Mr. Wadge's Math Shack
  • Welcome
  • Grade 12 Courses
    • Calculus 12 >
      • Projects
      • Ch 0: PreCalculus Review >
        • 0.0 One-Day Review
        • 0.1 PreCalculus Review (part 1)
        • 0.2 PreCalculus Review (part 2)
        • 0.3 PreCalculus Review (part 3)
        • 0.4 PreCalculus Review (part 4)
        • 0.5 PreCalculus Review (part 5)
      • Ch 1 Limits and Rates of Change >
        • 1.1 & 1.2 Tangent Problem / Limit of a Function
        • 1.3 One-Sided Limits
        • 1.3 (part 2) Intermediate Value Theorem
        • 5.1 Vertical Asymptotes
        • 5.2 Horizontal Asymptotes
        • 1.4 Using Limits to Find Tangents
        • 1.5 Velocity and Other Rates of Change
        • 1.8 Review Exercises / 1.9 Chapter Test
      • Ch 2 Derivatives >
        • 2.1 Derivatives
        • 2.2 The Power Rule
        • 2.3 The Sum and Difference Rules
        • 2.4 The Product Rule
        • 2.5 The Quotient Rule
        • 2.6 The Chain Rule
        • 2.7 Implicit Differentiation
        • 2.8 Higher Derivatives
        • 2.9 Review Exercises / 2.10 Chapter Test
      • Ch 3 Applications of Derivatives >
        • 3.1 Velocity
        • 3.2 Acceleration
        • 3.3 Rates of Change in the Natural Sciences
        • 3.5 Related Rates
        • 3.6 Newton's Method
        • BONUS: Local Linear Approximation
        • 3.7 Review Exercises / 3.8 Chapter Test
      • Ch 4 Extreme Values >
        • 4.1 Increasing and Decreasing Functions (part 1 of 2)
        • 4.1 Increasing and Decreasing Functions (part 2 of 2)
        • 4.2 Maximum and Minimum Values
        • 4.0 Existence Theorems
        • 4.3 The First Derivative Test
        • 4.4 Applied Maximum and Minimum Problems (part 1 of 2)
        • 4.4 Applied Maximum and Minimum Problems (part 2 of 2)
        • 4.6 Review Exercises / 4.7 Chapter Test
      • Ch 5 Curve Sketching >
        • 5.0 Review
        • 5.3 Concavity and Points of Inflection
        • 5.4 The Second Derivative Test
        • 5.5 A Procedure For Curve Sketching (part 1 of 2)
        • 5.5 A Procedure For Curve Sketching (part 2 of 2)
        • 5.6 Slant Asymptotes
        • 5.7 Review Exercises / 5.8 Chapter Test
      • Ch 6 Trigonometry Review >
        • 6.0 Review (part 1)
        • 6.0 Review (part 2)
        • 6.0 Review (part 3)
      • Ch 7 Derivatives of Trigonometric Functions >
        • 7.1 Limits of Trigonometric Functions
        • 7.2 Derivatives of the Sine and Cosine Functions (part 1 of 2)
        • 7.2 Derivatives of the Sine and Cosine Functions (part 2 of 2)
        • 7.3 Derivatives of Other Trigonometric Functions
        • 7.4 Applications
        • 7.5 Inverse Trigonometric Functions (part 1 of 2)
        • 7.5 Inverse Trigonometric Functions (part 2 of 2)
        • 7.6 Derivatives of the Inverse Trigonometric Functions
        • 7.7 Review Exercises / 7.8 Chapter Test
      • Ch 8 Exponential and Logarithmic Functions >
        • 8.1 Exponential Functions
        • 8.2 Derivatives of Exponential Functions
        • 8.0 Review of Logarithms
        • 8.3 Logarithmic Functions
        • 8.4 Derivatives of Logarithmic Functions
        • 8.6 Logarithmic Differentiation
        • BONUS: Indeterminate Forms and L'Hôpital's Rule
        • 8.7 Review Exercises / 8.8 Chapter Test
      • Ch 9 Area Under Curves >
        • 9.1 Riemann Sums
        • 9.2 The Trapezoidal Rule
        • 9.3 Sigma Notation
        • 9.4 Limit of Riemann Sums
      • Ch 10 Integration >
        • 10.1 Antiderivatives
        • 10.2 The Fundamental Theorem of Calculus
        • 10.3 The Substitution Rule
        • 10.4 Integration by Parts
      • Ch 11 Applications of Integrals >
        • 11.1 The Average Value Theorem
        • 11.2 Volume of Rotational Solids
        • 11.3 Volume of Rotational Solids (part 2)
        • 11.4 Volume of Rotational Solids (part 3)
        • 11.5 Differential Equations
        • 11.6 Slope Fields
      • Ch 12 Cumulative Review >
        • 12.1 Cumulative Review for Chapters 1 – 3
        • 12.2 Cumulative Review for Chapters 4 – 7
        • 12.3 Cumulative Review for Chapters 8 – 9
    • PreCalculus 12 >
      • Term Project Options
      • Review of Grade 11
      • Chapter 1: Sequence and Series >
        • 1.1 Arithmetic Sequences
        • 1.2 Arithmetic Series
        • 1.3 Geometric Sequences
        • 1.4 Geometric Series
        • 1.5 Infinite Geometric Series
        • 1.6 Chapter Review
      • Ch2: Transformations (First Half) >
        • 2.1 Functions and Relations (review)
        • 2.2 Arithmetic Combinations of Functions
        • 2.3 Composite Functions
        • 2.5 Inverse Functions (Part 1 of 2)
        • 2.5 Inverse Functions (Part 2 of 2)
        • 2.7 Chapter Review
      • Ch2: Transformations (Second Half) >
