total

Part I: Multiple Choice Questions

1 (5 points). Find the domain of the function y =

x^2 โˆ’ 1

(a) (โˆ’โˆž, โˆ’1] โˆช [1, โˆž) (b) [โˆ’ 1 , 1] (c) (โˆ’โˆž, โˆ’1) โˆช (1, โˆž) (d) (โˆ’ 1 , 1) (e) (1, โˆž)

2 (5 points). Determine which graph represents a one-to-one function.

x

y

x

y

x

y

(a) (b) (c)

x

y

x

y

(d) (e)

3 (5 points). Find the inverse function of f (x) =

2 x โˆ’ 1 x โˆ’ 3

(a) f โˆ’^1 (x) =

x โˆ’ 3 2 x โˆ’ 1

(b) f โˆ’^1 (x) =

1 โˆ’ 2 x x โˆ’ 3

(c) f โˆ’^1 (x) =

2 x + 1 x + 3

(d) f โˆ’^1 (x) =

3 x โˆ’ 1 x โˆ’ 2

(e) f โˆ’^1 (x) =

x โˆ’ 2 3 x โˆ’ 1

7 (5 points). Find the vertical asymptote to the graph of the function y =

2 x โˆ’ 6 4 x + 8

(a) x = โˆ’ 2 (b) x = 12 (c) x = 2 (d) x = โˆ’^34 (e) x = 3

8 (5 points). Find the solution set of the inequality ex^2 โˆ’^3 โ‰ค 1.

(a) x โ‰ค โˆ’ 2 or x โ‰ฅ 2 (b) โˆ’ 2 โ‰ค x โ‰ค 2 (c) x โ‰ค โˆ’

3 or x โ‰ฅ

(d) โˆ’

3 โ‰ค x โ‰ค

(e) x โ‰ค 2

9 (5 points). Find the solution set of the inequality log 2 (x + 1) < 2.

(a) x < 1 (b) x > โˆ’ 1 (c) x < 3 (d) โˆ’ 1 < x < 3 (e) โˆ’ 1 โ‰ค x < 3

10 (5 points). The complex number i^25 is equal to

(a) 5 i (b) 1 (c) i (d) โˆ’ 1 (e) โˆ’i

Part II: Partial Credit Problems

11 (10 points). Questions (a) through (d) refer to the graph of the function y = f (x):

x

y

1

1

y = f (x)

(a) Write the domain of f using the interval notation [a, b]:.

(b) Write the range of f using the interval notation [a, b]:.

(c) Find the average rate of change of f over its domain.

Solution.

(d) On which interval is f decreasing?

Answer.

12 (10 points). Let f (x) = x^2 + 3x and g(x) = x โˆ’ 2.

(a) Find f (โˆ’2).

Solution.

(b) Find the difference quotient

f (x + h) โˆ’ f (x) h

. Simplify the answer.

Solution.

(c) Find (f โ—ฆ g)(x). Simplify the answer.

Solution.

15 (14 points). Questions (a) through (d) refer to the function:

y = ln(x + 1) โˆ’ 1

(a) Graph the function y = ln(x + 1) โˆ’ 1.

x

y

1

1

(b) Write the domain and range of y = ln(x + 1) โˆ’ 1 using the interval notation [a, b].

Domain: Range:

(c) Find an equation of the vertical asymptote to the graph of y = ln(x + 1) โˆ’ 1.

Vertical Asymptote:

(d) Find the x- and y-intercepts of the graph of y = ln(x + 1) โˆ’ 1. Show all your work.

Solution.

x-Intercept: y-Intercept:

16 (9 points). Suppose that b is a positive constant greater than 1, and let A, B, and C be defined as follows: logb 2 = A logb 3 = B logb 5 = C

Use the properties of logarithms to evaluate each expression in terms of A, B, and/or C.

(a) logb 12

Solution.

(b) logb 0. 8

Solution.

(c) log 3 b 3

Solution.

17 (8 points). Solve the equation log 5 (x โˆ’ 1) + log 5 (x + 3) = 1 for x.

Solution.