A

MATH 101 FINAL EXAM PRINT ______________________ 4/25/08 NAME NO CALCULATOR ALLOWED. Part 1: In problems 1 - 9, show work on this test paper. Put answers in the blanks provided. Work on scratch paper will NOT be graded. ___________________________________________________________________________________ 1. Factor the following expression completely: 2x3 + 5x2 + 2x . (5 pts.) Answer: ______________________________ 2. Find the quotient and remainder 2x2 – 5x – 4 is divided by x – 2. Show how you got your answer. (5 pts.) Quotient: ___________________________ Remainder: ___________________________ 3. Add the following two rational expressions and simplify by combining like terms and factoring and

canceling terms if possible: 3x + 2

+5x –1x – 3

.

(5 pts.) Answer: ______________________________ 4. Find the center (h, k) and the radius r of the circle with equation x2 + y2 + 2x – 6y – 6 = 0 . Show how you got your answer. (5 pts.) Center: __________________ Radius: __________________

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5. Solve for x in the equation x + 3 = 4 x . What is/are the real solution(s)? Show how you got your answer. (5 pts.) Answer: ______________________________ 6. Solve for x in the following inequality and write your answer in interval notation: 3 – 5x < 13 . (5 pts.) Answer: ______________________________

7. Find the domain of the function f (x) = 2xx2 – 1

. Show how you got your answer.

(5 pts.) Answer: _____________________ 8. Find the domain of the function f (x) = x –10 . Show how you got your answer. (5 pts.) Answer: _____________________

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9. Use the graph of the function f shown below to answer parts (a) – (d). (a) Find f(–2). (3 pts.) Answer: __________ (b) What is the domain of f? (4 pts.) ____________________________ (c) For what numbers x is f(x) > 0? (4 pts.) ____________________________ (d) How often does the line y= 2

intersect the graph? (4 pts.) ____________________________ ___________________________________________________________________________________ Part 2: In the remaining problems, put the letter of the best answer on the answer sheet. (5 points each) 1. The diameter of a circle is 6 feet. Which of the following is the best estimate of the circle's area? A. 9 square feet B. 18 square feet C. 27 square feet D. 36 square feet E. 100 square feet 2. If a is –5 and b is –3, the value of 3a – 2b –1 is which of the following? A. 5 B. 8 C. 10 D. 12 E. 22

3. Simplify the expression: 5b–8

b2

A. 1

5b10 B. 5

b4 C. 5

b10 D. 5b6 E. 1

5b6

4. Simplify the expression: 2x3y2( )3 y4 A. 8x9y10 B. 6x6y20 C. 8x6y24 D. 6x9y20

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A

5. Simplify the expression: 16x14( )1/2 A. 8x7 B. 8x28 C. 4x12 D. 9x14 /3 E. 4x7 6. What are all the real solutions for x for the equation 2x2 – 3x –1 = 0 ?

A. 1 and 12

B. –3+ 54

and –3 – 54

C. –2 + 17

6 and

–2 – 176

D. 3+ 174

and 3 – 174

E. There are no real solutions

7. The length of the hypotenuse of a right triangle is 10 cm and that the length of one of the other sides

is 8 cm. What is the length of the third side?

A. 5 cm B. 6 cm C. 8 cm D. 9 cm E. It cannot be determined from the information given 8. If 5 – 3(x – 1) = 6x + 1, then x equals: A. 7

9 B. 7 C. – 1

2 D. 1

9 E. None of these

9. Perform the indicated operations and simplify the result.

�

x – 2x

• x5

x2 + x – 6

A.

�

x4

x – 3 B.

�

x6

x2 +1 C.

�

x6

x – 3 D.

�

x4

x + 3 E. 5

x + 3

10. Rationalize the denominator and simplify your answer: 13 – 5

.

A. 3+ 5–2

B. 3 – 5–2

C. 5–2

D. 3 – 54

E. 3+ 54

11. Simplify the expression: –27a53 A. –9a a23 B. – 3a a23 C. –3a2 a3 D. –9a2 a3

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12. Determine whether the graph shown below is symmetric with respect to the x-axis, the y-axis, and/or the origin.