        • 2.4 Transformations of Graphs (Part 1 of 2)
        • 2.4 Transformations of Graphs (Part 2 of 2)
        • 2.6 Combined Transformations
        • 2.7 Chapter Review
      • Ch3: Polynomials >
        • 3.1 Polynomials
        • 3.2 Graphing Polynomial Functions
        • 3.3 Division of Polynomials
        • 3.4 The Remainder and Factor Theorems
        • 3.5 Polynomial Applications
        • 3.6 Chapter Review
      • Ch4: Radicals & Rational Functions >
        • 4.1 Radicals
        • 4.2 Graphing and Solving Radical Equations
        • 4.3 Rational Functions
        • 4.4 Graphing Rational Functions
        • 4.5 Chapter Review
      • Ch5: Logarithms >
        • 5.1 Exponents
        • 5.2 Logarithmic Functions and their Graphs (Part 1 of 2)
        • 5.2 Logarithmic Functions and their Graphs (Part 2 of 2)
        • 5.3 Properties of Logarithms
        • 5.4 Exponential and Logarithmic Equations
        • 5.5 Applications of Exponential and Logarithmic Functions
        • 5.6 Chapter Review
      • Ch6: Trigonometry (Pt. 1) >
        • 6.1 Angles and their Measure
        • 6.2 Trigonometric Functions of Acute Angles
        • 6.3 Trigonometric Function - General & Special Angles
        • 6.4 Graphing Basic Trigonometric Functions (part 1 of 3)
        • 6.4 Graphing Basic Trigonometric Functions (part 2 of 3)
        • 6.4 Graphing Basic Trigonometric Functions (part 3 of 3)
        • 6.5 Application of Periodic Functions
        • 6.6 Chapter Review
      • Ch7: Trigonometry (Pt. 2) >
        • 7.1 Trigonometric Identities and Equations
        • 7.2 Verifying Trigonometric Identities
        • 7.3 Trigonometric Equations (part 1 of 2)
        • 7.3 Trigonometric Equations (part 2 of 2)
        • 7.4 Sum and Difference Identities (part 1 of 2)
        • 7.4 Sum and Difference Identities (part 2 of 2)
        • 7.5 Double Angle Identities
        • 7.6 Chapter Review
      • Old Curriculum Material >
        • 7.1 Fundamental Counting Principle (part 1 of 2)
        • 7.1 Fundamental Counting Principle (part 2 of 2)
        • 7.2 Permutations
        • 7.3 Combinations
        • 7.4 Binomial Theorem
        • 7.5 Pathway Problems
        • 7.6 Chapter Review
      • Final Exam
    • Foundations 12 >
      • Ch 1: Logical Reasoning and Set Theory >
        • 1.1 Connecting Words "And", "Or", "Not"
        • 1.2 Set Theory (Part 1 of 2)
        • 1.2 Set Theory (Part 2 of 2)
        • 1.3 Venn Diagrams - Part One
        • 1.4 Venn Diagrams - Part Two
        • 1.5 Conditional Statements
        • 1.6 Chapter Review
      • Ch 2: Permutations and Combinations >
        • 2.1 The Fundamental Counting Principle (part 1 of 2)
        • 2.1 The Fundamental Counting Principle (part 2 of 2)
        • 2.2 Factorial Notation and Permutations (part 1 of 2)
        • 2.2 Factorial Notation and Permutations (part 2 of 2)
        • 2.3 Permutations with Restrictions
        • 2.4 Permutations with Repetitions
        • 2.5 Combinations - Part 1
        • 2.6 Combinations - Part 2
        • 2.7 Problem Solving with Permutations and Combinations
        • 2.8 Chapter Review
      • Ch 3: Probability >
        • 3.1 Probability Terminology and Notation
        • 3.2 Odds and Probability
        • 3.3 Mutually Exclusive Events and the Event "A ∪ B"
        • 3.4 Independent / Dependent Events and the Event "A ∩ B"
        • 3.5 Solving Problems Using Tables and Diagrams
        • 3.6 Probability Involving Permutations and Combinations
        • 3.7 Chapter Review
      • Ch 4: Exponential and Logarithmic Functions >
        • 4.1 Review and Preview (part 1 of 2)
        • 4.1 Review and Preview (part 2 of 2)
        • 4.2 Analyzing Exponential Functions (part 1 of 2)
        • 4.2 Analyzing Exponential Functions (part 2 of 2)
        • 4.3 Analyzing Logarithmic Functions (part 1 of 2)
        • 4.3 Analyzing Logarithmic Functions (part 2 of 2)
        • 4.4 Interpreting Graphs of Exponential and Logarithmic Functions
        • 4.5 Modelling Data Using Exponential and Logarithmic Functions
        • 4.6 Chapter Review
      • Ch 5: Polynomial and Sinusoidal Functions >
        • 5.1 Polynomial Functions of Degree Zero, One, and Two
        • 5.2 Polynomial Functions of Degree Three
        • 5.3 Modelling Data Using Polynomial Functions
        • 5.4 Angular Measure - Degrees and Radians (part 1 of 2)
        • 5.4 Angular Measure - Degrees and Radians (part 2 of 2)
        • 5.5 Amplitude and Period
        • 5.6 Horizontal & Vertical Shifts
        • 5.7 Modelling Data Using Sinusoidal Functions
        • 5.8 Chapter Review
      • Ch 6: Financial Mathematics >
        • 6.1 Simple Interest andCompound Interest
        • 6.2 Investments Using Compound Interest
        • 6.3 Basic Loans Using Compound Interest (part 1 of 2)
