Download Name:_________________________ Date:________ Algebraic Expressions and Real Numbers

Name:_________________________
Date:________
Practice Set 1.1
Algebraic Expressions and Real Numbers
Translate each English phrase into an algebraic expression. Let x represent the number.
1.
A number decreased by seven.
1. _______________
2.
Eighteen more than a number.
2. _______________
3.
Five times a number increased by four.
3. _______________
4.
Six less than the quotient of a number and five.
4. _______________
5.
The difference of nine and three times a number.
5. _______________
6.
Twice the sum of a number and twelve.
6. _______________
Evaluate each algebraic expression for the given values of the variables.
7.
6 x − 14 if x = 4
7. _______________
8.
12 ÷ 3x if x = – 2
8. _______________
9.
x 2 − x if x = –3
9. _______________
10.
x 2 − y 2 if x = –5 and y = 4
10. _______________
11.
2 x 2 + 3xy − y 2 if x = –2 and y = –3
11. _______________
Determine whether the inequality is true of false. If it is false, rewrite it so that it is true.
12.
–8 > –4
12. _______________
13.
−3 −7
>
4
8
13. _______________
14.
–4.6 < –2.1
14. _______________
15.
0 < –5.3
15. _______________
1
Name:_________________________
Date:________
Use the given set to answer the following questions.
{–18, –0.42,
−1
,
8
6 , 5.8, 9, 0, 0.32 ,
1
5
, –7.36, , 210}
5
3
16.
Name the integers.
16. _______________
17.
Name the rational numbers.
17. _______________
Use the given set to answer the following questions.
{
π
6
,
4
− 15
0
, –8.3,
, 25,
, –10,
7
16
2
2 , 1, π , 0.6 , 17.2}
18.
Name the irrational numbers.
18. _______________
19.
Name the natural numbers.
19. _______________
Determine whether each statement is true of false.
20.
Every whole number is an integer.
20. _______________
21.
Some rational numbers are irrational.
21. _______________
22.
All natural numbers are rational numbers.
22. _______________
23.
Zero is a natural number.
23. _______________
24.
Irrational numbers are not real numbers.
24. _______________
25.
Whole numbers are positive and negative integers.
25. _______________
2
Name:_________________________
Date:________
Practice Set 1.2
Operations with Real Numbers and Simplifying Algebraic Expressions
Fill in the blanks.
1.
Absolute value is always _______________.
2.
When two negative numbers are added, the sum will be _______________.
3.
Reciprocals always have the _______________ _______________ because the product
of reciprocals is positive _______________.
4.
The product of a negative number and a negative number is _______________.
5.
Division by zero is _______________.
6.
The quotient of a negative number and a positive number is _______________.
Add, subtract, multiply or divide.
7.
18 – (–12)
7. _______________
8.
–16 (–4)
8. _______________
9.
125 ÷ –5
9. _______________
10.
–3.7 – 2.4
10. _______________
11.
–6 (–3)(0)(–2)(4)
11. _______________
12.
− 5 − 25
÷
8
26
12. _______________
3
Name:_________________________
Date:________
Simplify each algebraic expression using the order of operations.
13.
10 − 5(6 2 ÷ 4 + 5)
13. _______________
14.
5 + 82 ÷ 4 + 3
− 4 2 + 10 ÷ 2 + 3
14. _______________
15.
14x – 3(3x – 6) – 10
15. _______________
16.
18 – |32 – 7·2|
16. _______________
17.
(10x – 15 + 3x) – (5x – 4 + x)
17. _______________
18.
16 – 4[18 – 3(42 – 14 ÷ 2)] ÷ 22
18. _______________
19.
Use the commutative property of addition to write
an equivalent express to 3x + 18.
19. _______________
20.
Use the distributive property to write an equivalent
expression to –6(3x – 4).
20. _______________
4
Name:_________________________
Date:________
Practice Set 1.3
Graphing Equations
Match each equation with its corresponding graph.
______ 1. y = x 2 + 4
______ 2. y = x – 1
______ 3. y = – x
______ 4. y = – x 2 + 2
______ 5. y = 2x – 3
______ 6. y = –
1 2
x
4
______7. y = x + 2
______ 8. y = –
2
x –1
3
______ 9. y = x 3 + 1
______ 10. y = x
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
5
Name:_________________________
Date:________
Graph each equation.
