Algebra Question

Course Name: Second Year Algebra 2Course ID: MTHH040059
Student: Daimon Gardner
Student ID: G83165467
Generated Date: October 08, 2021
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. Write a function that models inverse variation if x = −6 when y = −2.
A. y = 12x
B.
C.
D. y = −12x
____ 2. What are the points of discontinuity of this function:
A. 2, −2
B. 4, −4
C. −4, 16
D. none
____ 3. Write this expression in a single logarithm: log 8 + log 3.
A. log 83
B. log 11
C.
D. log 24
?
____ 4. Which graph matches the equation
?
A.
B.
C.
D.
____ 5. Mr. Andersen put $2000 into an account that earns 3.5% annual interest. The
interest is compounded annually and there are no withdrawals. How much
money will be in the account at the end of 25 years?
A. $5715.30
B. $2820.75
C. $1397.24
D. $4726.49
____ 6. What are the points of discontinuity of this function:
A. –2, 1
B. –1, 2
C. −2, −1
D. 2, 1
?
____ 7. Which exponential equation goes through the points (2, 24) and (4, 864)?
A.
B.
C. y = 6(3)x
D.
____ 8. 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.
____ 9. Expand the logarithm logb 3x3y7.
A. log 3 + log x3 + log y7
b
b
b
B. 3 logb x3 + 3 logb y7
C. logb 3 + 3 logb x + 7 logb y
D. logb 3 + logb 3x + logb 7y
____ 10. Write the equation 100 = 102 in logarithmic form.
A. log2 10 = 100
B. log 2 = 100
C. log2 100 = 10
D. log 100 = 2
____ 11. Solve the equation log x + log 2 = 5.
A. 100
B. 50,000
C. 5,000
D. 2.5
____ 12. What are the points of discontinuity of this function:
?
A. −4
B. 8
C. −4, −8
D. −8
____ 13. Solve the equation
.
A. −7, 4
B. −4, 7
C. 2, −7
D. −2, 7
____ 14. Solve the equation
.
A. −1
B. −4
C. 4
D. 1
____ 15. You place $800 in an investment account that earns 5% interest compounded
continuously. Find the balance after 4 years.
A. $977.12
B. $5911.24
C. $2183.92
D. $646.71
____ 16. How is the graph of
translated from the graph of
?
A. 3 units left
B. 3 units right
C. 3 units down
D. 3 units up
____ 17. 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
____ 18. Subtract and simplify:
.
A.
B.
C.
D.
____ 19. You roll two six-sided number cubes. What is the probability that at least one
of the numbers is prime or even?
A.
B.
C.
D.
____ 20. 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. 2853
B. 600
C. 3690
D. 1244
____ 21. 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 / m2
B. 40 W / m2
C. 240 W / m2
D. 180 W / m2
____ 22. Write this expression in a single logarithm: 2 log x – 4 log y.
A. log x2 y4
B.
C. log (x2 – y4)
D. log (x2 + y4)
____ 23. Which of the following describes the function y = 10x?
A. exponential decay
B. exponential growth
C. quadratic
D. linear
____ 24. The population of Blinsk was 28,520 in 2000. In 2008, the population was
33,760. Find the growth function P(x) that models the population.
A. P(x) = 33,760(1.021)x
B. P(x) = 28,520(1.021)x
C. P(x) = 28,520(8)x
D. P(x) = 33,760(8)x
____ 25.
Write the equation
in logarithmic form.
A.
B.
C.
D.
____ 26. 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. independent
B. dependent
____ 27. Solve the equation e4x = 24.
A. −6.00
B. 0.34505
C. 6.00000
D. 0.79451
____ 28. Simplify the expression:
.
A.
B.
C.
D.
____ 29. Which of the following describes the function y = 1.023(0.98)x?
A. exponential decay
B. exponential growth
C. quadratic
D. linear
____ 30. Solve the equation
.
A. 105
B. −20
C. −105
D. 20
____ 31. Simplify the expression:
.
A. x – 3
B. x + 5
C. x + 15
D. x – 5
____ 32. 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?
A.
B.
C.
D.
____ 33. Expand the logarithm logb (3mn)3.
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)
____ 34. What are the asymptotes of the function
?
A. x = −7, y = 6
B. x = 1, y = −7
C. x = 6, y = 1
D. x = 6, y = −1
____ 35. How is the graph of y = log6 (x + 1) – 4 translated from the graph of y =
log6 x?
A. right 1 unit and up 4 units
B. left 1 unit and up 4 units
C. right 1 unit and down 4 units
D. left 1 unit and down 4 units
____ 36. What are the asymptotes of the function
?
A. x = −4, y = 5
B.
C.
D.
____ 37. Simplify the expression:
A.
B.
C.
D.
.
____ 38. Classify this pair of events: A main dish is selected at random; a type of salad
is selected at random.
A. independent
B. dependent
____ 39. Write a function that models inverse variation if x = 5 when y = 8.
A.
B. y = 40x
C.
D. y = −40x
____ 40. Solve the equation: log 5x = −2.
A. 0.005
B. 20
C. 500
D. 0.002
____ 41. Add and simplify:
.
A.
B.
C.
D.
____ 42. Add and simplify:
A.
B.
C.
D.
.
____ 43. Write the equation 64 = 1296 in logarithmic form.
A. log4 6 = 1296
B. log6 1296 = 4
C. log1296 6 = 4
D. log6 4 = 1296
____ 44. Write a function that models inverse variation if x = –8 when y = 3.
A.
B. y = −24x
C.
D. y = 24x
____ 45. The adult population of a city is 1,250,000. A consultant to a law firm uses the
function P(t) = 1,250,000(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 80% of the population to have been
exposed to news of the crime?
A. 54 days
B. 7 days
C. 23 days
D. 39 days
____ 46. Write this expression in a single logarithm: log 3 + log 6 – log 7.
A.
B. log 2
C. log −126
D.
____ 47. Solve the equation ln 2 + ln 4 = x.
A. 0.693
B. 1.386
C. 2.079
D. 8
____ 48. Expand the logarithm:
.
A. 4(logb x + logb y) – logb 2
B. 4logb x + logb y – logb 2
C. 4logb xy – logb 2
D. 4logb xy + logb 2
____ 49. Which graph matches the equation y = 3x?
A.
B.
C.
D.
____ 50. Which of the following graphs best represent the equation y = log7 x?
A.
B.
C.
D.
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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