        • 6.3 Basic Loans Using Compound Interest (part 2 of 2)
        • 6.4 Mortgages
        • 6.5 Buying, Renting, and Leasing
        • 6.6 Investment Portfolios
        • 6.7 Chapter Review
  • Grade 11 Classes
    • PreCalculus 11 >
      • Review (what you should already know)
      • Ch1: Factoring and the Quadratic Function >
        • 1.1 Factoring
        • 1.2 Factoring (More Complicated Types)
        • 1.3 Properties of Quadratic Functions
        • 1.4 The Standard Form of a Quadratic Function
        • 1.5 Chapter Review
      • Ch2: Quadratic Transformations >
        • 2.1 Finding the Equation of a Parabola
        • 2.2 General Form to Standard Form
        • 2.3 Vertex of a Parabola
        • 2.4 Applications of Quadratic Functions
        • 2.5 Chapter Review
      • Ch3: Quadratic Equations >
        • 3.1 Solving Quadratic Equations by Factoring
        • 3.2 Completing the Square and Square Root Property
        • 3.3 The Quadratic Formula
        • 3.4 Graphing Calculator and the Discriminant
        • 3.5 Applications of Quadratic Equations
        • 3.6 Chapter Review
      • Ch4: Systems of Equations >
        • 4.1 Graphing Non-Linear Systems of Equations
        • 4.2 Solving Non-Linear Systems Algebraically
        • 4.3 Graphing Linear Inequalities in Two Variables
        • 4.4 Graphing Non-Linear Inequalities
        • 4.5 Applications of Inequalities
        • 4.6 Chapter Review
      • Ch5: Radicals >
        • 5.1 Radical Operations (Part 1 of 2)
        • 5.1 Radical Operations (Part 2 of 2)
        • 5.2 Simplifying Radicals
        • 5.3 Adding and Subtracting Radical Expressions
        • 5.4 Multiplying and Dividing Radical Expressions (Part 1 of 2)
        • 5.4 Multiplying and Dividing Radical Expressions (Part 2 of 2)
        • 5.5 Radical Equations
        • 5.6 Chapter Review
      • Ch6: Rational Functions >
        • 6.1 Properties of Rational Expressions
        • 6.2 Multiplication and Division of Rational Expressions
        • 6.3 Sums and Differences of Rational Expressions
        • 6.4 Mixed Operations
        • 6.5 Rational Equations
        • 6.6 Graphing Rational Functions
        • 6.7 Applications of Rational Equations
        • 6.8 Chapter Review
      • Ch7: Trigonometry >
        • 7.1 Angles and their Measure
        • 7.2 The Three Trigonometric Functions
        • 7.3 Special Angles
        • 7.4 & 7.5 Oblique Triangles / Law of Sines (Part 1)
        • 7.5 Law of Sines (Part 2)
        • 7.6 Law of Cosines
        • 7.7 Chapter Review
      • Ch8: Finance >
        • 8.1 Investments and Loans
        • 8.2 Effective Interest Rates and Annuities
        • 8.3 Stocks and Bonds
        • 8.4 Instalment Loans
        • 8.5 Canadian Mortgages
        • 8.6 Chapter Review
      • Final Exam Review
      • Old Curriculum Material >
        • 1.1 Absolute Value
        • 4.3 Absolute Value Functions
        • 4.4 Solving Absolute Value Equations
        • 4.5 Rational Functions
        • 4.6 Reciprocal Functions (Part 1 of 2)
        • 4.6 Reciprocal Functions (Part 2 of 2)
        • 4.7 Chapter Review
    • Foundations 11 >
      • Ch 1: Rates and Scale Factor >
        • 1.1 Ratios and Rates
        • 1.2 Visualizing Rates
        • 1.3 Similar Figures
        • 1.4 Perimeter, Area and Surface Area of Similar Figures
        • 1.5 Volume of Similar Figures
        • 1.6 Chapter Review
      • Ch 2: Geometry >
        • 2.1 Geometry
        • 2.2 Proofs
        • 2.3 Polygons
        • 2.4 Compass and Straightedge Construction
        • 2.5 Chapter Review
      • Ch 3: Non-Right Angle Triangles >
        • 3.1 Review of Sine, Cosine and Tangent for Right Triangles
        • 3.2 Law of Sines (Part 1 of 2)
        • 3.2 Law of Sines (Part 2 of 2)
        • 3.3 Law of Cosines
        • 3.4 Applied Problems
        • 3.5 Chapter Review
      • Ch 4: Analyze Puzzles and Games >
        • 4.1 Patterns
        • 4.2 Inductive Reasoning
        • 4.3 Deductive Reasoning
        • 4.4 Puzzles and Games of Strategy
        • 4.5 Chapter Review
      • Ch 5: Statistics >
        • 5.1 Mean, Median and Mode
        • 5.2 Standard Deviation
        • 5.3 The Normal Distribution (Part 1 of 2)
        • 5.3 The Normal Distribution (Part 2 of 2)
        • 5.4 Confidence Interval for Means
        • 5.5 Chapter Review
      • Ch 6: Linear Systems >
        • 6.1 Review: Graphing a Linear Equation (Part 1 of 2)
        • 6.1 Review: Graphing a Linear Equation (Part 2 of 2)
        • 6.2 Linear Inequalities
        • 6.3 Linear Programming
        • 6.4 Application of Linear Programming
        • 6.5 Chapter Review
      • Ch 7: Quadratic Functions >
        • 7.1 Quadratic Functions (Part 1 of 3)
        • 7.1 Quadratic Functions (Part 2 of 3)
