Download Algebra 2 - Alliance Ouchi-O`Donovan 6

CHAPTER
ADDITIONAL RESOURCES
• Chapter 3 Resource Book
Chapter Test (3 levels) (p. 93)
SAT/ACT Chapter Test (p. 99)
Alternative Assessment (p. 100)
•
Test and Practice Generator
3
Chapter Standardized Test
TEST-TAKING STRATEGY If you find yourself spending too much time on one test question and
getting frustrated, move on to the next question. You can revisit a difficult problem later with a
fresh perspective.
1. MULTIPLE CHOICE Which ordered pair is a
solution of the following system of linear equations?
C
2x º 5y = º12
ºx + 4y = 9
A
¡
D
¡
(º6, 0)
(º9, 0)
B
¡
E
¡
(3, 3)
C
¡
6. MULTIPLE CHOICE Which linear equation is
graphed below? D
z
(0, 2, 0)
(º1, 2)
y
(4, 0, 0)
(2, 2)
x
2. MULTIPLE CHOICE How many solutions does the
Qu. Standard
Qu. Standard
8x º 4y = 20
2x º y = 5
A
¡
D
¡
B
¡
E
¡
0
4
1
C
¡
2
infinitely many
3. MULTIPLE CHOICE A total of $6500 is invested in
two funds. One fund pays 4% interest annually and
the other fund pays 6% interest annually. The
combined annual interest earned is $350. How much
of the $6500 is invested in one of the funds? A
A
¡
D
¡
$2000
$4000
B
¡
E
¡
$2500
C
¡
$3250
$5500
4. MULTIPLE CHOICE Which ordered pair is not a
A
¡
C
¡
E
¡
x º 2y º z = 4
x + 2y º z = º4
x ≥ º2
y ≥ º3
y < 3x + 3
A
¡
D
¡
(4, º3)
(5, 17)
B
¡
E
¡
(0, 0)
C
¡
(1, 6)
(º1, º1)
5. MULTIPLE CHOICE What is the minimum value of
the objective function C = 4x + 3y subject to the
following constraints? C
190
0
18
B
¡
E
¡
2
36
x º 2y + z = º4
x + 2y º z = 4
7. MULTIPLE CHOICE At which point does the graph
of 15x º 6y º 3z = 30 cross the y-axis? E
A
¡
C
¡
E
¡
B
¡
D
¡
(0, º6, 0)
(0, º3, 0)
(2, 0, 0)
(0, 0, º10)
(0, º5, 0)
8. MULTIPLE CHOICE Which ordered triple is a
solution of the following linear system? A
2x + 5y + 3z = 10
3x º y + 4z = 8
5x º 2y + 7z = 12
A
¡
C
¡
E
¡
B
¡
D
¡
(7, 1, º3)
(7, 1, 3)
(7, º1, º3)
(7, º1, 3)
(º7, 1, º3)
9. MULTIPLE CHOICE A cashier at a restaurant made
the chart below for popular lunch combinations.
What is the individual price of soup? B
x≥0
y≥0
2x + 3y ≤ 18
3x + y ≥ 6
A
¡
D
¡
B
¡
D
¡
ºx + 2y + z = 4
solution of the following system of linear
inequalities? C
190
(0, 0, ⫺4)
following system have? E
Lunch Combinations
Soup + Salad = $4.25
Soup + Sandwich = $4.75
Salad + Sandwich = $5.50
C
¡
8
A
¡
D
¡
$1.50
$2.50
Chapter 3 Systems of Linear Equations and Inequalities
B
¡
E
¡
$1.75
$3.00
C
¡
$2.25
QUANTITATIVE COMPARISON In Exercises 10 and 11, choose the statement
that is true about the given quantities.
A
¡
B
¡
C
¡
D
¡
The quantity in column A is greater.
The quantity in column B is greater.
The two quantities are equal.
The relationship cannot be determined from the given information.
