Mathematics 12 (WCP) Year Plan
Resources:
Prepared by: June Wong
Pure Math Grade 12 Workbook, Addison-Wesley Mathematics 12
Exam Specs, Ray Mickelson Math 12 Student Workbook
Open Learning Agency Notebook Templates, Coles’ Notes
Week 1: Week of January 13
Topics:
Intro./Warm-up Exercise
Review transformation of parabolas y=a f(x-p)2+q
Apply to functions in general
Review domain & range
Translation techniques: y=f(x-p), y=f(x)+q
Reflection: y=-f(x), y=f(-x)
Transformation
Review concept of inverse x=f(y)
7 Sessions (x2x50)
Reflection of inverses x=f(y)
Investigating stretching af(x) and f(bx)
Stretching techniques
Use of terms: Compression, Expansion, factors
Combination of transformation & order of operations (GEDMAS)
The importance of using standard form: y = a [b f(x-p)]+q
Week 2: Week of January 20
Topics:
Graphing Absolute-Value Functions
Notes on y=f(|x|) (optional)
Investigating Reciprocal functions (trends and asymptotes)
Graphing Calculator Skills
Guidelines for sketching Reciprocal functions
Review: difference between 1/f(x) and f-1(x)
Transformation Test
Review: difference between 1/f(x) and f-1(x)
Worksheet:
Introduce conics sections: dissecting a cone: Icecream cone? Carrots?
Review parabolas
Sketching x=a(y-p)2+q, locating vertex
Graphing basic circles and rectangular hyperbolas x2  y2=  c2
Hand-sketching and graphing calculator skills
Properties of hyperbolae:
Transverse/conjugate axis, equations of asymptotes, generalization
Transformation: Translation of conics
Conic Section Handout
Conics generalization centre (0,0)
Week 3: Week of January 27
Topics:
Stretching: circle--> ellipse, major/minor axes
Applying principle to hyperbolas
Review completing the square
Standard form/General form conversion
Conics:
5 Sessions (x2x50)
Special case of hyperbola: y=1/x (Where’s the box?)
Studying general form Ax2+By2+Cx+Dy+E=0
Practice writing examples of each type of conic sections.
Warm-up: Laws of Exponents
Introduce concept of logarithm as the inverse of exponential (2.2)
Domain and Range
Working with common log and different bases/Calculator Skills
Worksheet: Common log
Laws of Logarithm: Product/Quotient/Power
Solving Exponential Equations using the power rule(2.11)
Test Conics
Logarithm and Banking:
8.5 Sessions (x2x50)
Week 4: Week of February 3
Topics:
Change of base rule (2.3)
Applications: Banking & Compound Interest (Review+ problem: p.84 #12)
Introduce continuous growth/ e and ln x/ Calculator skills
Solving log equations, proofs of identities/format (2.12)
Worksheet:
Laws of Logarithm: True or false
Compound Interest/Continuous growth worksheets
Compound Interest from Mickelson’s Math 11 Workbook
Week 5: Week of February 10
Topics:
Graphs of exponential and log functions, inverses (2.6, 2.10)
Test Log/e
Intro to Sequences & Series/Notations
Arithmetic Sequence (quickie review)
Geometric Sequence and Series (2.7, 2.8)
Infinite Geometric Series (2.9)
Worksheet:
Matching Exponential functions and its inverses
Week 6: February 17
Sigma Notation
Applications of logarithm/half-life, doubling time formulas (2.4)
Real life applications: Richter scale/pH/deciBels (2.5)
Further work on continuous decay and growth
Worksheet: Sue Harberger’s supplement, half-life worksheet
Trigonometry (Chapter 3)
Radian Measure/Arclengths/Calculator skills (3.2)
Angles in Standard Position/+,- angles/Coterminal Angles
Worksheets: Conversion from Degrees to Radians
Sequence & Series:
5 Sessions (x2x50)
Week 7: Week of February 24
Topics:
Reference Angles
Quickie review: Primary Trig Functions: SOHCAHTOA
Introducing Reciprocal Trig Functions/Calculator skills (3.9)
Test Sequence & Series/Applications
Trig Graphs, Angles:
8 Sessions (x2x50)
Introduction to Unit Circle (3.3)
Finding Trig ratios of special angles: Using reference angles (Ref angle of 900?)
