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
  • Contact Mr. Wadge

Student of the Week

26/12/2019

0 Comments

 
Picture
This week's Student of the Week is Betty M (Ryan O comes through again with a photo! But Luciana send in an even BETTER one!!).

I have taught Betty Math in all of her high school years. In grade 8 she was in my Math 8 Core class (the Core class does not even exist anymore). Betty was there because she had been identified (not by me! Likely by grade 7 teachers and counsellors) as being particularly weak in Math. All the students in the class were there for the same reason. It was a tough class to teach due to some of the "livelier" personalities (not Betty! She was - and IS - an angel) but we got lots of work done and I think many students' confidence when it came to Math really increased.

Betty was one of the students who improved... was she ever!! Since that time Betty has stayed in the "regular Math" and PreCalculus stream, all the way to PreCalculus 12!! And she's getting a friggin' A in PreCalculus 12. AN "A" IN PRECALCULUS 12!!!! 

I am so proud of Betty! This is not supposed to happen! Students taking Core 8 are not supposed to be getting HIGH marks in PreCalculus 12. They are not supposed to be taking PreCalculus 12 at all! It is a testament to Betty's work ethic, her unwavering belief in herself, and her resiliency. Did I mention how PROUD I am of Betty!!! I honestly find it inspiring to think about how far she has come in the past five years. And I KNOW if she can do such things in Math then she can do it in all areas of her life. Betty is going to do great things in the world. She is unstoppable! (Again, I am NOT joking!!)

Betty is such a sweet person. Every time she enters my classroom she shoots me a smile and a "Hi, Mr Wadge". She is quick with a laugh (and is able to laugh at herself). She is funny and honest and charismatic and kind. 

I remember in grade 8 when I offered to take the Core class out for ice cream (I wasn't above bribing that class from time to time). Someone suggested we go to Dairy Queen and that Betty's mom might be working. I was sort of nervous (personally, I would NOT have wanted to go to my parents' place of work in grade 8 with my classmates) but away we went. I was so struck by how happy Betty was to see her mom, how fond of each other they obviously were, how comfortable Betty was in spite of her peers being there (also, Betty's mom was super nice). I am a big fan of people who love their parents / siblings / friends and aren't afraid to show it.

I will miss you so much next year, Betty. It is students like you who make "high school teacher" the best job in the world (again, I am NOT joking). Thank you for giving me the sense of "making a difference". There is no better feeling in the world and I owe it to students like you. You have made a difference in my life and I am forever grateful. I am so proud of you (can't help but say it a third time) and I love you!
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The Shazzys!!! Albums #15 - #1!!

26/12/2019

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Last week I counted down albums #30 - #16 (see way down below somewhere). Now we get to the REALLY good stuff! Top 15 albums of the year. It was surprisingly easy to make the list this year, with the possible exception of the top 6 which I kept flipping (and flopping!) around. But I feel good about the final list... and I hope you will check out a few of these albums. Also: send me your recommendations. What did I miss? Always eager to discover new music!

15. Ari Lennox - Shea Butter Baby

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The debut album from the R&B / soul singer is warm, infectious, and - at times - pretty darn funky. Great stuff!

14. Brittany Howard - Jaime

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The lead singer of Alabama Shakes releases her first solo album. Such a powerful voice! This is quite a varied album. There are parts that rock out and others that are much more subtle. Killer songwriting from a true musical force!

13. King Princess - Cheap Queen

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ANOTHER debut album makes the top 15, this one from New York based, "genderqueer icon", Mikaela Mullaney Straus. Her sound is pretty 80-ish (maybe that's why it appeals to me so much) and isn't short on hooks. Catchy!

12. Nilüfer Yanya - Miss Universe

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Whoa! This is crazy! ANOTHER debut album. I swear I did not plan this. Talk about a talented musician; her style ranges from pop to rock to soul to hip hop. You need to listen to this album a few times... and there will still be so much to discover. 

11. Angel Olsen - All Mirrors

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Her last album won rave reviews but I was kind of luke warm. This, on the other hand, is right up my alley. Epic soundscapes, dramatic crescendos, warm strings, soaring vocals. What a triumph!

10. FKA twigs - MAGDALENE

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At first I thought this album was headed for the "Most Disappointing" list. But - after a few more listens - it kind of "clicked" for me. What was never in doubt was FKA twig's beautiful voice. I was definitely late to the party with this album but it's become one of my favourites of the entire year.

