﻿ Grade 10, Math 10C Curriculum (Free Resources)

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math 10C (gr 10)
math 20-1 (gr 11)
math 30-1 (gr 12)

# Math 10C

## Stuck with Homework?

Submit a grade 10-12 homework question!

## Digital Tools

Alberta Program Overview

Specific Units:

Online Lessons:

BC Math: Math 10

Recommended Text Book
Mathematics 10 Practice and Homework Book: Exercise and Homework Book  ## 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: http://www.math.ucalgary.ca/community_outreach/math_nite

# Competitions

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.

Shortcuts

 3D Geometry Equations Irrational Numbers Linear Functions      see also Divisibility Surface Area and Volume See also exponent and radicals index cards. Additional Books for Math 10C FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS 10 WORKBOOK by Greg Ranieri, Alan Appleby # Topics

## 3D Geometry

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

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)

## 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.

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 https://www.mathsisfun.com/converting-decimals-fractions.html

## 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)

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

Lessons and other resources

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/

Videos:
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 http://map.mathshell.org/lessons.php?unit=9220&collection=8

Practice: Parallel Lines
Practice Exercises
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.

https://njctl.org/courses/math/geometry/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
Graphing a linear equation

Practice EXAM https://courses.lumenlearning.com/epcc-atdcoursereview-collegealgebra-1-2/chapter/linear-functions-practice-test/
(press Next at the bottom for solutions to this exam)

## Equations

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Linear Equations with Two Variables http://map.mathshell.org/lessons.php?unit=9235&collection=8

## Systems of Equations

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Systems of Linear Equations https://njctl.org/courses/math/algebra-i/systems-of-linear-equations/
Solve linear systems visually/graphically

Solving linear systems by substitution

Solving systems of equations by elimination

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