Math questions and answers selected

Math questions and answers selected

MATH 100 -- Practice Test 1
Millersville University
Ron Umble, Instr.
Name___________________________________
INSTRUCTIONS: Turn off and stow all cell phones and pagers.  Calculators may be used, but cell phone may not be used as
calculators.
MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.
List the elements in the set.
1) {x | x is an integer between -2 and 2}
A) {-1, 0, 1, 2} B) {-2, -1, 0, 1, 2} C) {-2, -1, 0, 1} D) {-1, 0, 1}
1)
Complete the blank with either ∈ or ∉ to make the statement true.
2) 2     {11, 10, 9, 8}
A) ∈ B) ∉
2)
Write the set in set-builder notation.
3) {2, 4, 6, 8}
A) {x | x is an even natural number}
B) {x | x is an even natural number less than 10}
C) {x | x is an even integer less than 10}
D) {x | x is an even whole number less than 10}
3)
Find n(A) for the set.
4) A = {x | x is a month in the year}
A) n(A) = 12 B) n(A) = 52 C) n(A) = 1 D) n(A) = 24
4)
5) A = 1
2 , 1
3 , 1
4 , 1
5 , ..., 1
29 , 1
30
A) n(A) = 31 B) n(A) = 29 C) n(A) = Infinite D) n(A) = 30
5)
Decide whether ⊆, ⊂, both, or neither can be placed in the blank to make a true statement.
6) {11, 12, 13}      {10, 11, 12, 13}
A) ⊂ B) Neither C) ⊆ D) Both ⊂ and ⊆
6)
Solve the problem.
7) List all possible subsets of the set {m, n}.
A) {m}, {n}, ∅ B) {m}, {n}
C) {m}, {n}, {m, n}, ∅ D) {m}, {n}, {m, n}
7)
Find the number of subsets of the set.
8) {6, 7, 8}
A) 6 B) 7 C) 8 D) 3
8)
Find the number of proper  subsets of the set.
9) {poetry, drama, speech, art, film}
A) 31 B) 24 C) 16 D) 32
9)
1
Let U = {1, 2, 4, 5, a, b, c, d, e}. Find the complement of the set.
10) Q = {2, 4, b, d}
A) {1, 3, 5, a, c, e} B) {1, 5, a, c, e}
C) {1, 5, a, e} D) {1, 2, 4, 5, a, b, c, d, e}
10)
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}.
11) (A ∩ B)ʹ
A) {q, s, t, u, v, w, x, y} B) {s, u, w}
C) {r, t, u, v, w, x, z} D) {t, v, x}
11)
12) Cʹ ∪ Aʹ
A) {q, r, s, t, u, v, x, z} B) {w, y}
C) {s, t} D) {q, s, u, v, w, x, y, z}
12)
13) (Aʹ ∪ C) ∩ Bʹ
A) {v, x} B) {r, t, v, w, x}
C) {r, t, u, v, w, s, y, z} D) {y, z}
13)
Find the Cartesian product.
14) A = {12, 9, 10}
B = {14, 4}
Find A × B.
A) {(12, 14), (9, 10), (10, 14)}
B) {(12, 14), (9, 4)}
C) {(14, 12), (14, 9), (14, 10), (4, 12), (4, 9), (4, 10)}
D) {(12, 14), (12, 4), (9, 14), (9, 4), (10, 14), (10, 4)}
14)
Find the indicated cardinal number.
15) Find n(A × B) given that A = {2} and B = {1, 3}.
A) 2 B) 1 C) 4 D) 3
15)
Determine whether the sets are equal, equivalent, both, or neither.
16) {72, 40, 27} and {40, 27, 72}
A) Equivalent B) Equal C) Neither D) Both
16)
Show that the set is infinite by placing it in a one -to-one correspondence with a proper subset of itself. Be sure to show
the pairing of the general terms in the sets.
