Navigating Through this Site: Finding What You Need

Exercises and Solutions

Below you will find the exercises and solutions available for The Language of Mathematics. Over time, more will be added and those in draft form will be finalized.

Please keep in mind that like most people, I am prone to making silly mistakes, so take the answers with a grain of salt. Corrections and suggestions are always welcome.

Series I - Description, Videos.

Series II - Description, Videos.

Series IIIa - Description, Videos.

Series IIIb - Description, Videos.

Series IV (open)

Series I

Section 2: The Real Number Set

Exercises: Which number set do the following numbers belong to.

Solutions.

Section 4: Basic Operations

Exercises: Basic Operations.

Solutions to:

i) Adding,

ii) Subtracting,

iii) Multiplying,

iv) Dividing,

v) Simplifying.

Section 5: Prime Numbers

Exercises: Break down the following into their Prime factors.

Solutions.

Section 6: Fractions

Exercises:

i) Reducing Fractions,

ii) Multiplying and Dividing Fractions,

iii) Adding and Subtracting Fractions.

Solutions to:

i) Reducing Fractions,

ii) Multiplying and Dividing Fractions,

iii) Adding and Subtracting Fractions.

Section 7: Trigonometry

Exercises: Find the missing variables, and solve the following right triangles.

Solutions.

Section 8: Basic Geometry

Exercises:

i) Parallel Lines,

ii) Congruent and Similar Triangles.

Solutions to:

i) Parallel Lines,

ii) Congruent and Similar Triangles.

Section 9: Coordinate Geometry

Exercises:

i) Plotting Points and Lines,

ii) Finding Slope, Midpoint, and Distance of a Line.

Solutions to:

ia) Small Grid,

ib) Large Grid,

ic) Plotting Lines,

iia) Finding Slope and Midpoint of a Line,

iib) Finding Distance of a Line.

Section 10: Proofs

Exercises:

i) Proofs Involving Triangles,

ii) Proofs Involving a Line,

iii) Coordinate Geometry Proof.

Solutions to:

i) Proofs Involving Triangles,

ii) Proofs Involving a Line,

iii) Coordinate Geometry Proof.

Series II

Section 1: Exponents and Radicals

Exercises:

i) Adding and Subtracting,

ii) Multiplying and Dividing,

iii) Exponents to Exponents,

iv) Reducing Radicals,

v) Simplifying Radicals.

Solutions to:

i) Adding and Subtracting,

ii) Multiplying and Dividing,

iii) Exponents to Exponents,

iv) Reducing Radicals,

v) Simplifying Radicals.

Series IIIa

- No exercises available for this series at the moment.

Series IIIb

- No exercises available for this series at the moment.

Series IV

- No exercises available for this series at the moment.

About Math in Real Life

In much the same manner that the industrial revolution brought about a surge of literacy in natural languages, the advent of the Internet in combination with low-cost computing has brought about a surge in the need to be literate in the language of mathematics. Due to these advancements, math has become an integral part of our society and the need to be literate in this language a necessity.

There are, however, some major problems. Many education systems, across the globe, are under stress and failing. The causes are vast and varied, so we’ll refrain from discussing the details of this collapse but instead focus on possible solutions to our predicament.

It is my belief that access to a good education is a human right, an obligatory gift from one generation to the next, and as long as we have access to an open, unfiltered, and uncensored Internet, then we, as a global community, can make a difference. We can fill the gap left behind by our governments and institutions by becoming proactive educators.

For my part, I will try and show how beautiful, how powerful, how useful and how easy it is to learn the bare minimum we need to know about the language of mathematics to enhance our lives. To achieve this task I am producing instructional videos for all major topics covered in secondary school math curriculums in Canada and the United State, i.e., all major topics starting with The Real Number Set up to and including an introductory course in Calculus and one for Probability and Statistics.

Content is being presented in an online video text book format and organized into two main Tables of Contents: One geared towards teaching the rules and principles that we use in math, and the other geared towards applying this information in real life. This is the essence of this site, teaching The Language of Mathematics to those who want to use Math in Real Life.

As for how you can support this project: It takes a tremendous amount of time and energy to produce this work, and it would make my job a lot easier if the necessities of life were not my main concern. So, if you enjoy this work, if you are finding the information on this site useful, and if you would like to support this project, and can afford it, then please consider making a donation.

Peace

chycho

Table of Contents

The following are the two main tables of contents for this site:

1. The Language of Mathematics
2. Math in Real Life

The Language of Mathematics is geared towards teaching the syntax of this language, the rules and principles that we use in math. This project began in 2007 with The Real Number Set and will conclude with an introductory series on Calculus and one for Probability and Statistics.

Math in Real Life, started in 2012, is in its infancy and will continue indefinitely. The content in this section is geared towards using The Language of Mathematics to enhance our lives.

Lessons are also accessible through the tree menu provided in the left column. Specific topics can be found through the Index (left column).

Math in Real Life: Table of Contents

By far the most common question that I have been asked over the years regarding mathematics has been, ”When am I going to use math in real life?” That is, at least, the way I choose to perceive it. Unfortunately, more often than not, this question has come my way in the form of the following absurd absolute statement, “I’m never going to use this in real life!”

This erroneous perception of math’s practical usage has been the most prevalent problem in our education system, and by addressing it, the beauty of mathematics and its relevance reveals itself. Information gets absorbed faster. The details get scrutinized and people begin to recognize the occasions for which they have, can, and are already using math in their own lives.

This is the ultimate purpose of this section, to apply what we have learned from studying The Language of Mathematics to enhance our lives.

Content for this section will be organized in the following categories:

1. Games and Gambling
2. Personal Finance
3. Food and Fitness
4. Economics and Politics
5. Business and Investment
6. Energy and Environment
7. Art and Music
8. Science and Technology
9. Construction and Engineering
10. Miscellaneous

I. Games and Gambling

Section 1: Shooting Dice, Playing Craps

- coming soon

II. Personal Finance

Section 1: Time Management

- coming soon

III. Food and Fitness

- In the works

IV. Economics and Politics

- In the works

V. Business and Investment

- In the works

VI. Energy and Environment

- In the works

VII. Art and Music

- In the works

VIII. Science and Technology

- In the works

IX. Construction and Engineering

- In the works

X. Miscellaneous

- How to Study: Tip #2: Longer is Better - Introduction to Efficiency