        • 7.1 Quadratic Functions (Part 3 of 3)
        • 7.2 General Form of a Quadratic Function
        • 7.5 Application of Quadratic Functions & Equations (part 1 of 2)
        • 7.0 Graphing Non-Linear Systems of Equations (Part 1 of 2)
        • 7.0 Graphing Non-Linear Systems of Equations (Part 2 of 2)
        • 7.6 Chapter Review
      • Ch8: Math Research Project
      • Old Curriculum Material >
        • 7.3 Quadratic Equations
        • 7.4 Solving Quadratic Equations (part 1 of 2)
        • 7.4 Solving Quadratic Equations (part 2 of 2)
        • 7.5 Application of Quadratic Functions & Equations (part 2 of 2)
    • Workplace 11 >
      • Ch 1: Slope and Rate of Change >
        • 1.1 Ratios and Proportions
        • 1.2 Rates / Solving Problems with Proportions
        • 1.3 Slope
        • 1.4 Angle of Elevation
        • 1.5 Pitch, Grade, and Drop
        • 1.6 Calculating Slope on a Coordinate Plane
        • 1.7 Calculating Slope from Ordered Pairs
        • 1.8 Rate of Change
        • 1.9 Interpolation and Extrapolation
      • Ch 2: Graphs and Statistics >
        • 2.1 Broken Line Graphs
        • 2.2 Bar Graphs
        • 2.3 Pictographs
        • 2.4 Histograms
        • 2.5 Review of Percents / Circle Graphs ​(part 1 of 2)
        • 2.5 Making Circle Graphs (part 2 of 2)
        • 2.6 Graphs and Technology
        • 2.7 Other Types of Graphs
        • 2.8 Misleading Graphs
        • 2.9 Mean, Median, Mode, and Range
        • 2.10 Standard Deviation
      • Ch 3: Scale Factor and Representations >
        • 3.1 Scale Factor
        • 3.2 Scale Diagrams
        • 3.3 One-Point Perspective
        • 3.4 Two-Point Perspective
        • 3.5 Exploded Views and Component Parts
        • 3.6 Orthographic Drawings
        • 3.7 Isometric Drawings
        • 3.8 Oblique Drawings
      • Ch 4: Financial Literacy >
        • 4.1 Financial Institutions
        • 4.2 Bank Accounts
        • 4.3 Bank Statements
        • 4.4 Simple Interest
        • 4.5 Compound Interest
        • 4.6 Compounding Periods
        • 4.7 Credit
        • 4.8 Loans
        • 4.9 Mortgages
        • 4.10 Mortgage Payments
        • 4.11 Investments
  • Grade 8, 9, 10 Classes
    • Foundations & PreCalculus 10 >
      • Problem Sets
      • Review (what you should already know)
      • Ch 1: Measuring Systems, Surface Area, and Volume >
        • 1.1 Metric Systems
        • 1.2 Imperial Systems
        • 1.3 Converting Metric and Imperial Systems
        • 1.4 Surface Area and Volume of Prisms (part 1 of 2)
        • 1.4 Surface Area and Volume of Prisms (part 2 of 2)
        • 1.5 Surface Area and Volume of Pyramids
        • 1.6 Surface Area and Volume of Cylinders, Cones, and Spheres
        • 1.7 Chapter Review
      • Ch 2: Radicals >
        • 2.1 Number Systems
        • 2.2 Greatest Common Factor and Least Common Multiple (part 1 of 2)
        • 2.2 Greatest Common Factor and Least Common Multiple (part 2 of 2)
        • 2.3 Squares and Square Roots
        • 2.4 Rational And Irrational Numbers
        • 2.5 Simplifying Radicals
        • 2.6 Exponential Notation (part 1 of 3)
        • 2.6 Exponential Notation (part 2 of 3)
        • 2.6 Exponential Notation (part 3 of 3)
        • 2.7 Chapter Review
      • Ch 3: Polynomials >
        • 3.1 Classifying Polynomials (part 1 of 2)
        • 3.1 Classifying Polynomials (part 2 of 2)
        • 3.2 Multiplying Polynomials
        • 3.3 Removing Common Factors
        • 3.4 Factoring x^2 + bx + c (part 1 of 2)
        • 3.4 Factoring x^2 + bx + c (part 2 of 2)
        • 3.5 Factoring ax^2 + bx + c
        • 3.6 Special Factors
        • Algebra Tiles
        • 3.7 Chapter Review
      • Ch 4: Relations and Functions >
        • 4.1 Relations
        • 4.2 Functions
        • 4.3 Linear Equations
        • 4.4 Non-Linear Equations
        • 4.5 Graphing with a Calculator
        • 4.6 Chapter Review
      • Ch 5: Linear Functions >
        • 5.1 Slope
        • 5.2 Rate of Change
        • 5.3 Graphing Linear Functions
        • 5.4 Parallel and Perpendicular Lines
        • 5.5 Applications of Linear Relations
        • 5.6 Chapter Review
      • Ch 6: Linear Equations >
        • 6.0 Rewriting Equations
        • 6.1 Different Forms of Linear Equations (part 1 of 2)
        • 6.1 Different Forms of Linear Equations (part 2 of 2)
        • 6.2 Special Cases of Linear Equations
        • 6.3 Equations of Parallel and Perpendicular Lines
        • 6.4 Linear Applications and Modelling
        • 6.5 Function Notation
        • 6.6 Chapter Review
      • Ch 7: Solving Linear Systems >
        • 7.1 Solving Linear Systems by Graphing
        • 7.2 Solving Linear Systems by Addition
        • 7.3 Solving Linear Systems by Substitution
        • 7.4 Problem Solving with Two Variables
