The Binomial Theorem.notebook
January 15, 2013
1
The Binomial Theorem.notebook
January 15, 2013
2
The Binomial Theorem.notebook
January 15, 2013
3
The Binomial Theorem.notebook
January 15, 2013
4
The Binomial Theorem.notebook
January 15, 2013
5
The Binomi
PC11
Quadratics
Lesson 5: MaxIMin Word Problems ll: Revenue Problems
Example 1: A bus company carries about 15 000 riders per day for a fare of $0.80. A
survey indicates that if the fare is increased by $0.05 the number of riders
will decrease by 1000. Wh
PC11
Quadratics
Lesson 1: Introduction to Quadratic Functions
A quadratic function is a function of degree 2 (the highest exponent on the variable is 2).
The equation of a quadratic function can be written in the form y = axz + bx + c, where a, b,
and c a
PC11
Quadratics
Lesson 3: Changing From General to Standard Form
Any quadratic written in the form y = axz + bx + c, is written in the General Form
ofa Parabola. The general form gives us very little useful information so we need
to be able to change to
PC1 1
Quadratics
Lesson 4: Mafoin Word Problems |
Example 1: A ball thrown upward reaches a height of h meters after t seconds
according to the function h(t) = -5t2 + 10t + 2. F' M w
MaxiMuM MW 0 He '0.
k({-\= - 515 + rat 4-7.
m
=-s(t-2+_+| ~13 +2.
"56234
PC11
Sequences and Series
Lesson 1: Arithmetic Seguences
Example 1: The Chinese calendar identies years with animals. There are 12
animals, and this year (2012) is the year of the Dragon.
a) What are the next three years of the dragon?
2017., 2°24, 2034.
PC11
Quadratics
Lesson 9: The Discriminant
Find the roots of the quadratic equaiion:
i) by graphing and
ii) by the quadratic formula.
a) 2x3 Sx+2=0
n in M2 i.=-8 o2
= 2 [email protected]
= .27 x 3.73
Number of solutions: 2
b) 2.6" 8x+8= 0
n in M7. v.=-8 :58
=
PC11
Quadratics
Lesson 2: Standard Form of a Quadratic Function
w (uulcx fuck
y = a(.1' p]3 +q
a< o oPux'ma Jean
'3 00+ co.\ (Winn [(000
M} uukx C 99
Example 1: On the grid provided sketch the ollowing parabolas and label the vertex and the
axis of
PC11
Quadratics
Lesson 7: Solving Quadratic Eguations ll Completing the Square
Solving a Quadratic Algebraically (not on GC)
If a quadratic is factorable then it can be solved by factoring, but if it is not factorable we
can use the Completing the Square
PC11
Quadratics
Lesson 6: Solvin QuadraticE uations I: Usin the GC
Quadratic Function Quadratic Equation
Example =2xz+3x5 x2+3 5=0
WIRES d° Y. = 2945* S 2x+ 3x- 5 = o
(2x+5)(2x 235°
2
f R 'o (2x +$\Cx- 50
-2 .<. l _ -
a, I
3:112? x-mwavk/ was
é=
PC11
Quadratics
Lesson 8: Solving Quadratics Ill: The Quadratic Formula
The Quadratic Formula: to solve forx if ax" +bx+c = 0, where a > 0, use:
a) 3x2+x2=0 &. 1'
_ -| 4.- Pam234
_ 2(3; "115s 2;
c.
-2 X=-It52s_\:s= 4 4.
e 6 i», c'.
b) 536b+7=0
X :
FOM12
Trigonometry
Lesson 5: Using ASTC to Find AiSP
1. Find the reference Angle.
2. Sketch reference angle in
approprlate quadrants.
3. Find angles in standard
DOSlth C) cos-6 = 0.33
e,=7l°
62:28'10
e) ta119=3.34 =
f) tan=0.55 e, :
G
Permutations of identical Objects.notebook
January 08, 2013
1
Permutations of identical Objects.notebook
January 08, 2013
2
Permutations of identical Objects.notebook
January 08, 2013
3
Adding and Subtracting Functions.notebook
February 05, 2014
1
Adding and Subtracting Functions.notebook
February 05, 2014
2
Adding and Subtracting Functions.notebook
February 05, 2014
3
Foundations of Math 11: Unit 5 - Logic
Sardis Secondary
Unit 1 Overview Logic
Learning Outcomes
D1. Demonstrate an understanding of normal distribution, including: standard
deviation and z-scores.
Math 11 Foundations
Sardis Secondary
Chapter 3: Trigonometry
3.7 Cosine Law
For non-right triangles that cant be solved with the sine law
SAS
SSS
Cosine Law can be proven based on the _ Theorem
mr.sutcliffe.ca
Math 11 Foundations
Sardis Secondary
Example
Math 11 Foundations
Sardis Secondary
Chapter 4: Trigonometry (Obtuse)
3.6 Sine Law: The _ Case
Say you have a triangle where A=30 and b= 12 What is the height?
What happens if a is 4?
What happens if a is 6?
What happens if a is 8?
What happens if a is 15
Math 11 Foundations: Unit 3&4 - Trigonometry
Sardis Secondary
Chapter 3: Trigonometry
3.4 Sine Law
For solving some types of _ triangles
Sine law is related to the height of a triangle.
h
mr.sutcliffe.ca
Math 11 Foundations: Unit 3&4 - Trigonometry
Sardis
Math 11 Foundations: Unit 3&4 - Trigonometry
Sardis Secondary
Chapter 3: Trigonometry
3.1 Trigonometric Ratios
A Triangle with a given angle always has the same ratios:
Example: Tangent Ratio
10
6
2
A
3
9
15
Small triangle: tanA =
Medium triangle: tanA =
Math 11 Foundations: Unit 5 - Statistics
Sardis Secondary
Unit 1: Logic
1.2 Conjecture
If the same result occurs over and over again, we may conclude that it will always occur.
This kind of reasoning is called INDUCTIVE reasonin
Math 11 Foundations: Unit 5 - Statistics
Sardis Secondary
Unit 1: Logic
1.3 Counter Examples
Optical Illusions:
Inductive reasoning can easily lead to _
We know that inductive reasoning can lead to a conjecture, which may or m
Math 11 Foundations: Unit 5 - Statistics
Sardis Secondary
Unit 1: Logic
1.5 Fallacies
A fallacy is usually an improper argument in reasoning that usually results in a
wrong conclusion. A single fallacy (error) in a deducti