Download Algebra II Honors Test Review 3-4 to 3-6

Name: ________________________ Class: ___________________ Date: __________
ID: A
Algebra II Honors Test Review 3-4 to 3-6
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. The maximum value of a linear objective function ____ occurs at exactly one vertex of the feasible region.
a. always
b. sometimes
c. never
2. Which of the following points lies in the plane represented by 6x + 4y + 7z = 2?
a. (–5, –8, 8)
b. (8, –5, 9)
c. (2, 1, –2)
d. (–8, 4, –3)
3. The solution to a system of three equations in three variables is ____ one point.
a. always
b. sometimes
c. never
Short Answer
Solve the system by the method of substitution.
ÏÔÔ
ÔÔ −x − y + 2z = −10
ÔÔÔ
z = −6
4. ÔÌÔ
ÔÔ
ÔÔÔ −x + 2y − z = 2
Ó
Use the elimination method to solve the system.
ÏÔÔ
ÔÔ 3x + 5y + 4z = 13
ÔÔÔ
5. ÔÌÔ 5x + 2y + 3z = −9
ÔÔ
ÔÔÔ 6x + 3y + 4z = −8
Ó
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Name: ________________________
ID: A
6. Graph the point (–2, 0, 4).
7. Describe the location of the point in coordinate space.
(8, –10, –4)
8. Graph −x + 2y + 2z = 6.
9. Find the equation of each trace of 3x − 2y + 12z = 24
10. Find the values of x and y that maximize the objective function P = 2x + 3y for the graph. What is the maximum
value?
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Name: ________________________
ID: A
11. Given the system of constraints, name all vertices. Then find the maximum value of the given objective
function.
ÏÔ
ÔÔÔ x ≥ 0
ÔÔ
ÔÔÔ y ≥ 0
ÌÔÔ
ÔÔ 3x + 2y ≤ 12
ÔÔÔ
ÔÔÔ
Óx + y ≤ 5
Maximum for P = 3x + 5y
12. Suppose you make and sell skin lotion. A quart of regular skin lotion contains 2 c oil and 1 c cocoa butter. A
quart of extra-rich skin lotion contains 1 c oil and 2 c cocoa butter. You will make a profit of $10/qt on regular
lotion and a profit of $8/qt on extra-rich lotion. You have 24 c oil and 18 c cocoa butter. How many quarts of
each type of lotion should you make to maximize your profit? What is the maximum profit?
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Name: ________________________
ID: A
13. A food store makes a 10-lb mixture of peanuts, cashews, and raisins. Peanuts cost $1.00 per pound, cashews cost
$2.00 per pound, and raisins cost $1.00 per pound. The mixture calls for twice as much peanuts than cashews.
The total cost of the mixture is $12.00. How much of each ingredient did the store use?
14. The sum of three numbers is -2. The sum of three times the first number, twice the second number, and the third
number is 9. The difference between the second number and half the third number is 10. Find the numbers.
15. You have $36 to spend on a party. Pizzas cost $12 each, chips cost $2.25 per bag, and soda costs $2 per bottle.
a.
b.
c.
Write an equation in three variables for the number of pizzas, bags of chips, and bottles
of soda you can buy.
Find the intercepts of the equation.
Graph the equation.
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ID: A
Algebra II Honors Test Review 3-4 to 3-6
Answer Section
MULTIPLE CHOICE
1. B
2. C
3. B
SHORT ANSWER
4. (0, –2, –6)
5. (–3, 6, –2)
6.
7. From the origin, move 8 units forward, 10 units left, and 4 units down.
8.
9. 3x − 2y = 24
−y + 6z = 12
x + 4z = 8
maximum value at (0, 8); 24
(0, 0), (4, 0), (2, 3), (0, 5); maximum value of 25 at (0, 5)
10 qts of regular skin lotion and 4 qts of extra-rich skin lotion will give you a maximum profit of $132.
4 lb peanuts, 2 lb cashews, 4 lb raisins
10.
11.
12.
13.
14. 3, 5, and -10
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ID: A
ESSAY
15.
[4]
a. 12p + 2.25c + 2s = 36
b. p = 3, c =16, s = 18
c.
[3]
[2]
[1]
only two parts correct
only one part correct
correct answers, but no work shown
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