Download 1. Write the given English phrase as an expression or equation: a

1. Write the given English phrase as an expression or equation:
a. the sum of five and three times a number
ans: 5 + 3x or 3x + 5
b. the product of three and a number, decreased by ten, is 25
ans: 3x − 10 = 25
c. The difference of a number and twelve.
ans: x − 12
d. Fourteen subtracted by a number times three.
ans: 3x − 14
e. The product of ten and Four less than a number.
ans: 10(x − 4)
f. The quotient of a number and 5.
x
ans:
5
g. When a number is decreased by four, the result is twenty.
ans: x − 4 = 20
h. The sum of ten and three times a number is five more than twice the number.
ans: 10 + 3x = 5 + 2x
i. The quotient of a number and seven, increased by five, is three less than twice the number.
x
ans: + 5 = 2x − 3
7
2. Consider the following numbers:
√ 2 0 2
√
10
2
{−10, −8, −5, − , 0, 1, 2, , , , π, 16, }
3
3 3 0
5
a. List all the natural numbers
√
10
=2
ans: 1, 16 = 4,
5
b. List all the integers
√
10
0
ans: 1, 16 = 4,
= 2, −10, −8, −5, 0, = 0
5
3
c. List all the rational numbers
√
10
0
2 2
ans: 1, 16 = 4,
= 2, −10, −8, −5, 0, = 0, − ,
5
3
3 3
d. List all the irrational numbers
√
ans: 2, π
e. List all the real numbers
√
10
0
2 2 √
ans: 1, 16 = 4,
= 2, −10, −8, −5, 0, = 0, − , , 2, π
5
3
3 3
3. Consider the following numbers:
1
1 √
2
101
,
2,
, π,
,
4
1
21
a. List all the natural numbers
2
ans: = 2
1
b. List all the integers
−5, −1, 0,
5
0
2
= 2, −5, −1, 0
1
c. List all the rational numbers
1 101
2
ans: = 2, −5, −1, 0, ,
1
4 21
d. List all the irrational numbers
√
ans: 2, π
ans:
e. List all the real numbers
2
1 101 √
ans: = 2, −5, −1, 0, ,
, 2, π
1
4 21
4. Consider the given numbers:
√
1
2
8
, 1,
, 4,
−3, − ,
2,
4
3
3
a. List all the natural numbers.
π,
√
−2
ans: 1, 4
b. List all the integers.
8
= −2
4
c. List all the rational numbers.
8 1 2
ans: 1, 4, −3, − , ,
4 3 3
d. List all the irrational numbers.
√
ans: 2, π
ans: 1, 4, −3, −
e. List all the real numbers.
8 1 2 √
ans: 1, 4, −3, − , , , 2, π
4 3 3
2
5. Which of the following are natural number:
I −2
II 3
III 25
a. I only
b. I and II only
them are natural numbers
c. II and III only
d. they are all natural numbers
e. None of
ans: c
6. Which of the following are integer:
I −5
4
II
2
III 0
a. I only
integer
b. I and III only
c. III only
d. They are all integers
e. None of them is an
ans: d
7. Which of the following are rational number:
−3
1
II
4
III π
I
a. I only b. I and II only
a rational number
c. II only
d. They are all rational numbers
e. None of them is
ans: b
8. Which of the following are real number:
0
4
5
II
0
π
III
2
a. I only b. I and II only
is a real number
I
c. I and III only
d. They are all real numbers
ans: c
3
e. None of them
9. Which of the following statement(s) is/are true?
I A real number is always a rational number.
II An integer is never a natural number.
III An irrational number is always a real number.
a. I only
b. II only
c. III only
d. They are all true
e. They are all false
ans: c
10. Which of the following statement(s) is/are true?
I An irrational number is never a rational number.
II A real number is always an integer.
