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Math 10C

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Stuck with Homework?

Submit a grade 10-12 homework question!


Digital Tools

Alberta Program Overview

Specific Units:

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


Online Lessons:

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

Mathematics 10C: Videos


BC Math: Math 10

Recommended Text Book
Mathematics 10 Practice and Homework Book: Exercise and Homework Book

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Worksheets and Automated Quizzes

Grade 10 Worksheets (+answers and automated tests)

Nelson Mathematics 10 Online Study Guide


Tests Online

10 ACT Practice Tests (PDF)


Math 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:


Cayley Contest Mathematics Contests, for Grade 10

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.


3D Geometry

Algebraic Expressions


Exponent Laws

Irrational Numbers

Linear Functions

Polynomials and Factoring

     see also Divisibility

Right Triangle Trigonometry

Surface Area and Volume

Systems of Equations 

See also exponent and radicals index cards Additional Books for Math 10C
by Greg Ranieri, Alan Appleby


3D Geometry

(back to Shortcuts...)

  Activity Use Tinkercad to identify the cross section of 3D objects.
  Build a hypercube

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Alberta Education Diploma Math 30
  Cavalieri's Principle (Volume)
  The Volume of a Cone

Exponent Laws

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The rules:
  What is an "Integral exponent"? An "Integral exponent" is an exponent that is a whole number
(in contrast to the powers of radicals for example which are 1/n, i.e. fractional)
  see also  Exponent and radicals index cards 

Irrational Numbers

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To understand irrational numbers, first we must understand rational ones. Definition: Rational Numbers

Do not think "rational" as in logical. Think as in "ratio", a.k.a. fraction.
Rational numbers as such that can be accurately reverse engineered from their decimal form back into their fraction, or rather ratio - and thus are rational. Any decimal number with a finite number of digits is such, and any decimal with a group of digits that infinitely repeat after the decimal point is also such.

Definition: Irrational Numbers Irrational is the opposite of Rational. That is you cannot accurately reverse engineer from the decimal form back to a parent ratio (or fraction) - and thus such number is not rational, or we say it is rather irrational.
You can create a fraction that is an approximation of that decimal, but it will not be an exact value and when reverting the fraction back into decimal you may get a somewhat different rounding than the one you started with.

How do Irrationals look like typically?
Irrational numbers appear as decimals with an infinite number of digits that do not repeat, and cannot be predicted. Such decimal number was most likely accomplished via a division that never stopped, and you were forced to round up so you can stop dividing.
An example is Pi = π = 3.14159.... π  is calculated via the division of any circle's circumference by its diameter. Another example is e, Euler's number, the same e as seen in natural logarithms.
Read more about irrational numbers here.

The problem is how do we know that a number is truly irrational and it's not that we just gave up to soon on the steps of a division?
The number e bears Euler's name because he was the first to prove the number has an infinite number of decimals and there is no pattern of repetitions, and thus is irrational.
  Converting Decimals to Fractions


Linear Functions

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  Explaining functions:
                        y = f(x)

  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.

  Lesson (slide show)

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Diploma Prep Courses
  Problem solving
Find the intercepts and draw the graph y = 4x-8

Lessons and other resources


Graphing Linear Equations
Solving and Graphing Linear Inequalities

An Introduction To Solving Linear Inequalities - Example 1
An Introduction To Solving Linear Inequalities - Example 2
An Introduction To Solving Linear Inequalities - Example 3

Solving Linear Compound Inequalities - Example 1
Solving Linear Compound Inequalities - Example 2
Solving Linear Compound Inequalities - Example 3

  Parallel and Perpendicular Lines
Practice: Parallel Lines
  Practice Exercises
    (PDF download)
  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.

  see also:

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
  Graphing a linear equation


  Practice EXAM
(press Next at the bottom for solutions to this exam)


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  Lessons and Tools
  Linear Equations with Two Variables

Systems of Equations

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  Systems of Linear Equations
  Solve linear systems visually/graphically 
Solving linear systems by substitution
  Solving systems of equations by elimination

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