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Postsecondary Math
Lending Library

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Topic Shortcuts

(In Alphabetical Order)

Algebraic Expressions


Complete the Square...



Exponent Laws (gr 10)

Functions (transformations, inverse, ...)

Function Catalogue


Geometry, 3D

Inductive Reasoning and Making a Conjecture

Linear Functions (gr 10)

    see also Equations

Polynomials (gr 10)

Polynomials, Factoring (gr 10)

     see also Divisibility

Probability and Statistics


Radicals and Square Roots

Sequences and Series

Three-dimensional Vectors

Trigonometry (gr 12)

Imaginary and Complex Numbers


Books and Articles

Grade 10-12 Math Curriculum

Alberta Program Overview

Specific Units:

10-Level Courses (follow the link to read about 10C, 10-3 and 10-4 program of studies).

20-Level Courses

30-Level Courses

Online Lessons

Mathematics 10C: Explained  

Math 20-1 Lessons (YouTube videos)

Mathematics 30-1: Explained

Math 10C, 10-3, 20-1, 20-2, 30-1

BC Math: Math 10, Math 11, Math 12

Topics on Mr. Jones' Classroom

Algebra I, Lessons


AP Calculus AB Course

AP Calculus BC Course

"Better Explained" - Calculus Learning Guide

Algebra and Functions


Stuck with Homework?

Submit a grade 10-12 homework question!


If you are serious about Math...

Don't just follow the normal curriculum, aim higher, try for example competition material.

American Mathematics Contest 10/12 (AMC 10/12)

AMC Problems and Solutions:

AMC 10 Problems and Solutions by AoP (Text version).

Many of these problems also have solutions presented in video tutorials on the AoP YouTube channel. Search the channel to check in a solution is available, for example:

Video Solution: Art of Problem Solving: 2017 AMC 10 A #22

Text version: select the year here, test A or B, next pick the problem or answer key: for ex. problem 22 solution in text version is here.


Digital Tools

Additional Competitions

Cayley Contest Mathematics Contests, for Grade 10

Fermat Contest Mathematics Contests, for Grade 11

Euclid Contest Mathematics Contests, for Grade 12


Worksheets and Automated Quizzes

Grade 10 Worksheets (+answers and automated tests)

Nelson Mathematics 10 Online Study Guide

Various Quizzes organized by Unit


Tests Online


10 ACT Practice Tests (PDF)

Assessment: Chinook Learning Services: Mathematics 20-1 or 20-2 or 20-3 Placement Test

In Person...

Math Nite will be running every Wednesday from 6pm-8pm in MS-431 at the University of Calgary, from the following dates:
September 20th, 2017 to December 6th,
2017 January 17th, 2018 to April 11th, 2018.
More detailed information about Math Nite can be found here:


See also the JAMES Mathematics Circle.



Does our approach to teaching math fail even the smartest kids?

Why Science Majors Change Their Minds (It’s Just So Darn Hard) (2011)


"...The excitement quickly fades as students brush up against the reality of what David E. Goldberg, an emeritus engineering professor, calls “the math-science death march.” Freshmen in college wade through a blizzard of calculus, physics and chemistry in lecture halls with hundreds of other students. And then many wash out."




Specific Topics

(see Shortcuts)



(back to Shortcuts...)

Try the activities first.

Scroll further down for lesson.



Experiment with the circle.


Play with the parameters that influence the parabola, find the roots.

  Focus of the Parabola
- use the mouse to drag the Focus and see the effect on the parabola's curve.
  Experiment with the effect of coefficient a on the parabola.
("standard form")

when messing with the b of this function, the Min point of the parabola moves along its own similar parabola.
Use Desmos and your own calculations to figure out what is the formula/function for the trajectory that the Min point incurs during changes to b.
Click here for one possible solution.

  Use your 3D printer to create a "live" parabola.
Interactive Tool: Manipulate the Sections of a Cone
Interactive Tool: Manipulate the Sections of a Cone

Conics in Generals

see also these formulas:

or on
Conic Sections (animation)

Lessons on Conics

Activities and Exploration

Use Google SketchUp (free)
(see also SketchUp tutorials)
  Project: Using Conics to build Baymax

Complete the Square

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How to complete_the_square.html
Mathisfun, Examples how to solve
Exercises on IXL

Linear Functions

(see first: Functions)

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What does "Linear" mean?
"Linear" is anything that represents the formula of a line. This can be linear equations, linear graphs, linear progressions, etc.

