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Chapter 5 Sample Exam: Mathematics Problem Solving - Prof. John Redden, Exams of Algebra

A sample mathematics exam focusing on problem-solving skills, including simplification, addition, subtraction, multiplication, and division of algebraic expressions, as well as finding the maximum and minimum values of functions. The exam also includes a projectile motion problem.

Typology: Exams

Pre 2010

Uploaded on 08/16/2009

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Chapter 5_ Sample Exam
Please answer all the questions and show work where appropriate.
1. Simplify:
3
2
3
3
2โŽŸ
โŽŸ
โŽ 
โŽž
โŽœ
โŽœ
โŽ
โŽ›
y
x
2. Simplify: 343 )5( โˆ’โˆ’ zxy
3. Given 923)( 2โˆ’+โˆ’= xxxf find )2(
โˆ’
f.
4. Add: )775()923( 22 +โˆ’โˆ’+โˆ’+ xxxx
5. Subtract: )532()435( 22 โˆ’โˆ’โˆ’+โˆ’โˆ’ xxxx
6. Multiply: )1523(2 232 +โˆ’+โˆ’ xxxx
7. Multiply: 3
)32( โˆ’x
8. Divide: 3
356
2
41820
x
xxx โˆ’+
9. Divide: 23
391343 234
โˆ’
++โˆ’+
x
xxxx
10. A projectile is fired from the top of an 80 ft building with an initial velocity of 64
feet per second. The height of the projectile, in feet, after t seconds is given by the
function 806416)( 2++โˆ’= ttth graphed here.
a. Use the graph to determine how long it takes to
reach the maximum height.
b. How long will it take to hit the ground?
c. What is the height of the projectile after 4
seconds?
pf2

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Chapter 5 _ Sample Exam

Please answer all the questions and show work where appropriate.

  1. Simplify:

3 2

3

3

y

x

  1. Simplify: ( 5 xy โˆ’^3 z^4 )โˆ’^3
  2. Given f ( x )= โˆ’ 3 x^2 + 2 x โˆ’ 9 find f (โˆ’ 2 ).
  3. Add: ( 3 x^2 + 2 x โˆ’ 9 )+(โˆ’ 5 x^2 โˆ’ 7 x + 7 )
  4. Subtract: ( โˆ’ 5 x^2 โˆ’ 3 x + 4 )โˆ’( 2 x^2 โˆ’ 3 x โˆ’ 5 )
  5. Multiply: โˆ’ 2 x^2 ( 3 x^3 + 2 x^2 โˆ’ 5 x + 1 )
  6. Multiply: ( 2 x โˆ’ 3 )^3
  7. Divide: (^3)

6 5 3

2

x

x + x โˆ’ x

  1. Divide: 3 2

x

x x x x

  1. A projectile is fired from the top of an 80 ft building with an initial velocity of 64 feet per second. The height of the projectile, in feet, after t seconds is given by the function h ( t )= โˆ’ 16 t^2 + 64 t + 80 graphed here.

a. Use the graph to determine how long it takes to reach the maximum height. b. How long will it take to hit the ground? c. What is the height of the projectile after 4 seconds?

Chapter 5 _ Sample Exam Answers

9

27

y

x

9

125 x z

y

  1. โˆ’ 2 x^2 โˆ’ 5 x โˆ’ 2
  2. โˆ’ 7 x^2 + 9
  3. โˆ’ 6 x^5 โˆ’ 4 x^4 + 10 x^3 โˆ’ 2 x^2
  4. 8 x^3 โˆ’ 36 x^2 + 54 x โˆ’ 27
  5. 10 x^3 + 9 x^2 โˆ’ 2

x

x x x

  1. a. t = 2 seconds b. t = 5 seconds c. h ( 4 )= 80 feet