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Chapter 9 Sample Exam: Mathematics Problem Solving - Prof. John Redden, Exams of Algebra

A sample mathematics exam covering topics such as simplification, graphing functions, rationalization, and problem solving. Students are required to answer all questions and show their work where appropriate.

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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Chapter 9_ Sample Exam
Please answer all the questions and show work where appropriate.
1. Simplify: a. yx3
32 b.
356
16 yxโˆ’
2. Simplify:
()
5
3
623
25 zyx
3. Graph the function 2)( += xxf and state the domain.
Assume all variables are positive.
4. Simplify: 2
(
)
xyxxyx 36499 53 โˆ’โˆ’
5. Multiply:
()
2
223 yx โˆ’
6. Rationalize: a. 52
5
27
23
xy
xyโ‹… b. 23
2
โˆ’
7. Simplify: a. 153 โˆ’โ‹…โˆ’ b. i
i
+
+
4
32
8. Solve: 02)72(2
3=โˆ’โˆ’xx
9. Solve: 1312 =+โˆ’โˆ’ xx
10. What length must a pendulum be in order for one complete cycle to take 1.2
seconds? (Use 32
2L
T
ฯ€
=where T is in seconds and L is in feet.)
pf2

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Chapter 9 _ Sample Exam

Please answer all the questions and show work where appropriate.

  1. Simplify: a. x y

3 32 b.

3 6 5 โˆ’ 16 x y

2. Simplify: ( )

5

3 3 2 6 25 x y z

  1. Graph the function f ( x )= x + 2 and state the domain.

Assume all variables are positive.

4. Simplify: 2 9 x y ( 49 x x 36 xy )

3 5 โˆ’ โˆ’

5. Multiply: ( )

2 3 2 x โˆ’ 2 y

  1. Rationalize: a. 5 2

5

xy

โ‹… xy b.

3 2

  1. Simplify: a. โˆ’ 3 โ‹… โˆ’ 15 b.

i

i

  1. Solve: 3 2 x ( 2 x โˆ’ 7 )โˆ’ 2 = 0
  2. Solve: 2 x โˆ’ 1 โˆ’ x + 3 = 1
  3. What length must a pendulum be in order for one complete cycle to take 1.

seconds? ( Use 32

L

T = ฯ€ where T is in seconds and L is in feet. )

Chapter 9 _ Sample Exam Answers

  1. a. 4 x 2 xy b.

2 3 2 โˆ’ 2 x y โ‹… 2 y

3 5 4 3 5 xyz โ‹… 5 x yz

  1. Domain: [ โˆ’ 2 ,โˆž)
  2. x xy x x

2 12 โˆ’ 7

  1. 18 x โˆ’ 12 xy + 2 y
  2. a.

y

y

5 4 18 b. 6 + 2

  1. a. โˆ’ 3 5 b. i 17

10 17

11

1 โˆ’

  1. 1.17 ft

x

y

-3 -2 -1 0 1 2 3 4 5

1

2

3