Unit 0: Review
Days
1
2
3
4
5
6
7
8
9
(9 days)
Learning Goals
Introduction to Course
Review
Success Criteria
Worksheet
A, B
C, D
Unit 1: Trigonometric Ratios
Day
1
1.1
Learning Goals
Sine, Cosine, and Tangent of Special Triangles
-special triangles and ASTC rule
-given pt on the unit circle (x, y): cosθ = x, sinθ =y and tanθ =y/x
-drawing angles in standard position
Success Criteria
p.2 #1-6, 8-10, 16,
18
-finding reference angle:
R= 180 – angle (II)
= angle – 180 (III)
= 360 – angle (IV)
-using reference angle to find trig ratios of angles greater than 90
degrees.
Angle = 180 – ref (II)
Angle = 180 + ref (III)
Angle = 360 – ref (IV)
2
1.2 – Sine, Cosine, and Tangent of Angles from 0 to 360 degrees
-calculator VS. exact
-finding trig ratios given a point (x, y)
e.g. #4
p. 5 #1-4, 6*, 8, 9,
12, 15- 17
3
1.3 – Trigonometry of Angles
-find angles given ratio or coordinate
p. 9 # 6-11, 13, 16,
17*, 18*
4
1.4 – Solving Problems Using Primary Trig Ratios
-finding side
p. 12 #1-5, 7-10,
16, 17
5
-finding angle
side: #1, 4, 7a, 8,
9, 10
6
1.5 –Solving Problems Using the Sine Law
angle: #2, 3, 5, 7b,
16, 17
p. 17 #1-13
Finding missing side
side: #1, 3, 10-13
Finding angle/solving triangle
angle: #2, 4-9
Ambiguous case:
If a, b and A are known and if a<b:
7
1. a < bsinA, no triangle is possible (a = 6, b = 10, A= 50o)
2. a = bsinA, only one triangle is possible (a = 4, b = 5,
A= 53o)
3. a > bsinA, two possible triangles (ambiguous case)
(a = 6, b = 10, A= 30o)
8
9
10
11
1.6 – Solving Problems Using the Cosine Law
p. 20 #1-12
Finding side
side: #1, 3, 5, 7-9
Finding angle/solving triangle
Review
Test
angle: #2, 4, 10-12
Unit 2: Sinusoidal Functions
Day
1
Learning Goals
2.1 –Graphs of Sinusoidal Functions
Success Criteria
p. 24 #1 , 2, 4, 6, 7
(group work)
-sine and cosine graphs
-unit circle (#1)
-max/min, amplitude, period, domain/range, intercepts
2
2.2 – Translations of Sinusoidal Functions
p. 28 #3 –13
-d-value (phase shift)
-c-value (vertical shift)
-how does domain and range change?
-Period/Amplitude (no change)
*graphing two transformations/writing equation of function
Range: -1 + c < y < l +c
3
2.3 – Stretches, Compressions and Reflections of Sinusoidal
Functions
a changes AMPLITUDE (multiply AMP by a)
k changes PERIOD (divide period by k)
p. 31 #1-3, 6-8, 1013
*finding equation
Range: -a < y < a
4
2.4 Combining Transformations of Sinusoidal Functions
p. 34 #4-10, *12,
13-16
x

 d , ay  c 
k

Apply transformations to key points using: 
Range: -a + c < y < a+c
5
Quiz
6
2.5 Representing Sinusoidal Functions (writing equations)
Amplitude =
max  min
2
Period =
2
k
k=
2
P
p. 36 #2-7, *9/10,
11-18
c= equation of axis of graph
= max – amplitude OR
7
max  min
2
2.6 Solving Problems Involving Sinusoidal Functions
p. 40#1, 3-11
Unit 3: Model With Vectors
Learning Goals
Lesson
Number
1
2
Success Criteria
3.1
Vectors
-vectors (magnitude and direction) and
scalars (magnitude only)
-true bearings (begins N and rotated
clockwise)
-quadrant bearings (east or west of northsouth line)
-parallel vector
-equivalent vectors (equal in magnitude and
direction)
-opposite vectors (equal in mag. with opposite
direction)
Components of Vectors
3.2
p. 45-46 #1-9, 11, 13
p. 48-49 #1-9, 11-14
-horizontal component =vcosӨ
-vertical component= vsinӨ
3
Adding Vectors
-Addition: head-to-tail (triangle) method or
parallelogram method
3.3
p. 52-53 #1-12, 15
3.4
p. 55-56 #1-10
3.5
p. 58-59 #1, 3-8, 10-14
-zero vector
-commutative property, associative property,
identity property
4
Subtracting Vectors
-Subtraction: add the opposite or using the
tail-to-tail method
5
Solving Problems Involving Vectors
-finding resultant vector and direction
*airplane question (resolve into rectangular
components)
6
Test
Unit 4: Solving Exponential Equations
Days
1
Learning Goals
4.1 –The Exponent Laws
-multiplication/division
Success Criteria
p. 61-62 #1 –8, 1012
(product/quotient law)
-power of a power (power law)
-negative exponents
-fraction as base
-fraction as exponent
-zero exponent
*example #10 (changing base)
2
4.2 –Solving Exponential Equations Graphically
-exponential growth/decay
-finding equation given the graph
p. 66-67 #1, 2, 5-9,
10a, 11
*example #11 (using calculator)
3
4.3 –Solving Exponential Equations Numerically
