Based on the readings and content for this course.docxBased on.docxikirkton
Based on the readings and content for this course.docx
Based on the readings and content for this course, which topic did you find most useful or interesting? How will you use it later in life? What makes it valuable?
Ans:
Well, there are many small but significant things in real life, that I understand, are related to maths.
For example the screen size of a TV or a laptop. When we say 14 inch laptop we mean the diagonal of the screen is approximately 14 inches.
This is a direct application of Pythagorean Theorem.
And depending on the shape of the room determines the formula for area that I use. For example, if our room was a perfect square (which none of them are) I would utilize the formula a = s^2, since our rooms our rectangle, the formula we more commonly use is a = lw.
Again I understand the amount of money we spend on gas can be modeled by a mathematical function.
When we throw a ball up, the time taken for it to come down can be modeled by a quadratic equation.
There are so many things.
I won't pick up any particular thing.
But after this course, I am able to look at many things in a more analytical way.
I can understand the mathematical logic behind them.
So all these are valuable to me
Do you always use the property of distribution when multiplying monomials and polynomials.docx
Do you always use the property of distribution when multiplying monomials and polynomials? Explain why or why not. In what situations would distribution become important? Provide an example for the class to practice with.
Ans:
The property of distribution is one important tool in solving the polynomial multiplications.
For example:
3x*(x+5) = 3x*x + 3x*5 = 3x^2 +15x
But this property is used only when one of the bracketed terms contains two or more terms of different order.
For example in the above case, the bracket consists of two different order terms, x and 5.
Let’s take another case:
3x*(x+2x)
This can be solved in two ways.
3x(x+2x) = 3x*x + 3x*2x = 3x^2 +6x^2 = 9x^2
Or we can say:
3x(x+2x) = 3x*3x = 9x^2
So in the 1st method we used the distribute property.
But in the 2nd case we did not.
So it depends on the particular problem and looking at the different terms we can decide whether or not to use distributive property.
Explain how to factor the following trinomials forms.docx
Explain how to factor the following trinomials forms: x2 + bx + c and ax2 + bx + c. Is there more than one way to factor this? Show your answer using both words and mathematical notation
Ans:
Actually I am not very sure how to answer this.
For me x2 + bx + c and ax2 + bx + c are not different from each other.
The 1st one is a special case of the second expression where a=1.
To factor the expression ax^2 + bx + c we first need to factor the middle term bx cleverly.
Now it's to be understood that not all trinomials can be factored. But some of them can be.
Basically, we have to write b in the form b= p+q so that p*q= a*c. This is the only trick.
Then ...
1. Today:
Submit all Outstanding Forms...
Literal Equations
Khan Academy Review
2. Formulas & Vocabulary Page
1. Dimension:
The measure of a thing in a given direction.
The dimensions of a 2-dimensional object are?
Length & Width.
The dimensions of a 3-dimensional object are?.
Length, Width, & Height
2. Volume:
The amount of space, measured in cubic units, (lwh) that
an object or substance occupies.
3. Formula for the volume of a rectangular 3-dimensional
object is:
Length x Width x Height
Most grocery products are “sold by weight, not by
volume” Why?
3. Formulas:
b. Find the height of a cylinder with
volume of 3140 feet and radius of 10 ft.
4. Class Notes:
Tips for Solving Literal & Other Equations:
Literal Equations:
1. If the variable you are solving for is inside the
parenthesis, you must distribute first. 9p = 3(k + 5) for k
We need to separate the ‘k’ from the 5 in this case.
Solve the equation.
2. If the variable you are solving for is outside the
parenthesis, simply perform the opposite operation.
9 = k(p + 5) for k
3. When clearing fractions, if the denominator being
multiplied has two or more terms, it must be distributed on
the other side.
5k( 2p + 4) = 9
ퟓ풌
ퟑ
=
ퟑ
ퟐ풑+ퟒ
for p
5. Class Notes:
Class Notes:
Tips for Solving Literal & Other Equations:
4. Always check to see if every term has something in
common. You can then factor the common part out.
3kp – 7km – 9k – 1 = -7p + 10 for k
first
3kp – 7km – 9k = -7p + 11 Then,
k(3p – 7m – 9) = -7p + 11 Now What?
k= -7p + 11
(3p – 7m – 9)
6. Class Notes:
Tips for Solving Literal & Other Equations:
5. If an entire term can be factored out, replace it
inside the parenthesis with a ‘1’
2p + 8px = ? 2p(1 + 4x) check by distributing the 2p again.
6. When solving fractional equations, you may have to
clear fractions more than once.
4 – 2x =
ퟏ
ퟓ
ퟔ − ퟑ풙
ퟑ
20 – 10x = 5
ퟔ −ퟑ풙
ퟑ
Complete the first step. Now we distribute the....
Solve for x.
7. Class Notes:
Tips for Solving Literal & Other Equations:
7. Two equal fractions is called a proportion.
Proportions can be solved by cross multiplying.
The following is not a proportion.
How must this problem be
solved?
Finish It
푺+ퟒ
ퟑ
=
ퟑ푺
ퟑ
solve
10. Warm-Up: Literal Equations
Solve for a: Q = 3a + 5ac
What can be factored out of both terms?
Solve for h: A =
ퟏ
ퟐ
ah -
ퟏ
ퟐ
bh
L = 19
Find the missing dimension: P = 60
Same Rules; don’t do anything different!
Lastly, this beauty...
−ퟑ
ퟓ
ퟓ − ퟏퟎ퐱
ퟑ
ퟒ
ퟐퟒ퐱 + ퟒ
11. 1st & 2nd Periods;
Complete class work from yesterday
3rd & 4th Periods;
Mixed Equation/Formula Practice
