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FINAL EXAM

MATH 105

Name___________________________________

Section___________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the equation. Check your solution.

1) 3x – 7(3 + x) = -4(x + 7)

A)

C) {-28}

B) all real numbers

D) {-21}

Provide an appropriate response.

2) Equation of a line: 5x + 3y = 30

(a) Solve for y.

(b) Find y when x = 4.

5

A) (a) y = – x + 30

3

(b) y =

(b) y =

2)

B) (a) y = –

70

3

C) (a) y = –

1)

5

x + 10

3

(b) y = 10

5

x + 10

3

D) (a) y =

10

3

(b) y =

5

x + 10

3

50

3

Solve the inequality and express the solution in set-builder notation and interval notation. Graph the solution set on a

real number line.

3) -4(5x – 8) -24x + 28

3)

A) {x|x -1}; (- , -1]

B) {x|x < -1}; (- , -1)
C) {x|x -1}; [-1, )
D) {x|x > -1}; (-1, )

Perform the indicated operation.

4) (8x – 3)2

A) 8×2 + 9

B) 64×2 + 9

C) 64×2 – 48x + 9

1

D) 8×2 – 48x + 9

4)

Simplify the expression. Write the answer with only positive exponents. All variables are nonzero.

4

-1

5) (20×2 y4 ) (4×2 y)

256 0

64 6

64 0

256 6

x

x

x

x

A)

B)

C)

D)

5

5

5

5

Perform the indicated operation. Express the answer in scientific notation.

6 × 10 -8

6)

12 × 103

A) -1.3

B) 5.0 × 10-12

C) 1.7 × 104

6)

D) 3.0 × 105

Factor the polynomial completely. If the polynomial cannot be factored, say it is prime.

7) 16×2 + 81

A) (4x + 9)2

8) 8×2 + 18x + 9

A) (2x – 3)(4x – 3)

A) {0, 2, 3}

7)

B) (4x – 9)2

C) (4x + 9)(4x – 9)

D) prime

B) (8x + 3)(x + 3)

C) prime

D) (2x + 3)(4x + 3)

B) {-2, -3}

1

C) – , -3

2

Solve the equation by factoring.

9) 20×3 + 100×2 + 120x = 0

5)

8)

9)

D) {0, -2, -3}

Perform the indicated operation.

15×4

10)

4×3

A)

11)

10)

12×2

20×5

4×4

25

B)

25×8

4

C)

180×2

80

D)

25×4

4

x2

10x – 16

2

x – 64

x2 – 64

A)

x-2

x+8

11)

B)

x+8

x-2

C) undefined

D) 0

Perform the indicated operation and simplify. Assume all variables represent positive real numbers.

12) 7 · 42

A) 7

B) 294

C) 7 6

D) 42

13) (2 13 + 9)(3 13 + 8)

12)

13)

A) 150 + 43 13

B) 72 + 6 132 + 16 13

C) 94 13

D) 78 13 + 16

2

Find n(A) for the set.

14) A = {2, 2, 3, 3, …, 6, 6}

A) n(A) = 6

B) n(A) = 3

C) n(A) = 10

D) n(A) = 5

Let U = {1, 2, 4, 5, a, b, c, d, e}. Find the complement of the set.

15) W = {1, 5, e, d, a}

A) {2, 3, 4, a, b, c}

B) {2, 4, b, c}

C) {2, 3, 4, b, c}

D) {1, 2, 4, b, c}

Solve the problem.

16) List all possible proper subsets of the set {2, 6, 7}.

A) , {2}, {6}, {7}, {2, 6}, {2, 7}, {6, 7}

C) {2}, {6}, {7}, {2, 6}, {2, 7}, {6, 7}

B) , {2}, {6}, {7}, {2, 6}, {2, 7}, {6, 7}, {2, 6, 7}

D) {2}, {6}, {7}, {2, 6}, {2, 7}, {6, 7}, {2, 6, 7}

14)

15)

16)

List the elements in the set .