11. y = x − 3
12. y = − x − 3
13. y = x 2 + 1
14. y = x 2 − 1
15. y = |x+ 3|
16. y = |–x – 2|
17. y = –x
18. y =
6
1
x−3
2
Name:_________________________
Date:________
Practice Set 1.4
Solving Linear Equations
Answer the question with yes or no.
1.
Is 8 a solution to the equation − 4 x + 20 = 2 x − 16 ?
1. _______________
2.
Is –4 a solution to the equation 18 − 3 x + 30 = −2(5 x − 10) ?
2. _______________
(a.) Solve each equation. (b.) Then state whether the equation is an identity, a conditional
equation, or an inconsistent equation.
3.
5( x – 3) = 15
3a. _______________
b. _______________
4.
5 + 2( 4 x – 4) = 3( 2 x – 1)
4a. _______________
b. _______________
5.
1
1 3
5
y– = y–
2
8 8
8
5a. ______________
b. _______________
6.
5(2a – 1) + 1 = 2a – 4 + 8a
6a. _______________
b. _______________
7.
6 – 2(5 y – 1) + 4 y = 20
7a. _______________
b. _______________
8.
8 + 2 x 3x – 5
=
+2
3
5
8a. _______________
b. _______________
9.
20 = 8 – 5( 2 x – 3) + 4 x
9a. _______________
b. _______________
10.
4(3a + 1) + 6 = 5 + 2(6a − 5)
10a. _______________
b. ______________
7
Name:_________________________
11.
Date:________
0.04 x – 0.06( x − 3) = 0.16 x
11a. ______________
b. ______________
12.
3x – 3
4x + 1
–2=
6
15
12a. ______________
b. ______________
13.
5( y – 2) – 2( 2 y + 3) = 5 y – 4
13a. ______________
b. ______________
14.
2x – 1 x − 3 x + 8
−
=
5
4
10
14a. ______________
b. ______________
15.
6 x − 3( x + 4) = x + 2( x + 6)
15a. ______________
b. ______________
16.
1
2
x + 8 = 10 − x
3
3
16a. ______________
b. ______________
17.
5 – 4(x – 2) = 12x – 3
17a. ______________
b. ______________
18.
x 1 x
− =
+1
5 3 15
18a. ______________
b. ______________
19.
4x – 7 = 4(x – 3) + 5
19a. ______________
b. ______________
20.
8.1x – 3.7 = 2.4x + 2
20a. ______________
b. ______________
8
Name:_________________________
Date:________
Practice Set 1.5
Problem Solving and Using Formulas
Choose the correct equation for each word problem.
______ 1. One number exceeds another by 12. The sum of the numbers is 19.
a. x + 12 = 19
b. x + ( x + 12) = 19
c. x = x + 12 + 19
______2. When four times the sum of a number and 3 is increased by 8, the result is 4.
b. 4 x + 3 = 8 + 4
a. x + 3( 4) + 8 = 4
c. 4( x + 3) + 8 = 4
______3. When 20% of a number is added to the number, the result is 330.
a. 0.20 x = 330
b. x + 20 x = 330
c.
x + 0.20 x = 330
______4. The second angle in a triangle is ten degrees more then the first and the third angle is
twice the first increased by ten degrees. The sum of the degrees of any triangle is 180 D .
a. 3x = 180
b. ( x ) + ( x + 10) + ( 2 x ) = 180
c. x + ( x + 10) + (2 x + 10) = 180
______5. After a 20% reduction, you purchase a watch for $88 .What was the original cost of
the watch?
a. x – 0.20 x = 88
b. x – 20 = 88
c. x – 0.20 = 88
______6. Including an 12% sales tax, a hotel charges $210.80 per night. Find the hotel’s nightly
charge before the tax was added.
a. x + 0.12 x = 210.80
b. x + 0.12 = 210.80
c. x + 12 x = 210.80
______7. The length of the vacant lot is three times as long as the width. If the perimeter is
152 ft., find the measurements of the lot.
a. x + 3x = 152
b. x (3 x ) = 152
c. 2 x + 2(3 x ) = 152
______8. This month’s cell phone bill is $45.00 The base charge is $20 per month with each
minute costing 5¢. Find how many minutes where used this month.
a. 20 + .05 = 45
b. 20 + 0.05x = 45
9
c. 20 x + .05x = 45
Name:_________________________
Date:________
Write an equation for each situation. Then solve.