III A natural number is always a rational number.
a. I only
b. II only
c. III only
d. I and III only
ans: d
11. True of False:
a. A natural number is never an integer.
ans: False
b. A natural number is never negative.
ans: True
c. An integer is a always rational number.
ans: True
d. A rational number is never irrational.
ans: True
e. A real number is never irrational.
ans: False
f. An irrational number is never an integer.
ans: True
g. A rational number is sometimes an integer.
ans: True
4
e. II and III only
12. Perform the Operation:
a. 3 − 5
ans: −2
b. −3 + −5
ans: −8
c. 3 + −5
ans: −2
d. −5 − (−3)
ans: −2
e. 14 + −6
ans: 8
f. −12 − (−24)
ans: 12
g. 14 + −3
ans: 11
h. −17 − 4
ans: −21
i. −22 + 32
ans: 10
j. −4 · −3
ans: 12
k. 4 · −3
ans: −12
l. −2 · 3
ans: −6
m. −15 ÷ −5
ans: 3
n. 24 ÷ −12
ans: −2
o. −4 ÷ −3
4
ans:
3
p. 12 ÷ −8
ans: −
q.
3
2
−3 2
·
4 3
5
ans: −
1
2
5
7
·
21 −4
5
ans:
12
12
−3
·−
s. −
8
5
9
ans: −
10
11
22
t.
·−
18
15
121
ans: −
135
−30 14
u.
·
7
3
ans: −20
12
v.
÷3
5
4
ans:
5
21
w. −7 ÷
4
4
ans: −
3
−30 14
x.
÷
7
3
45
ans: −
49
24
13
y. − ÷ −
5
23
552
ans:
65
10 21
z. − ÷
49
6
20
ans: −
343
r. −
6
13. Evaluate the expression:
a. 12 − 32 + 2(4 − 2) − 12 ÷ 3 · 2 + 1
ans: 0
b. 4 + 3 · −24 − 2 · 52 − (22 + 6)
ans: −104
c. 23 −
4 − 52
− 4 · 2 + 22
6 + −3
ans: 11
d. 3 − (3 + 4 · −6) + −33 − 22 · (5 − 11)
ans: 21
e. 4 − 42 + (12 +
ans:
22 + −32
· 2) + 21
12 − 32
53
3
f. 2(3 − 12 · 4
−6 + 42
+ 1) − 8 · −3
(2 − 4)2
ans: −208
g. (10 + 2) − 10 − (42 − 10) − (−42 − 5)
ans: 17
h. 2 + 3 · 4 + (5 − 6) · 72 − 8
ans: −43
14. Evaluate the expression if x = −1, y = 2, and z = −2
a. x2 − 4(y − 2) + z − 3
ans: −4
xy 2 − z
+ 4x − 2
2x + z − 3
40
ans: −
7
3
c. 3x − 4y + 5z 2 −
+ 3 − 2y
1−z
ans: 7
−x + z
d. 2x2 z − yz + 3 − (2y + z) −
2
3
ans:
2
b.
e. 10x − 3y − z 3 + 6(x + 3) − 9x
ans: 13
15. Which of the following is/are example(s) of the associative property of addition?
I 3 + (x + y) = (x + y) + 3
7
II (a + b) + 4 = a + (b + 4)
III a(bc) = (ab)c
a. I only
b. II only
c. I and III
d. They all are
e. None of them is
ans: b
16. Which of the following is/are example(s) of the commutative property of multiplication?
I 3(x + y) = 3x + 3y
II a(x + 4) = (x + 4)a
III x(yz) = (xy)z
a. I only
b. II only
c. I and III
d. They all are
ans: b
8
e. None of them is
17. The equation −2(x + 3) = −2x − 6 is an example of which property of the real numbers?
ans: distributive property
18. State the property of the real numbers that justify the statement:
x(y + 3) = (y + 3)x
ans: commutative property of multiplication
19. State the property of the real numbers that justify the statement:
2a(b − 1) = 2ab − 2a
ans: distributive property
20. State the property of the real numbers that justify the statement:
x + (y + 2) = (x + y) + 2
ans: associative property of addition
21. Simplify the expression:
a. 4x + 5x
ans: 9x
b. −x − 3(x + 2)
ans: −4x − 6
c. 4x − 3x + 3 + 9 − 4(x − 4)
ans: −3x + 28
d. 3[x + 4(3x − 7) + 5(2x + 1) − 2] + 4x − 1
ans: 73x − 76
e. 10 − 5(3x − 2) − 4(x + 3) + 9 − 4(2x − 1)
ans: −27x + 21
f. x − x + 1 − [x + 2 − (x − 3 − x + 4 − [x − 5 + (x − 6)] + 7x − 8 + 9 − 10x) − 11 + 12x] + 13
ans: −18x + 36
9