Let U = {q, r, s, t, u, v, w, x, y, z}

A = {q, s, u, w, y}

B = {q, s, y, z}

C = {v, w, x, y, z}.

17) A B’

A) {r, s, t, u, v, w, x, z}

C) {q, s, t, u, v, w, x, y}

17)

B) {u, w}

D) {t, v, x}

18) A’ – C

A) {q, s, u}

B) {r, t}

C) {v, x, z}

D) {q, s, u, v, x, z}

19) A (B C)

A) {q, s, w, y}

B) {q, s, u, w, y, z}

C) {q, r, w, y, z}

D) {q, y, z}

Shade the regions representing the set.

20) A’ B’

18)

19)

20)

A)

B)

C)

D)

3

Find the cardinal number of the set.

21) The numbers in the Venn Diagram below represent cardinalities.

21)

Find n(A B’).

A) 24

B) 28

C) 4

Find the cardinal number of the indicated set. Use the cardinal number formula.

22) If n(A) = 40, n(B) = 117 and n(A B) = 137, what is n(A B)?

A) 60

B) 22

C) 20

D) 20

D) 10

Solve the problem.

23) In a survey of 280 people, a travel company asked people about places they plan to visit in the next

5 years. The results were as follows:

48 plan to visit Europe

58 plan to visit Latin America

34 plan to visit Asia

14 plan to visit Europe and Latin America

12 plan to visit Latin America and Asia

11 plan to visit Europe and Asia

4 plan to visit all three

How many people plan to visit exactly two of these places?

A) 37

B) 25

C) 18

23)

D) 29

Convert the symbolic compound statement into words.

24) p represents the statement : “x < 2"
q represents the statement: "y > 2″

Translate the following compound statement into words:

p ~q

A) x is less than 2 and y is not greater than 2.

C) x is less than 2 or y is not greater than 2.

22)

24)

B) x is less than 2 or y is less than 2.

D) x is not less than 2 and y is not less than 2.

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound

statement.

25) (p ~q) r

25)

A) False

B) True

Let p represent 7 < 8, q represent 2 < 5 < 6, and r represent 3 < 2. Decide whether the statement is true or false.
26) (~p q) ~r
26)
A) False
B) True
4
Construct a truth table for the statement.
27) ~s (~p s)
A) s p ~s (~p s)
T
T
F
F
C) s
T
F
T
F
p
T
T
F
F
T
F
T
F
F
F
T
T
~s (~p
s)
T
T
T
T
B) s
p
~s
(~p
s)
T
T
F
F
D) s
T
F
T
F
p
F
T
T
T
~s (~p
s)
T
T
F
F
T
F
T
F
T
F
T
T
Tell whether the conditional statement is true or false.
28) (5 = 5) (4 = 3)
A) True
B) False
Construct a truth table for the statement.
29) ~s (~s q)
A) s q ~s (~s q)
B) s
q
~s (~s q)
T
T
F
F
D) s
T
F
T
F
q
T
T
T
T
~s (~s q)
T
T
F
F
T
F
T
F
T
T
F
F
C) s
T
F
T
F
q
T
T
F
F
T
F
T
F
T
T
T
F
~s (~s q)
F
F
T
F
28)
29)
T
F
T
F
Write the converse, inverse, or contrapositive of the statement as requested.
30) If you like me, then I like you.
Converse
A) If I like you, then you like me.
C) If you don't like me, I don't like you.
27)
30)
B) I like you if you don't like me.
D) I don't like you if you don't like me.
31) He who laughs last, laughs loudest.
31)
Inverse
A) If he doesn't laugh loudest, he doesn't laugh last.
B) If he doesn't laugh last, he doesn't laugh loudest.
C) If he laughs last, he doesn't laugh loudest.
D) If he laughs loudest, he laughs last.
32) Love is blind.
32)
Contrapositive
A) If it is not love, it is not blind.
C) If it is not blind, then it is not love.
B) If it is blind then it is not love.
D) If it is blind then it is love.
5
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Tags:
scientific notation
interval notation
positive real numbers
Real number line
Graph the solution set
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