9.
One number is five times another. Their sum is 72.
Find the numbers.
_______________
10.
Twice the sum of a number and eight is thirty-six.
Find the number.
_______________
11.
The length of a rectangle is four times the width. The
perimeter of the rectangle is 55 inches. Find the
dimensions of the rectangle.
_______________
12.
When a number is increased by 8% of itself, the result
is 54. Find the number.
_______________
13.
The monthly cell phone bill is $85 which includes taxes,
surcharges and 300 text messages. Any text messages
after 300 cost $0.10 each. If the bill for one month is $107,
find the total number of text messages.
_______________
14.
The price of a new refrigerator is $1295. If the store is
having a 20% off sale, find the sale price of the refrigerator.
_______________
Solve each formula for the specified variable.
15.
d = rt for t
_______________
16.
P = a + b + c for c
_______________
17.
V =
1
Br for B
3
_______________
18.
F=
9
C + 32 for C
5
_______________
19.
A=
n
πr 2 for n
360
_______________
20.
A=
1
h( B + b) for B
2
_______________
10
Name:_________________________
Date:________
Practice Set 1.6
Properties of Integral Exponents
Use the exponent rules to simplify each expression.
1.
y6 ⋅ y2
1. _____________________
2.
a4 ⋅ a7 ⋅ a
2. _____________________
3.
(6 x 2 y 3 )(13x 4 y 5 )
3. _____________________
4.
(−8 xy 5 )(3 x 4 y )
4. _____________________
5.
⎛ −3⎞
⎟
⎜
⎝ 4 ⎠
5. _____________________
6.
⎛2⎞
⎜ ⎟
⎝5⎠
7.
(− 4 x y )
7. _____________________
8.
( −5 x 3 y ) 3
8. _____________________
9.
25 x 6 y 5
5x 2 y
9. _____________________
10.
30 x 4 y −3
10 x − 4 y −6
10. _____________________
3
−2
6. _____________________
2
4 2
11
Name:_________________________
Date:________
11.
3 x 0 + 31 − 3 0
11. _____________________
12.
5 0 + 5 x 0 − (5 x) 0 + x 0
12. _____________________
13.
(−3) −4
13. _____________________
14.
(5 x) −3
14. _____________________
15.
(3 x 3 y −4 ) −2
(9 x − 4 y ) − 2
15. _____________________
16.
(2 x −3 y 5 ) 2
(3x 5 y −3 ) − 2
16. _____________________
17.
18m 3 n −5
− 3m 3 n −8
17. _____________________
18.
24a −3b 4 c −8
4a 3 b 2 c − 4
18. _____________________
19.
(4 x 2 y 4 )(−3 x 3 y −2 ) 2
19. _____________________
20.
(6 x 5 y )(2 x 3 y −6 ) −2
( x 3 y −6 )(3 xy 7 ) − 2
20. _____________________
12
Name:_________________________
Date:________
Practice Set 1.7
Scientific Notation
Rewrite each number in scientific notation.
1.
58,000
1. ______________
2.
93,000,000
2. ______________
3.
0.00004
3. ______________
4.
0.0000083
4. ______________
5.
–8,230,000
5. ______________
Rewrite each number in decimal notation.
6.
6.7 × 10 4
6. _______________
7.
3.9 × 10 −5
7. _______________
8.
8 × 10 −7
8. _______________
9.
1.43 × 10 6
9. _______________
10.
– 5.4 × 10 3
10. ______________
13
Name:_________________________
Date:________
Perform the indicated operations. Give answers in scientific notation.
11.
(3.6 × 10 9 )(2 × 10 −4 )
11. _______________
12.
5.4 × 10 4
3 × 10 6
12. _______________
13.
8.4 × 10 5
2.1 × 10 −3
13. _______________
14.
(6.3 × 10 5 )(3.1 × 10 3 )
14. _______________
15.
(1.7 × 10 −6 )(5.8 × 10 −3 )
15. _______________
16.
7.2 × 1012
8 × 10 4
16. _______________
Rewrite each number in scientific notation. Then perform the indicated operation and give the
answer in scientific notation.
17.
(38,000,000)(0.0002)
17. _______________
18.
0.00000325
0.000000013
18. _______________
19.
4,200,000,000
0.000016
19. _______________
20.
(0.0000083)(0.00000045)
20. _______________
14