MATH TUTOR
ONLINE MATH TUTOR RESOURCES
There were two important strategies I was taught when I first entered the teaching world:
1. There is no need to reinvent the wheel 2. It’s not about “what” you say, but “how” you say it
To address the first point, and bring relevancy to education and tutoring, there are a myriad of resources and problems out there which students can use to practice. However, sometimes information is not communicated in a way that the student understands, and every student is different. You can be a forefront mathematician working on disproving Fermat’s Theorem, but explaining fundamental concepts at a level that a student in grade 10 or 11 math can understand may be tricky (or not!). Here, you will find some helpful handouts and practice problems (with solutions!) for MATH problems.
Grade 12 Advanced Functions Resources
Unit 1 - Characteristics & Properties
11 Functions
12 Exploring Absolute Value
13 Properties of Graphs of Functions
14 Sketching Graphs of Functions
15 Inverse Functions
16 Piecewise Functions
17 Exploring Operations with Functions
Unit 2 - Understanding Rates of Change
21 Understanding Rates of Change
22 Estimating Instantaneous Rate of Change
Unit 3 - Polynomial Functions
31 Exploring Polynomial Functions
32 Characteristics of Polynomail Functions
33 Polynomial Functions in Factored Form
34 Transformations of Cubic and Quartic Functions
35 Dividing Polynomials
36 Factoring Polynomials
37 Factoring a Sum or Difference of Cubes
Unit 4 - Polynomial Equations & Inequalities
41 Solving Polynomial Equations
42 Solving Linear Inequalities
43 Solving Polynomial Inequalities
Unit 5 - Rational Functions
51 Graphs of Reciprocal Functions
52 Exploring Quotients of Polynomial Functions
53 Graphs of Rational Functions of the form f(x) = (ax + b) over (cx + d)
54 Solving Rational Equations
55 Solving Rational Inequalities
Unit 6 - Trigonometric Functions
61 Radian Measure
62 Radian Measure and Angles on the Cartesian Plane
63 Exploring Graphs of the Primary Trigonometric Functions
64 Transformations of Trigonometric Functions
65 Exploring Graphs of Reciprocal Trigonometric Functions
66 Modelling with Trigonometric Functions
Unit 7 - Trigonometric Identities & Equations
72 Compound Angle Formulas
73 Double Angle Formulas
74 Proving Trigonometric Identities
75 Solving Linear Trigonometric Equations
76 Solving Quadratic Trigonometric Equations
77 Inverse Trigonometric Functions
Unit 8 - Exponential & Trigonometric Functions
80 Exponential Functions
81 Exploring the Logarithmic Function
82 Transformations of Logarithmic Functions
83 Evaluating Logarithms
84 Laws of Logarithms
85 Solving Exponential Equations
86 Solving Logarithmic Equations
87 Solving Problems with Exponential and Logarithmic Functions
Unit 9 - Combinations of Functions
91 Exploring Combinations of Functions
92 Combining Two Functions - Sums and Differences
93 Combining Two Functions - Products
94 Exploring Quotients of Functions
95 Compositions of Functions
Grade 12 Calculus and Vectors Resources
Unit 1 - Introduction to Calculus & Limits
11 Radical Expressions
12 Slope of Tangent
13 Rate of Change
14 Limit of a Function
15 Properties of Limits
16 Continuity
Unit 2 - Derivative Rules
21 Derivative Function
22 Derivative of Polynomial Functions
23 Product Rule
24 Quotient Rule
25 Chain Rule
Unit 3 - Applications of Derivatives I
31 Higher Order Derivatives Velocity and Acceleration
32 Maximum and Minimum on an Interval Extreme Values
33 34 Optimization
Unit 4 - Applications of Derivatives II
41 Increasing and Decreasing Functions
42 Critical Points Local Maxima and Minima
43 Vertical and Horizontal Asymptotes
44 Concavity and Points of Inflection
45 An Algorithm for Curve Sketching
Unit 5 - Transcendental Functions & Optimization
53 Optimization
Derivative of Logarithmic Functions
52 Derivative of Exponential Functions
5.5 Derivative of Trigonometric Functions
Functions
Unit 6 - Vectors
61 An Introduction to Vectors
62 Addition and Subtraction of Geometric Vectors
63 Multiplication of a Vector by a Scalar
64 Properties of Vectors
65 Vectors in R2 and R3
66 Operations with Algebraic Vectors in R2
67 Operations with Algebraic Vectors in R3
Unit 7 - Applications of Vectors
71 Vectors as Forces
72 Velocity
73 Dot Product of two Geometric Vectors
74 The Dot Product of Algebraic Vectors
75 Scalar and Vector Projections
76 Cross Product
77 Applications of the Dot and Cross Product
Unit 8 - Equations of Lines & Planes
81 Vector and Parametric Equations of a Line in R2
82 Cartesian Equation of a Line
83 Vector Parametric and Symmetric Equations of a Line in R3
84 Vector and Parametric Equations of a Plane
85 Cartesian Equation of a Plane
Unit 9 - Relationships Between Points, Lines and Planes
91 Intersection of a Line with a Plane
91 Intersection of two Lines
93 Intersection of two Planes
94 Intersection of three Planes
95 Distance from a Point to a Line
96 Distance from a Point to a Plane
Affiliated Math Resources Site Meant4Teachers.ca
The following documents were obtained from La-Ctiadelle, at La Citadelle, Ontario, Canada (la-citadelle.com)