Welcome to the Pre-Calculus page!
OBJECTIVES:
The basic objectives of this course are to:
1. review, consolidate and enrich essential algebra skills required in college mathematics courses, such as calculus
2. acquire new mathematical concepts to be better prepared for college calculus
3. improve mental math skills
FORMAT:
There will be:
1. one module per cycle
2. one test at the end of each module
3. one WEBWORK assignment per module (webwork tutorial)
4. final group assignment tbc
EVALUATION:
Students will be evaluated:
1. on the full completion of each module, with complete work shown
2. all modules will last one 6-day cycle with the exception of more detailed modules
2. based on a modular test (no memory aids are permitted)
TUTORIALS:
1. daily at lunch
2. Google Virtual tutorials
3. Algebra Videos
MATERIALS:
1. pencils, binder, copybooks, graph paper
2. calculators will NOT be permitted in this course
3. Algebra notes
4. Grading Rubric
5. Advanced Review Package
6. Algebra Review 2
MATH CONTEST:
Fermat (Grade 11) - February 27, 2018
Practice Tests
University of Waterloo Visit - February 22, 2018 period 1
COURSE MODULES:
MODULE A: Basic Operations with Integers and Rational Numbers
Operations
Absolute Value
Square Roots Estimating
MODULE B: Algebraic Substitution and Quadratic Formula
Substitution
MODULE C: Linear Equations y = mx + b; general and point slope form; Parallel and Perpendicular lines; Inequalities
Linear Equations and Inequalities
MODULE D: Systems of Linear Equations (2 and 3 variables); Semi-Linear Equations with Curve Sketching and Visualization of Area between Curves
Systems of Equations - All
Curve Sketching and Systems
Determining Number of Solutions
MODULE E: Analytic Geometry
Analytic Geometry 1
Analytic Geometry 2
Analytic Geometry 3
Analytic Geometry 4
Analytic Geometry 5
MODULE F: 1st Degree Equations
1ST DEGREE EQUATIONS
MODULE G: Solids: Volume; Area, Similarity; Equivalence
VOLUME & AREA OF SOLIDS
SIMILARITY
MODULE H: Transformations in a Cartesian Plane
RULES
TRANSLATIONS, REFLECTIONS & ROTATIONS
SIMILARITY TRANSFORMATIONS
MODULE I: Sequences and Series; Factorials
OVERVIEW
GEOMETRIC AND ARITHMETIC SEQUENCES
GEOMETRIC AND ARITHMETIC SERIES
Factorials 1
Factorials 2
Factorials 3
Complex Numbers
MODULE J: Matrices (introduction) and Cramer's Rule
MATRIX OPERATIONS & CRAMER'S RULE
COURSE NOTES AND EXAMPLES
MODULE 1: Exponents, Rational Exponents (module 1 correction key q 31-40)
Exponents worksheet
QUIZ FEBRUARY 10, 2020 MODULE 1 VIDEO
MODULE 2: Radicals
Rationalizing Denominators and Numerators
Rationalizing Denominators and Numerators 2
QUIZ FEBRUARY 19, 2020 MODULE 2 VIDEO
MODULE 3: Polynomial Operations
Literal Equations 1
Literal Equations 2
QUIZ FEBRUARY 28, 2020 MODULE 3 VIDEO
MODULE 4: Factoring, including Sum and Difference of Cubes
Factoring Polynomials
Advanced Factoring
Factoring with Rational Exponents
QUIZ MARCH 16, 2020 MODULE 4 VIDEO
MODULE 5: Rational Expressions
Complex Fractions
Rational Expressions Worksheet
QUIZ MARCH 24, 2020 MODULE 5 VIDEO
MODULE 6: Synthetic Division
Synthetic Division
Synthetic Division
Synthetic Division
Remainder Theorem
Factor Theorem and Special Factoring
QUIZ APRIL 3, 2020 MODULE 6 VIDEO
MODULE 7: Partial Fraction Decomposition 1
Partial Fraction Decomposition 2
Partial Fraction Decomposition 3
