Algebra II Midterm Review
𝑥≥5
1. Solve the system of inequalities by graphing: {
𝑥+𝑦 ≤3
A.
B.
C.
D.
𝑥 + 3𝑦 ≤ 15
2. Solve the system of inequalities by graphing: {
4𝑥 + 𝑦 ≤ 16
A.
B.
C.
D.
3. Mrs. Fernandez’s Cookie Factory makes different –sized packages of cookies that
contain a combination of chocolate chip and peanut butter cookies. Mrs. Fernandez
places at least three of each type of cookie in each of the combination packages. The
largest package, the “Baker’s Dozen”, contains thirteen cookies. It costs Mrs.
Fernandez $0.19 to make a chocolate chip cookie and $0.13 to make a peanut butter
cookie. She sells them for $0.44 and $0.39 respectively. Let c represent the number
of chocolate chip cookies and let p represent the number of peanut butter cookies.
What is the equation that represents the objective quantity function to find the
profit?
A. 𝑃 = 25𝑐 + 26𝑝
C.
𝑃 = 19𝑐 + 13𝑝
B. 𝑃 = 0.44𝑐 + 0.39𝑝
D.
𝑃 = 19𝑐 + 39𝑝
4. Dolores arrives at school late because her car broke down, and therefore, has
only 45 minutes to complete a history exam. The exam has 2 open-ended questions
and 30 multiple-choice questions. Each correct open-ended question is worth 20
points, and each multiple-choice question is worth 2 points. She knows that it
usually takes her 15 minutes to answer an open-ended question and only one
minute to answer a multiple-choice question. Assume that for each question
Dolores answers, she receives full credit. Let x represent the number of open-ended
questions answered, and let y represent the number of multiple-choice questions
answered. All of the following represent inequalities for this problem EXCEPT:
A. 0 ≤ 𝑥 ≤ 2
C.
0 ≤ 𝑦 ≤ 30
B. 15𝑥 + 1𝑦 ≤ 45
D.
20𝑥 + 2𝑦 ≤ 45
5. Is (x + 1) a factor of (x3 + 4x2 + 2x - 1)?
A) no because there is no remainder
B) no because there is a remainder
C) yes because 1 is a root
D) yes because there is no remainder
6. F(x) = x + 2 and G(x) = x4 ; find F(G(2))
7. g(x) = 4x and f(x) = 4x – 1 find 6g(x) – f(x)
8. f(x) = 15(x2 + 8x + 15) and g(x) = 5(x + 3) ; find
f ( x)
g ( x)
Solve
9. √2𝑥 + 4= 6
4x  3  2  5
10.
11.
3
13x  1  4  0
Simplify
12.
4
m18 n8
13.
3
27 y15
14.
3 x 4 . 24 x 3
15.
5a 3 . 20a
Factor Completely.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
6x2 – 20x
x2 + 6x + 8
x2 – 4x + 3
3x2 – 3x – 36
4x2 – 28x + 49
2x2 + 9x + 7
2x2 – 5x – 3
9x2 – 6x + 1
If the area of a square is 25x2 – 81, what is the length of one side?
If the area of a rectangle is x2 – 15x + 56, what are its dimensions?
Simplify Completely.
26.
27.
28.
29.
30.
31.
7i + (-5 – 3i)
2i (9 – i)
2i + (-4 – 2i)
8 – ( -7 – 5i) + (-10 + 2i)
(5 + 9i)(-4 + i)
6 – 2i
3i
32. -2 + 5i
4 + 3i
33. 6 + i
-5 – 2i
The trajectory of a water balloon launched can be modeled by the quadratic function
and graph provided.
34a. From what height is the water balloon launched? Provide answer to the
nearest foot.
34b. How could you estimate starting height from the graph?
35a. How long does it take for the water balloon to reach its maximum height?
Show calculation. Round to the nearest hundredth of a second.
35b. How could you estimate the time to reach max height from the graph?
36a. What is the maximum height that the water balloon will reach? Show
calculation. Round to the nearest foot.
36b. How could you estimate the maximum height from the graph?
37a. What is the height of the water balloon after 5 seconds? Show your calculation
37b. How could you estimate the height after 5 seconds from the graph?
38a. Calculate how long after the launch it will take for the water balloon hit the
ground. Show calculation
38b. Support your answer with an approximation using the graph.