9. Kanye West - Jesus is King

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I know, I know. Everyone HATED this album. But there were a few of us who liked it... a lot! The choir is rather soul-stirring and Kanye's production - as always - is worth listening to the album alone. Lots of people slamming to vocals on this record... good thing I don't really listen to the lyrics at all - but the music is fantastic!

8. Bon Iver - i,i

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I do believe that Bon Iver is incapable of writing a bad song. It's virtually a guarantee that every one of Justin Vernon's albums will end up near the top of my end of the year list. Weird and wonderful!

7. Lizzo - Cuz I Love You

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I KNOW you heard parts of this album this year. Talk about a commercial success! And critical success too! So catchy. So positive. So fun. So good!

6. Tool - Fear Inoculum

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We waited over 13 years for this album and - somehow! - it lived up to the hype. It's the same old Tool: loooong songs building toward towering crescendos, multiple time signatures and key changes in the same song, Maynard's howling vocals, and the best drummer in rock n' roll (all hail Danny Carey!!). What a triumph!

5. Raphael Saadiq - Jimmy Lee

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​The album is named after Saadiq's brother, who died of a heroin overdose after contracting HIV. Amazing that such a sad set of circumstances could lead to this true work of art. Raphael Saadiq has been around forever (used to be a part of Tony! Toni! Toné! in the early 90's) but he is releasing better music than ever!

4. Nick Cave and the Bad Seeds - Ghosteen

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Somehow I made it through my teens and early 20's without hearing more than a few Nick Cave songs. What a treat, then, to discover all his outstanding music over my recent years. 2019's Ghosteen continues on the theme of loss (after the tragic passing of his son). It's truly beautiful music while also capturing sadness and disbelief.

3. Dawn Richard - new breed

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When I compile my annual list, I always check professional critics' Best Of lists (mostly to see if there are albums I have missed). And every year there are a few albums on MY list that don't show up anywhere else (The Chemical Brothers, RY X, Black Pumas). But it is very rare for such an album to show up near the very top of my list. But so it goes with Dawn Riachard's "new breed". I'm not sure what everyone else missed (or what is wrong with me) but there is no album I listened to MORE this year (thanks, in part, to its release near the start of the year but - most of all - because I just love it). It's a bit odd at times (the Black Indians of New Orleans??? Whaaaat?!?) and it's too short but the songs are strong, the bass kicks butt, and Ms Richard commands your attention.

2. Michael Kiwanuka - KIWANUKA

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A few years ago, Michael Kiwanuka topped my list with his album Love & Hate. This year, he takes the #2 spot. No shame in that! I actually feel the album starts a bit slow but part way through it picks up steam... and then some! If anyone can get me a ticket to his show next month at the Commodore I would be forever grateful. Can't believe Michael Kiwanuka isn't more a household name. How can someone so talented still be somewhat anonymous?

1. Lana Del Ray - Norman F*****g Rockwell

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I didn't have high hopes for this album. I have found much of Lana Del Ray's work hit or miss. Some fantastic stuff and a lot of filler. The album title was not encouraging. Even the album cover was / is kind of cheesy. So when I finally got around to listening to "Norman F*****g Rockwell" I was pretty pessimistic. But the first two songs alone completely blew me away. Mesmerizing! Hypnotic! Gorgeous! The rest of the album is (almost) just as good; an incredible achievement. I am so impressed and very thankful for this album. Congrats Ms Del Ray, you made the #1 album of 2019! The shiniest Shazzy of all goes to you!
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Song of the Week

26/12/2019

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For all the dog-lovers out there...

26/12/2019

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When your dog eyes your plate and notices that you have five pieces of turkey left on it, do they see that as “5”, and can they think that if you eat two more, that leaves three for them? That may be exactly what’s going on in their brains, according to new research by Emory University. Dogs use a similar part of their brain to process numbers of objects as humans do
“Our work not only shows that dogs use a similar part of their brain to process numbers of objects as humans do — it shows that they don’t need to be trained to do it,” says Gregory Berns, Emory professor of psychology and senior author of the study.
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Six-year-old putting us all to shame

26/12/2019

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At six, a boy from South Korea makes solving complex math problems such as gamma functions and Euler's functions appear as easy as playing a game of tic-tac-toe.
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Nice job, Sir!

