Final Exam Review Part 1 #1
Intermediate Algebra / MAT 135 Spring 2017 Master ( Master Templates)
Student Name/ID:
1. Solve the compound inequality.
2x + 5 ≥ 3 and 4x + 2 ≤ 18
Graph the solution on the number line.
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
2. Solve the compound inequality.
4u − 3 > −7
or
2u + 1 ≤ 7
Write the solution in interval notation.
If there is no solution, enter ∅.
3. Solve for x.
−2 3x + 6 = −24
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4. Graph the solution to the inequality on the number line.
2w − 8 ≥ 12
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
1 2
3 4
5 6
7 8
9 10 11
5. Solve.
6 x + 9 + 4 > 34
6. Find an equation for the line that passes through the points
−2, −6
and
7. Write equations for the horizontal and vertical lines passing through the point
4, −4
.
−2, −8
.
horizontal line:
vertical line:
8. Consider the line
−6x − 7y = 8.
(a) Find the equation of the line that is perpendicular to this line and passes through the point
(b) Find the equation of the line that is parallel to this line and passes through the point
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H
−4, 5
−4, 5
.
.
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9. Suppose that the relation
H is defined as follows.
H = 6, 0 , 2, q , 7, q
Give the domain and range of H.
Write your answers using set notation.
10. Find the domain of the function.
h x = 42 − 7x
Write your answer using interval notation.
11. Suppose that the credit remaining on a phone card (in dollars) is a linear function of the total calling time (in
minutes). When graphed, the function gives a line with a slope of
There is $27.73 in credit remaining on the card after
minutes of calls?
−0.13. See the figure below.
21 minutes of calls. How much credit was there after 9
Remaining
credit
in dollars
27.73
21
Calling time
in minutes
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12. Use substitution to solve the system.
5x + 3y = −17
3y − 7 = x
x=
y=
13. The Royal Fruit Company produces two types of fruit drinks. The first type is 45% pure fruit juice, and the
second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 90% pure
fruit juice. How many pints of each of the two existing types of drink must be used to make
that is 90% pure fruit juice?
First fruit drink:
160 pints of a mixture
_____ pints
Second fruit drink: _____ pints
14. Solve the following system of equations.
−4x + 5y = 25
−2x − 3y = 7
3 pounds of almonds and 2 pounds of jelly beans,
the total cost is $14. For 5 pounds of almonds and 6 pounds of jelly beans, the total cost is $28. Find the cost for
15. A store is having a sale on almonds and jelly beans. For
each pound of almonds and each pound of jelly beans.
16. Factor.
1 + v3
u
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17. Solve for u.
2
9u = 30u − 25
18. Solve for
v.
2v 2 + v − 6 = v + 2
2
If there is more than one solution, separate them with commas.
19. The area of a rectangle is 21
dimensions of the rectangle.
2
yd , and the length of the rectangle is 1 yd less than twice the width. Find the
20. For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
12
7
x
21. Find all excluded values for the expression.
That is, find all values of t for which the expression is undefined.
2t + 3
2t + 8
If there is more than one value, separate them with commas.
g
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g is defined below.
22. The function
g x =
x+7
x 2 − 25
Find all values of x that are NOT in the domain of g.
If there is more than one value, separate them with commas.
23. Multiply.
3x + 15 7x − 2
·
49x 2 − 4 2x − 7
Simplify your answer as much as possible.
24. Multiply.
7x − 28 2x
·
6
x−4
Simplify your answer as much as possible.
25. Divide.
2
x−1
x + 2x − 3
÷
3x − 9 x 2 − 2x − 3
Simplify your answer as much as possible.
26. Divide.
4x − 24y
2
x − 4y
2
÷
2
x − 6y
x − 8x y − 20y
2
Simplify your answer as much as possible.
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27. Subtract.
7
5
−
x x+2
Simplify your answer as much as possible.
28. Subtract.
4x
5x
−
x+3 x−2
Simplify your answer as much as possible.
29. Subtract.
6
x
−
4 − 7x 7x − 4
Simplify your answer as much as possible.
30. Add.
2
1
3x + 13x + 12
+
2
2
3x − 2x − 8
Simplify your answer as much as possible.
31. Simplify.
2v
v+8
2
4v
2
v + 16v + 64
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32. Simplify.
9
+3
x−9
24
+8
x−9
33. Simplify.
7
x−2
7
1−
x+2
1+
34. Simplify.
1 2
−
v u
7
1
− 2
v u
35. Simplify.
2
−1
2
−1
y −x
x +y
Write your answer using only positive exponents.
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36. Divide.
3
2
2
4x − 10x − 10x + 2 ÷ 2x + x
Your answer should give the quotient and the remainder.
