Review Supplement Unit 1a: Equations, Inequalities, Systems

Review Supplement
Unit 1a: Equations, Inequalities, Systems
You will be able to create an equation in
one variable from a real-world context
Algebra II Textbook P. 62: 23, 24; P. 63:
32, 33
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
You will be able to create equations in
two variables to represent relationships
between quantities
Algebra II Textbook P. 103: 50, 52, 54
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
You will be able to solve an equation in
one variable
Algebra II Textbook P. 62: 17-22 (Some)
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
You will be able to graph two-variable
equations
Algebra II Textbook P. 103: 50, 52, 54
(Graph the equations)
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
1.
Solve for .
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2.
Solve for .
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You will be able to write, solve, and
graph absolute value equations
Algebra II Textbook P. 64: 41-43
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
You will be able to solve and graph
absolute value inequalities
Algebra II Textbook P. 64: 44-47
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
3.
Kenny’s mom requires that he retake
any math quiz with a grade between
55 and 85, inclusive. Write an
absolute value inequality
representing the grade range for
which Kenny must retake a quiz.
4.
Referring to Q3, write an absolute
value inequality representing the
grade range for which Kenny does not
have to retake a quiz.
5.
Solve for .
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6.
You will be able to find the domain and
range of a relation (or function)
Solve for .
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More Practice With Domain and Range
Worksheet (Online)
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
Use the graph below to answer Q7-Q9.
7.
Identify the domain of the function.
8.
Identify the range of the function.
9.
Does the graph represent a function? Explain your
reasoning.
6
4
2
10
5
5
2
10
4
6
You will be able to tell if a relation is a
function
Algebra II Textbook P. 141: 5 and 6
10. What makes a relation a function?
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
11. Mrs. Sherwin buys paint for $22 per gallon. The function
gives the cost of buying gallons of paint.
a) Write the equation for
b) Determine whether
is continuous or discrete
c)
State a reasonable domain
d) State a reasonable range
12. Steel cable that is 3/8 inch in diameter weighs 0.24 pounds
per foot. The function
gives the weight of feet of
steel cable.
a) Write the equation for
b) Determine whether
is continuous or discrete.
c)
State a reasonable domain
d) State a reasonable range
You will be able to graph equations on
coordinate axes with labels and scales
See the previous objective that was
essential the same as this one.
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
You will be able to use a graphing
calculator to graph a scatter plot and to
find a line of best fit
Algebra II Textbook P. 145: 27
13. Use your equation (from Q27 on P.
145) to predict the speed of a
computer with 200 million
transistors.
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
You will be able to find the slope of a line
tangent to a nonlinear curve
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
15. Find the slope of the line tangent to
the point (2, 0).
at
14. A circle has its center at (-3, 5). Find
the slope of the line tangent to the
circle at (3, -3), assuming that point is
the other endpoint of the radius.
16. If a stone is dropped from a height of 275 feet, its distance
from the ground
can be modeled by the function
, where is time, measured in seconds.
Find the speed of the rock at
seconds. In other words,
find the slope of the tangent line at the point (2,
).
You will be able to represent constraints
by equations or inequalities
Algebra II Textbook P. 172: 34
17. Graph the system of inequalities. In
square units, what is the area of the
region that contains all of the solutions to
this system?
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
You will be able to use a graph to
determine solutions to a system of
inequalities
Algebra II Textbook P. 172-173: 35, 36, 37
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
You will be able to solve a system of
equations by graphing
Algebra II Textbook P. 157: 37; P. 222: 5
18. Write and graph a dependent,
consistent system of linear equation.
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
19. Write and graph an inconsistent
system of linear equation.
20. Write a system of linear equations
with the point (1, 5) as the solution.
21. Write a system of equations
(different from Q20) with the point
(1, 5) as the solution.
You will be able to solve a system of
equations using substitution
Algebra II Textbook P. 166: 60
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
22. If 6a – b2 = 22 and 6b + b2 = 50, then
what is the value of a + b?
23. If
and
, the what is
the value of ?
You will be able to solve a system of
equations by elimination
Algebra II Textbook P. 166: 57; P. 223: 8
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
24. Find the values of x and y that make
the triangle equilateral.
25. Let
. Find the values of
so that
.
a
2x - 4
5x - 4y
x+y
117°
63°
and
b
c
(5x + y)°
26. The price of refrigerator A is $600,
and the price of refrigerator B is
$1200. The cost of electricity needed
to operate the refrigerators is $50 per
year for refrigerator A and $40 per
year for refrigerator B. Which
refrigerator should you buy and why?
(13x y)°
d
You will be able to geometrically
interpret the solution to a linear system
in three variables
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
27. Graph
You will be able to solve a linear system
in three variables using substitution
Algebra II Textbook P. 224: 14
28. For what values of , , and does
the linear system shown have
(−1, 2, −3) as its only solution?
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
You will be able to solve a linear system
by Gaussian elimination
Algebra II Textbook P. 224: 15
29. Solve (if you dare):
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
30. Solve:
31. Solve:
32. In Bisbee, Arizona, an old mining
town, you can buy souvenir nuggets
of gold, silver, and bronze. For $20,
you can buy any of these mixtures of
nuggets: 14 gold, 20 silver, 24 bronze;
20 gold, 15 silver, 19 bronze; or 30
gold, 5 silver, 13 bronze. What is the
monetary value of each souvenir
nugget?
You will be able to define a matrix and its
key parts
Algebra II Textbook P.
33. Give an example of a 5 x 2 matrix.
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
You will be able to add and subtract
matrices and multiply them by a scalar
Algebra II Textbook P. 225: 18-23
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
34. Evaluate:
[
]
([
]
[
])
35. Solve for
[
and .
]
[
36. Solve for
]
[
([
]
and .
]
You will be able to multiply matrices
Algebra II Textbook P. 225: 24-27
[
])
[
]
37. The order of matrix is 7x3, and the
order of matrix is 3x12. What is the
order of
?
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
38. The order of matrix is 1x9, and the
order of matrix is 1x5. What is the
order of , if
?
41. Let , , and be square matrices.
Find a counterexample to disprove
that
39. Find [
] , showing your work.
40. Find the value of
[
][
and .
]
[
]