Ch. 0 Chapter R: Review
0.1 Real Numbers
1 Work with Sets
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set.
1) B ∪ C
A) {1, 2, 3, 4, 5, 7, 9} B) { } C) {0} D) {1, 2, 3, 5, 7, 9}
2) A ∪ C
A) {1, 2, 3, 4, 5, 8, 9} B) {4, 6, 7, 9} C) {1} D) {1, 2, 3, 5, 7, 9}
3) A ∩ B
A) {2, 3, 5} B) {1, 2, 3, 5, 7, 8} C) {2, 3, 5, 7} D) {1, 2, 3, 5, 8}
4) A ∩ C
M
A) {1} B) {1, 2, 3, 4, 5, 7, 8, 9}
C) {4, 6, 7, 9} D) {1, 2, 3, 5, 7, 9}
5) (A ∩ B) ∪ C
EL
A) {1, 2, 3, 4, 5, 9} B) {1, 2, 3, 5} C) {1, 2, 3} D) {2, 3, 5}
6) (B ∪ C) ∩ A
AN
A) {1, 2, 3, 5} B) {1, 2, 3, 4, 5, 7, 9} C) { } D) {1, 2, 3}
7) B
A) {0, 1, 4, 6, 8, 9} B) {1, 4, 6, 8, 9} C) {0, 1, 4, 6, 7, 8, 9} D) {0, 1, 4, 6, 9}
8) A ∪ B
IE
A) {0, 4, 6, 9} B) {4, 6, 9} C) {1, 4, 6, 8, 9} D) {1, 2, 3, 5, 7, 8}
9) A ∩ C
??
A) {0, 2, 3, 4, 5, 6, 7, 8, 9} B) {1}
C) {1, 2, 3, 4, 5, 7, 8, 9} D) {1, 2, 3, 4, 5, 6, 7, 8, 9}
10) B ∩ C
??
A) {0, 6, 8} B) {6, 8} C) {1, 2, 3, 4, 5, 7, 9} D) { }
2 Classify Numbers
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
List all the elements of B that belong to the given set.
3 5
1) B = 8, 7, -23, 0, , - , 8.7
5 3
Integers
A) {8, -23, 0} B) {8, 0} C) {8, -23} D) {8, 0, 7}
Page 1
, 1
2) B = 12, 8, -20, 0, , -4, 8.5
4
Natural numbers
A) {12} B) 12, 0, - 4 C) {12, 0} D) {-20, 0, 12}
0
3) B = 17, 6, -18, 0,
3
Real numbers
0 0
A) 17, 6, -18, 0, B) {17, -18, 0} C) 17, -18, 0, D) 17, -18
3 3
0
4) B = 8, 8, -8, 0, , 0.85
9
Rational numbers
M
0 0
A) 8, -8, 0, , 0.85 B) {8, 0} C) { 8} D) 8, , 0.85
9 9
0
5) B = 10, 5, -14, 0,
EL
, 0.02
3
Irrational numbers
AN
0 0
A) { 5} B) { 5, 0.02} C) 5, D) 5, , 0.02
3 3
5 9
6) B = {16, 6, -7, 0, , - , 5.1, 16π, 0.166166166...}
9 5
Integers
IE
A) {16, -7, 0} B) {16, 0} C) {16, -7} D) {16, 0, 6}
1
7) B = {6, 7, -19, 0, , -8, 7.1, 7π, 0.747474...}
??
8
Natural numbers
A) {6} B) 6, 0, - 8 C) {6, 0} D) {-19, 0, 6}
??
0
8) B = {9, 6, -11, 0, , 16, 0.17, -6π, 0.161616...}
2
Rational numbers
0 0
A) 9, -11, 0, , 16, 0.17, 0.161616... B) 9, -11, 0, , 0.17
2 2
0 0
C) 9, -11, 0, , 0.17, 0.161616... D) 9, -11, 0, , 16, 0.17, -6π, 0.161616...
2 2
0
9) B = {11, 8, -4, 0, , , 0.21, -8π, 0.444...}
9
Irrational numbers
0
A) { 8 , -8π} B) { 8} C) 8, , -8π D) { 8, -8π, 0.444...}
9
Page 2
,Approximate the number rounded to three decimal places, and truncated to three decimal places.
10) 3.4748
A) 3.475 B) 3.476 C) 3.475 D) 3.474
3.474 3.474 3.475 3.475
11) 1.14285714
A) 1.143 B) 1.144 C) 1.143 D) 1.142
1.142 1.142 1.143 1.143
20
12)
9
A) 2.222 B) 2.223 C) 2.222 D) 2.223
2.222 2.222 2.223 2.223
3 Evaluate Numerical Expressions
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
M
Write the statement using symbols.
1) The sum of 28 and 7 is 35.