Worksheets:
The Six Trig Functions of Special Angles: leading to ASTC rule/graphs
Extension: ASTC rule
Trig Functions of Angles in Standard Position: non-special angles
Investigating Graphs of Trig Functions (3.6, 3.8, 3.9)
Activity: Graphing Exercise: Sketching y=sin x, y=|sin x|, y=csc x y=|csc x| etc…on three pieces
of graph paper (1 day classwork)
Recap: Basic Periodic Functions (Chapter 3, 4.1, 4.6, 4.7) Bring your graphs!
Properties of Trig Graphs: Amplitude, Period, Phase Shift, Vertical displacement,
(Review transformation terms and concepts!) Asymptotes (4.2, 4.3, 4.6)
Investigating Transformation of Trig Functions: y=a sin b (x-c) + d
How to find period given value of b
Graphing Calculator Skills
Graphing Cont: Transformation of Reciprocal Functions. Lots of Practice!
Worksheet:
Investigating properties of basic trig functions (4.1, 4.6, 4.7)
Investigating transformation of trig functions (4.2, 4.3)
Dates: Week of March 3
Topics:
Functions in the form y=sin(2/p), Meaning of sin2x and sin-1x
Quiz graphing & angle measures
Solving simple trig equations such as sin= k including exact values
Solving Trig Equations by Graphing and Algebra (including general solutions,
restricted domains, multiple angles such as y=sin nθ and second degree equations)
Graphing Calculator Skills
Trig Identities: odd-even, tan=sin/cos, sin2 +cos2 =1 Prove by geometry
Two-Column Proof Format
Dates: Week of March 10
Trig Equations/Identities:
6 Sessions (x2x50)
Sum & Difference/Double Angle Identities (Derived by Two-column proof format)
24-hour clock. Word Problems (4.5)
Test Trig Equations and Identities
Intro to Combinatorics/Probability: Mindset for studying these topics
Bring Die/Poker!
The Fundamental Counting Principle
Tree Diagrams/Working with factorials!
Permutations: different objects, Calculator Skills (MATH/PRB menu)
Dates: Week of March 17
Topics:
Permutations: identical objects
649/Lottery examples/Sitting in rows and circles (Controversial!)
Pascal’s Triangle: Solving Pathway Problems, Chess Problems
Combinations:
The Binomial Theorem (Expansions/finding a term)
6 Sessions (x2x50)
More applications/Fun: World Cup Soccer
Test Combinatorics
Worksheet: Binomial Further Practice
Probability (Chapter 7) Chance of Raining
Experimental and Theoretical Probability
Venn Diagram/Tree Diagram/Sample Space/ (7.1, 7.2)
Addition/Multiplication Law
Dates: Week of March 24
Topics:
Notations: P(A), 7.3 P(A or B), 7.4 P(A&B)
Multi/Flip/Roll Experiment
Independent/Dependent/Mutually Exclusive Events
Complement of P(A)
7.5 Conditional Probability, P(A|B)P(B)=P(A&B)/Medical Test
7.6 Probabilities using Permutation and Combination
7.7 Binomial Probability
Birthday Problem?
Probability:
6 Sessions (x2x50)
Test Probability
Worksheet: Conditional Prob Supplement/What was wrong with?
Date: Week of March 31
Topics:
(8.1-8.3) Discrete and Continuous Distribution
Population vs Sample
Mean and Standard Deviation for a sample
Binomial Distribution: Mean and Deviation
Calculator Skills
First Stat Quiz
Statistics:
6 Sessions (x2x50)
Worksheet: Linda Rajotte’s “Making Connections”
(8.4-8.7) Normal (Continuous) Distribution
Standard Normal (z-values using tables and graphing calculators)
Modelling Real Situations using Normal Distribution
Using Normal to Approximate Binomial (binompdf, binomcdf)
Calculator Skills (DISTR, normalcdf, invNorm etc)
Second Stat Quiz
April 7, 8
April 9
Exam preparation/Year End Reinforcements
Final Exam
Enrichment/Review Materials
Transformation:
Logarithm:
Problem Set 2001#6 (Math Mouse) & Problem Set 1999
Problem Set 2001#2, Problem Set 1999 (A System of log equations)
Graph log y=log x etc
Sequence/Series
Antique Worksheets, Mickey Mouse Fractals
Trigonometry
Wenny’s question, Antique Worksheets, Problem Set 2001#7
Rewriting y=sin2x in standard form.
Combinatorics
Problem Set 2001#5 (Poker Hands) and accompanying teaching notes
World Cup 1st round
Probability
Dave’s Cupcake Problem. Problem Set 2001#4
Fun: Probability of getting 85% before and after provincial exam
Breathalyzer extra practice
Selections from Alberta Math 30 Exams