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Sample Midterm Exam: Mathematics Cumulative Review (Chapters 8-10) - Prof. John Redden, Exams of Algebra

A sample midterm exam for students in mathematics, focusing on topics from chapters 8-10. The exam includes various mathematical problems, such as factorization, solving equations, rationalization, graphing, and quadratic equations. Students are required to answer all questions and show their work.

Typology: Exams

Pre 2010

Uploaded on 08/16/2009

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Chapters 8 โ€“ 10 _ Cumulative Review
Sample Midterm Exam
Please answer all the questions and show work where appropriate.
Factor:
1. 1553 23 โˆ’โˆ’+ xxx
2. 31512 2+โˆ’ xx
3. 116 4โˆ’x
Solve:
4. )1(3)42(35 โˆ’=โˆ’โˆ’ xxx
5. 0123 2=+โˆ’ xx
6. 1
12
2
5
3=
โˆ’
+
โˆ’
โˆ’
xx
x
7. 087 3
1
3
2=โˆ’+ xx
8. 232 =โˆ’+x
9. 1332 <+x
10. 0
5
6
2โ‰ฅ
โˆ’
โˆ’+
x
xx
11. The height of a triangle is 3 less than five times the length of its base. If the area is
55 square inches, find the length of the base and the height.
12. Working together Norm and Cliff can paint the office in 4 hours. Working alone,
Norm can paint the office in three hours less time than Cliff. How long would it
take Norm, working alone, to paint the office?
pf3

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Sample Midterm Exam

Please answer all the questions and show work where appropriate.

Factor:

  1. 3 5 15 3 2 x + x โˆ’ x โˆ’

2 x โˆ’ x +

4 x โˆ’

Solve:

  1. 5 x โˆ’ 3 ( 2 x โˆ’ 4 )= 3 ( x โˆ’ 1 )

2 x โˆ’ x + =

x x

x

1 3

2 x + x โˆ’ =

  1. x + 2 โˆ’ 3 = 2
  2. 2 x + 3 < 13

2 โ‰ฅ โˆ’

x

x x

  1. The height of a triangle is 3 less than five times the length of its base. If the area is

55 square inches, find the length of the base and the height.

  1. Working together Norm and Cliff can paint the office in 4 hours. Working alone,

Norm can paint the office in three hours less time than Cliff. How long would it take Norm, working alone, to paint the office?

Sample Midterm Exam Page 2

Rationalize:

x y

x

  1. Graph: 2 2 12

2 y = โˆ’ x + x +

  1. Solve by Graphing:

โŽญ

x y

x y

  1. Solve:

โŽช โŽญ

x y z

x y z

x y z

  1. Find a quadratic equation, with integer coefficients, that has solutions { 3 i , โˆ’ 3 i }.
  2. The formula for the period T of a pendulum given its length, in feet, is

L

T = ฯ€. If a pendulum has a period of^ ฯ€^ seconds find its length L.

  1. The height, in feet, of an object shot into the air is given by h ( t ) 16 t 160 t 2 = โˆ’ +.

At what time will the object be 300 feet in the air?