Download Practice Exam #2 #5

Practice Exam #2 #5
Pre-Algebra and Introductory Algebra / MAT 99 Fall 1, 2016 ( Master Templates)
Student Name/ID:
1. Translate the sentence into an equation.
Eight times the difference of a number and
Use the variable
9 is equal to 7.
y for the unknown number.
2. Translate this phrase into an algebraic expression.
Seven less than the product of 9 and Malik's savings
Use the variable
m to represent Malik's savings.
3. Solve for u.
−
3
3
5
u+ =−
5
2
6
Simplify your answer as much as possible.
4. Solve for y.
2y − 10 = 18
Simplify your answer as much as possible.
5. Solve for
w+
w.
5 1
=
8 2
Simplify your answer as much as possible.
Practice Exam #2 #5
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c = −2
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6. Evaluate the expression when
c = −2.
c 2 + 5c + 7
7. Evaluate the expression when
a = 7 and c = −4 .
−7a + c
8. Solve the inequality for x.
−8 ≤ −4x + 4
Simplify your answer as much as possible.
9. Solve the inequality for
w.
11 − 6w ≤ 5 − 8w
Simplify your answer as much as possible.
10. Solve for y.
9y − 30 = 5y − 6
Simplify your answer as much as possible.
Practice Exam #2 #5
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11. Fill in the table using this function rule.
y = 3x − 3
x
y
−2
−1
0
1
12. Graph the line.
y = −3x − 1
y
8
6
4
2
x
-8
-6
-4
-2
2
4
6
8
-2
-4
-6
-8
Practice Exam #2 #5
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13. Graph the line.
y=−
4
x−1
3
10
y
8
6
4
2
-10
-8
-6
-4
-2
x
2
-2
4
6
8
10
-4
-6
-8
-10
14. Graph the line.
3x + y = 6
y
8
6
4
2
x
-8
-6
-4
-2
2
4
6
8
-2
-4
-6
-8
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15. The equation of a line is given below.
3x + y = −1
Find the slope and the y-intercept.
Then use them to graph the line.
slope: _______________
y-intercept: _______________
10
y
8
6
4
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
-8
-10
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16. The equation of a line is given below.
−2x + 5y = 5
Find the slope and the y-intercept.
Then use them to graph the line.
slope: _______________
y-intercept: _______________
10
y
8
6
4
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
-8
-10
17. Write an equation in slope-intercept form for the line with y-intercept
18. A line passes through the point
−10, 6
and has a slope of
−
−2 and slope −3.
1
.
2
Write an equation in slope-intercept form for this line.
19. Find an equation for the line that passes through the points
Practice Exam #2 #5
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2, −6
and
−4, −4
−8, 6
.
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20. Write equations for the horizontal and vertical lines passing through the point
−8, 6
.
horizontal line:
vertical line:
21. Use substitution to solve the system.
2x − 5y = −16
3x − 2 = y
x=
y=
22. Solve the following system of equations.
x + 7y = 17
−x − 9y = −21
23. Solve the following system of equations.
9x + 4y = −20
4x + 7y = 12
24. Simplify.
u
2
2v
4
3
Write your answer without parentheses.
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25. Simplify.
81v
9v
6
4
26. Simplify.
ab
6
7 5
a b
27. Rewrite the following without an exponent.
5−2
28. Rewrite the following without an exponent.
−3
2
3
29. Simplify.
a
−6 −1 −7
b
c
2 4 8
a b c
Write your answer using only positive exponents.
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30. Simplify.
u
−2
·u
−3
Write your answer with a positive exponent only.
31. Multiply.
6a + b a − 5b
Simplify your answer.
32. Rewrite without parentheses and simplify.
6x + y
2
33. Divide.
8u 5 + 24u 4 + 21u 3
4u 3
Simplify your answer as much as possible.
34. Divide.
7 7
2 7
7 2
−9v z + 14v z + 21v z
4 3
÷ −3v z
Simplify your answer as much as possible.
4
35. Find the greatest common factor of 12x and
Practice Exam #2 #5
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16x
3
.
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36. Find the greatest common factor of these two expressions.
18x 8 y 2
and
3x y 7 u 6
37. Factor by grouping.
3
2
5w − 2w + 30w − 12
38. Factor.
2
y + 3y − 18
39. Factor completely.
2
3u − 51u + 90
40. Factor by grouping.
30x + 5w x + 18 + 3w
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41. Factor by grouping (sometimes called the ac-method).
6x 2 + 11x + 5
First, choose a form with appropriate signs.
Then, fill in the blanks with numbers to be used for grouping.
Finally, show the factorization.
Form:
6x 2 +
___
x +
___
x + 5
6x
2
+
___
x −
___
x + 5
6x
2
−
___
x +
___
x + 5
6x
2
−
___
x −
___
x + 5
Factorization:
_________________________
Practice Exam #2 #5
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Practice Exam #2 #5 Answers for class MAT 99 Fall 1, 2016
1. 8
y−9 =7
2. 9m − 7
3. u =
35
.
9
4. y = 14
5. w = −
1
8
6. 1
7.
−53
8. 3 ≥ x
9. w ≤ −3
10. y = 6
11.
x
y
−2
−9
0
−3
−1
1
Practice Exam #2 #5
−6
0
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12.
y
8
6
4
2
x
-8
-6
-4
-2
(0, -1)2
4
6
8
-2
(1, -4)
-4
-6
(2, -7)
-8
13.
10
y
8
6
4
2
x
-10
-8
-6
-4
-2
(0, -1) 2
4
6
8
10
-2
-4
(3, -5)
-6
-8
(6, -9)
-10
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14.
y
8
0, 6
6
4
1, 3
2
2, 0
-8
-6
-4
-2
2
x
4
6
8
-2
-4
-6
-8
−3
y-intercept: −1
15. slope:
10
y
8
6
4
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
-8
-10
2
Practice Exam #2 #5
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2
5
y-intercept: 1
16. slope:
10
y
8
6
4
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
-8
-10
17. y = −3x − 2
18. y = −
1
x+1
2
19. y = −
1
16
x−
3
3
20. horizontal line: y = 6
vertical line: x = −8
21.
x=2
y=4
22.
x =3
y =2
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23.
x = −4
y=4
24.
u8
16v
25. 9v
26.
2
b
a6
27.
1
25
28.
27
8
29.
30.
12
1
8 5 15
a b c
1
u
5
31. 6a
2
32. 36x
− 29a b − 5b 2
2
+ 12x y + y 2
33. 2u
2
34. 3v
3 4
35. 4x
3
+ 6u +
z −
36. 3x y
21
4
14z
4
3v 2
7v
−
z
3
2
Practice Exam #2 #5
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37.
5w − 2 w 2 + 6
38.
y−3 y+6
39. 3
40.
u − 2 u − 15
6 + w 5x + 3
41.
Form:
6x 2 +
5x +
6x + 5
6x 2 +
___
x −
___
x + 5
6x
2
−
___
x +
___
x + 5
6x
2
−
___
x −
___
x + 5
Factorization:
6x + 5 x + 1
Practice Exam #2 #5
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