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Questions for Final Exam - College Algebra | MATH 1050, Exams of Algebra

Material Type: Exam; Class: College Algebra (QL); Subject: Mathematics; University: Salt Lake Community College; Term: Fall 2006;

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

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******************************************************************************************************************
PART III: Questions 21 - 30, Self select
Choose FIVE out of the next TEN questions to complete. You must show all your work and
clearly indicate your answer for full credit. CROSS OUT the problems that you do not want
graded.
******************************************************************************************************************
Find the inverse of the matrix without using your calculator.
21)
-2 2
-6 1
Write the partial fraction decomposition of the rational expression.
22) x
(x - 6)(x - 7)
Use synthetic division and the Factor theorem to determine whether x - c is a factor of f(x).
23) f(x) = x3 + 4x2 - 10x + 12; x + 6
Math 1050 - Final Exam - Fall 2006 - Form E - Page 1
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PART III: Questions 21 - 30, Self select

Choose FIVE out of the next TEN questions to complete. You must show all your work and clearly indicate your answer for full credit. CROSS OUT the problems that you do not want graded.


Find the inverse of the matrix without using your calculator.

-2 2 -6 1

Write the partial fraction decomposition of the rational expression.

  1. x (x - 6)(x - 7)

Use synthetic division and the Factor theorem to determine whether x - c is a factor of f(x).

  1. f(x) = x^3 + 4x^2 - 10x + 12; x + 6

Find the center (h, k) and radius r of the circle. Graph the circle.

  1. x 2 + y^2 - 2x - 12y + 21 = 0

x

y

x

y

Solve the problem.

  1. Find the amount earned at the end of 4 years if $6000 is invested at a rate of 8.5% compounded monthly.

The sequence is defined recursively. Write the first four terms.

  1. a 1 = 3 and a (^) n = 4a (^) n-1 - 2 for n ≥ 2

Graph BOTH functions below. For each function list at least three ordered pairs that lie on the graph.

  1. f(x) = log 3

x g(x) = 3x

-5 5 x

y 5

-5 5 x

y 5

-5 5 x

y 5

-5 5 x

y 5

Answer Key Testname: MATH 1050 FALL 2006 FINAL EXAM FORM E PART 3

1 10

-^1

-^1

x - 6

x - 7

  1. (^) Yes
  2. (h, k) = (1, 6); r = 4

-10 -5 5 10 x

y 10

5

-10 -5 5 10 x

y 10

5

  1. $8419.
  2. 3, 10, 38, 150
  3. 3
  4. Exact answers may vary. x = ln 2ln2 - ln

, x ≈ 3.

  1. {16, 25}

-5 5 x

y 5

-5 5 x

y 5

-5 -4 -3 -2 -1 1 2 3 4 5 x

5 y 4 3 2 1

-5 -4 -3 -2 -1 1 2 3 4 5 x

5 y 4 3 2 1

f(1/3) = -1, f(1) = 0, f(3) = 1, etc. g(-1) = 1/3 , g(0) = 1 , g(1) = 3 , etc.