Name ________________________________
Algebra 2 Exam Review Part 1 – December 2015
All correct algebraic support is required for credit. Show work on a separate piece of paper.
12. Solve the following inequality for w.
1. Solve
│x + 9│ > 15
2. Solve
│x + 5│ = 8
2
8  3w  13  5 Write the solution set for the
3
3. The horizontal bar used in gymnastics events
should by placed 110.25 inches above the
ground, with a tolerance (margin of error) of
0.4 inches. Write an absolute value inequality
for the acceptable heights.
4. A battery operated car, the Tesla Model S,
has a cost that ranges from $69,900 to
$104,500 depending on the battery capacity.
Write an absolute value equation describing
the maximum and minimum cost.
5. The recommended oven setting for cooking a
pizza in a professional brick-lined oven is
between 550 degrees F and 650 degrees F,
inclusive. Write an absolute value inequality
for this temperature range.
6. A car is 500 feet from Krista and driving
toward her at 32 feet per second. At what
times will the car be exactly 50 feet from her?
Write and solve an absolute value equation
for this situation.
7.
What is the
8. Given:
solution of 2│x│ < -4 ?
 5 2 x  1  3  10
Which is the
solution set for x?
9. Given the following absolute value equations
or inequalities:
I
1
7 9
x2  
4
8 16
II
III
 5 x  1  4  16
10.1  x  4.3  10.1
Which of these have no solution?
10. Solve
│x - 4│ = -12
11. Solve
│x + 4│ ≥ -20
function as an inequality, as an interval, in set
notation and on a number line,
13. Write an absolute value inequality to describe
the graph. Write an absolute value inequality
that would take 3 or more steps to solve to
describe the graph.
14. A speech teacher has 24 students in her
class. She has 50 minute periods and has set
3 class periods aside for her students to give
their final speeches. If she has given each of
her students a minimum time requirement of
3 minutes per speech and a maximum based
on her amount of time and number of
students, write an absolute value function
would represent the minimum and maximum
speech times, t.
15. Solve the absolute value equation. Graph the
solution on a number line.
16. What is the sum of the solutions of
?
17. What is the graph of the absolute value equation
given?
18. Graph the function
coordinates of the vertex.
and find the
19. Determine how many units and in which direction
the function
translates the parent
function
.
20. Find the x and y intercepts of the function
.
21. Find the domain and range of the function
.
22. Explain how the equation of the line of symmetry
relates to the equation of an absolute value function
. The equation for the line of
symmetry is ________. The line of symmetry occurs
when x equals _____.
23. Find the equation of the line of symmetry for the
function
30. Graph the function
x-axis.
reflected about the
31. Compare the function, 𝑦 = |− 7𝑥 + 3| + 6, with
the parent function. Determine the vertex, axis of
symmetry and transformations of the parent
function.
.
32. Plot
set of axes.
24. Determine the range for each function.
A f x   2 x  3  5
B
f x   2 x  5  3
C
f x   2 x  5  3
D
f x   2 x  3  5
and
on the same
33. Given an absolute value function,
f x   x  4  3 , give 4 functions that would
share the same maximum point. Use each of the
following representations, graph, table, equation
using function notation and equation using y = .
25. Find the maximum value of
the interval
.
on
34. An absolute value function, f(x), is given below.
Write an absolute value equation would have at least
one equivalent x-intercept as f(x).
26. A student records the height of the water in a pool
each day for seven days. The same amount of water
is removed from the pool each day for four days.
Then the same amount of water is added into the
pool for the last three days. The function
models the height of the water h
(in feet) in the pool after t days. Find the domain and
range for this function and interpret their meaning in
the context of the problem.
27. Describes the translation of
?
to
35. Graph the absolute value equation given
28. What is the equation of the absolute value function
graphed below?
12
y
8
4
–10 –8
–6
–4
–2
2
x
–4
–8
–12
–16
29. Which transformations to the graph of
f x   3 x  2  1 create a function whose vertex is
 2,1 ?
36. A student records the height of a toy submarine for
10 seconds. The function ℎ(𝑡) = −|𝑡 − 5| − 10
models the height h (in feet) of the submarine after t
seconds. What is the difference between the
submarine’s greatest height and least height during
the 10 second period?
37. A company produces widgets that are 2.25 inches
tall and they are manufactured with the following
