This video models solving linear equations of the form x + a = b using algebra tiles. It shows three examples of equations solved concretely with tiles: x + 3 = 7, r + 5 = -2, and 3x - 4 = 5. The tiles represent integers and unknowns, with an equals sign separating the left and right sides. Solving involves using the zero property to isolate the unknown, requiring adding the same amount to both sides to maintain balance.
College Algebra MATH 107 Spring, 2020Page 1 of 11 MA.docxmary772
College Algebra MATH 107 Spring, 2020
Page 1 of 11
MATH 107 FINAL EXAMINATION
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator. You must complete the exam individually.
Neither collaboration nor consultation with others is allowed.
Record your answers and work on the separate answer sheet provided.
There are 30 problems.
Problems #1–12 are Multiple Choice.
Problems #13–21 are Short Answer. (Work not required to be shown)
Problems #22–30 are Short Answer with work required to be shown.
MULTIPLE CHOICE
1. Determine the domain and range of the piecewise function. 1. ______
A. Domain [– 4, 2]; Range [– 2, 4]
B. Domain [– 2, 4]; Range [– 2, 1]
C. Domain [– 2, 4]; Range [– 4 , 2]
D. Domain [0, 2]; Range [– 2, 0]
2. Solve: 3 10x x+ = − 2. ______
A. No solution
B. –2, 5
C. 5
D. –2
-2 2 4 -4
-2
-4
2
4
College Algebra MATH 107 Spring, 2020
Page 2 of 11
3. Determine the interval(s) on which the function is decreasing. 3. ______
A. (–1, 3)
B. (–2, 4)
C. (–3.6, 0) and (6.7, )
D. (–, –2) and (4, )
4. Determine whether the graph of 2y x= + is symmetric with respect to the origin,
the x-axis, or the y-axis. 4. ______
A. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and
not symmetric with respect to the origin
B. symmetric with respect to the x-axis only
C. symmetric with respect to the y-axis only
D. symmetric with respect to the origin only
5. Solve, and express the answer in interval notation: | 5 – 6x | 13. 5. ______
A. (–, 3] [−4/3, )
B. (–, −4/3] [3, )
C. [4/3, )
D. [–4/3, 3]
College Algebra MATH 107 Spring, 2020
Page 3 of 11
6. Which of the following represents the graph of 8x − 3y = 24 ? 6. ______
A. B.
C. D.
College Algebra MATH 107 Spring, 2020
Page 4 of 11
7. Write a slope-intercept equation for a line parallel to the line x + 7y = 9 which passes through
the point (28, –3). 7. ______
A. 25y x=− +
B.
1
1
7
y x= − +
C.
1
3
7
y x= − −
D.
1
7
7
y x= −
8. Which of the following best describes the graph? 8. ______
A. It is the graph of a function but not one-to-one.
B. It is the graph of a function and it is one-to-one.
C. It is not the graph of a function.
D. It is the graph of an absolute value relation.
.
College Algebra MATH 107 Spring, 2020
Page 5 of 11
9. Write as an equivalent expression: log (x – 3) – 8 log y + log 1 9. ______
A.
log( 3)
log(8 )
x
y
−
B.
2
log
8
x
y
−
C.
8
3
log
x
y
−
D. ( )log 2 8x y− −
10. Which of the functions corresponds to the graph? 10. ______
A. ( ) 2 xf x e−=
B. ( ) 2 xf x e−= +
C. ( ) 2 xf x e= −
D. ( ) 2xf x e−=
College Algebra MATH 107 Spring, 2020
Page 6 of 11
11. Suppose that for a function f, the equation f (x) = 0 has no real-number solution.
Which of the following statements MUST be tr.
3D Representation
Read chapter 10 in Computer Science: note especially section 10.2. Create a 2-page document which will summarize the three steps involved in producing an image using 3D graphics. After you describe each step, give a good example of each. The examples should be different from the one given in the text.
Find a recent news article (not a tutorial or description) that relates to 3D graphics. Explain how any aspect of the news article relates to one of the steps you summarized above.
The document should be clear and concise, free from syntax and semantic errors.
Please submit the document on time please.
College Algebra MATH 107 Spring, 2017, V.1.3
Page 1 of 11
MATH 107 FINAL EXAMINATION
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator. You must complete the exam individually.
Neither collaboration nor consultation with others is allowed.
Record your answers and work on the separate answer sheet provided.
There are 30 problems.
Problems #1–12 are Multiple Choice.
Problems #13–21 are Short Answer. (Work not required to be shown)
Problems #22–30 are Short Answer with work required to be shown.
MULTIPLE CHOICE
1. Determine the domain and range of the piecewise function. 1. ______
A. Domain [– 3, 3]; Range [– 1, 3]
B. Domain [– 3, 1]; Range [– 3, 3]
C. Domain [– 1, 0.5]; Range [–1, 0]
D. Domain (–∞, 3]; Range [–1, ∞)
2. Solve: 10 3x x− = − 2. ______
A. –5, 2
B. 5/2
C. –5
D. No solution
2 4 -4
-2
-4
2
4
-2
College Algebra MATH 107 Spring, 2017, V.1.3
Page 2 of 11
3. Determine the interval(s) on which the function is increasing. 3. ______
A. (–∞, –1)
B. (– 2, 2)
C. (–∞, – 3) and (1, ∞)
D. (– 4.5, – 1) and (2.5, ∞)
4. Determine whether the graph of ( )
2
4xy −= is symmetric with respect to the origin,
the x-axis, or the y-axis. 4. ______
A. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and
not symmetric with respect to the origin
B. symmetric with respect to the x-axis only
C. symmetric with respect to the y-axis only
D. symmetric with respect to the origin only
5. Solve, and express the answer in interval notation: | 6 – 5x | ≤ 14. 5. ______
A. (–∞, −8/5] ∪ [4, ∞)
B. (–∞, –8/5]
C. [4, ∞)
D. [–8/5, 4]
College Algebra MATH 107 Spring, 2017, V.1.3
Page 3 of 11
6. Which of the following represents the graph of 7x + 4y = 28 ? 6. ______
A. B.
C. D.
College Algebra MATH 107 Spring, 2017, V.1.3
Page 4 of 11
7. Write a slope-intercept equation for a line parallel to the line x – 3y = 5 which passes through
the point (6, –8). 7. ______
A.
1
8
3
y x= −
B.
1
10
3
y x= −
C.
1
6
3
y x= − −
...
1. Grade 7 Video Outcomes
P7.4 Demonstrate an understanding of linear equations of the form x a b (where a
and b are integers) by modeling problems as a linear equation and solving the problems
concretely, pictorially, and symbolically.
Synopsis
Clip P7.4 models the three questions listed below with Algebra Tiles that are red on one
side and a different color on the other side. The red sided tiles are treated as positive and
the other sided color tiles are negative. The small square tiles represent the positive and
negative integers and the rectangular tiles represent the unknowns. Each equation is
modeled with the tiles and an equals sign separates question and answer. Using algebra
tiles in this way helps students understand that when you use the zero principle to isolate
the unknown you must also add that integer to the answer side of the equation to maintain
a balanced equation. Once the unknown is isolated it is simply a matter of adding or
subtracting integers on the opposite side of the equation.
Problems
x+3=7
r + 5 = -2
3x – 4 = 5
Concrete Manipulatives: Algebra Tiles, equal sign between left and right side of the
equation.
Virtual Manipulatives
Algebra Tiles
http://nlvm.usu.edu/en/nav/frames_asid_189_g_1_t_2.html?open=activities&from=topic
_t_2.html
1