MA004-FinalExam-Answers

Solve: 10x +1 < x - 8 AND x - 1 > -5.

Choose one answer.

	a. x < -1
	b. x > -4
	c. -4 < x < -1
	d. -4 > x > -1
	e. x > -3

Question 2

Solve: -1-3x>2 OR 2x-2<-2

Choose one answer.

	a. x<-1
	b. x<0
	c. x>0
	d. x>-1
	e. None of the above

Question 3

Solve and express the answer in interval notation: |2x-1|+3<4.

Choose one answer.

	a.
	b.
	c. (0,1)
	d. [0,1)
	e. (0,1]

Question 4

Solve the system of equations by substitution: 4x+y=4 x+3y=1.

Choose one answer.

	a. x=1,y=2
	b. x=0, y=1
	c. x=2,y=1
	d. x=1, y=0
	e. There is no solution.

Question 5

Simplify:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 6

Simplify:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 7

Simplify completely:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 8

Multiply, and then simplify completely:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 9

Multiply and then simplify completely:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 10

Simplify:

Choose one answer.

	a.
	b.
	c.
	d.
	e. None of the above

Question 11

Solve for x:

Choose one answer.

	a. 0
	b. 5
	c. 33
	d. 4
	e. 1

Question 12

Find all solutions:

Choose one answer.

	a. x=-1, x=2
	b. x=-1
	c. x=2
	d. x=5,x=-1
	e. x=3

Question 13

Solve:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 14

If Jim can mow the yard in 2 hours and Jim Junior can mow the yard in 3 hours, then how long will it take them to mow the yard together?

Choose one answer.

	a. 1 hour and 12 minutes
	b. 2 hours
	c. 1 hour and 24 minutes
	d. 2 hours and 15 minutes
	e. 1 hour

Question 15

John went on a bike ride of 48 miles. He realized that if he had gone 4 mph faster, then he would have arrived 6 hours sooner. How fast did he actually ride?

Choose one answer.

	a. 4 mph
	b. 8 mph
	c. 6 mph
	d. 2 mph
	e. 12 mph

Question 16

Solve:

Choose one answer.

	a. n=-3
	b. n=3
	c. n=2
	d. n=-2
	e. There is no solution.

Question 17

Give the domain of the function:

Choose one answer.

	a.
	b.
	c.
	d.
	e. There is no restriction on the value of x.

Question 18

Evaluate

for the function

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 19

Solve

Choose one answer.

	a. x=-2
	b. x=2
	c. x=3
	d. x=-3
	e. x=6

Question 20

Solve for the base in the equation

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 21

You need a 60% alcohol solution. On hand, you have a 360 mL of a 45% alcohol mixture. How
much pure alcohol will you need to add to obtain the desired solution?

Choose one answer.

	a. 135
	b. 216
	c. 100
	d. 54
	e. 28

Question 22

A bank loaned out $10,000, part of it at the rate of 5% annual interest, and the rest at 10%
annual interest. The total interest earned for both loans was $650.00. How much was loaned at
each rate?

Choose one answer.

	a. $7000 at 5%, $3000 at 10%
	b. $7000 at 10%, $3000 at 5%
	c. $6500 at 5%, $3500 at 10%
	d. $3500 at 5%, $6500 at 10%
	e. $6500 at 10%, $0 at 5%

Question 23

Solve: -5-3x

4 AND x+3 < -5

Choose one answer.

	a. x < -8
	b. x -3
	c. x -3
	d. x > -8
	e. No solution

Question 24

Solve: -5-3x

4 OR x+3 < -5

Choose one answer.

	a. x -3
	b. x < -8
	c. x -3
	d. x > -8
	e. No solution

Question 25

Solve and express answer in interval notation: 2-|-2x+1|

-5.

Choose one answer.

	a. [-3.4]
	b. (-3,4)
	c. (,-3)
	d. [4,)
	e. (,)

Question 26

Solve the system of equations by addition: 3x+y=3 x-y=1

Choose one answer.

	a. x=0, y=1
	b. x=1, y=0
	c. x=1, y=1
	d. x=0, y=0
	e. No solution

Question 27

If Sally has 3 times as many dimes as quarters and she has a combined value of 330 cents, how many of each coin does she have?