tolerance: |𝑙 − 2.25| ≤ 0.08. The widgets are
stacked for storage to a target stack length of 96.75
inches with tolerance |ℎ − 96.75| ≤ 0.5. What is the
maximum possible number of pellets in a stack?
38.
39. Which inequality does the graph
represent?
45. Solve the system.
46. Solve the system.
𝑦 = 𝑥 2 − 12𝑥 + 36
{
𝑥 + 𝑦 = 18
40. The shaded area below contains the points that
3
satisfy both of the inequalities 𝑦 ≤ 4 − |𝑥 − 1| and
2
𝑦 ≥ 𝑎. What is the value of a?
47. Write an equation for a quadratic function if
the graph has a vertex at (3, 5) and is
stretched vertically by a factor of 2?
48. Matt has a neighborhood lawn business for
the summer. He has a weekly schedule where
he can mow at most 20 lawns per week and
weed at most 8 lawns per week. Matt charges
$10 for each lawn mowed and $55 for
weeding each yard. If m represents the
number of lawns mowed and w represents the
number of lawns weeded, write a system of
inequalities would represent all the possible
lawns that will earn Matt at least $400 per
week?
49. Which quadrants contain the solutions to this
system of inequalities?
y0
41. Assume that x and y are whole numbers. Use
a table to solve the system of inequalities.
y  5 x  14
4 x  7 y  28
42. Solve the system by substitution
𝑦 = 13 − 3𝑥
{
2𝑥 + 9𝑦 = −8
43. Solve the system by graphing.
6𝑥 + 𝑦 = 31
{
𝑥 + 5𝑦 = −19
50. Find the sum of the x-coordinates of the
solutions to the system of equations.
–x + y = 2
Y = x2 – 4
51. A right triangle is formed below. Write a
system of inequalities that would represent
44. In 1972, city #1 and city #2 had the same
population. The population of city #2
continued to increase steadily, while the rate
of population growth of city #1 (although
initially less than that of city #2) eventually
overtook the growth rate of city #2. The
populations of two cities are modeled by the
following equations:
City #1
City #2
𝑦 = 2𝑥 2 + 15𝑥 + 1080
𝑦 = 25𝑥 + 1080
where x=0 corresponds to the year 1972. In
what year after 1972 did the cities have the
same population?
the triangle.
52. Your club is baking vanilla and chocolate
cakes for a bake sale. They need at most 22
cakes. You cannot have more than 8
chocolate cakes. Write and graph a system of
inequalities to model this system.
Let x = the number of vanilla cakes.
Let y = the number of chocolate cakes.
53. The table on the next page contains solutions
to a system of inequalities. Write two possible
systems.
x
-3
-2
0
1
y
1
4
3
2
54. Solve the system of inequalities by graphing.
57. Two skaters are practicing at the same time
on the same rink. One skater follows the path
𝑥 2 + 𝑦 2 = 45, while the other skater follows
a straight path that begins at ( - 1, - 2) and
ends at (5, 10). Which of the following best
describe this situation?
A The skaters will not cross paths while
practicing because the functions that
represent their paths do not
intersect.
B The skaters will cross paths once at
(3, 6) because the skaters path
begins at ( - 1, - 2).
C The skaters will cross paths twice, at
(-3, - 6) and (3, 6) because the
linear function through at ( - 1, - 2) and
(5, 10) has a domain of all real numbers.
D The skaters will cross paths once at
(5, 45) because the skaters path
ends at (5, 10).
58. Solve the system of inequalities by graphing.
55. Jana graphs the system of constraints to find
the minimum value of an objective function.
Explain Jana’s error.
59. When using Gaussian elimination to solve a
system of three variables, why is it important
to have all 0’s, except for a single 1, in each
row, except for the last element?
56. If Jana correctly calculates the
maximum value given the objective
function 𝑃 = 3𝑥 + 4𝑦. What is the
maximum value she calculated?
A
The 0’s represent the value of the
variables being solved for. The 1’s
represent the values of the other
variables. These rows represent the
coefficients of the variables.
B
Each 1 represents the value of the
variable being solved for. The 0’s are
the values for the other variables.
These rows represent equations in
which every variable except one has
been eliminated.
C
The 0’s represent the coefficient of
the variable being solved for. The 1’s
are the other variables’ coefficient.
These rows represent the coefficients
of the variables.
D
Each 1 represents the coefficient of
the variable being solved for. The 0’s
are the other variables’ coefficient.
These rows represent equations in
which every variable except one has
been eliminated.
4𝑥 + 4𝑦 + 4𝑧 = −4
3𝑥 + 5𝑦 + 4𝑧 = 0
2𝑥 + 2𝑦 + 5𝑧 = 7
{
67. Write a matrix equations that can be used to
represent the system below?
60. Write the system of equations represented by
the augmented matrix below.
0  2  6 4 
0 1
4  5

