Algebra Final Exam



Name: __________________________

COLLEGE ALGEBRA MIDTERM STUDY GUIDE

QUARTER 1 / SEMESTER 1

30 Multiple Choice Questions

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I. Problem Solving and Critical Thinking

• Estimation, graphs, and mathematical models

• Problem solving

II. Algebraic Expressions

• Evaluating expressions

• Distributive property

• Combining like terms

• Translating from word problems to expressions

III. Algebraic Linear Equations

• Solving one step and two-step equations including fractions

• Solving multi-step equations with distributive property and combining like terms

• Solving multi-step equations with variables on both sides of the equation

• Solving multi-step equations with no solutions or infinite solutions

• Solving literal equations

• Applications of linear equations

IV. Functions

• Function notation

• Evaluating functions

• Vertical line test

• Function mapping

• Domain and range

Problem Solving and Critical Thinking

1. Write an algebraic rule for the total number of tiles, T, in terms of the figure, n.

[pic]

A. n2 + 4

B. 2n + 2

C. 2(n + 1)

D. 3n + 2

2. Write an algebraic rule for the total number of tiles, T, in terms of the figure, n.

[pic]

A. n + 1

B. n(n + 1)

C. 3n

D. n2 + 1

3. Which equation best describes the relationship between the values of x and y shown in the table?

|x |y |

|-1 |-7 |

|0 |-5 |

|2 |-1 |

|4 |3 |

A. y = x – 5

B. y = 2x – 5

C. y = 3x – 7

D. y = 4x – 7

Algebraic expressions

4. Two enterprising college students decide to start a business. They will make up and deliver helium balloon bouquets for special occasions. It will cost them $39.99 to buy a machine to fill the balloons with helium.

They estimate that it will cost them $2.00 to buy the balloons, helium and ribbons needed to make each balloon bouquet. Which of the following expressions could be used to model the total cost for producing b balloon bouquets?

A. $2.00b + $39.99

B. $37.99b

C. $39.99b + $2.00

D. $41.99b

5. A plumber charges $13.50 per hour for a plumbing job that requires more than 3 hours to complete. For any job requiring 3 hours or less, there is a flat charge of $40.50. If h represents the number of hours the job requires, which of the following expressions gives the charge, in dollars, for a job requiring more than 3 hours to complete?

A. 13.5h + 40.5

B. 13.5h

C. 13.5h – 40.5

D. 40.5

6. You help in the school cafeteria by emptying the trash barrels. You are paid $4 for each day you work. Let d be the number of days you work in a month. Which of the following expressions represent your pay for that month, in dollars?

A. d4

B. [pic]

C. 4 + d

D. 4d

7. What is the value of the expression (x – y)2 when x = 5 and y = -1?

A. 4

B. 16

C. 24

D. 36

8. If a = -[pic], b = 4, and d = -3, what is the value of [pic]?

A. -25[pic]

B. -6

C. 75

D. 102

9. What is the value of [pic] if x = 6?

A. -3

B. 3

C. 6

D. 9

10. For all x, 5 – 3(x – 4) = ?

A. -3x + 17

B. -3x – 7

C. -3x + 1

D. -3x – 4

11. (6x – 4) – (2x + 8) is equivalent to:

A. 4(x + 4)

B. 4(x – 1)

C. 4(x – 3)

D. 4(x – 12)

12. The expression (3x2 + 5x – 12) – 2(x2 + 4x +9) is equivalent to which of the following:

A. x2 – 3x – 30

B. x2 + 13x + 6

C. 5x2 + x – 18

D. x2 + 3x – 21

Algebraic Linear Equations

13. A Fahrenheit temperature F can be approximated by doubling the Celsius temperature C and adding 32. Which of the following expresses this approximation method?

A. F = [pic]C + 32

B. F = 2C + 32

C. F = 2(C + 32)

D. F = C2 + 32

14. Roy is saving to buy a new bike, which costs $258. He has $16 towards this purchase. Express how much more Roy needs in the form of an equation.

A. x + 258 = 16

B. x – 16 = 258

C. x = 258 + 16

D. x + 16 = 258

15. Solve for r: 3r + 2 – r = -4

A. 3

B. -3

C. 4

D. -4

16. Patricia pays $1.19 each to download songs to her MP3 player. If n is the number of downloaded songs, which equation represents the cost C in dollars?

A. C = 1.19n

B. n = 1.19C

C. C = 1.19 ÷ n

D. C = n + 1.1

17. Solve the equation[pic].

A. [pic]

B. [pic]

C. [pic]

D. [pic]

18. An equation is shown below:

-2x + 9 = -17

What is the solution to the equation?

A. x = -13

B. x = -4

C. x = 4

D. x = 13

19. If a + b = 6, then [pic]

A. 3

B. 7

C. 10

D. 14

20. Solve for y: 3x – 4y = 12

A. y = 3x – 4

B. [pic]

C. [pic]

D. 3x – 4y = 12

21. The sum of one fifth of a number and three is equal to half of the number. What is the number?

A. 5

B. 10

C. 15

D. 20

22. Given y + 36 = 102, y + 14 = ? (Hint: solve for y first, then find y + 14)

A. 66

B. 76

C. 80

D. 124

23. When n basketball uniforms are purchased, the cost, C, of each uniform is given by the equation[pic]. If the cost of each uniform was $60, how many uniforms were purchased?

A. 5

B. 6

C. 8

D. 13

E. 26

Functions

24. What is the value of f(2) if f(x) = [pic]?

A. [pic]

B. 15

C. 125

D. 500

25. What are the domain and range for the relation[pic].

A. Domain = {all real numbers}

Range = {all real numbers}

B. Domain = {all real numbers ≠ 5}

Range = {all real numbers}

C. Domain = {all real numbers ≠ −5}

Range = {all real numbers}

D. Domain = {all real numbers}

Range = {all real numbers ≠ 5}

26. If f(x) = 3x – 2, find f(8) – f(-5)

A. 7

B. 9

C. 37

D. 39

27. If f(x) = 2x – 4 find f(q + 1):

A. 2q + 4

B. 2q + 2

C. 2q – 6

D. 2q – 2

28. If f(x) = -4x2 + 15, then f(-3) = ?

A. -21

B. -9

C. 39

D. 51

29. Find the range of the function given the domain: f(x) = 5 – 4x; domain = {-1, 0, 1}

A. {1, 5, 3}

B. {9, 5, 1}

C. {9, 5, 3}

D. {1, 5, 5}

30. A function g(x) = [pic]. For which value of x will g(x) = 0?

A. x = [pic]

B. x = -1

C. x = [pic]

D. x = 0

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