Choose one answer.

	a. 9 quarters, 3 dimes
	b. 18 quarters, 6 dimes
	c. 4 quarters, 12 dimes
	d. 12 quarters, 4 dimes
	e. 6 quarters, 18 dimes

Question 28

Solve the system of equations:
x+y-z=4
x-2y+3z=-6
2x+3y+z=7

Choose one answer.

	a. x=1,y=2,z=-1
	b. x=2,y=1,z=-1
	c. x=-1,y=2,z=1
	d. x=2,y=2,z=-1
	e. x=1,y=-1,z=2

Question 29

Stacy invested $15000 in two accounts paying 5% and 8%. How much was invested in each account if, after 1 year, the total interest was $900?

Choose one answer.

	a. $5000 at 5%, $10000 at 8%
	b. $10000 at 5%, $5000 at 8%
	c. $15000 at 5%, $0 at 8%
	d. $0 at 5%, $10000 at 8%
	e. $1000 at 5%, $14000 at 8%

Question 30

Solve: -3x-5<4 AND -x-1 < -5

Choose one answer.

	a. x>4
	b. x>-3
	c. -3
	d. x<-3
	e. x<4

Question 31

Solve: -3x-5<4 OR -x-1 < -5

Choose one answer.

	a. -3
	b. x>4
	c. x>-3
	d. x<4
	e. x<-3

Question 32

Solve: x-4<|2-x|

Choose one answer.

	a. x<-4
	b. x<3
	c. Any number
	d. No solution
	e. -2

Question 33

Solve the system by any method: 3x+6y=15 -5x-10y=-25

Choose one answer.

	a. x=5, y=0
	b. No solution
	c. x=3, y=5
	d. x=5, y=3
	e. Infinite number of solutions

Question 34

Pam would like a 25% concentration of sulfuric acid. She has 10 liters of 10% concentration. How much pure sulfuric acid must be added to a 10% concentration?

Choose one answer.

	a. 20 liters
	b. 1/2 liters
	c. 4 liters
	d. 2 liters
	e. 3 liters

Question 35

Sherry has been saving her coins for a special treat. She noted that she has 10 nickels for each dime. Her total amount of all nickels and dimes is $12.00. How many of each does she have?

Choose one answer.

	a. 200 nickels, 20 dimes
	b. 20 nickels, 200 dimes
	c. 100 nickels, 10 dimes
	d. 10 nickels, 100 dimes
	e. 100 nickels, 30 dimes

Question 36

Solve the system of equations: 2x=-2y+2z+2 3y=-8x+6z+1 3z=4x+y+1

Choose one answer.

	a. x=4,y=3,z=2
	b. x=2,y=3,z=4
	c. x=1,y=2,z=3
	d. x=3,y=2,z=1
	e. x=2,y=2,z=4

Question 37

Simplify the expression $\frac{x^{\frac{3}{2}}y^{\frac{5}{3}}}{{x^{\frac{4}{3}}y^{\frac{1}{2}}}$ .

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 38

Simplify the expression $\frac{t^{\frac{-3}{8}}v^{\frac{5}{4}}}{{t^{\frac{-2}{3}}v^{\frac{-1}{2}}}$ .

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 39

Simplify the expression $\left(\frac{t^{\frac{3}{8}}v^{\frac{-5}{4}}}{{t^{\frac{2}{3}}v^{\frac{1}{2}}}\right)^{\frac{-2}{3}}$ .

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 40

Simplify

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 41

Rationalize the denominator:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 42

Rationalize the denominator:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 43

Rationalize the denominator:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 44

Simplify completely:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 45

Simplify completely:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 46

Multiply, and then simplify completely:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 47

Multiply, and then simplify completely:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 48

Simplify, including reducing the index:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 49

Simplify, including reducing the index: $(\sqrt[4]{x^{12}y^{10}$ .

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 50

Simplify, including reducing the index: $\sqrt[21]{x^7y^{14}$ .

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 51

Simplify:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 52

Simplify:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 53

Multiply the following and simplify: (1+2i)(2-i).

Choose one answer.

	a. 2
	b. 1-3i
	c. 1+3i
	d. 4-3i
	e. 4+3i

Question 54

Express the following as a complex number:

Choose one answer.

	a. 1-4i
	b. 1+4i
	c. 1+16i
	d. 1-16i
	e. 5i

Question 55

Express the following as a complex number:

Choose one answer.

	a. 4
	b. 144i
	c. 1+12i
	d. 1-12i
	e. 13i

Question 56

Solve the following by completing the square:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 57

Solve the following by completing the square:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 58

Find all solutions to the following using the quadratic formula:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 59

Find all solutions to the following using the quadratic formula:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 60

Solve for the unknown in the following equation:

Choose one answer.

	a. 2
	b. 4
	c. 0
	d. 1
	e.

