Algebra 2 Combined Review
Name: ________________________
1. Find the point-slope form of the equation of the line passing through the points (–6, –4) and
(2, –5).
2. Write the equation for the translation of y = |x|.
3. Write the equation that is the translation of y = |x| left 2 units and up 2 units.
Solve the system.
4. x − y = −4
2x − 2y = −8
6.
4x + 2y = 20
7x − 3y = 9
5.
x + y = −6
x − 4y = −1
7.
−x − 3y = 4
x + 3y = 7
8. A system of two linear inequalities ____ has a solution.
a. always b. sometimes c. never
9. Given the system of constraints, name all vertices. Then find the maximum value of the given
objective function.
x≥ 0
y≥ 0
6x − 2y ≤ 12
Maximum for C = 4x − 3y
4y ≤ 4x + 8
10. Dalco Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be
approximated by the formula P = −3x2 + 6x + 10, where x is the number of units produced
per week, in thousands.
a. How many units should the company produce per week to earn the maximum profit?
b. Find the maximum weekly profit.
11. Graph y = −2(x − 2)2 – 4.
12. Use vertex form to write the equation of the parabola.
13. Identify the vertex and the y-intercept of the graph of the function y = −3(x + 2)2 + 5.
Factor the expression.
14. 4x2 + 20x + 25
15. 4x2 − 25
16. Solve by factoring. 4x2 − 30x − 100 = 0
Solve the equation by finding square roots.
17. 3x2 = 21
Simplify the expression.
18. (−2 + i) + (−2 − 2i)
19. (1 + 3i) − (6 + 2i)
20. (−8i)(4i)
21. (−5 − 5i)(−2 + 6i)
Solve the equation.
22. 36x2 + 9 = 0
23.
24. x2 + 4x − 3 = 0
25. x2 + 6x + 16 = 0
26. −2x2 + x + 8 = 0
27. Find the zeros of y = x(x + 4)(x + 3). Then graph the equation.
28. Write a polynomial function in standard form with zeros at 5, –3, and 1.
29. Find the zeros of f(x) = (x + 5)2(x − 4)4 and state the multiplicity.
30. The numbers of cookies in a shipment of bags are normally distributed, with a mean of 64
and a standard deviation of 4. What percent of bags of cookies will contain between 60 and 68
cookies?
31. A bag contains 6 red marbles, 6 white marbles, and 4 blue marbles. Find P(red or blue).
Simplify the radical expression. Use absolute value symbols if needed.
32.
Multiply and simplify if possible.
33.
34.
35. Simplify
. Assume that all variables are positive.
Simplify.
36.
Multiply.
37.
Solve. Check for extraneous solutions.
38.
39. Let f(x) = 3x + 5 and g(x) = 4x + 7. Find f(x) + g(x).
40. Let f(x) = 3x + 2 and g(x) = −7x − 6. Find f g and its domain.
41. Let f(x) = −4x − 5 and g(x) = −2x − 6. Find (f
g)(−3).
Write the equation in logarithmic form.
42. 72 = 49
Evaluate the logarithm.
43. log5
44. log7343
Write the expression as a single logarithm.
45. 4 logbv + 3 logbx
46. log280 – log210
Expand the logarithmic expression.
47. log 7
48. Solve ln(3x − 1) = 1. Round to the nearest thousandth.
49. Solve ln 2 + ln x = 5.
Simplify the rational expression. State any restrictions on the variable.
50.
Multiply or divide. State any restrictions on the variables.
51.
Add or subtract. Simplify if possible.
52.
Solve the equation. Check the solution.
53.
54.
55. Graph the system of constraints. Then find the values of x and y that maximize P = 40x + 0y.
x≥ 0
y≥ 0
−2x + 2y ≤ 4
x≤ 3
56. Graph y = 2x2 − 7.
57. In a baseball game, an outfielder throws a ball to the second baseman. The path of the ball is
modeled by the equation
, where y is the height of the ball in feet
after the ball has traveled x feet horizontally. The second baseman catches the ball at the same
height as the height at which the outfielder released it.
a. What was the maximum height of the ball along its path? Answer to the nearest foot.
b. How far was the second baseman from the outfielder at the time he caught the ball?
c. How high above the ground was the ball when it left the hand of the outfielder?
