Course Name: Second Year Algebra 2
Student: Aguistin Spaan
Course ID: MTHH040059
ID: G87557040
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.
Add and simplify:
+
a.
b.
c.
d.
____ 2.
Solve the equation: log 4x = −1.
a.
b.
c.
d.
0.25
0.025
25
−0.25
.
____ 3.
Which graph matches the equation y = −
?
a.
b.
c.
d.
____ 4.
Which of the following describes the function y =
a.
b.
c.
d.
exponential decay
exponential growth
quadratic
linear
?
____ 5.
Which exponential equation goes through the points (4, 12) and (7, 96)?
a.
y=
b.
y = 4(2)x
c.
d.
____ 6.
____ 8.
(4)x
y=
.
x+9
x+3
x+6
x–3
Write a function that models inverse variation if x = 3 when y = 4.
a.
y=
b.
y=
c.
d.
y = 12x
y = −12x
Mr. Andersen put $1000 into an account that earns 4.5% annual interest. The interest is compounded
annually and there are no withdrawals. How much money will be in the account at the end of 30 years?
a.
b.
c.
d.
____ 9.
y=2
Simplify the expression:
a.
b.
c.
d.
____ 7.
(2)x
$1300.25
$2051.67
$3745.32
$5431.67
What are the points of discontinuity of this function: y =
a.
b.
c.
d.
−4, −3
–3
–4
4
____ 10. Solve the equation log x + log 2 = 5.
a.
b.
c.
d.
100
50,000
5,000
2.5
?
____ 11.
Write the equation
a.
= 81 in logarithmic form.
−4 = 81
b.
log−4
c.
log81 −4 =
d.
= 81
81 = −4
____ 12. In her first 16 basketball games, Kimberly made 72.3% of her free throws. In the next game, she made 6 of
7 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?
____ 13.
a.
f(x) =
b.
f(x) =
c.
f(x) =
d.
f(x) =
Simplify the expression:
•
.
a.
b.
c.
d.
____ 14. The adult population of a city is 1,350,000. A consultant to a law firm uses the function P(t) = 1,350,000(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 70% of the population to have been exposed to
news of the crime?
a.
b.
c.
d.
36 days
20 days
12 days
40 days
____ 15. How is the graph of y = log6 (x + 1) – 4 translated from the graph of y = log6 x?
a.
b.
c.
d.
right 1 unit and up 4 units
left 1 unit and up 4 units
right 1 unit and down 4 units
left 1 unit and down 4 units
____ 16. Write this expression in a single logarithm: log 4 + log 7.
a.
b.
log 11
c.
d.
log 28
log
log 47
____ 17. Solve the equation x +
a.
b.
c.
d.
____ 18.
–
−42
42
210
−210
How is the graph of y = 4 •
a.
b.
c.
d.
= 50.
– 4 translated from the graph of y = 4 •
?
4 units left
4 units right
4 units up
4 units down
____ 19. 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, 2700 species live in 500 km2.
How many species would remain if half of the forest area were destroyed by logging and farming?
a.
b.
c.
d.
____ 20.
1595
4567
2641
2399
Simplify the expression:
÷
.
a.
b.
c.
d.
____ 21. 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
____ 22. Solve the equation
a.
b.
c.
d.
=
.
10
2
−2
−10
____ 23. Write a function that models inverse variation if x = 4 when y = −7.
____ 24.
____ 25.
a.
b.
y = −28x
c.
d.
y = 28x
y=
y=
Expand the logarithm:
a.
5logb xy + logb 3
b.
5logb x + 5logb y – 5logb 3
c.
5(logb x + logb y) – logb 3
d.
5logb x + logb y – logb 3
.
What are the points of discontinuity of this function: y =
a.
b.
c.
d.
36, −9
6, −6
3, −3
none
____ 26. Write the equation 10,000 = 104 in logarithmic form.
a.
log4 10,000 = 10
b.
log 10,000 = 4
c.
d.
log 4 = 10,000
log4 10 = 10,000
?
____ 27. Which of the following graphs best represent the equation y = log6 x?
a.
b.
c.
d.
____ 28. You roll two six-sided number cubes. What is the probability that both the numbers are greater than 2?
a.
b.
c.
d.
____ 29. Classify this pair of events: A main dish is selected at random; a type of salad is selected at random.
a.
b.
independent
dependent
____ 30. What are the asymptotes of the function y =
a.
b.
c.
d.
?
x = 3, y = 1
x = −5, y = −1
x = −5, y = 3
x = −5, y = 1
____ 31. Write a function that models inverse variation if x = −4 when y = –6.
a.
y=
b.
y=
c.
d.
y = 24x
y = −24x
____ 32. Write the equation
a.
= 5 in logarithmic form.
625 = 5
b.
log5 625 =
c.
log625 5 =
d.
log625
=5
____ 33. Write this expression in a single logarithm: 3 log x + 4 log y.
a.
log (x 3y 4)
b.
log (x 3 + y 4)
c.
log (x 3 – y 4)
log (12xy)
d.
____ 34. Which of the following describes the function y = 2x 2 + 7?
a.
b.
c.
d.
exponential decay
exponential growth
quadratic
linear
____ 35. 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 50 watts per square meter at 3
meters. What is the sound intensity at 5 meters?
____ 36.
a.
18 W / m 2
b.
48 W / m 2
c.
30 W / m 2
d.
24 W / m 2
What are the points of discontinuity of this function: y =
a.
b.
c.
d.
–2, 1
–1, 2
−2, −1
2, 1
____ 37. Expand the logarithm log 3x 3y 7.
b
a.
logb 3 + logb x 3 + logb y 7
b.
3 logb x 3 + 3 logb y 7
c.
logb 3 + 3 logb x + 7 logb y
d.
logb 3 + logb 3x + logb 7y
____ 38. Write this expression in a single logarithm: log 3 + log 6 – log 7.
a.
log −
b.
c.
d.
log 2
log −126
log
?
____ 39. Which graph matches the equation y = 3x?
a.
b.
c.
d.
____ 40.
Add and simplify:
a.
b.
c.
d.
+
.
____ 41. 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
____ 42. Solve the equation
a.
b.
c.
d.
=7+
.
−7, 4
−4, 7
2, −7
−2, 7
____ 43. You place $1000 in an investment account that earns 7% interest compounded continuously. Find the
balance after 6 years.
a.
b.
c.
d.
$1011.73
$1521.96
$2236.89
$2314.63
____ 44. Which exponential equation goes through the points (2, 128) and (−1, 16)?
a.
y = 64(2)x
b.
y = 32(2)x
c.
y = 16(2)x
d.
y = 8(4)x
____ 45. Solve the equation e3x = 20.
a.
b.
c.
d.
0.99858
1.22874
5.46874
6.667
____ 46. What are the asymptotes of the function y =
a.
b.
x = −4, y = 5
x=
,y=5
c.
x=
,y=5
d.
x=
,y=
?
____ 47. Subtract and simplify:
–
.
a.
b.
c.
d.
____ 48. A game-show spinner has 7 equal sections labeled with the colors red, orange, yellow, green, blue, indigo
and violet. What is the probability that on two consecutive spins you get University of Michigan’s colors
(blue and yellow)?
a.
b.
c.
d.
____ 49. Expand the logarithm log (3mn)3.
b
a.
3logb (3mn)
b.
logb 9 + 3 logb m + 3
logb n
c.
3(logb 3m + logb n)
d.
3(logb 3 + logb m + logb n)
____ 50. Solve the equation: ln 3 + ln 5 = x.
a.
b.
c.
d.
2.079
15
0.693
2.708
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.
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