MATH 105 LMU Equation of A Line & Interval Notation Exam Practice

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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 Purchase answer to see full attachment Tags: scientific notation interval notation positive real numbers Real number line Graph the solution set User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.