58. Use the graph of y = (x − 3)2 + 5.
a. If you translate the parabola to the right 2 units and down 7 units, what is the equation of
the new parabola in vertex form?
b. If you translate the original parabola to the left 2 units and up 7 units, what is the equation
of the new parabola in vertex form?
c. How could you translate the new parabola in part (a) to get the new parabola in part (b)?
59. Let f(x) =
and g(x) = 2x2 + 4.
a. Find f(g(x)).
b. Find g(f(x)).
60. A model for the height of a toy rocket shot from a platform is y = −16x2 + 145x + 7, where x
is the time in seconds and y is the height in feet.
a. Graph the function.
b. Find the zeros of the function.
c. What do the zeros represent? Are they realistic?
d. About how high does the rocket fly before hitting the ground? Explain.
61. Sketch a normal curve with a mean of 50 and a standard deviation of 2. Label the horizontal
axis at one, two, and three standard deviations from the mean.
62. Find the x-intercepts of the graph
63. Suppose you invest $200 into an account that earns 4.7% interest, compounded continuously.
Find the number of years for the investment to double.
64. A rectangular parking lot has a length that is 3 yards greater than the width. a) Write the
model b) If the area of the parking lot is 180 square yards, find the length and width.
65. Determine
66. Show
is a factor of
. Determine the remaining factors.
67. Solve the system and verify your solution:
For Questions 68 and 69 use the following information to answer the questions.
During the 2009-2010 basketball season, the number of points scored in each game by the Boston
Celtics was approximately Normally distributed with a mean of 99.2 points and a standard
deviation of 10.5 points.
68. What is the 33rd percentile of points scored by the Celtics?
69. The mean number of points scored by Los Angeles Lakers was 101.7. In what proportion of
their games did the Celtics score more than the Lakers’ mean score?
70. A survey of a random sample of 1280 student loan borrowers found that 448 had loans
totaling more than $20,000 for their undergraduate education. Construct and interpret a 95%
confidence interval to estimate the population proportion of student load borrowers who have
loans totaling more than $20,000.
71. Your school has 1000 students. You ask 80 of them, “Have you had a cold in the last three
months?” Fifty-six percent of them answered “yes.”
This is an example of
a. an experiment.
b. a census.
c. an observational study.
d. both (b) and (c).
e. none of these.
72. Kitchen appliances don’t last forever. The lifespan of all microwave ovens sold in the United
States is approximately Normally distributed with a mean of 9 years and a standard deviation of
2.5 years. What percentage of the ovens last more than 10 years?
a. 11.5%
b. 34.5%
c. 65.5%
d. 69%
e. 84.5%
73. A scientist selects 500 smokers to test how long they can hold their breath. Not surprisingly,
the smokers can't hold their breath for long. The average result was a measly 23 seconds. What
kind of study was this?
a. Randomized trial
b Double blind study
c. Observational study
d. An experiment
74. Which of the following is a random sample?
a. Picking out the best athletes from a track team to measure average performance
b. Selecting the closest people sitting next to you in class to determine the average GPA of the
entire class
c. Neither (A) nor (B)
d. Both (A) and (B)
75. Which of the following is a random sample?
a. Picking out the best athletes from a track team to measure average performance
b. Selecting the closest people sitting next to you in class to determine the average GPA of the
entire class
c. Neither (A) nor (B)
d. Both (A) and (B)
76. Your friend wants to show you a magic trick and takes out a coin from her wallet. The coin is
flipped several times in a row and all the results are heads. What do you think?
a.
b.
c.
d.
The coin is fair
The coin is unfair
This may have happened due to chance
All of the above
77. You and your entire class are stranded on a desert island. A rescue boat can save all of you
except for one, who will be left on the island forever. You have all decided that whoever picks a
number closest to the one that is randomly generated (luckily, someone brought a laptop) will
stay behind. What should be done to ensure a fair result?
a.
b.
c.
d.
Make sure that everyone looks at each other while guessing
Make sure that everyone writes their guesses down
Allow people to talk to one another
All of the above