FMPC10
Real Numbers
Lesson 6: Exgonent Laws Part 2 [Fractional Exgonentsl Radical Form Power Form
1
X3 Examghe 3: Simpify (write answer in radical form and power form]:
a) xy = =
PC12
Trigonometry
Lesson 5: Reciprocal Trigonometric Ratios
Cosecant:
Secant:
Cotangent:
Example 1: The point P (3, -5) is on the terminal arm of angle 6 in standard position.
Draw a diagram showing 8 in standard position and nd the six trig ratios
belo
P012
Trigonometry
Lesson 1: Radian Measure
Radians are a unit different than degrees for measuring angles.
1 Radian is the measure of the central angle that contains an are that is the same
length as the radius.
211' radians =3
w
v
To change from degrees
PC12
Trigonometry
Lesson 4: The Unit Circle
The Special Triangles: m
if
306090 Triangle [E and
A
454590 Triangle Unit Circle: a circle with a radius of 1
( I Examgle 1: Use the unit circle to determine the exact values for:
a)cossE='&=-L
PC12
Trigonometry
Lesson 2: An les in Standard Position
Let P(x, y) be a point rotating about the circumference of a circle centered at
0(0. 0) with radius r. P starts at the point AM
(f s 0
An angle is said to be in standard position if the initial arm
PC11
Trigonometry
Lesson 8: Phase Shift
How is the graph of the function y = si_n[6£] related to y = sin 6?
10(x-75 2
rij r;f%
How is the graph of the function y = sin[6+§] related to y = sin 6?
In General: The graph of y = sin(9 t) or y = 1305(61) is the
PC11
Radicals
Lesson 3: Multiplying Radicals
When multiplying mixed radicals multiply iniegertr'mes integer and radicand times radicand.
Example 1: Multiply then write your answer in simplest form.
a) [fa/$51 45): 35% b) BJEXx/2 3" H4 (5%
/\ A 2x
a x
P811
Radicals
Lesson 1: Simpliging Radicals
es/E
An expression of the form V? is called an entire radical.
An expression of the form ad? is called a mixed radical.
NOTE: ax]; = a - x/E i) 'Vigyib 7%
35" =Z-Z'V'Y37
Changing Mixed Radicals to Entire Radical
PC11
Radicals
Lesson 2: Adding and Subtracting Radicals
To add or subtract radicals the radicand (the number under the 3:15} must be the
Example 1: Simplify the following
mm 15-22 3545: I
c) éBisn2£= dim7+h3ri=
a? c,.3-s -2J'7 -SS§
+3 3 SJ?
yaw/274772 2
P011
Radicals
Lesson 3: Dividing Radicals Part | Rationalizing the denominator:
The process of eliminating radicals in the denominator.
Ifthe denominator is a monomial then multiply top and bottom by radical in denominator
(denominator needs to be in simp
P611
Sequences and Series
Lesson 2: The General Term of an Arithmetic Seguence
The General Term of an arithmetic se uence:
r=a+(n1]d
Where a is the 1' term, :1 is the term number (or number of terms). d is the common
difference, and in is the n term (
P011
Radicals
Lesson 7: Solving Radical Eguations
Example 1: Solve the following equations algebraically:
a) V5214 1. Isolate the radical
3 f I 2. Square both sides
3. Solve for x
2. 2. 4. Check answers.
r:=7 ~
b) 75 cuck: 57-? .- 7 =5? +7 HW: Worksheet
P011
Radicals
Lesson 5: Dividing Radicals Part II
Examgle 1: Expand the following then simplify.
a) (Ammo2) = '3 M q
W
= El
b) (3xfE2x/E)(3\/§+2\/§) = q .2 *M_q.s
\L/
3 2o =E
(a + b! and (a p) are called conjugates. When you multiply conjugates containi
FMPClO
Real Numbers
Lesson 4: Sim ii in Radicals
On a Calculator multiply: 15 x «If; = L! =
Multipiicatiori Property of Radicals:
%-%=m
An expression of the form «E is called an entire radical.
An expression of the form ad} is called a mixed radical.
Real Numbers
Lesson 1: Introduction to Radicals
NUMBER SYSTEMS:
Natural Numbers 1N1: counting numbers.
{I.2,3,l|. :-
Whote Numbers (t: The natural numbers and U.
{0.1.2,1'4, H l-
lntegers m: The positive and negative Whole Numbers.
{. . ~3,-?,-I,0,
FMPC'lO
Real Numbers
Lesson 3: GCF and LCM
Definitions:
Greatest Common Factor lGCFl: The largest numberthat divides into each of the given
numbers exactly. (lowest power of each prime factor)
Lowest Common Muitpile [LCM]: The smallest common nonzero mult
Rea] Numbers
Lesson 2: Prime Factorization
Prime Number: Awhoie number that is divisible by one and itself. it has exactly two
different factors. [2) 3 5) . . .
Comgosite Number: A whole numberthet is not prime. {Hes more than 2 factors)
or ,eJ . . .
Lesson 4: Functions
A relation is a rule that produces one or more output numbers for every valid
input number.
A function is a relation that produces one and only one output number y for every
valid input number x. (For every x-coordinate there is only o
Chapter 4: Relations and Functions
Lesson 2: Graphing Relations
Graphs are used in mathematics as a way of making comparisons, drawing
conclusions, and approximating quantities.
Cartesian Coordinate System:
Graphs can be created by plotting
points represe
Cheater 4: Relations and Functions
Lesson 3: Domain and Range
Domain: the set of xvalues represented by the graph of a relation
Range: the set of yvalues represented by the graph of a relation
Examgle 1: Determine the domain and range.
Domain;