algebra

please look in the attachment for the proper file.a.
b.
c.
d.Write this expression in a single logarithm: log 4 + log 2 – log 5.
____ 2.
____ 3.
a.
b.
c.
d.

log -30

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log1

c.
d.
log –
Write the equation
= 27 in logarithmic form.
log27 = -3
27 = -3
log3 27 = –
log-3 27 =
____ 4.
Expand the logarithm:
.

3logbx+3logby–3logb4

3logb xy + logb 4

3logb x+logb y–logb 4

3(logbx+logby)–logb4

____ 5.
Solvetheequation:ln2+ln6=x.

12

2.079

1.099

2.485

You place $900 in an investment account that earns 6% interest compounded continuously. Find the
balance after 5 years.

$906.05

$1546.78

$1214.87

$1006.58

Which of the following describes the function y = 1.023(0.98)x?

exponential decay

exponential growth

quadratic

linear

The adult population of a city is 1,150,000. A consultant to a law firm uses the function P(t) = 1,150,000(1 –
e-0.03t) to estimate the number of people P(t) who have heard about a major crime t days after the crime
was first reported. About how many days does it take for 60% of the population to have been exposed to
news of the crime?

46 days

15 days

31 days

19 days

Solve the equation e4x = 24.
____ 6.
____ 7.
____ 8.
____ 9.
____ 10.

-6.00

0.34505

6.00000

0.79451

Add and simplify:
a.
b.
c.
d.
+ .

____ 11.
b.
c.
d.
Solve the equation: =

-9

3

-3

9

Add and simplify:
a.
+
.
____ 12.
____ 13.
____ 14.
____ 15.
____ 16.
.
Which of the following describes the function y = 1x?

exponential decay

exponential growth

quadratic

linear

Which exponential equation goes through the points (4, 3072) and (-1, 3)?
a.
b.
c.
d.
y = 20(4)x
y = 8(4)x
y = 12(4)x
y = 16(4)x
Solve the equation log x + log 2 = 5.

100

50,000

5,000

2.5

What are the points of discontinuity of this function: y = ?

