MTH60 resources
- There is no need to purchase textbook or online access code.
Materials here are free!
- Go through each lesson's lecture notes and video lectures. Do homework
online to practice. If you made a mistake in a homework question, you can
try the same problem with different numbers, until you master the concepts.
- Log in at https://webwork.pcc.edu/webwork2/mthalc60-yao-f15/ to use the online homework system. You need a username and password. Email Carl Yao at
xiaolong.yao@pcc.edu to create
one.
Open all
Close all
3 means you won $3.
-4 means you lost $4.
3+(-4) means you won $3 and then lost $4, a net loss of $1. This is why 3+(-4)=-1.
Make sense?
Everyone loves fractions! This unit reviews fraction operations (add/subtract/multiply/divide).
We will learn some basic Algebra skills in this unit.
Solving linear equations is the foundation for all later mathematics.
Memorize the following steps: (There will be similar variations in these steps.)
1. Get rid of () by distributive property.
2. Combine like terms.
3. Move x terms to one side of =.
4. Move numbers to the other side of =.
5. Get rid of the number in front of x.
Here is an example:
3(x-3)+10 = x+7 To do Step 1: Get rid of () by distributive property.
3x-9+10 = x+7 To do Step 2: Combine like terms.
3x+1 = x+7 To do Step 3: Move x terms to one side of =.
3x+1-x = x+7-x
2x+1 = 7 To do Step 4: Move numbers to the other side of =.
2x+1-1 = 7-1
2x = 6 To do Step 5: Get rid of the number in front of x.
2x/2 = 6/2
x = 3
No one is born to solve word problems. You need to learn how to solve a few different types of word problems. At first, they seem unrelated to each other. However, once you see the similarity among different types of word problems, you will get the hang of solving them.
This unit will help you build a foundation for more difficult word problems in a later unit.
Solving linear inequalities follow the same procedures of solving linear equalities. Get rid of parentheses, ...
There is one major difference.
We know 2>1 is true. If we multiply -1 on both sides of 2>1, we have -2<-1. Notice that the direction of the inequality symbol changed!
Rule: When we multiple or divide a negative number on both sides of an inequality, we must switch the direction of the inequality symbol. Why? I just showed you with the 2>1 and -2<-1 example.
Assume your house is worth $200,000 and you paid $1,200 of property tax last year. Your neighbor's house is worth $240,000, and he paid $1,250 of property tax last year. Is it fair?
Proportion will tell you this is not fair: You are not paying your fair share! How can that be? Well, this unit will show you.
In this unit, we learn how to find the perimeter and area of some common shapes.
This unit is the core of Algebra. Math is used to model all types of real-life data. Linear model is a basic type.
For example, a tree was 2 feet tall when it was planted. It grows 0.4 feet every year. To model this situation, we use the equation y=0.4x+2.
0.4 is this line's slope, implying the tree grows 0.4 feet per year.
2 is this line's y-intercept, implying the tree was 2 feet tall when it was planted.
It would be very helpful if you understand and memorize this scenario. All the other linear models are similar.
Trigonometry sounds mysterious and difficult, but ...
they are simply ratios!
Unit 1: Positive and Negative Numbers