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Worksheet 1.1-1.4
name:
Algebra 2
Evaluate each expression if a = 4, b = -3, c = ½ , d = -2, e = 5, f = -6, g = 0 :
1.
a+b.d–e
2.
d – f + ac
5.
bd 2 - b3
c
6.
ge 2 + ab
d
3.
7.
2b2
4.
(2b)2
( f + d)2 - a3
bc
8.
abc
eg - g 2
Choose the correct answer:
9.
Decimals that terminate are ________________________ numbers.
a)
10.
rational
12.
irrational
c)
whole
d)
not real
d)
not real
Decimals that repeat are ________________________ numbers.
a)
11.
b)
rational
b)
irrational
c)
whole
Decimals that are non-repeating and non-terminating are ________________________ numbers.
a)
rational
b)
irrational
c)
whole
Fill in:
Rational numbers can be expressed as a ratio
d)
not real
a , where a and b are both _____________________ and
b
b is not _______________. (see page 11 in your textbook)
Name the sets of numbers to which each number belongs. There may be more than one answer:
(Choose from: natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, not real)
13.
-2.54
14.
0
18.
33.3
19.
0
23.
-8
24.
6
29.
62.5
28.
13
62
Simplify the expressions:
15.
7
0
184.005
16.
-5
17.
π
22.
-9
-8.26
27.
65,000
62.516
32.
- 3
20.
2
21.
- 36
25.
81
49
26.
30.
62.5
31.
4
33.
36.
1 (4j
5
+ 2k + 6j – 7k)
æa bö
12 ç - ÷
è3 4ø
34.
4(20 – 4p) –
37.
ö 1
5æ3
ç x +12y ÷ - ( 2x -12y)
ø 4
6è5
3
4
(4 – 16p)
35.
2(4z – 2x + y) – 4(5z + x – y)
38.
a2 – a + 4a – 3a2 + 1
Find the additive inverse and multiplicative inverse for each number:
39.
-
2
9
40.
1.4
Name the property illustrated by each equation (see 1.2 notes and 1.3 notes for properties)
41.
3a + 0 = 3a
42.
(6m + 8m) + 7m = (8m + 6m) + 7m
44.
æ1ö
5y ç ÷ = 1
è 5y ø
47.
If p = -5 and -5 = q, then p=q.
45.
(
)
5 x + 5 = 5x + 5
48.
If x – 5 = 13, then x = 18.
43.
(6m + 8m) + 7m = 6m + (8m + 7m)
46.
If 14 = -7x, then -7x = 14
49.
If
1
3
x = 9, then x = 27.
Write an algebraic expression to represent each verbal expression:
50.
8 less than the product of 5 and a number
51.
15 increased by the cube of a number
52.
4 more than the quotient of a number and 3
53.
6 decreased by twice the square of a number
Write a verbal sentence to represent each equation:
54.
55.
2(c– 1) = 3c
x
4
+ 8 = -16
Solve the equations:
56.
4n + 20 = 68 – 2n
57.
-3b + 7 = -18 + 2b
58.
100 = 20 – 5r
59.
62.
6y – 15 = -3(2y – 7)
63.
7–
1
2
x=3
Solve the equations:
60.
a-
2a
=3
5
61.
Solve for the specified variable:
64.
a = 3b – c, for b
67.
65.
A=
x + y , for y
2
66.
3x – 24 = -5x
H = vt – gt2, for v
(Draw a picture, and use algebra to solve this problem)
Robert’s father is five years older than three times Robert’s age. If the sum of their ages is 53, find the age of
Robert’s father.
69.
- 12 n = 85
The length of a rectangle is 10 cm longer than its width. If the total perimeter of the rectangle is 44 cm, find the
dimensions.
68.
3
4
(Use algebra to solve this problem)
Jason started with d dollars in his piggy bank. One week later, Jason had doubled the amount in his piggy bank.
Another week later, Jason was able to add $20 to his piggy bank. At this point the piggy bank has $50 in it. What
amount did Jason start with?
(Use algebra to solve this problem)
Evaluate each expression if w = -4, x = 2, y =
70.
|22y + z| + |yz|
71.
1
2
and z = -6:
3|wx| +
1
4
|4x + 8y|
72.
10 – |wy| + |z + x|
Solve each equation. Check your solutions:
73.
|x + 15| = 37
74. |y – 13| = -24
77. |4a + 3| = 15 – 2b
75.
|8d – 2| – 5 = 13
78. |5b + 9| + 16 = 2
76.
79.
-2|7 – 3y| – 6 = -14
|8 + p| = 2p – 3
_________________________________________________________________________________________________________
ANSWERS:
1) 5
2) 6
3) 18
4) 36
5) 30
6) 6
7) 0
8) undefined
9)
rational
10)
rational
11)
irrational
12) integers, zero
16) integer, rational, real
13) rational, real
15)
rational, real
20)
irrational, real
26)
rational, real
27) natural, whole, integer, rational, real
30)
rational, real
31) rational, real
36)
4a–3b
42)
commutative prop
43) associative property
44)
multiplicative inverse 45)
47)
transitive property
48)
49)
multipliation property
53)
6–2x2
60)
a=5
68)
41 years old
75)
d=5/2 or d=- 2
37)
21) rational, real
13y
38)
22) not real
n=¼
addition property
62)
69)
76)
32)
-2a2+3a+1
54) various answers
61)
17) irrational, real
y=3
$15.00
55)
63)
x=3
70)
8
y=1 or y=11/3
23)
AI: 2/9
71)
77)
b=
rational, real
33)
MI: -9/2
various answers
64)
18) rational, real
whole, integer, rational, real
19) whole, integer, rational, real
24) not real
25) rational, real
28) natural, whole, integer, rational, real
irrational, real
39)
14)
a+c
3
27
a=2 or a=-9
2j–k
40)
56) n=8
65)
72)
34)
29) rational, real
77–4p
35)
-8x+6y–12z
AI: -1.4 or -7/5 MI: 5/7
distributive prop
50)
5x–8
57)
b=5
y=2a–x
12 73)
78)
66)
v=
identity prop
46) symmetric property
51)
58)
41)
15+x3
52)
r=–16
59)
67)
H + gt 2
t
x/3 + 4
x=8
6 cm x 16cm
x=22 or x=-52
74)
no solution
no solution
79)
p=11