26/12/2019

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A Saskatoon math teacher has won a $25,000 prize from a U.S. math museum for his lesson plan, which used dice to teach students about probability by holding an auction of potential dice-rolling outcomes in class.
Nat Banting, 32, a faculty member in the college of education department of curriculum studies at the University of Saskatchewan in Saskatoon, also teaches at Marion M. Graham Collegiate in Saskatoon. He submitted his lesson plan months ago, and found out in early December that he won.
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Student of the Week

21/12/2019

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This week's Student of the Week is Chanelle C (who will send this week's photo?!)

The best thing about teaching at a true "high school", that starts at grade 8 and continues until grade 12 is that you get to see such amazing and dramatic changes in the students you teach. Think of the grade 8 boys that I am currently teaching. Right now, they are silly and loud and pretty goofy. And yet, over the next five years they will (or MOST will) turn into giant, calm, handsome, personable young men. It's pretty amazing to see.

The differences are most striking in boys to be sure (grade 8 girls are, on the whole, much more mature than the boys) but there are still lots of changes in the girls too.

Which brings me to Chanelle...

I have taught Chanelle for the past five years. She has always been a lovely student. In grade 8 she was a bit loud at times, lots of giggling, tended to lose focus sometimes. Nothing bad and nothing particular unique: MOST kids are like that in grade 8. 

Over the past five years Chanelle has become a lot quieter, more composed, introspective, poised. She has ALWAYS had a great sense of humour but now when she is laughing I can usually understand what she is laughing ABOUT. She is kind and intelligent and just a tiny bit mysterious (sometimes she has a little smile on her face that seems to suggest she knows something that I don't).

I remember in grade 9 or 10 when Chanelle asked me about the benefits of working ahead in her Math in Summer School. Even though it's a good idea (if you plan to take Calculus 12) I found it hard to say so to her (though I did!) because I knew it would mean she would no longer be in my class (I made the decision to stick with the Grad 2020 class early on). Happily she chose to take a Science class instead that Science.

It's been five wonderful years, Chanelle. Thanks for all your hard work and all your kind words over that time. May you never lose your gentle nature and your charming personality... I am sure that you will not. Love ya, CC!! 
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Best Albums of 2019 (#30 - 16)

20/12/2019

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The Shazzys are back!! The Shazzys are back!! Everyone loves the Shazzys!!

As you all know (how could you NOT?) the Shazzys are named after former music-loving students Izzy and Shami (who are probably the only two students who will actually read this). 

I believe this is year 6 (though the name "Shazzys" is only 3 years old) and over that time I have expanded from top 10 songs to top 20. Last year saw top 25 and this year... THE TOP THIRTY (30!!!!!!) albums. 

As always, these... ahem... awards are based on the albums I LISTENED to the most. I mean, there might be other albums with more artistic merit (Weyes Blood? Sharon Van Etten?) but if I'm not returning to them over and over (and over) then really... that's not so successful, is it?

These are the 30 albums from 2019 that I listened to - and enjoyed! - the most.

But first...


Purple Mountains - Purple Mountains

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​This is the first annual winner of the "Chaucer G award" which will hereby be awarded to great albums that I under-appreciate. The problem: I am not at all deep. I do not agonize over the deeper themes and meanings of the music I listen to. In fact, I hardly listen to the words at all. I just let the lovely noises wash over me and - whether they are singing about eternal love, our fleeting existence as human beings, or how some guy looks in tight jeans - I don't really care. I'm pretty sure these lyrics are super meaningful and important and YOU should listen to them and be blown away by them. I'll just enjoy the nice sounds.

30. The Chemical Brothers - No Geography

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I have a soft spot for the Chemical Brothers. They are probably well past their prime and much of their music sounds kind of similar... but it's so darn catchy!!! Like EDM music? Then you owe a big "thank you" to these guys. I don't know if I ever understood "The Drop" until I heard Block Rockin' Beats back in 1998. This is the music I am dancing around my bedroom to in my underwear (enjoy those visuals).  :)

29. Anderson.Paak - Ventura

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Mr. Smooooooth has released a LOT of new material over the past year. Some of it is good and most of it is better than that. This guy is so talented it is ridiculous. It seems like he isn't even trying that hard. Must be nice!