Question 61

Solve for the unknown in the following equation:

Choose one answer.

	a. 140.6
	b. 14.06
	c. .141
	d. 1.406
	e. 1

Question 62

Solve the following:

Choose one answer.

	a. 8.22
	b. 9
	c. .208
	d. 2.08
	e. 20.8

Question 63

Solve the following:

Choose one answer.

	a. 1.257
	b.
	c.
	d. 1.5
	e. -1.257

Question 64

Find all solutions to

Choose one answer.

	a. 0
	b. 0,-1
	c. -1
	d. 3
	e. 8

Question 65

Find all solutions to

Choose one answer.

	a. 1
	b. 5
	c. 1, 5
	d. 9
	e. 7

Question 66

The length of a rectangle is 8 inches longer than it is wide. If the area is 180 square inches, then what are the dimensions of the rectangle?

Choose one answer.

	a. length=22, width=14
	b. length=12, width=20
	c. length=20, width=12
	d. length=18, width=10
	e. length=10, width=18

Question 67

The width of a rectangle is 6 inches longer than it is long. If the area is 160 square inches, then what are the dimensions of the rectangle?

Choose one answer.

	a. length=10, width=16
	b. length=16, width=10
	c. length=12, width=18
	d. length=18, width=12
	e. length=6, width=16

Question 68

Simplify completely:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 69

Solve the following equation:

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 70

Solve the following equation:

Choose one answer.

	a. 2
	b. -2
	c. 0
	d. 1
	e. -1

Question 71

Solve the following equation:

Choose one answer.

	a. 1
	b. -4
	c. 4
	d. -6
	e. 6

Question 72

Solve the simultaneous product equations, and express the answer in ordered pair(s):

Choose one answer.

	a. (4,3) and (24,1/2)
	b. (3,4) and (1/2,24)
	c. (3,4) and (24,1/2)
	d. (1/2,24)
	e. (4,3)

Question 73

Solve the simultaneous product equations, and express the answer in ordered pair(s):

Choose one answer.

	a. (3,2) and (12,1/2)
	b. (2,3) and (1/2,12)
	c. (2,3)
	d. (3,2) and (12,1/2)
	e. (1,1)

Question 74

A number of students decided to split a purchase of $60. However, 15 students failed to pay their share, so each student had to pay $9 more. How many students were in the original group?

Choose one answer.

	a. 20
	b. 3
	c. 35
	d. 22
	e. 9

Question 75

A farmer bought a number of pigs for $260. However, 4 of them died before he could sell the rest at a profit of $8 per pig. His total profit was $76. How many pigs did he originally buy?

Choose one answer.

	a. 16
	b. 24
	c. 22
	d. 20
	e. 18

Question 76

A tourist bought a number of jars of honey, for which he paid $100. He keeps 4 jars of honey for his family and sells the remaining jars to his friends for $8 more per jar than he originally paid. He makes back what he originally paid plus a profit of $108. How many jars did he originally buy?

Choose one answer.

	a. 16
	b. 24
	c. 18
	d. 22
	e. 20

Question 77

Julie went on a trip of 480 miles. For the return trip, she realized that if she traveled at an average of 20 mph faster, then she would have arrived 2 hours sooner. How fast did she average going on her road trip?

Choose one answer.

	a. 40 mph
	b. 80 mph
	c. 70 mph
	d. 60 mph
	e. 50 mph

Question 78

Carrie went on a 100 mile trip to a soccer game. On the way back, due to road construction she had to drive 10 miles per hour slower. This made the trip take 5 hours longer. How fast did she drive to the soccer game?

Choose one answer.

	a. 18 mph
	b. 20 mph
	c. 16 mph
	d. 22 mph
	e. 24 mph

Question 79

Alison drives 400 miles at a certain speed to New York for a ski vacation. When she returns home, the weather is bad, so she drives 10 miles per hour slower and it takes her 2 hours longer. How fast did Alison drive to New York?