-make both sides of equation have the SAME base
4
4.4 – Points of Intersection
-find x algebraically and plug in to find y-value
*(using calculator find point of intersection)
5
4.5 – Logarithms
-logarithm is inverse of exponent (use graphs)
-converting exponential to logarithmic form and vice versa
-evaluating logs
p. 75 #1-9
6
4.6 – Solving Problems Using Logarithms
-change of base formula
-compound interest (take log of both sides or change to log
form)
-sound/pH/Richter scale
p.78-79 #1-3, 6-13
-half life/doubling time
p. 69-70 #1,2, 4, 5,
9, 10, *11
p. 72-73 #1- 10
p. 70 #8
p. 141-142 (sheets)
#8-10a, 14, 15a, 16,
17a, 18, 19
Unit 5: Polynomial Functions
Days
1
(11 days)
Learning Goals
5.1 – Identifying Polynomial Functions
Success Criteria
p. 82-84 #1-10, 1112 (not c)
-definition of a function (v. line test)
-what is a polynomial function (degree of function)
2
5.2 Graphs of Polynomial Functions
-even and odd degree polynomial functions
-end behaviour, domain and range
-finite differences
p. 86-89 #1-5, *6, 9,
13, 14
3
5.3 Comparing Polynomial Functions
p. 91-93 #1-6
1. Turning points:
#10-15 (graphing
calculator)
A polynomial func’n of degree n has at most
n – 1 turning points
(i.e. f(x) = x2 has ONE turning point)
MINIMUM: for odd, zero and for even, 1
2. Number of Zeros:
-degree n = up to n distinct zeros
-odd degree MUST have at least ONE zero
-even degree may have NO zeros
MINIMUM: for odd, 1 and for even, zero
Even and Odd Functions:
NOT the same as even and odd DEGREE functions.
Even/odd functions are defined by the symmetry or lack
of symmetry of the function.
Symmetry:
Plug in a –x and check:
-even functions, where f(-x) = f(x), are symmetrical in the y-axis
b(line symmetry)
-odd functions, where f(-x) = -f(x), have rotational symmetry
about the origin. (point symmetry)
-MOST poly func’ns have NO symmetry, neither odd nor even
with no rel’p between f(-x) and f(x)
*extra questions from
ad. functions
X-Intercept Orders: Odd VS Even order (odd=crosses axis while
even=only touches but does not cross)
-orders 1, 2, 3
4
5.4 Evaluating Polynomial Functions
-find y when x=? (algebraically and using VALUE/TABLE
functions in calc)
p. 95-97 #1-11, *14,
*15
5
5.5 Solving Problems Involving Polynomial Functions
-min/max
-initial
-when x=?
p. 99-100 #1-7, *8,
9-13
6
5.6 Factoring Polynomial Expressions
Two days?
5.7 Difference of Squares of Polynomial Expressions
p. 103-104 #1 –17
8
5.8 Intercepts of Polynomial Functions
-sketching a graph using the intercepts and end behaviours
p. 108-109 #1-5, 712, *13, *15
11
Test
7
Unit 6: Solve Polynomial Equations
p. 106#1- 8, 10, 12
(9 days)
Learning Goals
6.1 Simplifying Polynomial Expressions
-expanding
Success Criteria
p.112-113 #1-10,
12, *16
2
6.2 Strategies for Solving Polynomial Equations
-factoring
3
6.3 Solving Equations of the Form xn=a
4
6.4 Functions and Formulas (two days)
5
6.5 Solving Multi-Step Problems Using (two days)
Polynomials Equations
p. 115-116
11, 12
p. 118-119
7-10
p. 121-123
10 ,14
p. 125-127
11-13, 15
Days
1
#1-9,
#1-5,
#1-7,
#1-9,
Unit 7: Solving Problems Involving Geometry
Days
Learning Goals
7.1 Area of Two-Dimensional Objects
-conversions (imperial to metric and vice versa)
-area of circle, triangle, rectangle
Success Criteria
p. 130-134 #2-5, 9,
10
Word problems (day 2)
#12-23
2
7.2 Surface Area of Three-Dimensional Objects
-sphere, rectangular prism, cylinder
p. 136-138 #1-15
3
7.3 Volume of Three-Dimensional Objects
-conversions
-sphere, rectangular/triangular prisms, cylinder
p. 140-143 #1–12,
14-16, 18, *21, *23,
*24
1
4
5
6
10
(two days)
TEST
7.4 Properties of Circles
-chord, arc, segment
-tangent/secant
-sector, central angle
-inscribed angle
-arc length=fraction of circle x circumference
-area of sector (fraction of circle x area)/segment
7.5 Investigating Properties of Circles
-equal chords = equal distance from centre
-right bisector of chord =passes thru centre, perpendicular to
chord, passes thru midpoint
-same chord = inscribed is half central
-equal chord = central/inscribed angles are equal
-same chord = inscribed equal (if one same side of chord)
-inscribed angle subtended by diameter = right angle
7.6 Solving Problems Involving Properties
of Circles
Test
p. 146-147 #1-12
p. 150-151 #1-6, 1416
p. 153-154 #1-11