        • 7.5 Chapter Review
      • Ch 8: Trigonometry >
        • 8.1 Sine, Cosine, and Tangent for Right Triangles (part 1 of 2)
        • 8.1 Sine, Cosine, and Tangent for Right Triangles (part 2 of 2)
        • 8.2 Relationships Between Sine, Cosine, and Tangent
        • 8.3 Special Angles
        • 8.4 Applications of Trigonometry
        • 8.5 Compound Trigonometry Applications
        • 8.6 Chapter Review
    • Math 9 >
      • Ch 1: Square Roots, Powers, and Exponent Laws >
        • 1.1 Square Roots
        • 1.2 Square Roots of Big & Small Numbers
        • 1.3 Estimating Square Roots
        • 1.4 Powers
        • 1.5 Order of Operations
        • 1.6 Exponent Rules
        • 1.7 Power Rules
        • 1.8 Review
      • Ch 2: Finance >
        • 2.1 Salary and Wages
        • 2.2 Commission
        • 2.3 Tips and Piecework
        • 2.4 Deductions
        • 2.5 Simple Interest
        • 2.6 Budgeting
      • Ch 3: Rational Numbers >
        • 3.1 Rational Numbers
        • 3.2 Operations with Integers
        • 3.3 Operations with Decimals
        • 3.4 Dividing Decimals
        • 3.5 Multiplying and Dividing Fractions
        • 3.6 Adding Fractions
        • 3.7 Subtracting Fractions
        • 3.8 Adding and Subtracting Negative Rational Numbers
        • 3.9 Order of Operations with Rational Numbers
        • 3.10 Review
      • Ch 4: Polynomials >
        • 4.1 Defining Polynomials
        • 4.2 Simplifying Polynomials
        • 4.3 Adding & Subtracting Polynomials
        • 4.4 Multiplying Polynomials
        • 4.5 Dividing Polynomials
        • 4.6 Order of Operations with Polynomials
      • Ch 5: Linear Equations >
        • 5.1 One-Step Equations
        • 5.2 Two-Step Equations
        • 5.3 Using the Distributive Property
        • 5.4 Combining Like Terms
        • 5.5 Variables on Both Sides of an Equation
        • 5.6 Clearing Fractions
        • 5.7 Solving ANY Linear Equation
        • 5.8 Writing Algebraic Equations
      • Ch 6: Proportional Reasoning >
        • 6.1 Congruent Triangles
        • 6.2 Similar Triangles (Part 1 of 2)
        • 6.2 Similar Triangles (Part 2 of 2)
        • 6.3 Similar Polygons
        • 6.4 Scale Factor
        • 6.5 Scale Diagrams
        • 6.6 Unit Conversions
      • Ch 7: Statistics >
        • 7.1 Statistics
      • Ch 8: Linear Relations >
        • 8.1 Patterns (part 1 of 2)
        • 8.1 Patterns (part 2 of 2)
        • 8.2 Modeling Real-Life Situations
        • 8.3 Cartesian Plane
        • 8.4 Graphing a Table of Values
        • 8.5 Interpolation and Extrapolation
    • Math 8 >
      • Ch 1: Integers >
        • 1.1 Multiplying Integers
        • 1.2 Dividing Integers
        • 1.3 Adding Integers
        • 1.4 Subtracting Integers
        • Practice
      • Ch 2: Fractions >
        • 2.1 Basic Fraction Skills
        • 2.2 More Fraction Skills
        • 2.3 Multiplying Fractions
        • 2.4 Multiplying Mixed Fractions
        • 2.5 Dividing Fractions
        • 2.6 Dividing Mixed Fractions
        • 2.7 Adding and Subtracting Fractions
        • 2.8 Adding Mixed Fractions
        • 2.9 Subtracting Mixed Fractions
        • 2.10 Order of Operations with Fractions
        • Practice
      • Ch 3: Percent, Proportions, Ratio, and Rate >
        • 3.1 Converting Fractions, Decimals, & Percents
        • 3.2 Solving Proportions
        • 3.3 Percents
        • 3.4 Common Percent Problems
        • 3.5 Ratios
        • 3.6 Rates
        • 3.7 Proportion Problems
        • Handouts
      • Ch 4: Square Roots and the Pythagorean Theorem >
        • 4.1 Perfect Squares and Square Roots
        • 4.2 Estimating Square Roots
        • 4.3 Cube and Cube Roots
        • 4.4 The Pythagorean Theorem
        • 4.5 The Pythagorean Theorem (continued)
        • 4.6 Applications of the Pythagorean Theorem
        • Practice
      • Ch 5: Probability and Statistics >
        • 5.1 Probability
        • 5.2 Probability with Cards
        • 5.3 Tree Diagrams
        • 5.4 Independent and Dependent Events
        • 5.5 Dependent Events
        • 5.6 Measures of Central Tendency
      • Ch 6: Linear Equations and Relations >
        • 6.1 Algebraic Expressions
        • 6.2 Solving One-Step Equations
        • 6.3 Solving Two-Step Equations
        • 6.4 The Distributive Property
        • 6.5 The Cartesian Plane
        • 6.6 Linear Relations
        • 6.7 Linear Models
      • Ch 7: Geometry >
        • 7.1 Area Review
        • 7.2 Area of Composite Shapes
        • 7.3 Volume of Prisms
        • 7.4 Volume of Composite Shapes
        • 7.5 Surface Area of Prisms
        • 7.6 Surface Area of Cylinders
        • 7.7 Surface Area of Composite Shapes
  • (Retired) Blog
  • Marks
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Best Albums of the Year (#20 - 11)