Column A
1
5
1
ƒ(x, y) = ᎏᎏ(10 + 4x º 3y), ƒ(º2, º1)
2
ƒ(x, y) = ᎏᎏ(20 º 2x + y), ƒ(4, 8)
10.
11.
12b. Sample answer: x = 2y + 2, so
5(2y + 2) – 4y = 6y + 10 = –8.
6y = –18, or y = –3.
x = 2(–3) + 2 = –4.
The solution is (–4, –3).
12c. Sample answer: Multiply the
first equation by –2, and add
it to the second equation:
–2x + 4y = –4
5x – 4y = –8
3x =
–12
So x = –4. Then 2y = x – 2 =
–4 – 2 = –6, so y = –3.
12d. Sample answer: I prefer the
linear combination method,
since it works with any system
and usually yields a solution
easily, especially when only one
equation needs to be multiplied,
as here.
13d. For part (a), I started with a different linear combination of x
and y which would give a different slope, then seeing that (–3, 2)
is a solution of the given equation, I calculated the value of the
right-hand side to make it a solution of my equation as well. For
part (b), I made the left-hand side
–2 times the left-hand side of the
original equation, then picked a
completely different number for
the right-hand side. For part (c),
I made the whole equation –2
times the original equation.
y
14b.
Column B
1
5
1
ƒ(x, y) = ᎏᎏ(10 + 4x º 3y), ƒ(2, 1)
2
ƒ(x, y) = ᎏᎏ(20 º 2x + y), ƒ(º1, 3)
B
B
12. MULTI-STEP PROBLEM Use the following system of linear equations.
Equation 1
x º 2y = 2
5x º 4y = º8
Equation 2
a. Solve the system by graphing. (º4, º3)
b. Solve the system using the substitution method. Show your work. 12b–d. See margin.
c. Solve the system using the linear combination method. Show your work.
d.
Writing Which method do you prefer for solving this system? Explain.
13. MULTI-STEP PROBLEM Write an equation which, when paired with
º2x + 3y = 12 to form a system, has the given number of solutions.
a. exactly one solution x + 4y = 5
b. no solution 4x º 6y = 5
c. infinitely many solutions 4x º 6y = º24
d.
Writing Explain how you wrote each of the equations in parts (a)–(c).
See margin.
14. MULTI-STEP PROBLEM The cholesterol in your blood is necessary, but too
much cholesterol can lead to health problems. A blood cholesterol test gives three
readings: LDL “bad” cholesterol, HDL “good” cholesterol, and total cholesterol
(LDL + HDL). It is recommended that your LDL cholesterol be less than
130 milligrams per deciliter, HDL cholesterol be at least 35 milligrams per
deciliter, and total cholesterol be no more than 200 milligrams per deciliter.
(35, 130)
a. Write a system of three linear inequalities for the recommended cholesterol
readings. Let x represent HDL cholesterol and y represent LDL cholesterol. 0 ≤ y < 130; x ≥ 35; x + y ≤ 200
x ⫽ 35
(35, 0)
c. Are the cholesterol readings at the right within recommendations?
not within recommendations
y ⫽ 130
x ⫹ y ⫽ 200
b. Graph the system. Label any vertices of the solution region. See margin for graph.
d. Give an example of blood cholesterol test results in which the LDL
(70, 130)
100
0
LDL: 120 mg/dL
HDL: 90 mg/dL
Total: 210 mg/dL
100
(200, 0)
x
cholesterol is too high, but HDL and total cholesterol readings are fine.
Write a system of linear inequalities to describe all the examples of this type.
LDL: 135 mg/dL; HDL: 40 mg/dL; Total: 175 mg/dL; y ≥ 130; x ≥ 35; x + y ≤ 200
e. Another recommendation is that the ratio of total cholesterol to HDL
cholesterol be less than 4. Find a point in your solution region from part (b)
mg
total
that meets this recommendation and show that it does.
LDL = 120 }}, HDL = 40. Then }} = 3, and 3 < 4.
dL
HDL
Chapter Standardized Test
191
191