Second Semester Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. What is the solution of the equation? ____ 1. a. 36 b. 28 c. –2 d. 44 What is the solution of the equation? Eliminate any extraneous solutions. ____ 2. a. 1 b. 1 and 2 5 c. 1 d. 2 5 ____ 3. Let and . Find f(x) g(x). a. 10x – 8 b. 10x – 2 c. –2x – 8 d. –2x – 2 What is the inverse of the given relation? ____ 4. . a. c. b. d. ____ 5. For the function , find . a. 14 b. 5 c. –5 d. 25 Graph the equation. ____ 6. a. 2 4 –2 –4 x 2 4 –2 –4 y c. 2 4 –2 –4 x 2 4 –2 –4 y
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Second Semester Exam Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
What is the solution of the equation?
____ 1.
a. 36 b. 28 c. –2 d. 44
What is the solution of the equation? Eliminate any extraneous solutions.
____ 2.
a. 1 b. 1 and
2
5
c. 1 d.
2
5
____ 3. Let and . Find f(x) g(x).
a. 10x – 8 b. 10x – 2 c. –2x – 8 d. –2x – 2
What is the inverse of the given relation?
____ 4. .
a.
c.
b.
d.
____ 5. For the function , find .
a. 14 b. 5 c. –5 d. 25
Graph the equation.
____ 6.
a.
2 4–2–4 x
2
4
–2
–4
y
c.
2 4–2–4 x
2
4
–2
–4
y
b.
2 4–2–4 x
2
4
–2
–4
y
d.
2 4–2–4 x
2
4
–2
–4
y
Evaluate the logarithm.
____ 7.
a. –3 b. 5 c. –4 d. 4
Graph the logarithmic equation.
____ 8.
a.
2 4 6–2–4–6 x
4
8
12
–4
–8
–12
y
c.
2 4 6–2–4–6 x
4
8
12
–4
–8
–12
y
b.
2 4 6–2–4–6 x
4
8
12
–4
–8
–12
y
d.
2 4 6–2–4–6 x
4
8
12
–4
–8
–12
y
Write the expression as a single logarithm.
____ 9.
a. c.
b. d.
____ 10.
a. b. c. d.
Expand the logarithmic expression.
____ 11.
a. c.
b. d.
Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary.
____ 12.
a. 10.7722 b. 5 c. 2.7826 d. 0.6309
____ 13. Solve . Round to the nearest hundredth if necessary.
a. 28 b. 0.14 c. 3.57 d. 700
____ 14. Solve .
a. 6 b. 6e c. d. ln 6
Use natural logarithms to solve the equation. Round to the nearest thousandth.
____ 15.
a. –0.448 b. 0.327 c. 0.067 d. –0.046
____ 16. Suppose that x and y vary inversely, and x = 10 when y = 8. Write the function that models the inverse
variation.
a.
c.
b.
d. y = 0.8x
Sketch the asymptotes and graph the function.
____ 17.
a.
5 10–5–10 x
5
10
–5
–10
y
c.
5 10–5–10 x
5
10
–5
–10
y
b.
5 10–5–10 x
5
10
–5
–10
y
d.
5 10–5–10 x
5
10
–5
–10
y
Find any points of discontinuity for the rational function.
____ 18.
a. x = –2, x = –7 c. x = –8
b. x = 2, x = –7 d. x = 2, x = 7
____ 19. Describe the vertical asymptote(s) and hole(s) for the graph of .
a. asymptote: x = 5 and hole: x = 1
b. asymptote: x = –5 and hole: x = –1
c. asymptote: x = –3 and hole: x = 5
d. asymptote: x = 5 and hole: x = –1
____ 20. Find the horizontal asymptote of the graph of .
a. y = 1 c. no horizontal asymptote
b. y = 1 d. y = 0
What is the graph of the rational function?
____ 21.
a.
5 10–5–10 x
5
10
–5
–10
y
c.
5 10–5–10 x
5
10
–5
–10
y
b.
5 10–5–10 x
5
10
–5
–10
y
d.
5 10–5–10 x
5
10
–5
–10
y
Simplify the rational expression. State any restrictions on the variable.
____ 22.
a. c.
b. d.
What is the quotient in simplified form? State any restrictions on the variable.
____ 23.
a.
c.
b.
d.
Simplify the sum.