Partial Fraction Decomposition 4
Partial Fraction Decomposition 5
QUIZ APRIL 16, 2020 (KEY) MODULE 7 VIDEO
MODULE 8: Solving Second Degree Equations (square roots, factoring)
Completing the Square
Solving Second Degree Equations (Completing the Square)
QUIZ APRIL 24, 2020 MODULE 8 VIDEO
MODULE 9 & 10: (2 CYCLES) More Equations: Linear (fractional), Absolute Value, Rational, Radical, Exponential, Trigonometric, Logarithmic
QUIZ MAY 4, 2020 (KEY) MODULE 9 & 10 VIDEO
MODULE 11: Inequalities: Absolute Value, Compound, Linear, Systems, Quadratic (graphical)
Quadratic (algebraic)
Rational 1
Rational 2
QUIZ MAY 12, 2020 (KEY) MODULE 11 VIDEO
MODULE 12: Graphing Polynomial Functions
Graphing Polynomial Functions 2
Graphing Polynomial Functions 3
Graphing Polynomial Functions 4
Graphing Polynomial Functions 5
Graphing Polynomial Functions 6
Graphing Piece-Wise Functions (introduction to continuity)
Graphing Piece-Wise Functions 2
Graphing Rational Functions
Graphing Rational Functions 2
RATIONAL FUNCTIONS WORKSHEET
QUIZ MAY 22, 2020 (KEY) MODULE 12 VIDEO
MODULE 13: Exponential Functions
Logarithmic Functions
Logs 2
INTRODUCTION
Notes
QUIZ JUNE 1, 2020 (KEY)
MODULE 14: (2 CYCLES) Trigonometry: Reference angles, Graphing, Wrapping functions, Degrees and Radians
Graphing 2
Trig equations
QUIZ IN CLASS (KEY)
MODULE 15: Trigonometric Identities 1
Trigonometric Identities 2
Sum, Difference, Half and Double Angle Identities
Sum, Difference, Half and Double Angle Identities worksheet
QUIZ IN CLASS
MODULE 16: (2 CYCLES) Introduction to Limits 1
Introduction to Limits 2
Introduction to Limits 3
Introduction to Derivatives 1
Introduction to Derivatives 2
Introduction to Derivatives 3
REFERENCE
OBJECTIVES:
The basic objectives of this course are to:
1. review, consolidate and enrich essential algebra skills required in college mathematics courses, such as calculus
2. acquire new mathematical concepts to be better prepared for college calculus
3. improve mental math skills
FORMAT:
There will be:
1. one module per cycle
2. one test at the end of each module
3. one WEBWORK assignment per module (webwork tutorial)
4. final group assignment tbc
EVALUATION:
Students will be evaluated:
1. on the full completion of each module, with complete work shown
2. all modules will last one 6-day cycle with the exception of more detailed modules
2. based on a modular test (no memory aids are permitted)
TUTORIALS:
1. daily at lunch
2. Google Virtual tutorials
3. Algebra Videos
MATERIALS:
1. pencils, binder, copybooks, graph paper
2. calculators will NOT be permitted in this course
3. Algebra notes
4. Grading Rubric
5. Advanced Review Package
6. Algebra Review 2
MATH CONTEST:
Fermat (Grade 11) - February 27, 2018
Practice Tests
University of Waterloo Visit - February 22, 2018 period 1
COURSE MODULES:
MODULE A: Basic Operations with Integers and Rational Numbers
Operations
Absolute Value
Square Roots Estimating
MODULE B: Algebraic Substitution and Quadratic Formula
Substitution
MODULE C: Linear Equations y = mx + b; general and point slope form; Parallel and Perpendicular lines; Inequalities
Linear Equations and Inequalities
MODULE D: Systems of Linear Equations (2 and 3 variables); Semi-Linear Equations with Curve Sketching and Visualization of Area between Curves
Systems of Equations - All
Curve Sketching and Systems
Determining Number of Solutions