28
A) 28 + 7 = 35 B) =4 C) 28 ∙ 7 = 196 D) 28 - 7 = 21
7
EL
2) The difference 10 less 2 equals 8.
10
A) 10 - 2 = 8 B) =5 C) 10 + 2 = 12 D) 10 ∙ 2 = 20
AN
2
3) The product of 65 and 13 equals 845.
65
A) 65 ∙ 13 = 845 B) =5 C) 65 + 13 = 78 D) 65 - 13 = 52
13
IE
4) The quotient 14 divided by 7 is 2.
14
A) =2 B) 14 ∙ 7 = 98 C) 14 + 7 = 21 D) 14 - 7 = 7
7
??
5) The sum of four times x and 5 decreased by 7 is 8.
A) 4x + 5 - 7 = 8 B) 4(x + 5) - 7 = 8 C) 7 - (4x + 5) = 8 D) 4(x + 5 - 7) = 8
??
6) Three times the difference of x and 8 is -10.
A) 3(x - 8) = -10 B) 3 - x - 8 = -10 C) 3x - 8 = -10 D) 3 + x - 8 = -10
7) The quotient of x and the sum of 5 and x.
x x+5
A) B) x + 5 + x C) x(5 + x) D)
5+x x
Evaluate the expression.
8) 1 - 5 + 9
A) 5 B) -13 C) 15 D) -3
Page 3
, 4
9) 7 +
7
53 49 53 49
A) B) C) D)
7 7 4 4
10) 6 ∙ [6(3 - 5) - 8]
A) -120 B) 24 C) -60 D) 20
11) 5 ∙ [2 + 4 ∙ (7 + 3)]
A) 210 B) 300 C) 50 D) 296
12) 5 - (6 + 5 ∙ -5 + 9)
A) 15 B) -5 C) 33 D) 27
14 ∙ 2
13)
10 7
2 5 7 5
M
A) B) C) D)
5 2 5 7
2∙ 1
14) 1+
EL
3 2
2 1
A) 1 B) C) D) 3
3 2
AN
1∙ 1
15) 9- +8
6 3
85 55 50 17
A) B) C) D)
9 6 3 9
IE
7+1
16)
6+7
8 6
A) B) C) - 8 D) - 6
??
13 13
3-1
17)
1-3
??
A) -1 B) 3 C) - 3 D) 2
7 1
18) +
9 15
38 1 1 38
A) B) C) D)
45 3 45 3
8 2
19) -
9 7
38 2 2 38
A) B) C) D)
63 21 3 9
Page 4
0.1 Real Numbers
1 Work with Sets
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set.
1) B ∪ C
A) {1, 2, 3, 4, 5, 7, 9} B) { } C) {0} D) {1, 2, 3, 5, 7, 9}
2) A ∪ C
A) {1, 2, 3, 4, 5, 8, 9} B) {4, 6, 7, 9} C) {1} D) {1, 2, 3, 5, 7, 9}
3) A ∩ B
A) {2, 3, 5} B) {1, 2, 3, 5, 7, 8} C) {2, 3, 5, 7} D) {1, 2, 3, 5, 8}
4) A ∩ C
M
A) {1} B) {1, 2, 3, 4, 5, 7, 8, 9}
C) {4, 6, 7, 9} D) {1, 2, 3, 5, 7, 9}
5) (A ∩ B) ∪ C
EL
A) {1, 2, 3, 4, 5, 9} B) {1, 2, 3, 5} C) {1, 2, 3} D) {2, 3, 5}
6) (B ∪ C) ∩ A
AN
A) {1, 2, 3, 5} B) {1, 2, 3, 4, 5, 7, 9} C) { } D) {1, 2, 3}
7) B
A) {0, 1, 4, 6, 8, 9} B) {1, 4, 6, 8, 9} C) {0, 1, 4, 6, 7, 8, 9} D) {0, 1, 4, 6, 9}
8) A ∪ B
IE
A) {0, 4, 6, 9} B) {4, 6, 9} C) {1, 4, 6, 8, 9} D) {1, 2, 3, 5, 7, 8}
9) A ∩ C
??
A) {0, 2, 3, 4, 5, 6, 7, 8, 9} B) {1}
C) {1, 2, 3, 4, 5, 7, 8, 9} D) {1, 2, 3, 4, 5, 6, 7, 8, 9}
10) B ∩ C
??
A) {0, 6, 8} B) {6, 8} C) {1, 2, 3, 4, 5, 7, 9} D) { }
2 Classify Numbers
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
List all the elements of B that belong to the given set.
