Download Review Chapter 1

Math 152 A
Intermediate Algebra
Fall 2012
Study Guide for Exam 1
Exam 1 is scheduled for Thursday, September 6'''. You may use a 3" x 5" note card (both sides) and a
scientific calculator. You are expected to know (or have written on your note card) any formulas you may
need. Think about any rules and procedures you needed to know for homework. For example: exponent
rules, etc...
For Exam 1 you will need to be able to:
1. Compare numbers, including fractions and decimals using inequality symbols. 1.2
20
I
-V23
3.62
0
2
\ 2
"7 77
— r
-6
5
-4
-3
-2
-1
0
1
2
4.3
4-»4
.1
0
2. Given roster notation or set-builder notation graph the set on the number line and vice versa. 1.2
Roster Notation:
S = { - 1 , 0, 1,2,3}
Set-Builder Notation:
S = {;c 1 -2 < X < 4 and
X
e /}
3. Identify important sets of numbers. 1.2
HVMI N u n i i > t ; -
j
Raiion.il numbers
1.4,
f
Irrational numbers
2.35
Inlegcrs
5. i
m
V2
V3
Whole numbers
Natural
numbers
1.4.42
hilcgers
V2y
Rational
iuinibers
n
w
3
Real
Zero
Negative integers
N D m n l U i ' L T rati()n;t! n i i m h c r s
nun\bers
Irrational number^
(b)
*
*
*
*
Real numbers- every number on the number line.
Rational numbers- numbers that can be written as fractions, or the decimal representation ends or repeats. Ex: 1.4, Vi
Irrational numbers- numbers that cannot be written as fractions, the decimal representation never ends and never repeats.
Integers- positive and negative whole numbers. Ex: -5, 6, 0, -1000
4. Express in set builder notation each set of numbers that are indicated on the number line. 1.2
5. Know how to simplify numbers with exponents, absolute values, simplify statements using the order
of operations and how to complete inequality statements (including fractions and decimals). 1.3 & 1.4
Absolute Value:
anything = positive
- anything = negative
Order of Operations:
- grouping symbols (),[ ], {} (inside follow order of op. too)
- exponents and roots
- multiplication/division (left to right)
- addition/subtraction (left to right)
6. Know how to add, subtract, multiply, and divide positive and negative numbers (including fractions
and decimals), while simplify expressions and using the order of operations. 1.3 & 1.4
Addition/Subtraction: — ± — - '^^-^^ (ggj g common denominator, add/subtract numerators and keep denominator)
b d
ac
a c
Multiplication:
=
(multiply straight across the top and the bottom, unless you can cross cancel first)
b d
Division:
—
b
d
bd
bd
—^
b c
(flip the 2"** fraction and multiply)
be
Positive Fractions:
Negative fractions:
-a
a
a
-a
a
-b
b
b
b
-b
7. Translate phrases into mathematical statements. 1.3 & 1.4
* Subtract:
(2 subtract b means: a—b
* Subtracted from:
^subtracted from b means:
8. Negarive with exponents. 1.6
if n is even, the number is positive
if
is odd,J the
number —
is negative
— n
— —
.
9. Know the difference between -2^ = -4,
(-2)^ = 4,
and
{-xf
-{-If = -4 (exponents first!)
10. Evaluate an algebraic expression variables given specific values for the variables. 1.4
11. Simplify expressions using the rules of exponents, including expressions with both positive,
negative, and zero exponents. 1.5
•productrule: x"' -x" = x""*"
* power rule: {X ) =X
* zero exponent rule: x° = 1
* add/subtract with same base: x'" ±x"m rule!
quotient mle:
= x"
* expanded power rule:
ax
* negative exponent rule: x"" = -i^and—^ = x"
* fraction raised to negative exponent:
a'"x'"
a
bj
a
by.
12. Convert decimal numbers to scientific notation and convert scientific notation to decimal numbers. 1.6
if n > 0, the number is 1 or greater
if n < 0, the number is smaller than 1
* moving decimals:
subtract:
add:
ax 10"
3. Multiply and divide numbers in scientific notation. 6.3
*multiplying: iaxl(r)(bxl(r)
= abxl(r'^
^ ^
''^
^
" (/,xlO") b
Practice Problems
The solutions to all the problems listed below, are posted on my website. For those of you who have the Chapter
Test Prep Video cd that came with the book, you can use it to see someone solving each of the problems in the
Chapter Tests. If you don't have it, it is available at both tutoring centers (ILC, Watsonville; MLC, Aptos).
Intermediate Algebra
Chapter 1 Exam Review
Name
1. Insert > , <, or = between each pair to make a true statement.
23
a.) - 4 . 0 6
b.) - 4 . 2
-4.02
d.) 8 - | - 2 |
8-(-2)
5
c.) - ( - 5 )
--(-5)
2. Express the set in roster form.
I .X e TV and 3 < J < 7}
3. Express the set in set builder form.
{-1,0,1,2,3,4}
4. Consider the following set of numbers. < V9, - 3 ^ , -0.9, 0, 0.3, n, Vs, 3.9, - 2 , 10 >
a. List the rational numbers.
b. List the irrational numbers.
c. List the integers.
d. List the real numbers.
5. Express in set builder notation each set of numbers that are indicated on the number line,
a.
b.
-1
^-•1
-\•
V^—'T'
-.'1
-A
-l
-1
0
1
2
3
4
6. Arrange the numbers from smallest to biggest.
-(-1),
,1.2,4,-1-2
4
-t—1
-.^
-4
\
-3
'
-1
7. Simplify:
_(_5)2^5.(-2^)
1
-1
»
»
0
»
1
2
»
-
1
-
1
8.
Simplify:
18^(6)(3) + 18^(6-3)
9.
Simplify:
10-7-2(5-^27)
11. Simplify:
10. Simplify:
5-(2'-2')-(V8-5)
[-7 - (-2)]+[V81+V27 - 3)]+(-5^)
13. Simplify:
12. Simplify:
VT00-2(2'-5-2'')
4+ 3(2-5'^3)'
14. Divide:
-3.3(-3.3)
-3.3-(-3.3)
15. Divide:
16. Add:
17. Add:
'
3^
-- +
5 . 15.
2-[(^/9-5)-2^]
-3-2'-5
r 2^
I
18. Simplify:
[(3-(4-6))-2f
2[(32 + 4')-(2-4)]
3J
7
12
15
7
36
12
+-
19. Simplify:
2_2
1_4_3
3"4'2
6
8
4
22, Evaluate for x =-2.1;
-3J'+5JC + 8
23. Evaluate forx = 1.2 and;^
x~ +xy-2y~
24. Evaluate for x = 5 and y = -4 :
25. Evaluate for x = -2 andj'
26. Simplify.
27. Simplify.
-3-2°-3-2-^
28. Multiply.
29. Simplify.
30. Simplify.
31. Multiply.
(-2x'yz'f(-4x'y')
32. Simplify.
33. Simplify.
r
V
34. Simplify.
2x-VV^
35. Convert the following to scientific notation.
0.0000000978
4;c-^)/^2
36. Convert the following to standard form.
2.64x10'
38, Divide.
-4
2x10
4x10'
37, Multiply,
(2.5xl0')(3.4xl0-')
39, Simplify.
(2.5xl0'')(1.5xl0')
'
(7.5x10^)
40. There are 675,000,000 square feet of Wal-Mart to 300,000,000 U.S. citizens. Find how many square
feet per U.S. citizen in scientific notation.