30/12/2017

1 Comment

 
This is the fourth time I have made this end-of-the-year list (though I have expanded from top 10 to top 20!). It's high time I gave this list a fancy name... like the Emmys or the Oscars or something.

I hereby declare the albums on this list, winners of the annual SHAZZY awards!! (they are named after Shami and Izzy, the only two people who have ever actually expressed any interest in actually READING these lists. Thanks to you both. And congratulations: you are now immortalized. The SHAZZYs!! What an honour!)

A couple quick points before I start the actual list:
  1. way more good albums in the first 6 months of the year then the last 6 months
  2. some people claim "rock is dead" and maybe my list is a sign of this. I have always said that rock music (alternative, indie, classic, etc) is my favourite genre of music but there is (for the second year in a row) a LOT of R&B / soul music on my list. Plus a little electronic music (no EDM!). Still some rock in there but not a ton. Interesting.
  3. Lots of good albums this year but very few GREAT ones. To tell the truth, it would have been much easier to list these twenty albums "in no particular order". They are all strong albums but there is not a single one that I would call an instant classic (unlike previous years). But I know people like countdowns so I'll stick with that format.
  4. Last year it took me HOURS to write this list up. Considering how many people actually read it, I'm cutting down on the comments. 
  5. Let me know which albums I missed (Taylor Swift and Harry Styles, no doubt).

20. Miguel - War and Leisure

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It must be sweet to be this SMOOOOOTH. Miguel could probably sing a couple pages of the phone book and it would sound sultry and sexy. The guy can do no wrong. Er... wait a minute... I guess he can mess up sometimes... (video below)

19. Jhené Aiko - Trip

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Just heard this album this week. Loving it! Could have been ranked higher if I'd heard it earlier in the year (note to artists: improve your chances of winning a SHAZZY by avoiding November / December release dates).

18. Blanck Mass - World Eater

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Don't be scared by the album cover!

When most people think of electronic music they think of Tiesto or Diplo (or...ugh... The Chainsmokers). Hard to believe that this album falls into the same genre. Black Mass takes a little more patience to listen to than drop-heavy EDM but it's worth it. I'm predicting that this would be the LEAST favourite album on this list for most people but try it... you just might be impressed!

17. Julie Byrne - Not Even Happiness

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Nothing fancy here. One woman, her guitar and a gorgeous voice. This is the album my wife would like most on this list (check it out, Zan!). Folky, sparse... and beautiful!

