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Topic Shortcuts

(In Alphabetical Order)

Algebraic Expressions

Conics

Complete the Square...

Divisibility

Equations

Exponent Laws (gr 10)

Functions (transformations, inverse, ...)

Function Catalogue

Geometry

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

Quadratics

Radicals and Square Roots

Sequences and Series

Three-dimensional Vectors

Trigonometry (gr 12)

Imaginary and Complex Numbers

 


Books and Articles


Alberta:
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

Pre-Calculus

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

http://www.shodor.org/interactivate/tools/

https://www.desmos.com/

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

PRACTICE PSAT 2 (PDF)

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: http://www.math.ucalgary.ca/community_outreach/math_nite

 

See also the JAMES Mathematics Circle.

 

Articles

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."

Read more...

 

 

Specific Topics

(see Shortcuts)

     

Conics

(back to Shortcuts...)

Try the activities first.

Scroll further down for lesson.

   

Activity:
Circle

Experiment with the circle.
     

Activities:
Parabola

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.
ax2+bx+c
("standard form")
  ax2+bx+c

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. https://www.youtube.com/watch?v=-mqRisANuWE
     
Interactive Tool: Manipulate the Sections of a Cone https://illuminations.nctm.org/Activity.aspx?id=3506
Interactive Tool: Manipulate the Sections of a Cone http://www.shodor.org/interactivate/activities/CrossSectionFlyer/
     

Conics in Generals

see also these formulas:

or on .teacherspayteachers.com.
Conic Sections (animation)

Lessons on Conics

http://www.shelovesmath.com/precal/conics/
  https://njctl.org/courses/math/pre-calculus/conics/
  https://illuminations.nctm.org/Lesson.aspx?id=2907
   
   

Activities and Exploration

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

Complete the Square

(back to Shortcuts...)

How to complete_the_square.html
Mathisfun, Examples how to solve https://www.mathsisfun.com/algebra/completing-square.html
     
Exercises on IXL https://ca.ixl.com/math/grade-10/complete-the-square
 

Linear Functions

(see first: Functions)

(back to Shortcuts...)

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

http://mathsradical.weebly.com/functions.html

http://www.shelovesmath.com/algebra/beginning-algebra/coordinate-system-and-graphing-lines/

http://carlisleschools.ss13.sharpschool.com/cms/One.aspx?portalId=95563&pageId=768700

 

Graphing Linear Equations https://njctl.org/courses/math/algebra-i/graphing-linear-equations/
Solving and Graphing Linear Inequalities https://njctl.org/courses/math/algebra-i/solving-and-graphing-linear-inequalities/
  Parallel and Perpendicular Lines http://map.mathshell.org/lessons.php?unit=9220&collection=8
     
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
http://www.math10.ca/lessons//UnitBooks/Math10C_Workbook_Unit4.pdf
  Practice: Shortest Distance between a Point and Line - Equations of Lines
  Practice:
Given a line y = mx + b, find the formula of a parallel line at a distance d.
  Practice:
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 http://www.math10.ca/lessons/relationsAndFunctions/practiceExam/Math10C_PracticeExam_RelationsAndFunctions.pdf
     
 

Quadratics

(back to Shortcuts...)

Lessons and Notes

http://www.shelovesmath.com/algebra/intermediate-algebra/quadratics/

Graphing Quadratics: http://carlisleschools.ss13.sharpschool.com/cms/One.aspx?portalId=95563&pageId=768751

 

Math 20-1: https://www.sachs.gsacrd.ab.ca/eteachers/1151/math-20-1

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

 

Math 20-2: https://www.sites.google.com/site/sharonbarrymath/mathematics-20-2/chapter-7-quadratic-equations

 

  Art of Problem Solving: Vieta for Quadratics Part 1
  Art of Problem Solving: Vieta for Quadratics Part 2  
     
  Quadratic Function - Vertex Form https://mathbitsnotebook.com/Algebra1/Quadratics/QDVertexForm.html
     
     
  Desmos: Quadratic Classroom Activities https://teacher.desmos.com/quadratic
     
 
     
  Parabola Interactive Activity on Desmos https://teacher.desmos.com/activitybuilder/custom/56fade8fcd70f60d1ca0ca05
  Review: Quadratic Theory - Warm-up Questionnaire
     Answers
     
 
     

Functions

(back to Shortcuts...)