3 5
1) B = 8, 7, -23, 0, , - , 8.7
5 3
Integers
A) {8, -23, 0} B) {8, 0} C) {8, -23} D) {8, 0, 7}
Page 1
, 1
2) B = 12, 8, -20, 0, , -4, 8.5
4
Natural numbers
A) {12} B) 12, 0, - 4 C) {12, 0} D) {-20, 0, 12}
0
3) B = 17, 6, -18, 0,
3
Real numbers
0 0
A) 17, 6, -18, 0, B) {17, -18, 0} C) 17, -18, 0, D) 17, -18
3 3
0
4) B = 8, 8, -8, 0, , 0.85
9
Rational numbers
M
0 0
A) 8, -8, 0, , 0.85 B) {8, 0} C) { 8} D) 8, , 0.85
9 9
0
5) B = 10, 5, -14, 0,
EL
, 0.02
3
Irrational numbers
AN
0 0
A) { 5} B) { 5, 0.02} C) 5, D) 5, , 0.02
3 3
5 9
6) B = {16, 6, -7, 0, , - , 5.1, 16π, 0.166166166...}
9 5
Integers
IE
A) {16, -7, 0} B) {16, 0} C) {16, -7} D) {16, 0, 6}
1
7) B = {6, 7, -19, 0, , -8, 7.1, 7π, 0.747474...}
??
8
Natural numbers
A) {6} B) 6, 0, - 8 C) {6, 0} D) {-19, 0, 6}
??
0
8) B = {9, 6, -11, 0, , 16, 0.17, -6π, 0.161616...}
2
Rational numbers
0 0
A) 9, -11, 0, , 16, 0.17, 0.161616... B) 9, -11, 0, , 0.17
2 2
0 0
C) 9, -11, 0, , 0.17, 0.161616... D) 9, -11, 0, , 16, 0.17, -6π, 0.161616...
2 2
0
9) B = {11, 8, -4, 0, , , 0.21, -8π, 0.444...}
9
Irrational numbers
0
A) { 8 , -8π} B) { 8} C) 8, , -8π D) { 8, -8π, 0.444...}
9
Page 2
,Approximate the number rounded to three decimal places, and truncated to three decimal places.
10) 3.4748
A) 3.475 B) 3.476 C) 3.475 D) 3.474
3.474 3.474 3.475 3.475
11) 1.14285714
A) 1.143 B) 1.144 C) 1.143 D) 1.142
1.142 1.142 1.143 1.143
20
12)
9
A) 2.222 B) 2.223 C) 2.222 D) 2.223
2.222 2.222 2.223 2.223
3 Evaluate Numerical Expressions
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
M
Write the statement using symbols.
1) The sum of 28 and 7 is 35.
28
A) 28 + 7 = 35 B) =4 C) 28 ∙ 7 = 196 D) 28 - 7 = 21
7
EL
2) The difference 10 less 2 equals 8.
10
A) 10 - 2 = 8 B) =5 C) 10 + 2 = 12 D) 10 ∙ 2 = 20
AN
2
3) The product of 65 and 13 equals 845.
65
A) 65 ∙ 13 = 845 B) =5 C) 65 + 13 = 78 D) 65 - 13 = 52
13
IE
4) The quotient 14 divided by 7 is 2.
14
A) =2 B) 14 ∙ 7 = 98 C) 14 + 7 = 21 D) 14 - 7 = 7
7
??
5) The sum of four times x and 5 decreased by 7 is 8.
A) 4x + 5 - 7 = 8 B) 4(x + 5) - 7 = 8 C) 7 - (4x + 5) = 8 D) 4(x + 5 - 7) = 8
??
6) Three times the difference of x and 8 is -10.
A) 3(x - 8) = -10 B) 3 - x - 8 = -10 C) 3x - 8 = -10 D) 3 + x - 8 = -10
7) The quotient of x and the sum of 5 and x.
x x+5
A) B) x + 5 + x C) x(5 + x) D)
5+x x
Evaluate the expression.
8) 1 - 5 + 9
A) 5 B) -13 C) 15 D) -3
Page 3
, 4
9) 7 +
7
53 49 53 49
A) B) C) D)
7 7 4 4
10) 6 ∙ [6(3 - 5) - 8]
A) -120 B) 24 C) -60 D) 20
11) 5 ∙ [2 + 4 ∙ (7 + 3)]
A) 210 B) 300 C) 50 D) 296
12) 5 - (6 + 5 ∙ -5 + 9)
A) 15 B) -5 C) 33 D) 27
14 ∙ 2
13)
10 7
2 5 7 5
M
A) B) C) D)
5 2 5 7
2∙ 1
14) 1+
EL
3 2
2 1
A) 1 B) C) D) 3
3 2
AN
1∙ 1
15) 9- +8
6 3
85 55 50 17
A) B) C) D)
9 6 3 9
IE
7+1
16)
6+7
8 6
A) B) C) - 8 D) - 6
??
13 13
3-1
17)
1-3
??
A) -1 B) 3 C) - 3 D) 2
7 1
18) +
9 15
38 1 1 38
A) B) C) D)
45 3 45 3
8 2
19) -
9 7
38 2 2 38
A) B) C) D)
63 21 3 9
Page 4
