Download 1 # Algebra 2/Trig Name: Unit 1 Notes Packet Date: Period: Powers

Algebra 2/Trig
Unit 1 Notes Packet
Name:
Date:
Period:
Powers, Roots and Radicals
(1) Homework Packet
(2) Homework Packet
(3) Homework Packet
(4) Page 277 #4 – 10
(5) Page 277 – 278 #17 – 25 Odd, #37 – 61 Odd
(6) Page 277 – 278 #18 – 26 Even, #38 – 60 Even
(7) Worksheet evens
(8) Worksheet odds
(9) Page 411 #5 – 20
(10) Page 411 – 412 #22 – 79 Column
(11) Page 411 – 412 #23 – 47 Column, #51, 54, #57 – 73 Column, #77, 80
(12) Page 411 – 412 #25 – 49 Column, #52, 55, #59 – 81 Column
(13) Chapter Review ***TEST TOMORROW***
1
#
5.3 and Supplement Simplifying Radicals (Add, Sub, Conjugates – no variables)
Perfect Squares: A number whose square roots are integers or quotients of integers
(R,I,E/3)
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400... (Integers)
x2, x4, x6, x8, x10… (Variables)
1/4, 9/25, 4/49, 81/100…(Quotients of Integers)
An expression with radicals is in _______________________________ if the following are true:
1) All radicals are broken down
2) All coefficients are reduced
3) No radicals are in the denominator
Helpful Hint: It is often easier to break down radicals first in an attempt to make the numbers more
manageable.
E1) Simplify the expression √
P1) Simplify the expression √
E2) Simplify the expression
a. √
b.
√
c. √
b.
√
c. √
P2) Simplify the expression
a. √
E3) Simplify the expression √
P3) Simplify the expression √
2
E4) Simplify
√
a. √
√
b. √
√
b. 8√
√
P4) Simplify
a. √
√
√
E5) Simplify
a. √
√
b. √
√
√
c.
d. (
√ )
√
P5) Simplify
a. √
√
b. √
√
√
c.
E6) Simplify
a.
b.
√
√
P6) Simplify
a.
b.
√
3
√
d. (
√ )
√
5.4 Complex Numbers (powers of i)
Imaginary Numbers
The imaginary unit , is defined as
any negative number.
(I/3)
√
. The imaginary unit can be used to write the square root of
* Never leave an exponent other than 1 on the imaginary unit in simplest form*
(cycle)
Complex Numbers
A complex number in standard form, where
is the real part and
E1. Solve 3x2 + 10 = -26
is the imaginary part:
P1. Solve 2x2 + 26 = -10
E2. Write the expression as a complex number in standard form
a.
b.
c.
4
P2. Write the expression as a complex number in standard form
a.
b.
c.
E3. Write the expression as a complex number in standard form.
a.
b.
c.
P3. Write the expression as a complex number in standard form.
a.
E4. Write the quotient
b.
c.
in standard form
P4. Write the quotient
5
in standard form
7.1 nth Roots and Rational Exponents
(I/2)
Vocabulary:
⁄
√
Examples:
Radical Form (Rads)
Rational Exponent Form (No Rads)
√
⁄
√
⁄
√
⁄
⁄
⁄
⁄
√
⁄
⁄
⁄
⁄
or
⁄
⁄
⁄
⁄
Practice:
Express using rational exponents (no rads)
E2. √
E1. √
E3. √
E4. √
Express using radical notation (rads)
E5.
⁄
E6.
⁄
⁄
⁄
E7.
⁄
⁄
⁄
E8.
⁄
Simplify
E9. √
E10. √
E11.√
6
E12. √
⁄
⁄
Express in simplest radical notation (rads + simplify)
E13.
⁄
E14.
⁄
⁄
⁄
E15. √
E16.
⁄
⁄
Evaluate (with calculator). Round answers to the nearest hundredth (2 decimal places)
E18. √
E17. √
Evaluate (without calculator).
The following order might help without a calculator:
1) eliminate negative exp
2) change to radical form
E19. √
E21. √
E20.
3) simplify rad
4) simplify exp
E22. –
Solve the equation (use a calculator to approximate answers). Round answers to the nearest hundredth.
The following order might help
1) isolate exponent
2) destroy exponent
3) isolate variable (solve for x)
E23.
E24.
E25.
7
E26.
7.2 Properties of Rational Exponents (include examples with variables)
(I/4)
The properties of exponents can be applied to rational exponents to simplify the expression
E1. Use the properties of rational exponents to simplify the expression
a.
b.
c.
d.
e. (
)
d.
e. (
)
P1. Use the properties of rational exponents to simplify the expression
a.
b.
c.
E2. Use the properties of radicals to simplify the expression.
a. √
√
b.
√
√
P2. Use the properties of radicals to simplify the expression.
a. √
√
b.
8
√
√
E3. Write the expression in simplest form.
b. √
a. √
P3. Write the expression in simplest form.
b. √
a. √
E4. Perform the indicated operation
a. ( )
( )
b. √
√
b. √
√
P4. Perform the indicated operation
a. 5( )
( )
E5. Simplify the expression. Assume all variables are positive.
a. √
b
⁄
c. √
d.
P5. Simplify the expression. Assume all variables are positive.
a. √
c. √
b
9
d.
E6. Write the expression in simplest form. Assume all variables are positive.
a. √
b. √
P6. Write the expression in simplest form. Assume all variables are positive.
b. √
a. √
E7. Perform the indicated operation. Assume all variables are positive.
a. √
√
b.
c. √
√
c. √
√
P7. Perform the indicated operation. Assume all variables are positive.
a. √
√
b. 3g
10