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: 2x 3 + 5x 2 + 2x .
(5 pts.)
Answer: ______________________________
2. Find the quotient and remainder 2x 2 – 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
3
5x – 1
canceling terms if possible:
.
+
x+2 x–3
(5 pts.)
Answer: ______________________________
4. Find the center (h, k) and the radius r of the circle with equation x 2 + y 2 + 2x – 6y – 6 = 0 .
Show how you got your answer.
(5 pts.)
Center: __________________
A
Radius: __________________
2
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: ______________________________
2x
7. Find the domain of the function f (x) = 2
. Show how you got your answer.
x –1
(5 pts.)
Answer: _____________________
8. Find the domain of the function f (x) = x – 10 . Show how you got your answer.
(5 pts.)
Answer: _____________________
A
3
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
D. 36 square feet
C. 27 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
1
5b10
5
b4
B.
(
4. Simplify the expression: 2x 3 y 2
A. 8x 9 y10
A
E. 22
5b –8
b2
3. Simplify the expression:
A.
D. 12
B.
C.
)
3
5
b10
D. 5b 6
E.
1
5b 6
y4
6x 6 y 20
C.
8x 6 y 24
D. 6x 9 y 20
(
5. Simplify the expression: 16x
A. 8x 7
)
8x 28
B.
4
14 1/2
C. 4x12
D. 9x14 / 3
E. 4x 7
6. What are all the real solutions for x for the equation 2x 2 – 3x – 1 = 0 ?
–3 + 5
–3 – 5
–2 + 17
–2 – 17
1
B.
and
C.
and
4
4
6
6
2
3 + 17
3 – 17
D.
and
E. There are no real solutions
4
4
A. 1 and
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
1
9
D.
E. None of these
9. Perform the indicated operations and simplify the result.
A.
x4
x–3
B.
x6
2
x +1
x6
x–3
C.
D.
10. Rationalize the denominator and simplify your answer:
A.
3+ 5
–2
B.
11. Simplify the expression:
A. –9a 3 a 2
A
3– 5
–2
3
C.
5
–2
D.
x–2
x5
• 2
x
x + x–6
x4
x+3
5
x+3
E.
1
.
3– 5
3– 5
4
E.
–27a 5
B. – 3a 3 a 2
C. –3a 2
3
a
D. –9a 2
3
a
3+ 5
4
5
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).
29
1
1
29
1
29
A. y = 5x –
B. y + 7 = (x + 6)
C. y = – x –
D. y = x –
5
5
5
5
5
5
⎛ 7 ⎞
14. Find an equation of the line with slope undefined and containing the point ⎜ – , 4 ⎟ .
⎝ 8 ⎠
7
7
A. y = 4 B. y = –
C. x = –
D. x = 4
8
8
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) = –3x 2 – 4x + 5 .
A. –3x 2 – 3xh – 3h 2 – 4x – 4h + 5
C. –3x 2 – 6xh – 3h 2 – 4x – 4h + 5
B. –3x 2 – 3h 2 – 4x – 4h + 5
D. –3x 2 – 3h 2 – 10x – 10h + 5
9x + 7
2x
and g(x) =
. Find (f + g)(x).
7x – 5
7x – 5
7x – 7
11x + 7
A. ( f + g)(x) =
B. ( f + g)(x) =
7x – 5
7x – 5
11x – 7
–11x + 7
C. ( f + g)(x) =
D. ( f + g)(x) =
7x – 5
7x – 5
17. Let f (x) =
A
6
18. Find the midpoint of the line segment shown.
A. (–1, 8)
⎛ 9 ⎞
B. ⎜ – , 2 ⎟
⎝ 2 ⎠
19. Find all intercepts of the graph with equation y =
A. (–49, 0), (0, 0), (49, 0)
C. (0, 0)
C. (–9, 4)
⎛9 ⎞
D. ⎜ , 2 ⎟
⎝2 ⎠
7x
.
x + 49
2
B. (0, –7), (0, 0), (0, 7)
D. (–7, 0), (0, 0), (7, 0)
20. Find the vertex of the quadratic function f (x) = x 2 + 6x – 1 .
A. (3, –17)
B. (–3, 17)
C. (–3, –10)
D. (3, 10)
21. Find the inverse function of f (x) = 5x + 3 .
1
x–3
x–5
A. f −1 ( x ) =
B. f −1 ( x ) =
C. f −1 ( x ) =
5x + 3
5
3
–x + 5
–x + 3
D. f −1 ( x ) =
E. f −1 ( x ) =
3
5
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. 40x 2 – 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) + 4
2
B. y = – ( x − 1) + 4
2
C. y = – ( x + 1) + 4
2
D. y = ( x + 1) + 4
2
E. y = – ( x + 1) – 4
2
A
7
24. Solve the inequality (x + 5)(x + 2) > 0.
A. (–5, –2)
C. (2, ∞)
B. (–∞, –5)
D. (–∞, –2), (–5, ∞)
E. (–∞, –5), (–2, ∞)
25. Which polynomial function defines the graph below?
A.
B.
C.
D.
f (x) = ( x + 1) (x − 1)(x – 3)
f (x) = – ( x + 1) (x − 1)(x – 3)
f (x) = ( x + 1) (x − 1)(x + 3)
f (x) = – ( x + 1) (x − 1)(x + 3)
E. f (x) = ( x – 1) (x + 3)
2
26. Find any horizontal asymptote of f (x) =
A. x =
7
2
B. x = 9
2x – 7
.
x–9
C. y = 9
27. Find any vertical asymptotes of h(x) =
D. y = 2
2x + 5
.
8x – 16
1
C. x = 2
4
28. Find the exact value of log 3 9 .
A. y = 0
B. y =
A.
B. 2
3
C. 27
D.
E. y = 0
D. x = –
18
5
2
E. 12
29. Solve for x: 2 x – 5 = 8 x
A.
A
–
5
2
B. –4
C.
2
5
D.
–
1
3
E. 8
E. x =
1
2