1. Solve
│x + 9│ > 15
2. Solve
│x + 5│ = 8
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. 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.
5. 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.
6. What is the solution of 2│x│ < -4 ?
7. Given:  5 2 x  1  3  10
Which is the correct solution set for x?
8. Solve the following inequality for w.
2
8  3w  13  5
3
Which of the following represents the solution set to the inequality?
9. Solve the absolute value equation. Graph the solution.
10. What is the sum of the solutions of
?
11. Determine how many units and in which direction the function
.
12. Find the x and y intercepts of the function
translates the parent function
.
13. Find the domain and range in interval notation of the function
.
14. Find the equation of the line of symmetry for the function
15. Find the maximum value of
on the interval
.
.
16. 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.
17. Which of the following describes the translation of
to
?
18. 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
3
19. The shaded area below contains the points that satisfy both of the inequalities 𝑦 ≤ 4 − |𝑥 − 1|
2
and 𝑦 ≥ 𝑎. What is the value of a?
20. Assume that x and y are whole numbers. Use a table to solve the system of inequalities.
21. 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?
22. Solve the system.
𝑦 = 𝑥 2 − 12𝑥 + 36
{
𝑥 + 𝑦 = 18
23. Which quadrants contain the solutions to this system of inequalities?
y0
y  5 x  14
4 x  7 y  28
24. Find the sum of the x-coordinates of the solutions to the system of equations.
–x + y = 2
Y = x2 – 4
25. A right triangle is formed below.
Which set of inequalities would represent the triangle?
26. 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.
27. The table below contains solutions to which system of inequalities?(2A.3G)
x
-3
-2
0
1
y
1
4
3
2
A 3x  y  4
x  3 y  18
y  1
B 2x  y  3
x  2y  8
y 1
C 4x  y  6
x  4 y  20
y 1
28. Solve the system of inequalities by graphing.
29. Jana graphs the system of constraints to find the minimum value of an objective function.
Explain Jana’s error.
30. Solve the system of inequalities by graphing.
31.
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?
32.
Which represents matrices can be used to represent the system below?
33.
𝑥 + 4𝑧 = 43
𝑦
+ 2𝑧 = 18
Solve the following system, then give the value of x.
−3𝑦 + 𝑧 = 2
{
34.
Solve the following system, then give the value of y.
{
4𝑥 + 4𝑦 + 4𝑧 = −4
3𝑥 + 5𝑦 + 4𝑧 = 0
2𝑥 + 2𝑦 + 5𝑧 = 7
35. 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?
36. The following matrix equation can be used to represent a system of equations. Which of the following
would not be a correct first step if you were solving the system using Gaussian elimination?
A Multiply row 3 by 
B
1
8
Switch row 1 and row 2
1
6
D Add row 1 and row 3 to eliminate the
zeros
C
Multiply row 3 by
37.
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, 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?
38. Write the system
as an augmented matrix. Then identify the coefficient
matrix and the constant matrix.
a.
c.
coefficient matrix:
variable matrix:
variable matrix:
coefficient matrix:
constant matrix:
constant matrix:
b.
d.
variable matrix:
coefficient matrix:
constant matrix:
constant matrix:
coefficient matrix:
variable matrix:
39.
The steps shown below, use Gaussian elimination to solve the system:
2 0  3  14
2 6 7 24 


0 2 3 11 
Procedure
Multiply row 1
by -1 and add to
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
Math
Result
-2 0 3 14
2 0  3  14
0 6 10 38 


0 2 3 11 
 2 6 7 24
0 6 10 38
0  6  9  33
0
6
10
38
0
0
1
5
0
0
2
2
3
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 
Finish the problem to solve for y.
40.
Landon was asked to solve the following system for y using substitution. His answer does
not match the teacher’s answer.
System of Equations:
Steps
Step 1
Eq.1 : x  y  3z  8
Eq. 2 :
2 y  z  15
Eq. 3 :
3 x  2 z  7
Procedure
Solve Eq.1 for x
Substitute the result from step 1
Step 2
into Eq.3
Step 3
Distribute the 3
Step 4
Simplify Eq. 3
Step 5
Multiply Eq. 2 by 2
Step 6
Add Step 4 and 5
Answer
Solve for y
In what step did Landon first make a mistake?
Math
x  y  3z  8
3 y  3z  8  2z  7
3 y  9 z  24  2 z  7
 6 y  2 z  17
4 y  2 z  30
 2 y  47
y  23.5
41. What is the leading coefficient of the quadratic that contains the points 1,4,  1,2, 3,22 ?
42. What are the vertex and the axis of symmetry of the equation?
43. What is the vertex form of the equation?
44. Suppose a parabola has an axis of symmetry at
, a maximum height of 4 and also passes
through the point (3, 0). Write the equation of the parabola in vertex form.
45. Identify the maximum or minimum value and the domain and range of the graph of the function
.
46. Which representation correctly states the range for the function, f x   2 x 2  12 x  9 ?
47. Which of the following quadratic functions shares a vertex with f x   3x 2  12 x  1 ?
48. What is an equation of a parabola with the given vertex and focus? vertex:
; focus:
49. Graph the function. How is each graph a translation of
?
50. A diver jumped off of a platform and dove into the pool. The table below shows the relationship
between the elapsed time and the height of the diver above the pool.
Time after the
Height of the diver
diver jumped
above the pool
(seconds)
(feet)
0.25
26
0.5
25
0.75
22
1
17
1.25
10
If the height of the diver is a quadratic function of time, which of equations represents the data in
the table?
51. Find the solutions of the quadratic equation.
52. What is the number of real solutions?
53. Simplify the expression.
54. Simplify the expression.
55. Solve the inequality
56. Explain how you can use the table to help solve the inequality
x
y
–3
12
–2
0
–1
–6
0
–6
1
0
. Then solve.
2
12
a. I can use the table to identify the x-values
for which the corresponding y-values are
less than 0. The solution is
.
b. I can use the table to identify the x-values
for which the corresponding y-values are
greater than 0. The solution is
and
.
c. I can use the table to identify the x-values
for which the corresponding y-values are
less than 0. The solution is
.
d. I can use the table to identify the x-values
for which the corresponding y-values are
greater than 0. The solution is
.
57. Which expression is equivalent to  5  3i    3i   2  i  ?
58. What is the vertex form of the equation?
y = x2 – 6x + 19
59. Which representation correctly states the range for the function, f x   3x 2  12 x  17 ?
60. A diver jumped off of a platform and dove into the pool. The table below shows the relationship
between the elapsed time and the height of the diver above the pool.
Time after the
diver jumped
(seconds)
0.25
0.5
1
1.25
Height of the diver
above the pool
(feet)
16.5
16
9
2.5
If the height of the diver is a quadratic function of time, which of the following equations
represents the data in the table
61. Describe the domain of the function in words
explain the domain.
62. How does the graph of
. Use properties of square roots to
compare to its parent function?
63. Graph the relation and its inverse. Use open circles to graph the points of the inverse.
x
0
4
9
10
y
3
2
7
–1
64. How can you find the inverse of a function algebraically?
65. Find the equation, domain, and range of the inverse for the function
the inverse.
. Then graph
66. Are
with domain
and
inverse functions? Explain.
67. What is the solution of the equation?
68. What is the solution of
69. For
?
what is the domain and range?