Chapter 1:Unit 3. Math skills Required in this Course

Required Math Skills

1. Algebra: Algebra is used to solve equations by un-doing whatever is being done to an unknown variable. For example, if an equation has “x+2” then you would subtract “2” to solve for “x”.  Everything that is done to one side must be done to the other side of the equation as well.
2. Logarithm: logarithms are a way of counting of power of a base number.  If  then Y=b^x .  If no base is specified, it’s assumed to be 10.  A natural log (ln) uses the base of “e” (2.313).
3. Graphical Interpretation: A graph represents the relationship between two variables, either direct, inverse or exponential. A point on the line of the graph indicates the value of one variable with respect to the value of another variable.
4. Percentage Problem: Percents are a special kind of decimal. Most calculations involving percentages involve using the percent in its decimal form. This is achieved by dividing the percentage amount by 100. You may need to find the percent value of a number, find the percent rate of one number compared to another number, and find the original amount given the percent value and the percent rate.
5. Calculator tips: Ask your instructor on how to operate your calculator

Positive and negative numbers

In math, numbers greater than zero are referred to as positive numbers, and numbers less than zero are referred to as negative numbers.

On a number line, negative numbers are written on the left side of 0, indicating they are smaller than 0, while positive numbers that are bigger than 0 are written on the right side of 0.
When two positive numbers are multiplied or divided, the answer is a positive number. Similarly, when two negative numbers are multiplied or divided, the answer is a positive number.
Example: 15 x 5 = 75
15 ÷ 5 = 3
(-15) x (-5) = 75
(-15) ÷ (-5) = 3

When two numbers with different signs are multiplied or divided, the answer is a negative number.
Example: (-15) x 5 = -75
15 ÷ (-5) = -3
(-15) x 5 = -75
15 ÷ (-5) = -3
In the addition of two positive numbers, the answer is positive and the sum of those numbers. However, in the addition of two negative numbers, the answer is the negative sum of those numbers.
Example: 15 + 5 = 20
(-15) + (-5) = -20

In the addition of two numbers with different signs, the answer is always the difference of those two numbers. However, the answer will always have the sign of the number which is bigger in magnitude.
Example: (-15) + 5 = -10
(15) + (-5) = 10
In subtraction, you can first change the sign of the number you are subtracting and then follow the rule of addition.
Example: 15 – (5) = 15 -5 = 10
15 – (-5) = 15 + 5 = 20
-15 – (5) = -15 – 5 = -20
-15 – (-5) = -15 + 5 = -10

Percentage

Percentage represents the portion of a value out of 100. For example, if we have we have 20% maple trees in a forest, here 20% represents that if total there are 100 trees, out of that 20 will be maple trees.
To find the amount present in a certain quantity we can just multiply the percent with the number.
Example: A forest has 20% maple trees, find the total number of maple trees if there 400 trees in the forest.
400 x 20/100 = 80 Maple tree
Watch this video for a further understanding of percentages.

Scientific and Standard Notation

In science, numbers can be written in two different ways, scientific notation and standard notation. In scientific notation or exponential notation, a number is written as x*10y. Here, x is called the coefficient and y represents the exponent of 10. The value of x has to be 1 or more and less than 10. y, the exponent, can be any positive or negative whole number.
In standard or expanded notation, the exponent is not used. Both expanded and scientific notation forms of a number should contain the same number of significant figures if possible.
Example: There were 32500 gallons of water in a tank. Here the number is written in expanded form without any exponent, hence the notation is also called expanded or standard notation.
This number can also be written in scientific notation. To do so, we must make the value of the coefficient less than 10. Since there is no decimal in the number, we will place the decimal at the end of the number and move it as many places as needed to make the value of the coefficient less than 10. Here we will move it 4 places to the left to make the number 3.2500.
3 2 5 0 0.

Since we moved the decimal 4 places to the left our exponent will be 104, and we can write the number in scientific notation as 3.25 * 104.

Example: 600000 can be written as 6 * 105
0.00000328 can be written as 3.28 * 10-6

To multiply exponential term: we simply add the exponents.
To divide exponential terms: subtract the exponents.
Watch this out!

Questions:

Write each number in scientific notation:
95200
6780,000
0.000725

 Write the following using standard notation:
1.60 *10-9
5.2131*102
7.*10-5

Solving one Variable Equation

Very often in math, a variable is used to represent a quantity. You can solve for this variable’s value by rearranging the equation. The basic rule for solving one variable equation is to start with gathering like terms and isolating the variable on one side.
Example: 5X + 15 = 70
To isolate X we will start with gathering like terms. Here 15 and 70 are both numeric terms, we can gather them together.
To get rid of 15 from left side, subtract 15 from both sides.

5X + 15 = 70
-15 -15

5X = 55
To isolate X, Divide both sides with 5.

5X/5= 55/5

X = 11

Watch this YouTube video for further understanding of solving equations.

https://youtu.be/Z-ZkmpQBIFo?si=SXZpIPwc8R8GKQ4U
Graphs
Graphs are the pictorial representations of data to show the relationship between two variables. In graphs, independent variable is plotted on the horizontal axis or the x-axis and the dependent variable is plotted on the vertical y-axis.
Watch this video below to see an example of the interpretation of a graph.

Questions:

Q#1

1. Where can you find chemicals?

1. In laboratory
2. In grocery or hardware store
3. All around you and inside you
4. All of the above

Q#2

Which statement best defines chemistry?

1. The science that makes shampoo and drugs
2. The science that studies air and water pollution
3. The science that deals with reactions happening in laboratory
4. The science that connects properties of particles that compose matter with how things work in nature
5. All of the above

Q#3

According to the scientific method, what is a law?

1. A fact that cannot be changed
2. A model that gives insight to a natural process
3. An initial guess with explanatory power
4. A short statement that summarizes a large number of observations

Q#4

The graph below shows the value of one variable( along Y axis) as a function of its another variable(along X axis). What is the estimated value of Y when the value of X is= 3.2E-03?

The graph below shows the value of one variable( along Y axis) as a function of its another variable(along X axis). What is the estimated value of Y when the value of X is= 3.2E-03?

1. -8
2. -10
3. -12
4. None of the above

Q#5

What percent of 64 is 4?

a. 6.25

b. 2.56

c. 0.04

d. none of the above

Q#6

Solve the term AB/D= 36Y

for the term A.

a. A= 36YD/B

b. A= YD/36Y

c. A= 36YBD

d. none of the above

Q#7

18 is 40% of what?

a. 36

b. 2.125

c. 18

d. none  of the above

Q#8

1. The price of a pen can be determined by the equation: P = $2n, where P is the price and n is the number of pens. What is the constant of proportionality (unit rate)?

a. n

b. 1/2

c. 2

d. none of the above

Q.9

Find the constant of proportionality (k) for each linear relationship y=kx

11x= 77y

a. k=1/7

b. k= 7

c. k=11

d. all of the above

Q#10

You can bake 4 chocolate cakes every hour in your oven. Represent this relationship using an equation, table, and graph.