1 2
7  1
{
61. The augmented matrix for a three variable
0  2  6 4 
system is 0 1
4  5 . Pablo uses

1 2
7  1
Gaussian elimination and determine the
1 0 0 6 
augmented identity matrix is 0 1 0 7  .


0 0 1  3
What is the solution to the system? Write
your answer as an ordered triple.
62. Write an augmented matrix that can be used
to represent the system below?
63. Solve the following system, then give the
value of x.
𝑥 + 4𝑧 = 43
𝑦 + 2𝑧 = 18
−3𝑦 + 𝑧 = 2
{
64. Solve the following system, then give the
value of z.
1𝑥 + 1𝑦 − 1𝑧 = 4
𝑦=6
6𝑥 − 𝑦 + 3𝑧 = −9
{
65. Solve the following system. Give you answer
as an ordered triple.
−2𝑥 + 𝑦 + 3𝑧 = −2
𝑧=5
𝑥 − 2𝑦 = 10
{
66. Solve the following system, then give the
value of y.
68. Maria has some 49¢ stamps, some 32¢
stamps and some 25¢ stamps worth $25.65.
The number of 25¢ stamps is 10 less than the
number of 32¢ stamps. The number of 49¢
stamps is twice the number of the other
stamps combined. If x, y, and z represent the
number of 49¢, 32¢, and 25¢ stamps
respectively, which system of inequalities
could be used to solve for the number of 25¢
stamps that Maria has?
69. A food store makes a 11-lb mixture of
oatmeal (x), crispies (y), and chocolate chips
(z). The cost of oatmeal is $1.00 per pound,
crispies cost $3.00 per pound, and chocolate
chips cost $2.00 per pound. The mixture calls
for twice as much oatmeal as crispies. The
total cost of the mixture is $19.00. Write a
system of equations that could be used to
find out how much of each ingredient did the
store use?
70. A food store makes a 7-lb mixture of peanuts,
almonds, and raisins. The cost of peanuts is
$1.00 per pound, almonds cost $3.00 per
pound, and raisins cost $1.00 per pound. The
mixture calls for twice as many peanuts as
almonds. The total cost of the mixture is
$9.00. How much of each ingredient did the
store use?
71. The coach purchased a combined total of 58
small, large, and extra-large shirts for $1411.
The sum of twice the number of small and the
number of extra-large is five times the
number of large shirts. The cost of each is
shown below:



Small shirts cost $18.00 each
Large shirts cost $22.50 each
Extra-large shirts cost $25.00 each
Based on this information, give two possible
reasonable number of large shirts that he
purchased?
72. The following matrix equation can be used to
represent a system of equations. What are
three different possible first steps if you were
solving the system using Gaussian
elimination?
drinks, d, and quarts of ice cream, q, she
bought.
 8 2 4.5  p  105
 8  1 0   d    0 

    
 1 0 2  q   0 
If Nicole bought enough drinks for each
person at the party to have exactly two
drinks, how many people were at the party?
73. Nicole spent $105 to buy a combination of
pizza, drinks and ice cream for a party. Each
pizza cost $8, each drink cost $2, and each
quart of ice cream cost $4.50. For every
pizza she bought, she bought 8 drinks. She
bought 1 quart of ice cream for every 2
pizzas. The matrix equation below can be
used to determine how many pizzas, p,
75. Megan solved the following absolute value.
74. Write the system
as an
augmented matrix. Then identify the
coefficient matrix and the constant matrix.
2 x  1  x  3x  4 In which step did Megan first make a
mistake?
Step 1
2 x  1  4x  4
Step 2
x  1  2x  2
Step 3
x 1  2x  2 or x 1  2x  2
1  x  2 or 3x  1  2
3  x or 3x  1
Step 4
Step 5
Step 6
Step 7
x  3 or x 
1
3
 1
3, 
 3
76. The steps shown below, use Gaussian elimination to solve the system: Finish the problem to solve for
y.
2 0  3  14
2 6 7 24 


0 2 3 11 
Procedure
Math
Result
-2 0 3 14
Multiply row 1
2 0  3  14
by -1 and add
0 6 10 38 
 2 6 7 24
to


0 6 10 38
0 2 3 11 
row 2; replace
row 2
Multiply row 3
by -3 and add
to row 2;
replace row 3
Multiply row 3
by 3 and add to
row 1; take half
and replace
row 1
0  6  9  33
0
6 10 38
0
0
0
0
2
2
1
3
5
15
0  3  14
0
0
1
1
2
2 0  3  14
0 3 5 19 


0 0 1 5 
1 0 0 0.5
0 3 5 19 


0 0 1 5 