none

8, -8

4, -4

none
mthh040059_51_hassan_omar.pdf

Unformatted Attachment Preview

Course Name: Second Year Algebra 2
Student: Omar Hassan
Course ID: MTHH040059
ID: E93324820
Submittal: 51
Progress Test 1
Although the progress test is similar in style to the unit evaluations, the progress test is a closed-book test. It is
important that you do your own work. Select the response that best completes the statement or answers the question.
Your graphing calculator may be used on this progress test. You may also use scratch paper to work out the solutions.
____ 1.
A game-show spinner has 26 equal sections labeled with the letters of the English alphabet. What is the
probability that on two consecutive spins you get your first and last initials, in that order?
a.
b.
c.
d.
____ 2.
____ 3.
Write this expression in a single logarithm: log 4 + log 2 – log 5.
a.
b.
c.
log -30
log 1
d.
log –
Write the equation
a.
b.
____ 4.
log27
= 27 in logarithmic form.
= -3
27 = -3
c.
log3 27 = –
d.
log-3 27 =
Expand the logarithm:
a.
3logb x + 3logb y – 3logb 4
b.
3logb xy + logb 4
c.
3logb x + logb y – logb 4
d.
3(logb x + logb y) – logb 4
.
____ 5.
Solve the equation: ln 2 + ln 6 = x.
a.
b.
c.
d.
____ 6.
You place $900 in an investment account that earns 6% interest compounded continuously. Find the
balance after 5 years.
a.
b.
c.
d.
____ 7.
46 days
15 days
31 days
19 days
Solve the equation e4x = 24.
a.
b.
c.
d.
____ 10.
exponential decay
exponential growth
quadratic
linear
The adult population of a city is 1,150,000. A consultant to a law firm uses the function P(t) = 1,150,000(1 –
e-0.03t) to estimate the number of people P(t) who have heard about a major crime t days after the crime
was first reported. About how many days does it take for 60% of the population to have been exposed to
news of the crime?
a.
b.
c.
d.
____ 9.
$906.05
$1546.78
$1214.87
$1006.58
Which of the following describes the function y = 1.023(0.98)x?
a.
b.
c.
d.
____ 8.
12
2.079
1.099
2.485
-6.00
0.34505
6.00000
0.79451
Add and simplify:
a.
b.
c.
d.
+
.
____ 11.
Add and simplify:
+
.
a.
b.
c.
d.
____ 12. Solve the equation:
a.
b.
c.
d.
=
.
-9
3
-3
9
____ 13. Which of the following describes the function y = 1x?
a.
b.
c.
d.
exponential decay
exponential growth
quadratic
linear
____ 14. Which exponential equation goes through the points (4, 3072) and (-1, 3)?
a.
y = 20(4)x
b.
y = 8(4)x
c.
y = 12(4)x
d.
y = 16(4)x
____ 15. Solve the equation log x + log 2 = 5.
a.
b.
c.
d.
____ 16.
100
50,000
5,000
2.5
What are the points of discontinuity of this function: y =
a.
b.
c.
d.
none
8, -8
4, -4
none
?
____ 17. Write this expression in a single logarithm: 2 log x – 4 log y.
a.
b.
log x 2 y 4
log
c.
log (x 2 – y 4)
d.
log (x 2 + y 4)
____ 18. Solve the equation x +
a.
b.
c.
d.
____ 19.
–
= 50.
-42
42
210
-210
Simplify the expression:
a.
b.
c.
d.
.
x+6
x+4
x+2
x–6
____ 20. Expand the logarithm log (3mn)3.
b
____ 21.
a.
3logb (3mn)
b.
logb 9 + 3 log?b m + 3
logb n
c.
3(logb 3m + logb n)
d.
3(logb 3 + logb m + logb n)
What are the points of discontinuity of this function: y =
a.
b.
c.
d.
?
-4, -3
–3
–4
4
____ 22. Mr. Andersen put $500 into an account that earns 5.5% annual interest. The interest is compounded
annually and there are no withdrawals. How much money will be in the account at the end of 35 years?
a.
b.
c.
d.
$3256.91
$599.79
$4289.46
$859.14
____ 23. Subtract and simplify:
–
.
a.
b.
c.
d.
____ 24. Write the equation
a.
____ 25.
= 5 in logarithmic form.
625 = 5
b.
log5 625 =
c.
log625 5 =
d.
log625
=5
What are the points of discontinuity of this function: y =
a.
b.
c.
d.
?
4, -5
-4, 5
-4, -5
4, 5
____ 26. You roll two six-sided number cubes. What is the probability that both the numbers are greater than 2?
a.
b.
c.
d.
____ 27.
Which graph matches the equation y = –
?
a.
b.
c.
d.
____ 28. Write a function that models inverse variation if x = -4 when y = –6.
a.
y=
b.
y=
c.
d.
y = 24x
y = -24x
____ 29. How is the graph of y = log7 (x – 5) + 2 translated from the graph of y = log7 x?
a.
b.
c.
d.
right 5 units and down 2 units
left 5 units and down 2 units
right 5 units and up 2 units
left 5 units and up 2 units
____ 30. Classify this pair of events: A flavor of ice cream is selected at random; A topping for the ice cream is
selected at random.
a.
b.
independent
dependent
____ 31. Which of the following graphs best represent the equation y = log8 x?
a.
b.
c.
d.
____ 32. What are the asymptotes of the function y =
a.
b.
c.
d.
?
x = -7, y = 6
x = 1, y = -7
x = 6, y = 1
x = 6, y = -1
____ 33. Which exponential equation goes through the points (2, 24) and (4, 864)?
a.
y=6
b.
y=
c.
y = 6(3)x
d.
y=
(6)x
(12)x
____ 34. What are the asymptotes of the function y =
____ 35.
a.
x=
b.
c.
x = 3, y = 2
d.
x=
,y=
x=- ,y=
,y=3
Simplify the expression:
÷
a.
b.
c.
d.
____ 36. Solve the equation
a.
b.
c.
d.
?
-5, 8
2, 5
-8, 5
2, -5
=4+
.
.
____ 37. Classify this pair of events: A volleyball team is selected at random from the league; one of the remaining
teams is selected at random.
a.
b.
independent
dependent
____ 38. Which graph matches the equation y = 2x?
a.
b.
c.
d.
____ 39. Write this expression in a single logarithm: log 8 + log 3.
a.
b.
c.
d.
____ 40.
log 83
log 11
log
log 24
How is the graph of y = 4 •
a.
b.
c.
d.
translated from the graph of y = 4 •
?
3 units left
3 units right
3 units down
3 units up
____ 41. The population of Blinsk was 26,150 in 2000. In 2005, the population was 28,700. Find the growth function
P(x) that models the population.
a.
P(x) = 28,700(1.019)x
b.
P(x) = 26,150(5)x
c.
P(x) = 26,150(1.019)x
d.
P(x) = 28,700(5)x
____ 42. Write a function that models inverse variation if x = –8 when y = 3.
____ 43.
a.
y=
b.
c.
y = -24x
d.
y = 24x
y=
Simplify the expression:
a.
b.
c.
d.
•
.
____ 44. In her first 16 basketball games, Kimberly made 65.8% of her free throws. In the next game, she made 7 of
9 free throws. Let x be the number of free throws Kimberly tried in the first 16 games. What function
represents the percent of free throws made after 17 games?
a.
f(x) =
b.
f(x) =
c.
f(x) =
d.
f(x) =
____ 45. Expand the logarithm log 5x 4y 3.
b
a.
logb 5 + logb 4x + logb 3y
b.
logb 5 + 4 logb x + 3 logb y
c.
logb 5 + logb x 4 + logb y 3
d.
5 logb x 4 + 5 logb y 3
____ 46. Sound intensity is inversely proportional to the square of the distance from the source—the farther from the
source you are, the less intense the sound. Suppose the sound intensity is 60 watts per square meter at 6
meters. What is the sound intensity at 3 meters?
a.
120 W / m 2
b.
40 W / m 2
c.
240 W / m 2
d.
180 W / m 2
____ 47. Solve the equation: log 8x = -3.
a.
b.
c.
d.
0.008
0.000125
-2.6
8000
____ 48. You can use the equation N = k log A to estimate the number of species N that live in a region of area A.
The parameter k is determined by the conditions in the region. In a rain forest, 3200 species live in 600 km2.
How many species would remain if half of the forest area were destroyed by logging and farming?
a.
b.
c.
d.
2853
600
3690
1244
____ 49. Write a function that models inverse variation if x = 3 when y = 4.
a.
y=
b.
y=
c.
d.
y = 12x
y = -12x
____ 50. Write the equation 100 = 102 in logarithmic form.
a.
log2 10 = 100
b.
c.
log 2 = 100
log2 100 = 10
d.
log 100 = 2
Carefully review your answers on this progress test and make any corrections you feel are necessary. When
you are satisfied that you have answered the questions to the best of your ability, transfer your answers to the
online test submission page in the presence of your proctor.
The University of Nebraska is an equal opportunity educator and employer. ©2018, The Board of Regents of the
University of Nebraska. All rights reserved.

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