____ 24.
a.
c.
b.
d.
Simplify the difference.
____ 25.
a.
c.
b.
d.
Solve the equation. Check the solution.
____ 26.
a. 17
20
b. 47
4
c. 47
20
d.
47
4
____ 27.
a. –9 b. –6 c. –9 and –6 d. 6
____ 28. Write an equation of a parabola with a vertex at the origin and a directrix at y = 5.
a. c.
b.
d.
____ 29. What are the focus and directrix of the parabola with equation ?
a. focus: ; directrix: c. focus: ; directrix:
b. focus: ; directrix: d. focus: ; directrix:
____ 30. Use the graph to write an equation for the parabola.
2 4–2–4 x
2
4
–2
–4
y
a.
c.
b.
d.
____ 31. What is an equation of a parabola with a vertex at the origin and directrix x = 4.75?
a.
c.
b.
d.
Write an equation in standard form for the circle.
____ 32.
4 8 12–4–8 x
4
8
12
16
–4
y
a.
c.
b.
d.
What is the center and radius of the circle with the given equation?
____ 33.
a. center at (–4, –8); radius 9 c. center at (4, 8); radius 3
b. center at (4, 8); radius 9 d. center at (–4, –8); radius 3
What is the graph of the equation?
____ 34.
a.
8–8 x
8
–8
y c.
8–8 x
8
–8
y
b.
8–8 x
8
–8
y d.
8–8 x
8
–8
y
What is the standard-form equation of the ellipse shown?
____ 35.
4 8–4–8 x
4
8
–4
–8
y
a.
c.
b.
d.
What are the center, vertices, foci, and asymptotes of the hyperbola for the given equation? Sketch the
graph.
____ 36.
a.
8 16–8–16 x
8
16
24
–8
–16
y
Center:
Vertices: and
Foci: and
Asymptotes:
c.
8 16–8–16 x
8
16
24
–8
–16
y
Center:
Vertices: and
Foci: and
Asymptotes:
b.
8 16–8–16 x
8
16
24
–8
–16
y
Center:
Vertices: and
Foci: and
Asymptotes:
d.
8 16–8–16 x
8
16
24
–8
–16
y
Center:
Vertices: and
Foci: and
Asymptotes:
____ 37. A yogurt shop offers 6 different flavors of frozen yogurt and 12 different toppings. How many choices are
possible for a single serving of frozen yogurt with one topping?
a. 144 b. 72 c. 36 d. 665,280
____ 38. Verne has 6 math books to line up on a shelf. Jenny has 4 English books to line up on a shelf. In how many
more orders can Verne line up his books than Jenny?
a. 24 b. 720 c. 14 d. 696
____ 39. In how many ways can 12 basketball players be listed in a program?
a. 665,280 b. 1 c. 479,001,600 d. 12
____ 40. There are 10 students participating in a spelling bee. In how many ways can the students who go first and
second in the bee be chosen?
a. 1 way c. 3,628,800 ways
b. 90 ways d. 45 ways
____ 41. Evaluate .
a. 9 b. 1 c. 5,040 d. 7
Suppose S and T are mutually exclusive events. Find P(S or T).
____ 42. P(S) = 20%, P(T) = 22%
a. 2% b. 440% c. 42% d. 4.4%
____ 43. Joey’s sock drawer is unorganized and contains 7 black dress socks, 7 black ankle socks, 6 brown dress socks,
and 2 brown ankle socks. What is the probability that Joey will blindly reach into his sock drawer and pull out
a sock that is brown or a dress sock?
a. 15
22
c. 3
11
b. 4 d. 21
22
____ 44. The contingency table shows the results of a survey of college students. Find the probability that a student’s
first class of the day is a humanities class, given the student is male. Round to the nearest thousandth.
First Class of the Day for College Students
Male Female
Humanities 70 80
Science 50 80
Other 60 70
a. 0.171 b. 0.467 c. 0.269 d. 0.389
____ 45. On St. Patrick’s Day, you took note of who was coming into your restaurant wearing green. What is the
probability that someone was wearing green given that the customer is female?
Wearing Green Not Wearing Green
Male 56 70
Female 29 83
a. 0.5 b. 5.23 c. 0.259 d. 0.23
Make a box-and-whisker plot of the data.
____ 46. Average daily temperatures in Tucson, Arizona, in December: