Honors Advanced Algebra w/Trig
Chapters 3 and 4
#1
GROUP NUMBER_____________
NAMES:
WRITER/RUNNER______________CALCULATOR/TASK MASTER____________
NOTES PERSON_______________ CALCULATOR/TIMER__________________
_____________________________________________________________________________
Target Goals:
• Determine whether a system of linear equations is inconsistent, consistent, and dependent, or
consistent and independent. (3.1)
• Solve systems of linear equations by using substitution. (3.2)
_____________________________________________________________________________
MULTIPLE CHOICE
1.
2.
A system of linear equations may not have:
A
exactly one solution.
C
infinitely many solutions.
B
no solution.
D
exactly two solutions.
1.___________
Choose the correct description of the system of equations.
4x + 2y = -6
2x - y = 8
F
consistent and independent
H
consistent and dependent
G
inconsistent
J
inconsistent and dependent
2.___________
3-4
To solve each system of equations, which expression could be
substituted for x into the first equation?
3.
5x - 2y = 8
x-y=1
A
y+1
B
y-1
C
- x+1
D
x-1
3.___________
4.
4x - 3y = 12
x + 3y = -5
F
3y - 5
G
-3y - 5
H
y + 35
J
-5+3y
4.___________
Honors Advanced Algebra w/Trig
Chapters 3 and 4
#2
GROUP NUMBER_____________
NAMES:
WRITER/RUNNER______________CALCULATOR/TASK MASTER____________
NOTES PERSON_______________ CALCULATOR/TIMER__________________
_____________________________________________________________________________
Target Goals:
• Solve systems of linear equations by using elimination. (3.2)
• Solve a system of linear equations in three variables. (3.5)
• Use inverse matrices to solve a system of equations. (4.6)
_____________________________________________________________________________
MULTIPLE CHOICE
5-6
The first equation of each system is multiplied by 4. By what number would you
multiply the second equation in order to eliminate the x variable by adding?
5.
3x - 2y = 4
4x + 5y = 28
A
6.
3
B
-3
C
4
D
-4
G
6
H
-3
J
-6
5.___________
-6x -3y = 12
8x + 2y = 16
F
3
6.___________
7-8
Solve each system of equations.
7.
3x - 2y = 5
x=y+2
A
8.
(1, 1)
B
(2, -1)
C
(0, -2)
D
(1, -1)
7.___________
2x + y + z = 13
2x - y - 3z = -3
x - 2y - 4z = 20
F
(36, -126, -67)
G
(-36, -126, 67)
H
(36, 126, 67)
J
(36, -126, 67)
8.___________
Honors Advanced Algebra w/Trig
Chapters 3 and 4
#3
GROUP NUMBER_____________
NAMES:
WRITER/RUNNER______________CALCULATOR/TASK MASTER____________
NOTES PERSON_______________ CALCULATOR/TIMER__________________
_____________________________________________________________________________
Target Goals:
• Graph a system of inequalities. (3.4)
• Find the maximum and minimum values of a function over a region using linear programming
techniques. (3.6)
• Solve problems involving maximum and minimum values using linear programming
techniques. (3.7)
_____________________________________________________________________________
9-12 Linear Programming. Show all work in the spaces provided.
A college arena sells tickets to students and to the public. Student tickets are $8 each
and general public tickets are $32 each. The college sells at least 5000 tickets for
students. The arena seats 18,000. How many general public tickets should the college
sell to maximize revenue (amount collected.)? What is the maximum revenue?
Define the variable, arrange the information in a matrix, set up a system of
inequalities, set up a profit (cost) equation, graph the system of inequalities, name
all critical points, answer the problem.
Matrix for Data:
System of
Inequalities:
x = ________
y = _________
Profit (maximum
revenue) Equation:
Final Solution:
Honors Advanced Algebra w/Trig
Chapters 3 and 4
#4
GROUP NUMBER_____________
NAMES:
WRITER/RUNNER______________CALCULATOR/TASK MASTER____________
NOTES PERSON_______________ CALCULATOR/TIMER__________________
_____________________________________________________________________________
Target Goals:
• Solve application problems using 2 or more variables and 2 or more equations. (3.1, 3.2, 3.5)
• Solve a system of linear equations in three variables. (3.5)
• Use inverse matrices to solve a system of equations. (4.6)
_____________________________________________________________________________
Use for #13-16
The 300 students at Holmes School work a total of 5000 hours each month. Each student in the first group
works 10 hours, each student in the second group works 15 hours, and each student in the third group
works 20 hours each month. There are twice as many students in the second group as in the first group.
How many students are in the second group?
13. Define the variables.
14. Write a system of equations that will solve the problem.
15. Solve the system of equations.
16. Answer the problem.
Honors Advanced Algebra w/Trig
Chapters 3 and 4
#5
GROUP NUMBER_____________
NAMES:
WRITER/RUNNER______________CALCULATOR/TASK MASTER____________
NOTES PERSON_______________ CALCULATOR/TIMER__________________
_____________________________________________________________________________
Target Goals:
• Name a matrix by rows and columns. (4.1)
• Organize data using a matrix. (4.1)
• Find a determinant. (4.5)
_____________________________________________________________________________
17.
The rates to stay at the Star Beach Resort in summer are:
Single Room:
$55 on weekdays;
$74 on weekends
Double Room:
$65 on weekdays;
$84 on weekends
Suite:
$75 on weekdays;
$100 on weekends
Write a 2 x 3 matrix that represents the cost of each room.
17.____________________________________
18.
Write a 5 x 2 matrix that represents the five-day forecast of high (H) and low (L)
temperatures.
Monday
H 80
L 52
Tuesday
H 81
L 53
Wednesday Thursday
H 85
H 79
L 52
L 51
Friday
H 72
L 51
18.____________________________________
19.
Find the value of
4 5 6
−2 3 4 .
5 6 7
19._____________________
Honors Advanced Algebra w/Trig
Chapters 3 and 4
#6
GROUP NUMBER_____________
NAMES:
WRITER/RUNNER______________CALCULATOR/TASK MASTER____________
NOTES PERSON_______________ CALCULATOR/TIMER__________________
_____________________________________________________________________________
Target Goals:
• Add, Subtract and Multiply matrices. (4.2 & 4.3)
• Find the inverse matrix of a 2 x 2 matrix. (4.6)
• Prove that two matrices are inverses of each other. (4.6)
_____________________________________________________________________________
20.
 5
Find the inverse of 
 2
8
4

.

20._________________
21-22 Perform the indicated operations.
21.
 −1 1 2  8 3 1
− 

 2 0 −5  6 −7 2
4
21._________________
€
22.
€
23.
 0 1 2  2 −1

 

−5 3 0  • 1 4 
−1 4 −3 0 −3 
22.________________
4
Determine if the 2 matrices 
−1
are inverses of each other.
€
3
 and
2
2
11
1

11
−3
11 
4

11 
23._________________
Honors Advanced Algebra w/Trig
Chapters 3 and 4
#7
GROUP NUMBER_____________
NAMES:
WRITER/RUNNER______________CALCULATOR/TASK MASTER____________
NOTES PERSON_______________ CALCULATOR/TIMER__________________
_____________________________________________________________________________
Target Goals:
• Graph a system of inequalities. (3.4)
• Solve a system of linear equations by graphing. (3.1)
_____________________________________________________________________________
24.
Graph the following system of inequalities. Shade only the region of feasible
solutions and name all of the critical points.
y≤x
y > -2x + 5
x<6
25.
Solve the system of equations by graphing.
3x - 5y = -11
4x + y = 16
25.____________
Honors Advanced Algebra w/Trig
Chapters 3 and 4
Bonus (+2)
GROUP NUMBER_____________
NAMES:
WRITER/RUNNER______________CALCULATOR/TASK MASTER____________
NOTES PERSON_______________ CALCULATOR/TIMER__________________
_____________________________________________________________________________
Target Goals:
• State the domain and range of a relation. (2.1)
• Write and graph piecewise-defined functions. (2.6)
_____________________________________________________________________________
26. Graph the piecewise function. Name the domain and range:
x + 5
if − 3 < x ≤ 4

f (x) = −4
if x ≥ 4
−2x − 4 if x ≤ −3

Domain________________
Range_________________
Packet Activity Score Sheet
Group #__________Class Period____________Date____________
Group members names
__________________
__________________
__________________
__________________
#1______________(2 points)
#2______________(2 points)
#3______________(2 points)
#4______________(2 points)
#5______________(2 points)
#6______________(2 points)
#7______________(2 points)
Bonus______________(2 points)
Total______________