 
Explaining y = f(x)
 
Functions Catalog
 
  Functions vs. Relations http://www.learnalberta.ca/content/memg/Division04/Relation/index.html

http://carlisleschools.ss13.sharpschool.com/cms/One.aspx?portalId=95563&pageId=768692
     
  Piecewise Functions https://www.mathsisfun.com/sets/functions-piecewise.html
 
Function Transformations
Vertical and Horizontal Transformations
 
Stretch and Compression

 
  Transforming the square-root function
(Khan Academy)
 
https://www.khanacademy.org/math/algebra2/radical-equations-and-functions/graphs-of-radical-functions/v/flipping-shifting-radical-functions
 
  The Inverse of a Function The Inverse of a Square Root Function

https://www.mathsisfun.com/sets/function-inverse.html

Rational Functions
 
http://carlisleschools.ss13.sharpschool.com/cms/One.aspx?portalId=95563&pageId=768791
 
  Function Operation and Composition http://blumalg2.blogspot.com/2018/08/august-22-2018-function-operations-and.html

http://www.purplemath.com/modules/fcnops.htm 

https://www.mathsisfun.com/sets/functions-composition.html
     
  Reconstructing a function from its roots and y-intercept into factored form y = a(x - x1)(x - x2)
 
https://www.youtube.com/watch?v=ETexFVlpXYQ
  Graphing square root (radical) functions
see also radicals...
 
http://www.analyzemath.com/Graphing/graphing_square_root_func.html

https://www.mathway.com/popular-problems/Algebra/279714
 
 
     

Equations

(back to Shortcuts...)

   
  Lessons and Tools https://www.ck12.org/search/?q=equations&subject=algebra&subject=calculus&source=ck12&grade=10&grade=11&grade=12
  Linear Equations with Two Variables http://map.mathshell.org/lessons.php?unit=9235&collection=8
Systems of Linear Equations https://njctl.org/courses/math/algebra-i/systems-of-linear-equations/
 

Exponent Laws

(back to Shortcuts...)

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

(back to Shortcuts...)

   
  Lessons
 
http://carlisleschools.ss13.sharpschool.com/cms/One.aspx?portalId=95563&pageId=768844
Intro to Arithmetic Series on Khan Academy https://www.khanacademy.org/math/algebra/sequences/introduction-to-arithmetic-squences/v/arithmetic-sequences

  Intro to Geometric Series on Khan Academy https://www.khanacademy.org/math/algebra/sequences/introduction-to-geometric-sequences/v/geometric-sequences-introduction
 

Three-dimensional Vectors

(back to Shortcuts...)

 

 

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

Imaginary and Complex Numbers

(back to Shortcuts...)

 
  Complex Numbers: Introduction http://www.purplemath.com/modules/complex.htm
     

 

Lesson - Part I
(see the entire series here)
Complex Numbers http://www.mathsisfun.com/numbers/complex-numbers.html
     
 

Geometry

(back to Shortcuts...)

   
  General links on Geometry https://www.ck12.org/c/geometry/
  Interactive: Circle & Line Geometry
  Interactive: Incenter-Incircle
     
Interactive: Angle Bisector
  Mathematics Vision Project:
 
  Angles
Parallel Lines
Triangles
Similar Triangles and Trigonometry
Congruent Triangles
Circles
Transformations
Quadrilaterals
Area of Figures
 
https://njctl.org/courses/math/geometry/
  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

(back to Shortcuts...)

   
  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)

(back to Shortcuts...)

  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
https://njctl.org/courses/math/geometry/analytic-geometry/
 
     
     
Inductive Reasoning and Making a Conjecture

(back to Shortcuts...)

 
Khan Academy
https://www.khanacademy.org/math/algebra-home/alg-series-and-induction#alg-deductive-and-inductive-reasoning
  Activity: Leap Frog Numbers Patterns
(Needs Flash)
https://brocku.ca/mathematics/resources/learningtools/learningobjects/frogs/fullscreendemo.html
 
     
     
Probability and Statistics

(back to Shortcuts...)

 
Lessons
http://map.mathshell.org/lessons.php?unit=9400&collection=8&redir=1

https://njctl.org/courses/math/7th-grade/statistics-probability/

http://carlisleschools.ss13.sharpschool.com/cms/One.aspx?portalId=95563&pageId=768777

Khan Academy lessons https://www.khanacademy.org/math/statistics-probability

 

Articles

(back to Shortcuts...)

 

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

 

Books

 

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

Topics include:
Sierpinski Triangles,
Menger Sponge,
Fractals
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

(back to Shortcuts...)

   
         

 

(back to Shortcuts...)

 

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