Quotient:
Remainder:
37. Divide.
2x 2 + x − 23 ÷ x + 4
Your answer should give the quotient and the remainder.
Quotient:
Remainder:
4
3
38. Use synthetic division to find the quotient and remainder when 4x + 12x − x − 3 is divided by x + 3.
Specifically, complete the synthetic division table below, and write your answer in the following form:
Quotient +
Remainder
−3 4
x+3
.
12
0
−1
−3
4x 4 + 12x 3 − x − 3
=
x+3
x
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+
x+3
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39. Solve for x.
18
10
=
x+4
x
40. Solve for y.
−
7
3
+1=
2y + 12
y+6
41. Solve for u.
1
3
6
−
=
u + 4 u − 2 u 2 + 2u − 8
42. Solve for x.
−2
x
=
x
3x − 8
43. Solve for y.
y+1
y−1
−1=
y+2
y−6
v
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44. Solve for v.
w 3−v
=X
z
45. Solve for p.
8
9
7
= +
p m n
46. One hose can fill a small swimming pool in
70 minutes. A larger hose can fill the pool in 55 minutes. How long
will it take the two hoses to fill the pool working together?
Do not do any rounding.
50 miles while going with the current in the same amount of time as it took to row 25
miles going against the current. The rate of the current was 2 miles per hour. Find the rate of the rowing team in
47. A rowing team rowed
still water.
48. Simplify.
200
49. Simplify.
7 5
16s t
Assume that all variables represent positive real numbers.
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50. Write the following in simplified radical form.
4
162
51. Write the following as an exponential expression.
7
4
z
52. Evaluate.
256
1
4
=
____
125 3 =
____
1
53. Simplify. Write your answers without exponents.
3
1
9
32
2
−
=
3
5
=
54. Simplify as much as possible.
v
20w 3 + 5w
45w v 2
Assume that all variables represent positive real numbers.
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55. Simplify.
2
4
162 −
4
512
56. Simplify.
48 × 2 18
57. Simplify.
20x 7 u
5x 7 u
Assume that all variables represent positive real numbers.
58. Simplify.
75 − 20
25
59. Rationalize the denominator and simplify.
−9
4−2 x
Assume that the variable represents a positive real number.
60. Rationalize the denominator and simplify.
2
3 5 −6
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Final Exam Review Part 1 #1 Answers for class MAT 135 Spring
2017 Master
1.
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
2.
− ∞, ∞
3. x = 2,
−6
4.
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
5. x < −14 or
6. y =
x > −4
1
16
x−
3
3
7. horizontal line: y = −8
vertical line: x = −2
8.
Equation of perpendicular line: y =
Equation of parallel line:
7
29
x+
6
3
y=−
6
11
x+
7
7
= 6, 2, 7
= 0, q
9. domain
range
− ∞, 6
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10.
− ∞, 6
11. $29.29
12.
x = −4
y=1
13.
First fruit drink:
16 pints
Second fruit drink:
144 pints
14.
x = −5
y=1
15. Cost for each pound of almonds: $3.50
Cost for each pound of jelly beans: $1.75
16.
1 + v 1 − v + v2
17.
5
3
18. v = 5,
−2
19.
Length: 6
yd
Width: 3.5
yd
20. 9.75
21. t = −4
22. x = 5,
23.
−5
3 x+5
7x + 2 2x − 7
7x
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24.
7x
3
25.
x+1
3 x+3
26.
4 x − 10y
x − 2y
27.
2x + 14
x x+2
28.
29.
30.
−x x + 23
x+3 x−2
−6 − x
7x − 4
1
x−2 x+3
31.
v+8
2v
32.
3
8
33.
34.
x+2 x+5
x−2 x−5
u u − 2v
7u 2 − v
2
35.
y xy −1
x x2y + 1
36.
Quotient:
2x − 6
Remainder:
−4x + 2
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37.
2x − 7
Quotient:
Remainder: 5
38.
−3 4
12
−12
0
4
4
0
0
0
−1
0
−1
−3
3
0
3
4x + 12x − x − 3
0
3
= 4x − 1 +
.
x+3
x+3
39. x = 5
40. y =
1
2
41. u = −10
42. x = −8,
2
43. y = 2,
−4
44. v = −
Xz
+3
w
8m n
9n + 7m
45. p =
46. 30.8 minutes
47. Rate of the team in still water: 6 miles/hour
48. 10
2
49. 4s
3 2
50. 3
4
t
st
2
4
51. z
7
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52.
256
1
4
=4
1
125 3 = 5
53.
3
1
9
32
2
−
3
5
=
=
1
27
1
8
54. 17w v
55. 2
4
56. 24
2
6
57. 10x
58.
5w
7
u
3 −4
5
59.
−18 − 9 x
8 − 2x
60.
2 5 +4
3
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