A. origin only B. y-axis only C. x-axis only D. x-axis, y-axis, and origin E. None

13. Find the slope-intercept form of the equation of the line containing the points (–6, –7) and (4, –5).

A. y = 5x – 295

B. y + 7 = 15(x + 6) C. y = – 1

5x – 29

5 D. y = 1

5x – 29

5

14. Find an equation of the line with slope undefined and containing the point –78, 4⎛

⎝⎜⎞⎠⎟ .

A. y = 4 B. y = – 78

C. x = – 78

D. x = 4

15. Find the slope-intercept form of the equation of the line parallel to the line y = –4x – 1 and containing the point (2, 6). A. y = 4x – 14 B. y = –4x + 14 C. y = –4x + 26 D. y = 4x – 26 16. Find f(x + h) when f (x) = –3x2 – 4x + 5 .

A. –3x2 – 3xh – 3h2 – 4x – 4h + 5 B. –3x2 – 3h2 – 4x – 4h + 5 C. –3x2 – 6xh – 3h2 – 4x – 4h + 5 D. –3x2 – 3h2 – 10x –10h + 5

17. Let f (x) = 9x + 77x – 5

and g(x) = 2x7x – 5

. Find (f + g)(x).

A. ( f + g)(x) = 7x – 77x – 5

B. ( f + g)(x) = 11x + 77x – 5

C. ( f + g)(x) = 11x – 77x – 5

D. ( f + g)(x) = –11x + 77x – 5

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18. Find the midpoint of the line segment shown.

A. (–1, 8) B. –92, 2⎛

⎝⎜⎞⎠⎟ C. (–9, 4) D.

92, 2⎛

⎝⎜⎞⎠⎟

19. Find all intercepts of the graph with equation y = 7xx2 + 49

.

A. (–49, 0), (0, 0), (49, 0) B. (0, –7), (0, 0), (0, 7) C. (0, 0) D. (–7, 0), (0, 0), (7, 0) 20. Find the vertex of the quadratic function f (x) = x2 + 6x –1 .

A. (3, –17) B. (–3, 17) C. (–3, –10) D. (3, 10) 21. Find the inverse function of f (x) = 5x + 3 .

A. f −1 x( ) = 15x + 3

B. f −1 x( ) = x – 35

C. f −1 x( ) = x – 53

D. f −1 x( ) = –x + 53

E. f −1 x( ) = –x + 35

22. For the functions f (x) = 8x +13 and g(x) = 5x –1 , find the composite function ( f ! g)(x) . A. 40x + 5 B. 40x + 12 C. 40x + 21 D. 40x2 – 13 23. The graph of a quadratic function y = f(x) with vertex at (–1, 4) and y-intercept at (0, 3). Determine the equation of the graph.

A. y = x −1( )2 + 4

B. y = – x −1( )2 + 4

C. y = – x +1( )2 + 4

D. y = x +1( )2 + 4

E. y = – x +1( )2 – 4

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24. Solve the inequality (x + 5)(x + 2) > 0. A. (–5, –2) B. (–∞, –5) C. (2, ∞) D. (–∞, –2), (–5, ∞) E. (–∞, –5), (–2, ∞) 25. Which polynomial function defines the graph below?

A. f (x) = x +1( )(x −1)(x – 3) B. f (x) = – x +1( )(x −1)(x – 3) C. f (x) = x +1( )(x −1)(x + 3) D. f (x) = – x +1( )(x −1)(x + 3)

E. f (x) = x –1( )2 (x + 3)

26. Find any horizontal asymptote of f (x) = 2x – 7x – 9

.

A. x = 72

B. x = 9 C. y = 9 D. y = 2 E. y = 0

27. Find any vertical asymptotes of h(x) = 2x + 58x –16

.

A. y = 0 B. y = 14

C. x = 2 D. x = – 52

E. x = 12

28. Find the exact value of log3 9 . A. 3 B. 2 C. 27 D. 18 E. 12 29. Solve for x: 2x–5 = 8x

A. – 52

B. –4 C. 25

D. – 13

E. 8