Algebra II with Trigonometry
Name: _______________________
CHAPTER 1
Date: __________ Per.: _______
EQUATIONS AND INEQUALITIES
Study Guide will be collected on the day of the test (Tuesday, Oct. 16)
The following is a list of topics presented in Chapter 1. This list is intended to help guide
your preparation for the chapter test. Please note that any material presented within this
chapter, including notes, homework, do nows, and quizzes, can be assessed.
1-1
APPLY PROPERTIES
SKILLS:
1)
2)
3)
4)
5)
OF
REAL NUMBERS
Identify properties of real numbers
Classify real numbers
Rewrite decimals as fractions
Apply the order of operations to evaluate an expression
Convert units
1-2/4-5 RADICAL EXPRESSIONS
SKILLS:
1)
2)
Simplify radicals
Add, subtract, multiply, and divide radical expressions
4-6
COMPLEX NUMBERS
SKILLS:
1)
2)
3)
4)
1-3
SOLVE LINEAR EQUATIONS
SKILLS:
1)
2)
1-4
REWRITE FORMULAS
SKILLS:
1)
2)
Evaluate powers of i.
Simplify radicals with negative radicands
Add, subtract, multiply, and divide expressions containing complex numbers
Classify numbers within the complex number system
Solve equations
Classify solution within the complex number system
AND
EQUATIONS (LITERAL EQUATIONS)
Solve an equation or formula for a specified variable
Solve problems by rewriting a literal equation and evaluating for a set
of values.
1
Algebra II with Trigonometry
1-5
USE PROBLEM SOLVING STRATEGIES
SKILLS:
1)
2)
3)
AND
MODELS
Follow a problem-solving plan to find a solution to a word problem.
Declare a variable, write an equation, solve, and summarize solution
in a sentence with appropriate units.
Solve consecutive integers, geometry, and other types of word problems
1-6
SOLVE LINEAR INEQUALITIES
SKILLS:
1)
2)
3)
1-7
SOLVE ABSOLUTE VALUE EQUATIONS
SKILLS:
1)
2)
3)
4)
Solve simple inequalities and graph solution
Solve compound inequalities and graph solution
Follow problem-solving plan to solve a word problem involving an inequality
AND
INEQUALITIES
Solve absolute value equations
Solve absolute value inequalities and graph solution
Check for extraneous solutions
Follow problem-solving plan to solve a word problem involving an
absolute value inequality
Complete the problems that follow. If additional work space is needed, use notebook
paper and staple to this packet.
I.
State the property illustrated.
1)
(a x b) x c = c x (a x b)
_______________________
2)
812 + 0 = 812
_______________________
3)
w(3x – 2y) = 3wx – 2wy
_______________________
4)
¼x4=1
_______________________
5)
m + (c + v) = (m + c) + v
_______________________
6)
-918 + 23 is a unique real number
_______________________
2
Algebra II with Trigonometry
IIA. TRUE or FALSE
1)
3.168756…. is a real number.
___________
2)
63 is an irrational number.
___________
3)
If a number is a whole number, then it is an integer. ___________
4)
A real number is a complex number.
___________
5)
An imaginary number is irrational.
___________
IIB. Rewrite 0.16363636363…… as a rational number (fraction).
III. Simplify each radical expression.
1)
54 ________
2)
-150 ________
3)
-361 ________
4)
162
________
32
5)
12 - 5 24 - 11 75 ________
6)
8 · 7 63 ________
7)
( 6 11) ________
8)
-18 · -14 ________
9)
(2
10)
8
________
6
11)
13)
2
)(
)
7 - 3 5 + 7 ________
2 3
8
________
12)
5
________
6+ 3
4- 5
________
9-2 5
3
Algebra II with Trigonometry
IV. Answer each question involving complex numbers.
1)
(3 + 2i) + (5 + 7i) _________
2)
(5 + 4i) – (6 + 2i) _________
3)
i2(4 + i) _________
4)
3i(7 + 2i) _________
5)
(5 + 4i)(3 – 7i) _________
6)
(10 – 3i)(10 + 3i) _________
7)
(3 – i)² _________
8)
i243 _________
Give the conjugate of each number.
11.) 2 + 7i _________
12.) 3 – 5i _________
Simplify.
13)
5
_________
6i
14)
26
_________
-12i
15)
5
_________
7 - 2i
16)
3 - 4i
_________
2 + 5i
17.) If 5x + 2yi = 15 + 4i, what are x and y? _________
4
Algebra II with Trigonometry
VA. Classify each of eth following numbers using all the following words that apply:
natural, whole, integer, rational, irrational, real, pure imaginary, imaginary,
complex.
1)
5 – 9i
_____________________
2)
-3i
_____________________
3)
5.76
_____________________
4)
27
_____________________
5)
7+ i 3
6)
4.12345678101112… _____________________
_____________________
VB. Convert 67 miles/hour to ft/sec.
VI. Solve each equation and simplify all answers.
1) -5(x + 3) + 5 = -(x – 2) – 4(x + 3)
3)
3x - 4 x - 7 6x - 2
=
5
2
5
5) | 1 – 2x| = 13
2)
2æ 1
ö -5 æ -1
ö
ç x - 3÷ =
ç x - 1÷
3è2
ø 8 è3
ø
4) -(5x – 2) – x = -8(x + 1) + 2x
6)
2
x -7 =5
3
7) |3x + 5| = -9
5
Algebra II with Trigonometry
VII. For each equation, solve for x.
1) P = 2r + 2x
2)
a=
v- x
t
3)
1
(x - 3y ) = 7z
2
VIII. Solve each inequality and graph on a number line.
1)
2
1
(3 - 2x ) - (x + 2) > 9
3
4
2)
3x + 1 x - 5 x
³
2
4
3
3) 17x - 13 £ -47 or 5x + 1 ³ 6
4) 12 - 3x > 3 and 4x - 1 < 6x + 7
5) -8 < 3x - 1 < 11
6) 2x - 3 + 1 £ 14
7) 6 7 - 3x - 3 > 21
8)
IX.
1
1 1
x- <
4
3 3
For the following problems:
a) State the unknown the variable represents.
b) Write an equation for the problem.
c) Solve the equation.
d) Clearly state the solution of the problem.
1) Nick is selling cell phone contracts. He makes a weekly salary of $125 and receives
a commission of $15 for each contract sold. How many contracts did he have to sell
for his income to be $320?
2) Find 4 odd consecutive integers such that twice the sum of the first two is equal to the
sum of the last two.
6