Download Study Guide for Exam 1

Math 233A
Intermediate Algebra
Fall 2012
Study Guide for Exam 1
E x a m 1 is scheduled for Wednesday, September 12*. Y o u may use a 3" x 5" note card (both sides) and a
scientific calculator. Y o u 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 E x a m 1 you w i l l need to be able to:
1. K n o w 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:
Order of Operations:
anythin^= positive
- grouping symbols (),[ ], {} (inside follow order of op. too)
- exponents and roots
- anything = negative
- multiplication/division (left to right)
- addition/subtraction (left to right)
2. K n o w 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: ^ + — = at/ ± be ,
fd
.
. .
.
Multiplication:
a c
b d
Division:
=
ac
d
be
(multiply straight across the top and the bottom, unless you can cross cancel first)
bd
1^^^^.^^^
b
. ^ common denominator, add/subtract numerators and keep denominator)
bd
(flip the 2"^ fraction and multiply)
be
Positive Fractions:
Negative fractions:
-a
a
a
-a
a
-b
b
b
b
-b
3. Translate phrases into mathematical statements. 1.3 & 1.4
* Subtract:
a subtract b means: a — b
* Subtracted from:
a subtracted from b means: b — a
4. Negative with exponents. 1.6
if n is even, the number is positive
(-ay
if n is odd, the number is negative
5. K n o w the difference between -V = -4,
(-2)=' = 4,
and
{-xf
-(-2)^ = -4 (exponents first!)
6. Evaluate an algebraic expression variables given specific values for the variables. 1.4
7.
Simplify expressions using the rules o f exponents, including expressions with both positive,
negative, and zero exponents. 1.5
* product rule: x'" -x" = jc'"^"
* power rule: {x ) = x
* zero exponent rule:
* add/subtract with same base: x'" ± x" no rule!
1
1
* negative exponent rule: x " = — a n d - ^ = x"
=\
x"'
* quotient rule: — = x"' "
* expanded power rule:
'ax^
* fraction raised to negative exponent:
a'"x'"
a
b'"y"
b'"' a'"
8. Convert decimal numbers to scientific notation and convert scientific notation to decimal numbers.
1.6
axlO"
if n > 0, the number is 1 or greater
if n < 0, the number is smaller than 1
* moving decimals:
add:
<
subtract:
3. Multiply and divide numbers in scientific notation. 6.3
^multiplying: (axW"){bx\(r) =
abx\(r*"
*
dividing: (£^^1^ = ^x10'"-"
^ (^xlO")
b
Practice Problems
The solutions to all the problems listed below, are posted on my website. For those o f you who have the
Chapter Test Prep Video cd that came with the book, you can use it to see someone solving each o f the
problems in the Chapter Tests. If you don't have it, it is available at the Math Lab.
Intermediate Algebra
Chapter 1 Exam Review
Name
1. Insert > , <, or = between each pair to make a true statement.
a.)
-4.06
-(-5)
23
-(-5)
2. Arrange the numbers from smallest to biggest.
b.)
-4.2
-4.02
d.) 8 - - 2
8-(-2)
3.
-(_5)2^5.(_22)
-(-1),
4.
6.
Simplify:
!8^(6)(3) + 18^(6-3)
5.
Simplify:
7.
5-(2'-2')-(V8-5)
Simplify:
Simplify:
1 0 - 7-2(5-^27)
Simplify:
[-7 - (-2)]
+ [VsT + V27 - 3] +
(-5')
8.
Simplify:
9.
Simplify:
^/l00-2(2'•5-2')
10. Divide:
4+ 3(2-5'^3)'
11. Divide:
-^•X-^-^)
2-[(V9-5)-2']
-3.3-(-3.3)
12. A d d :
-3-2^-5
13. A d d :
—
_T_ 1 5 _ ^ _ f 5 '
+
5
15
14. Simplify:
[(3-(4-6))-2]^
2[(32^4^)-(2-4)]
16. Simplify:
12^36
("8,
15. Simplify:
1A1_1_1J_1
3
4 2
6
8
17. Simplify:
6 14
8-lof
3 (-4)+ 4
12
+-
9 •[
6
718
1 4
18. Evaluate for jc =-2.1:
-3x^ +
5JC +
8
20. Evaluate for x = 5 and;^ = -4 :
19. Evaluate for x = 1.2 andj^; = 3.4 :
x~+xy~2y~
21. Evaluate for x = -2 and _)/ == Vi:
-x~ -xy + Ay'
22. Simplify.
23. Simplify.
-3-2''-3-2-'
24. Multiply.
25. Simplify.
(-3x//)^
26. Simplify.
i-^x'y'zr
27. Multiply.
{-2x'yzyi:^x'/)
28. Simplify.
6x'y'z
30. Simplify.
29. Simplify.
M X
31. Convert the following to scientific notation.
0.0000000978
4x-\'i
32. Convert the following to standard form.
2.64x10'
33. Multiply.
34. Divide.
35. Simplify.
(2.5xl0')(3.4xl0-')
2x10"'
(2.5x10* )(1.5xltf)
4x10'
(7.5 xlO-")
36. There are 675,000,000 square feet o f Wal-Mart to 300,000,000 U.S. citizens. Find how
feet per U.S. citizen in scientific notation.