16. Daniel Caesar - Freudian

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Always good to get a Canadian artist on the SHAZZY list. Way to go, Sir. Great start to your career. Loving your voice and your gospel sound.

​Also: the woman (H.E.R.) in this song, would be #21 on my list of top albums (album also called H.E.R.). Must hurt to get THAT close to winning a SHAZZY and still miss! Imagine!

15. Curtis Harding - Face Your Fear

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This sounds like soul music from the 60's or 70's. Great tunes sung by someone who really means it! So good!

14. LCD Soundsystem - American Dream

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From a band that "ceased to exist" a few years back. Glad you were able to break your promise. Welcome back!

Also: still hoping "LCD" stands for "lowest common denominator"

13. Khalid - American Teen

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Betting lots of you know this album already. I heard the first few singles around a year ago and loved it. Still remember the day the album came out... I was driving somewhere at night and put on the BRAND NEW ALBUM (pumped!). And the first two songs STUNK!!! What a disappointment!! Thankfully the rest of the album lived up to the initial promise... enough so that it still makes this list (despite those first two songs). And to think he's still a TEENAGER!

12. The War on Drugs - A Deeper Understanding

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Their last album was extraordinary. This one is "merely" great. It's the most classic rock n' roll sounding album on this list, so if that's your thing....

11. Arcade Fire - Everything Now

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I think every critic HATED this album. I saw it on all sorts of "Most Disappointing Lists". But I LOVE it!! First time I heard it, I was driving around at night, picking up office chairs for my classroom on a hot summer night. How nerdy is that. Windows down. This song blaring. Excitedly driving to North Van for old chairs. Yahoo!

On a side note: ex-student Marija B gave me lots (LOTS!!) of grief for not being a fan of their last album. Hope this makes up for it MB!!  <3

​Next Week: the top 10 SHAZZYS!!!! (can you handle the anticipation!!)
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Student of the Week

23/12/2017

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This week's Student of the Week is Sophie W!!

A short aside to begin: Sophie is the 2017 - 2018 winner of the Grace Kingsley Award presented to the female King George student with the biggest potty-mouth in the school. You are following a true legend, Sophie, but I am sure that Grace would be impressed with your ability to curse, swear, and make inappropriate comments of all types. Congratulations... I guess.

My earliest memory of Sophie is a little odd. I never taught her in grade 8 but I definitely noticed her. She was always at school very early and would usually sit at a locker right near the office. She had a nice smile and seemed friendly but what I found most intriguing at that time was... her voice! It was pretty husky and super clear and confident. I LOVED it!! "This kid needs to be in radio" I'd think to myself. 

Full disclosure: sometimes I'd hang out by my mailbox in the office (pretending to look through papers) just to hear that voice a little longer. I asked a teacher at one point: who  is the cute little Chinese girl with the distinctive voice? The teacher answered with no hesitation: "that must be Sophie. She's so great!".

And she really is great! I was so excited when I finally got to teach her last year. I'd gotten to know her a tiny bit and Ms Sidhu had assured me that she was a wonderful student (though a bit talkative at times. hehehe). She started PreCalculus 11 a little slow but after a month or so she kicked it into gear and her effort since then (continuing into Calculus 12) is nothing short of amazing. What I admire most about Sophie is her willingness to keep working hard, even after getting marks that she considers disappointing (not that they are ever that bad). It's one thing to show determination and persistence when things are going well but it's quite another after experiencing disappointment. In my opinion, this is the number one indicator of future success: the ability to keep going and keep going and keep going, no matter how many challenges life throws at you.

And Sophie has had to deal with a LOT of challenges in her young life (of MUCH greater importance than her Math marks). Honestly, she is an extraordinarily brave, wise, and inspiring human being. The fact that she is at school every day, radiating positivity (bad language aside!), supporting friends and succeeding at her studies is almost incomprehensible to me. 

I was given some extremely bad news a couple months ago about my dad's health (he was diagnosed with an incurable degenerative disease). Obviously, this news left me (and still does) feeling helpless and upset and bitterly sad. In the days after I first found out, many friends and family tried to console me, to varying degrees of success. And then, one of the most magical things in my 21-years of teaching happened...

Sophie and (the wonderful) Anelia were in my classroom during my spare block and gently pressed me as to why I seemed to sad. Finally, I decided that I would tell them about my father's health. They were both so generous and comforting. And the things that Sophie said to me - drawing from her own experiences - made (and continue to make) more of a difference to me than what anyone else has said to me before or since. She told me things about making memories, and the importance of laughter, and the power of completion (getting to say everything you've ever wanted to say to someone). It was extremely powerful and meaningful to me. And the fact that it was a 17-year old student telling me EXACTLY WHAT I NEEDED TO HEAR will always make it memorable and extra-special to me.

Sophie, some people say (and I agree) that the greatest satisfaction you can experience in life is to make a tangible difference with another human being. I want you to know that you have made a difference in my life in how I will relate to my dad in however much longer I have to spend with him. I have thought about the things you said to me every day since then and I will continue to do so. I have nothing but love and admiration for you, Sophie. So happy to have gotten to teach you these past two years! You are amazing!
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HILARIOUS!! You should ALL understand this joke!