Choose one answer.

	a. 55 mph
	b. 40 mph
	c. 50 mph
	d. 60 mph
	e. 70 mph

Question 80

If Jenna cleans her house in 4 hours and Jodi, her daughter, cleans the house in 6 hours, then how long will it take for them to clean the house together?

Choose one answer.

	a. 2.4 hours
	b. 3 hours
	c. 3.4 hours
	d. 2.2 hours
	e. 3.8 hours

Question 81

If Sherri does a job in 10 hours and with the help of Susan they can do it
together in 6 hours, then how long would it take Susan to do it alone?

Choose one answer.

	a. 20 hours
	b. 19 hours
	c. 17 hours
	d. 15 hours
	e. 13 hours

Question 82

If Jodi mows her yard in 2 hours and her sister Sue can mow the yard in 3 hours, then how long will it take them working together to mow the yard?

Choose one answer.

	a. 1.4 hours
	b. 1.2 hours
	c. 1.8 hours
	d. 1.6 hours
	e. 1 hour

Question 83

A picture that measures 11 inches by 7 inches is placed in a frame of uniform thickness. If the area of the frame and picture together is 221 square inches, then how thick is the frame?

Choose one answer.

	a. 13 inches
	b. 13 inches
	c. 11 inches
	d. 19 inches
	e. 21 inches

Question 84

A frame that measures 14 inches by 13 inches is of uniform thickness. The area of the picture inside is 30 square inches. What is the length of the shorter side of the picture?

Choose one answer.

	a. 9 inches
	b. 8 inches
	c. 4 inches
	d. 6 inches
	e. 5 inches

Question 85

Give the domain of the function

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 86

Find f(2), if

Choose one answer.

	a. -1
	b. 0
	c. 1
	d. 2
	e. 3

Question 87

Find h(2), if

Choose one answer.

	a. 8
	b. 9
	c. 7
	d. 6
	e. 5

Question 88

Find h(2), if

Choose one answer.

	a. -2
	b. -1
	c. 3
	d. 1
	e. 2

Question 89

Find h(x), where

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 90

Find h(x), where

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 91

Find

Choose one answer.

	a.
	b.
	c.
	d.
	e.

Question 92

Give the vertex of the graph of

Choose one answer.

	a. (-1,2)
	b. (2,-1)
	c. (-2,1)
	d. (2,1)
	e. (-2,-1)

Question 93

Jane purchased a cd from her local bank. She invested $10,000 in the cd. The terms of the cd is to pay 4% interest compounded quarterly if she leaves the money in the bank for five years. How much will Jane be returned after the end of the five years?

Choose one answer.

	a. $12,201.90
	b. $1,201.90
	c. $21,201.90
	d. $12,201.00
	e. $12,209.00

Question 94

Maria purchased a cd from her local bank. She invested $12,000 in the cd. The terms of the cd is to pay 5% interest compounded quarterly if she leaves the money in the bank for four years. How much will Maria be returned after the end of the four years?

Choose one answer.

	a. $12,638.67
	b. $14,638.67
	c. $1,638.67
	d. $14,638.00
	e. $14,678.67

Question 95

Jane purchased a cd from her local bank. She invested $10,000 in the cd. The terms of the cd is to pay 4% interest compounded continuously if she leaves the money in the bank for five years. How much will Jane be returned after the end of the five years?

Choose one answer.

	a. $12,214.00
	b. $12,114.03
	c. $12,214.03
	d. $1,214.03
	e. $10,214.03

Question 96

Maria purchased a cd from her local bank. She invested $12,000 in the cd. The terms of the cd is to pay 5% interest compounded continuously if she leaves the money in the bank for four years. How much will Maria be returned after the end of the four years?

Choose one answer.

	a. $1,656.83
	b. $16,456.83
	c. $14,566.83
	d. $14,656.00
	e. $14,656.83

Question 97

Solve for x in the equation:

Choose one answer.

	a. 3.66
	b. .366
	c. .3
	d. .663
	e. 36.6

Question 98

Solve for x in the equation:

Choose one answer.

	a. 0
	b. 1
	c. 2
	d. 3.5
	e. 6

Question 99

Solve for x in the equation:

Choose one answer.

	a. 0
	b. 0.5
	c. 1
	d. 1.5
	e. 2

Question 100

Solve for x:

Choose one answer.

	a. 729
	b. 1/3
	c. 27
	d. 3
	e. 9