17) {5, 6, 7, 8, ...}
A) { 5, 6, 7, 8, ..., n + 4, ...}
↓↓↓↓ ↓
{ 4, 5, 6, 7, ..., n + 3, ...}
B) { 5, 6, 7, 8, ..., n + 4, ...}
↓↓↓↓ ↓
{ 6, 7, 8, 9, ..., n + 5, ...}
C) { 5, 6, 7, 8, ..., n + 4, ...}
↓↓↓↓ ↓
{ 6, 7, 8, 9, ..., n + 6, ...}
D) { 5, 6, 7, 8, ..., n + 5, ...}
↓↓↓↓ ↓
{ 4, 5, 6, 7, ..., n + 3, ...}
17)
2
Find the cardinal number of the set.
18) {8, 9, 10, 11, ...}
A) c B) 4 C) ℵ 0 D) 11
18)
19) {x | x is a decimal between 63 and 64}
A) 2 ℵ 0 B) c C) 2 D) ℵ 0
19)
For the given sets, construct a Venn diagram and place the elements in the proper region.
20) Let U = {1, 2, 3, 4, 5, 6, 7, 8}
A = {3, 6, 8}
B = {4, 6}
C = {1, 6, 7, 8}
A) B)
C) D)
20)
3
Solve the problem.
21) A local television station sent out questionnaires to determine if viewers would rather see a
documentary, an interview show, or reruns of a game show. There were 800 responses with the
following results:
240 were interested in an interview show and a documentary, but not reruns.
32 were interested in an interview show and reruns but not a documentary.
112 were interested in reruns but not an interview show.
192 were interested in an interview show but not a documentary.
80 were interested in a documentary and reruns.
48 were interested in an interview show and reruns.
64 were interested in none of the three.
How many are interested in exactly one kind of show?
A) 384 B) 394 C) 364 D) 374
21)
Let p represent the statement, ʺJim plays footballʺ, and let q represent the statement ʺMichael plays basketballʺ. Convert
the compound statement into symbols.
22) Jim does not play football and Michael does not play basketball.
A) ~p ∧ q B) ~p ∧ ~q C) ~(p ∧ q) D) ~p ∨ ~q
22)
Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound
statement.
23) ~p ∨ (q ∧ ~r)
A) False B) True
23)
Let p represent 7 < 8, q represent 2 < 5 < 6, and r represent 3 < 2. Decide whether the statement is true or false.
24) (~p ∧ q) ∨ ~r
A) True B) False
24)
Write a negation for the statement.
25) Some athletes are musicians.
A) Some athletes are not musicians. B) No athlete is a musician.
C) Not all athletes are musicians. D) All athletes are musicians.
25)
Construct a truth table for the statement.
26) ~r ∧ ~s
A) r   s  (~r ∧ ~s)
TT F
TF T
FT T
FF T
B) r s (~r ∧ ~s)
TT T
TF F
FT F
FF T
C) r s (~r ∧ ~s)
TT F
TF F
FT F
FF T
D) r   s (~r ∧ ~s)
TT F
TF F
FT F
FF F
26)
4
Use De Morganʹs laws to write the negation of the statement.
27) A day late and a dollar short.
A) A day late or not a dollar short. B) Not a day late and not a dollar short.
C) Not a day late and a dollar short. D) Not a day late or not a dollar short.
27)
Solve the problem.
28) Given that p ∨ q is false, what can you conclude about the truth values of p and q?
A) Exactly one of p and q is false B) At least one of p and q is false
C) Both p and q are false D) p and q have the same truth value
28)
Write the converse, inverse, or contrapositive of the statement as requested.
29) If I pass, Iʹll party.
Contrapositive
A) Iʹll party if I pass. B) If I donʹt pass, I wonʹt party.
C) If I party, then I passed. D) If I donʹt party, I didnʹt pass.
29)
30) If I were young, I would be happy.
Converse
A) If I were not happy, I would not be young.
B) If I were young, I would not be happy.
C) If I were not young, I would not be happy.
D) If I were happy, I would be young.