23/12/2017

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The Most Disappointing Albums of the Year

22/12/2017

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I know everyone (well, at least TWO of you) have been eagerly awaiting my unveiling of my Top Albums (Top 20? Top 25? We shall see) over the next two weeks. But today, we start with something a little less admirable: the five most disappointing albums of 2017. These are albums I had high hopes for over the past year but left me feeling "meh"... or worse! Honourable mentions to Beck, Grizzly Bear, and Spoon but these are the most disappointing of all...

5) St. Vincent - Masseduction

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First of all, you should listen to this album! Because some people loved it. MOST people loved it!! It's one of the highest rated albums of the year by critics. Some major publications named it the BEST album of the year. And yet...

For whatever reason, these songs did not capture me. St Vincent's last album was so unique, so catchy, so fun! This is a tougher listen and - sadly - it never grew on me. I haven't given up on it yet. I'll keep listening and maybe it will "click" one day.

One last comment: one time I was listening to this album and Zan came in to ask me to turn it off. There's lots of my music she does not like but that is pretty harsh!

4) Bjork - Utopia

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First of all - that album cover (scary!). 

You never know what you are going to get from Bjork. Some of her albums are warm and beautiful while others are stark and somewhat harsh. This one is kind of in a no-man's land. She calls it her "Tinder-album" (her last - amazing! - album was a "Breakup album"). I never imagined that Tinder could be this dull (but what do I know? I was married about 15 years before Tinder existed).

3) U2 - Songs of Experience

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I suppose this could be looked upon as progress. The companion album (Songs of Innocence) was released a couple of of years ago and was my most disappointing album of that year. This one's only the THIRD most disappointing.

To be fair, there are a couple songs on this album that are not bad at all (Lights of Home, Summer of Love). Bad the bad songs are AWFUL. Even Kendrick Lamar couldn't prevent this from being one of the worst U2 songs EVER...
If some new band released this album I'd probably be somewhat impressed. But this is from the band I adored in the 1980's. The band who made albums like The Joshua Tree, Achtung Baby, and the Unforgettable Fire. 

It's all further evidence that - with rare exceptions - rock artists do not age well. 

2) Fleet Foxes - 

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It was beginning to look like there would NEVER be a new Fleet Foxes album. So, when it was announced this year, I was equal parts surprised and delighted.

It starts VERY strong...
...but after that it kind of goes nowhere. I still have faith in these guys but this was a step in the WRONG direction.

1) Haim - Something to Tell You

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I was so PUMPED for this album. I'd been basically doing a countdown for about 6 months until the day it was released.

Then they teased it with this...
What a song!!! Bring on the album! This is going to be awesome!

First warning sign: for some unknown reason they didn't use the version of the song above. Instead they opted for some over-produced, excessive facsimile. Booo!

There is one other okay song (and amazing video)...
...but the rest is bad, bad, bad. Way too poppy, too many effects and layers of sound. Not enough substance. After all the anticipation, it's sad to admit that this was my Most Disappointing Album of 2017.
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Add this to my Christmas list!!

22/12/2017

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Student of the Week

9/12/2017

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This week's Student of the Week is Ysabel G!

Ysabel is a quiet but dependable student. She seldom asks for help and she certainly never causes any trouble. Plus I can count on her to always have her work done on time and to be well-prepared for every test. Such a good student!

One of my lasting images of Ysabel will be of her fighting off sleep in my class. So many times (especially last year) I'd look over, while I was giving the lesson, and see Ysabel's eyes C-L-O-S-I-N-G... so slowly. Then they'd whip back open, before starting their slow descent again. Hehehe! Sorry Ysabel. But I couldn't resist mentioning it.

Ysabel is so intriguing. She is quiet but funny. Unassuming but poised. Plus there is her name. Is it Ysabel like Isabelle or is it pronounced "why"-sabel? And how did it happen that so many people call her the latter name? And does this name bother her? So much mystery!

Thanks, Ysabel, for all your hard work and always being so pleasant and kind. It makes me very happy that you took Calculus 12 this year so I got to teach you for another year. Hope I don't put you to sleep too often!!  :)
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Song of the Week

9/12/2017

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I think there is a new one of these questions every week

9/12/2017

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The physics of milk in (on?) coffee

9/12/2017

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What do Rihanna and I have in common?

9/12/2017

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Can you spot the (unforgivable) error on the blackboard, above. C'mon RiRi!!
For article
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The scary Related Rates Questions

8/12/2017

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Mohsen mastered #8 (what a guy!)
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#8 is so hard that I'm posting it twice. Ysabel got it this time (Yahoo Ysabel!)
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Toma tackled #9 (terrific!)
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The spectacular Sophie solved #10 (amazing!)
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#11 was eradicated by Estella! Excellent Estella!
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#12 was jettisoned by Jordan! Joyous!!
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Amazing Anna attacked #13! Nice effort!
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#15 was ripped to shreds by Razmig! 
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#17 was conquered by Katarina! Great work!
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    P. Wadge

    I am your teacher. Obey me.

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