The typical formula for a line is given as:
y = mx + b, where m is the slope of the line and b is its y-intercept.
Lessons and other resources


Graphing Linear Equations
Solving and Graphing Linear Inequalities
  Parallel and Perpendicular Lines
Practice: Parallel Lines
  Practice Exercises
    Domain and range
    Plug in values
    Table of values
    Finding points on the graph
    Intercepts and points on the graph (p.17)
    Graphing volume (p.18)
    Interpreting Graphs
  Practice: Shortest Distance between a Point and Line - Equations of Lines
Given a line y = mx + b, find the formula of a parallel line at a distance d.
Shortest distance
between two parallel lines
(based on the solution above):

Problems that require finding the shortest distance between two parallel lines:
Using the above formula, we can isolate the distance d. This is assuming that the two line formulas are given. In other words:
- m & b1 are known,
- and b2 the parallel line's y-intercept is also given (or can be calculated).

Since the distance is a length, taking the positive value is what we want.
  Practice EXAM


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Lessons and Notes

Graphing Quadratics:


Math 20-1:

                    Scroll down to: Unit 3: Chapters 3 and 4 (these are Video presentations).


Math 20-2:


  Art of Problem Solving: Vieta for Quadratics Part 1
  Art of Problem Solving: Vieta for Quadratics Part 2  
  Quadratic Function - Vertex Form
  Desmos: Quadratic Classroom Activities
  Parabola Interactive Activity on Desmos
  Review: Quadratic Theory - Warm-up Questionnaire


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Explaining y = f(x)
Functions Catalog
  Functions vs. Relations
  Piecewise Functions
Function Transformations
Vertical and Horizontal Transformations
Stretch and Compression

  Transforming the square-root function
(Khan Academy)
  The Inverse of a Function The Inverse of a Square Root Function

Rational Functions
  Function Operation and Composition
  Reconstructing a function from its roots and y-intercept into factored form y = a(x - x1)(x - x2)
  Graphing square root (radical) functions
see also radicals...


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  Lessons and Tools
  Linear Equations with Two Variables
Systems of Linear Equations

Exponent Laws

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The rules:
  What is an "Integral exponent"? An "Integral exponent" is an exponent that is a whole number
(opposite to the powers of radicals for example which are 1/n, i.e. fractional)  .

Sequences and Series

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Intro to Arithmetic Series on Khan Academy

  Intro to Geometric Series on Khan Academy

Three-dimensional Vectors

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Activity Use Tinkercad to model 3D vectors from the video below.

Imaginary and Complex Numbers

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  Complex Numbers: Introduction


Lesson - Part I
(see the entire series here)
Complex Numbers


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  General links on Geometry
  Interactive: Circle & Line Geometry
  Interactive: Incenter-Incircle
Interactive: Angle Bisector
  Mathematics Vision Project:
Parallel Lines
Similar Triangles and Trigonometry
Congruent Triangles
Area of Figures
  Similarity in Triangles: What is necessary in two triangles to conclude similarity?
    SAS Triangle Similarity Theorem

SSS Triangle Similarity

AA Similarity
    read more on similarity...

3D Geometry

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  Activity Use Tinkercad to identify the cross section of 3D objects.
  Build a hypercube
  Cavalieri's Principle (Volume)
  The Volume of a Cone

Analytic Geometry (= Coordinate Geometry = Cartesian Geometry)

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  Origin of Analytic Geometry
Distance Formula
Midpoint Formula
Partitions of a Line Segment
Slopes of Parallel and Perpendicular Lines
Eq of Parallel and Perpendicular Lines
Triangle Coordinate Proofs
Equation of a Circle and Completing the Square
Inductive Reasoning and Making a Conjecture

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Khan Academy
  Activity: Leap Frog Numbers Patterns
(Needs Flash)
Probability and Statistics

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Khan Academy lessons



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Bad feelings about math beget bad grades — which beget more bad feelings

Girls rank themselves less competent in math than boys, even when getting the same grades

Stephen McCormick: a mathematician who nearly failed math

How math is helping sub-Saharan maize farmers




Free online version available..
This book is also available
in Kindle format.
Chapters have
Self Grading Quizzes

Topics include:
Sierpinski Triangles,
Menger Sponge,
Fibonacci and
The Golden Ratio.
Currently (Dec 2017),  free on Kindle.

Calculus Text Book - Western Canada High School

A Book of Abstract Algebra
Charles C. Pinter
Where can I find free Math books online?

Try the "Open Textbook Library".
Elementary Linear Algebra
Howard Anton, Chris Rorres
Make It Stick offers techniques for becoming more productive learners, and cautions against study habits and practice routines that turn out to be counterproductive By road testing many of the counterintuitive techniques described in this book, Carey shows how we can flex the neural muscles that make deep learning possible.    

Coding with MIT 3.0 Scratch



Extras for Fun

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Academix: Study, Explore, Engage...