30)
Use an Euler diagram to determine whether the argument is valid or invalid.
31) Not all that glitters is gold.
My ring glitters.                  
My ring is not gold.
A) Valid B) Invalid
31)
Use a truth table to determine whether the argument is valid.
32) p → q
q    
p
A) Valid B) Invalid
32)
Determine whether the argument is valid or invalid.
33) Lorettaʹs hobby is stamp collecting. If her husband likes to fish, then Lorettaʹs hobby is not stamp
collecting. If her husband does not like to fish, then Nathan likes to read. Therefore, Nathan likes to
read.
A) Valid B) Invalid
33)
Convert the Egyptian numeral to Hindu-Arabic form.
34)
A) 3670 B) 367 C) 3067 D) 3607
34)
5
Convert the Hindu-Arabic numeral to Egyptian form.
35) 367
A) B)
C) D)
35)
Convert the Roman numeral to Hindu-Arabic form.
36) CLXXXV
A) 185 B) 85 C) 105 D) 1085
36)
Convert the Hindu-Arabic numeral to Roman form.
37) 1867
A) MDCCLXVII B) MDCCLLXVII C) MDCCCLXVII D) MDCCCXLVII
37)
Convert the Chinese numeral to Hindu-Arabic form.
38)
A) 520 B) 920 C) 820 D) 620
38)
Convert the Hindu-Arabic numeral to Chinese.
39) 367
A) B) C) D)
39)
Write the number in expanded form.
40) 936
A) (9 ·  101) + (3 ·  102) + (6 ·  103) B) (9 ·  102) + (3 ·  101) + (6 ·  100)
C) (9 ·  103) + (3 ·  102) + (6 ·  101) D) (9 ·  100) + (3 ·  101) + (6 ·  102)
40)
Identify the number represented on the abacus.
41)
A) 515 B) 191 C) 151 D) 919
41)
6
Solve the problem.
42) Write (in the same base) the counting numbers just before and just after 3246seven.
A) 3254seven, 3250seven B) 3245seven, 3247seven
C) 165seven, 166seven D) 3245seven, 3250seven
42)
Convert the number to decimal form.
43) 275eight
A) 283 B) 189 C) 112 D) 1512
43)
Convert the decimal number to the given base.
44) 503 to base five
A) 4003five B) 3004five C) 4030five D) 3040five
44)
Convert from binary form to the indicated base.
45) 11100two to base eight
A) 21eight B) 42eight C) 168eight D) 34eight
45)
Convert the number to binary form.
46) FA6sixteen
A) 111010110110two B) 111110000011two
C) 111110100110two D) 111110110110two
46)
Determine the letters or numbers.
47) Write the binary code for the letter Q.
A) 1010010 B) 1010001 C) 100100 D) 1010100
47)
48) Break 110001011001011100100 into groups of seven digits and write as lower case letters.
A) arm B) bed C) cue D) bad
48)
Find all natural number factors of the number.
49) 42
A) 1, 7, 42 B) 1, 2, 3, 7, 6, 14, 21, 42
C) 1, 2, 3, 7, 6, 14, 28, 42 D) 7, 6, 14, 42
49)
Give the prime factorization of the number. Use exponents when possible.
50) 396
A) 24 · 11 B) 34 · 11 C) 23 · 32 · 11 D) 22 · 32 · 11
50)
7
Answer Key
Testname: MATH 100‐‐PRACTICETEST1‐‐2012
1) D
2) B
3) B
4) A
5) B
6) D
7) C
8) C
9) A
10) B
11) C
12) A
13) B
14) D
15) A
16) D
17) B
18) C
19) B
20) A
21) A
22) B
23) A
24) A
25) B
26) C
27) D
28) C
29) D
30) D
31) B
32) B
33) A
34) C
35) C
36) A
37) C
38) D
39) A
40) B
41) A
42) D
43) B
44) A
45) D
46) C
47) B
48) B
49) B
50) D
8