28. Bruce Springsteen - Western Stars

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Hey! Big news this year! Lots of old guys made my list! Way to go Old Guys! I'm not the hugest Bruce Springsteen fan in the world (though he put on the greatest show I ever saw in my life) but this album is fantastic. Love all the strings. And Bruce's voice sounds as strong (though weathered) as ever. This is why they call him The Boss!

27. Neil Young & Crazy Horse - Colorado  

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If I had to pick a single artist to listen to for the remainder of my life it would probably be Neil Young. I absolutely adore the man's music. Well, most of it. Even the most ardent Neil Young fan has to admit that he has released a great deal of crap over the years. Heck... even Neil would agree to that! Sadly, the great songs (nevermind albums) have not been as common the past decade but this is a return to form... and with the Mighty Crazy Horse no less! I saw Neil two times this year... here's hoping I get to see him again in 2020 with Crazy Horse!!

26. Sudan Archives - Athena 

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"Violinist and singer". So reads the credentials of American singer Sudan Archives. You don't see that often and you don't hear music like this either. Funky R&B with violin interspersed throughout. Unique and compelling!

25. Fontaines D.C. - Dogrel

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This album makes me want to be young (I'm not), Irish (I'm 1/8), and capable of playing guitar (not yet). What a voice (love the Irish brogue) and what an album. No wonder all the critics loved this album.

24. Black Pumas - Black Pumas

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Mr Eckert - yes! Mr Eckert!! - told me about these guys and I am pretty darn thankful. Gotta love the funk and soul sound. Great voices and a tight sound. I bet their NEXT album will be BIG!

23. 75 Dollar Bill - I Was Real

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Strange band: one guy plays the guitar (VERY WELL!) and the other (who is something like 30 years older) bangs on a wooden crate (instead of drums). Some of their songs are VERY long and quite repetitive but it becomes quite mesmerizing. No idea what the band name refers to. Like I said: strange band.

22. James Blake - Assume Form

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This must have been released VERY early in 2019 because I feel like I have been listening to it FOREVER!! Still enjoy it immensely. James Blake is best when he is performing with someone else. The King of the "Featuring" song!

21. Bob Dylan - The Rolling Thunder Revue

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Another absolute legend! Another total "hit or miss" artist the past few decades. This is an absolute win. I love the energy, the exuberance, the slightly-out-of-control pace and power. Must have been incredible to see these shows. Sadly, I was only 3 at the time.

20. RY X - Unfurl

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I am not claiming that this is an incredible artistic statement nor that anyone else actually likes it. But I listened to it SO MANY TIMES this year. There is something comforting and soothing about it. Great background music, working music, relaxing music. 

19. Thom Yorke - ANIMA

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Radiohead's lead singer releases another solo album. What's impressive about Thom Yorke's solo stuff is how DIFFERENT it sounds than Radiohead and yet it still works. I saw these songs in concert this year and it was even better live. Thom Yorke is a genius!!

18. Prince - Originals 

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Old songs. All written by Prince. Many originally sung by others. How did he write SO MANY incredible tunes. Supremely gifted and funky, gone far too soon. Thankfully, we have his music (and newly released music like this) to enjoy forever.

17. Jamila Woods - LEGACY! LEGACY!

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Each song on this album is named after an important black artist. There is a lot of anger, hope, and warmth in these songs. Jamila Woods is an important and inspiring artist. 

16. Sault - 5

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Who is this band?!? Nobody really knows. But who cares? All that is important is the quality of the music. Soul, funk, post punk... it's all here. I just discovered it last week so I can't say I listened to it a lot this year... but I am confident that I soon will!

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Song of the Week

19/12/2019

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Great article (especially for Foundations 12 students)!

19/12/2019

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The immediate math to be done with those numbers is the total number of ways you can scramble a Rubik’s cube: 43,252,003,274,489,856,000. Written in a more mathematical way, that number is (388!)(21212!)/12. Here’s how that comes together.
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You had to know this would happen...

19/12/2019

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Using Math to save lives

19/12/2019

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By combining RNA sequencing, bioinformatics and mathematical modeling, University of California San Diego School of Medicine and Moores Cancer Center researchers identified a sudden transcriptomic switch that turns healthy liver tissue cancerous. The finding was used to develop a quantitative analytical tool that assesses cancer risk in patients with chronic liver disease and to predict tumor stages and prognosis for patients with liver cancer.
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