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Math 130T College Algebra Practice Exam 1

1. Where does the functionx

xxf

+=

2

6)( have a vertical asymptote?

a. x = 2 d. y = 2

b. x = 3 e. x =

2c. y = 3

2. Which one of the following is equal to loga(xy)?

a. (xy)a d. (ax)(ay) b. logax + logay e. None of these

c. (logax)(logax)

3. Which one of the following is equivalent to 200 ?

a. 2 10 d. 20

b. 10 2 e. None of these

c. 14

4. Which one of the following is equal to ?))(( 325 xyyx

a. d.65

yx16

yx

b. e.15 yx 66 yx

c. x5y

5. What is the solution to ln(x + 1) = 0?

a. 2 d. 1b. 1 e. None of these

c. 0

6. Which one of the following represents the complete factorization ofx2

+ 6x + 5?a. x(x + 6 + 5) d. (x + 1)(x + 5)

b. (x + 6)(x + 5) e. (x + 2)(x + 3)

c. (x2

+ 6)(x + 5)

7. What is the simplest form of 2(x + 2y) 3(x y) 7y +x?

a. 0 d. 2xb. 4y e. 2x 4y

c. 8y

8. Which one of the following is equal to ?yxa +

a. ax + ay d. ax + y b. (a

x)(ay) e. None of these

c. ax + ay

Math 130T College Algebra Practice Exam 1.doc Page 1 of 5


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9. Which one of the following is equal to (a + b)0

when a and b are positive numbers?

a. a + b d. 1

b. a0

+ b0

e. None of thesec. 0

10. If log10x = 0.8762, what does log10 100x equal?a. 2.8762 d. 87.62

b. 3.8762 e. 100.8762

c. 8.762

11. Which of the following is the simplest form of

105

10

2

42

xx

x?

a. 2 d.x

x 2

b. 2 e. x + 2

c.x

x 2+

12. Which of the following is the solution set ofx2 9 = 0?

a. {3 1 } d. {3} b. {9} e. {3,3}c. {3}

13. What is the slope of the line through the points (0, 1) and (4, 2)?

a.4

3 d.

3

4

b.4

3e.

3

4

c. 3

14. Which one of the following is equal to3

5?

a.3

22d.

9

5

b.3

15e.

3

5

c.95

15. What is the solution set of32

32

+

x

x= 3?

a. The empty set d. {2} b. {3} e. {3}

c. {2}



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16. Which one of the following lines intersects 2x + 3y + 4 = 0?

a. x y + 1 = 0 d. 4x + 6y + 9 = 0

b. 2x + 3y + 2 = 0 e. 6x + 9y + 10 = 0c. 4x + 6y + 3 = 0

17. If (3x 5) and (x + n) are factors of 3x2

+ 16x 35, what does n equal?

a. 7 d. 16

b. 5 e. 30c. 7

18. The domain of the function4

3)(

+=

xxf is

a. all real numbers d. all positive real numbers

b. all real numbers except 0 e. all real numbers except4

c. all real numbers greater than 3

19. Which one of the following is a factor of both 9x 24 and 9x2

64?

a. 3 d. 9x2

+ 9x 88

b. 3x + 8 e. 81x3

216x2 576x + 1536

c. 3x 8

20. Ifx2

+ 2x 8 = 0, then which one of the following must be true?a. x = 0 d. x = 2 orx = 4

b. x = 1 orx = 8 e. x = 2 orx = 4

c. x = 1 orx = 8

21. In which quadrants are there no points in the solution ofx +y < 9?

III

III IV

y

x

a. I only d. IV only

b. II only e. II and IV onlyc. III only

22. If ln (x + 1) = 1, what is the value ofx?a. 0 d. e 1

b. 1 e. None of these

c. 9



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23. The equationy = |x 6| is equivalent to:

a. y =x 6 d. y =x + 6

b. y = 6 x e. None of thesec. y =x 6 ory = 6 x

24. If , then2log5 =x

a. x = 25 d. x = 52

b. x = 10 e. x = 0

c. x = 32

25. Which one of the following is not a real number?

a. 2 d. 5

b. 0 e. 5

c.2

1

26. For what value ofx is the function1

)(+

=x

xxf undefined?

a. 2 d. 1

b. 1 e. None of thesec. 0

27. Which one of the following represents the complete factorization ofxy + 2xy2

+ 3xy3?

a. xy(2y + 3y2) d. xy(1 + 2y + 3y

2)

b. (xy + 2xy)(y + 3xy2) e. x(y + 2y

2) +y

2(2x + 3xy)

c. (xy + 2x)(y + 3xy3)

28. What is the degree of the expression 3x4 + 6x2 + 9?a. 2 d. 6

b. 3 e. 9c. 4

29. Which of the following is equal to (a 2b)(a2

+ b2)?

a. a3

+ ab2

2a2b 2b

3d. a 2b + a

2+ b

2

b. a3

+ ab2

2a2b + 2b

3e. None of these

c. a3

2b3

30. Which one of the following is closest in value to a solution of |x 3| = 12?

a. 10 d. 20 b. 0 e. 30c. 10



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31. Which one of the following ordered pairs is a solution of this system of inequalities?

>+

53

02

yx

yx

a. (1, 3) d. (4, 0)

b. (1, 3) e. (2, 2)

c. (0, 2)

32. Which of the following sets is equal to {a | a is a positive integer}{b | b is a negative integer}?a. {c | c is a negative integer} d. The empty set

b. {c | c is a rational number} e. {0}

c. {c | c is a positive integer}

33. What is when))(( xgf o 3)( xxf = and 27)( = xxg ?

a. 273 x d. 9x

b. 33 x e. None of these

c. 3 27x

34. The inequality 705 >+x is equivalent to which of the following?

a. d. 705 >705 >+x +x or 705 x 5 > x and 705

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