MODULE E: Analytic Geometry
Analytic Geometry 1
Analytic Geometry 2
Analytic Geometry 3
Analytic Geometry 4
Analytic Geometry 5
MODULE F: 1st Degree Equations
1ST DEGREE EQUATIONS
MODULE G: Solids: Volume; Area, Similarity; Equivalence
VOLUME & AREA OF SOLIDS
SIMILARITY
MODULE H: Transformations in a Cartesian Plane
RULES
TRANSLATIONS, REFLECTIONS & ROTATIONS
SIMILARITY TRANSFORMATIONS
MODULE I: Sequences and Series; Factorials
OVERVIEW
GEOMETRIC AND ARITHMETIC SEQUENCES
GEOMETRIC AND ARITHMETIC SERIES
Factorials 1
Factorials 2
Factorials 3
Complex Numbers
MODULE J: Matrices (introduction) and Cramer's Rule
MATRIX OPERATIONS & CRAMER'S RULE
COURSE NOTES AND EXAMPLES
MODULE 1: Exponents, Rational Exponents (module 1 correction key q 31-40)
Exponents worksheet
QUIZ FEBRUARY 10, 2020 MODULE 1 VIDEO
MODULE 2: Radicals
Rationalizing Denominators and Numerators
Rationalizing Denominators and Numerators 2
QUIZ FEBRUARY 19, 2020 MODULE 2 VIDEO
MODULE 3: Polynomial Operations
Literal Equations 1
Literal Equations 2
QUIZ FEBRUARY 28, 2020 MODULE 3 VIDEO
MODULE 4: Factoring, including Sum and Difference of Cubes
Factoring Polynomials
Advanced Factoring
Factoring with Rational Exponents
QUIZ MARCH 16, 2020 MODULE 4 VIDEO
MODULE 5: Rational Expressions
Complex Fractions
Rational Expressions Worksheet
QUIZ MARCH 24, 2020 MODULE 5 VIDEO
MODULE 6: Synthetic Division
Synthetic Division
Synthetic Division
Synthetic Division
Remainder Theorem
Factor Theorem and Special Factoring
QUIZ APRIL 3, 2020 MODULE 6 VIDEO
MODULE 7: Partial Fraction Decomposition 1
Partial Fraction Decomposition 2
Partial Fraction Decomposition 3
Partial Fraction Decomposition 4
Partial Fraction Decomposition 5
QUIZ APRIL 16, 2020 (KEY) MODULE 7 VIDEO
MODULE 8: Solving Second Degree Equations (square roots, factoring)
Completing the Square
Solving Second Degree Equations (Completing the Square)
QUIZ APRIL 24, 2020 MODULE 8 VIDEO
MODULE 9 & 10: (2 CYCLES) More Equations: Linear (fractional), Absolute Value, Rational, Radical, Exponential, Trigonometric, Logarithmic
QUIZ MAY 4, 2020 (KEY) MODULE 9 & 10 VIDEO
MODULE 11: Inequalities: Absolute Value, Compound, Linear, Systems, Quadratic (graphical)
Quadratic (algebraic)
Rational 1
Rational 2
QUIZ MAY 12, 2020 (KEY) MODULE 11 VIDEO
MODULE 12: Graphing Polynomial Functions
Graphing Polynomial Functions 2
Graphing Polynomial Functions 3
Graphing Polynomial Functions 4
Graphing Polynomial Functions 5
Graphing Polynomial Functions 6
Graphing Piece-Wise Functions (introduction to continuity)
Graphing Piece-Wise Functions 2
Graphing Rational Functions
Graphing Rational Functions 2
RATIONAL FUNCTIONS WORKSHEET
QUIZ MAY 22, 2020 (KEY) MODULE 12 VIDEO
MODULE 13: Exponential Functions
Logarithmic Functions
Logs 2
INTRODUCTION
Notes
QUIZ JUNE 1, 2020 (KEY)
MODULE 14: (2 CYCLES) Trigonometry: Reference angles, Graphing, Wrapping functions, Degrees and Radians
Graphing 2
Trig equations
QUIZ IN CLASS (KEY)
MODULE 15: Trigonometric Identities 1
Trigonometric Identities 2
Sum, Difference, Half and Double Angle Identities
Sum, Difference, Half and Double Angle Identities worksheet
QUIZ IN CLASS
MODULE 16: (2 CYCLES) Introduction to Limits 1
Introduction to Limits 2
Introduction to Limits 3
Introduction to Derivatives 1
Introduction to Derivatives 2
Introduction to Derivatives 3
REFERENCE
