Fundamental Counting Principle (FCP) & Tree Diagrams

Experimental probability is the likelihood that an event will occur based on the outcomes on previous results.

Sample space is the total number of outcomes of an event

There is a general method that you following when discovering the fundamental counting principle (FCP).

ex. 4 hoagies: 3 types of meat, four types of cheeses

How many different combinations can you make ?

MEAT: turkey, ham, liverwurst                 CHEESE: provolone, cheddar, American, swiss

First method: match each meat with each type of cheese using a tree diagram

Second method: multiply the total # of meats by the total # of cheeses

FCP = 3 (# of meats)  x 4 (# of cheeses) = 12 combinations

For more information –>http://www.basic-mathematics.com/fundamental-counting-principle.html

BASIC SCIENCE

You may have been introduced to some of the algebra concepts that you are using now in class early on in your school years. Perhaps you knew about scientific notation in the second grade or the quadratic formula in the eighth grade. So, you can use these lessons as a “refresher.” Here are just a few terms that I am sure that you are familiar with.

Scientific Notation: an expression that allows you to write very small and very large numbers in multiples of 10. When an exponent is negative, you move your decimal place to the right. When the exponent is positive, you move your decimal place to the left.

Adding and Subtracting Positive and Negative Numbers: Just a reminder…

Positive + Positive = Positive

Negative – Negative= Negative

(Negative)(Negative) = Positive

(Positive)(Negative) = Negative

System of Equations: Just to note, there are three methods for solving systems of equations. First, you can choose to graph your system and write each equation in y-intercept form. Secondly, you can solve the system of equations by using the substitution method. Lastly, you can use elimination to isolate x or y by itself and solve for the opposite variable. For instance, if you eliminate x, you have to solve for y first. If you eliminate y, you have to solve for x first.

Polynomials: A polynomial is an expression written with more than one term. For instance 2x^3 + 5x is a polynomial because it has two terms written as an expression. There are three types of polynomials and you will learn them all this year if you have not already.

• Monomial- the prefix mono meaning “one.”A monomial has only one term.
  
• Binomial- the prefix bi meaning “two.” A binomial has two terms.
• Trinomial- the prefix tri meaning “three.” A trinomial has three terms.

You may be ask to factor or simply polynomials. Each action offers a different result.

Example: Simplify (2x+5)(2x-3)    =

In order for you to simplify this expression, you must know the FOIL method. This tool is helpful for solving factoring problems.

F: First (multiply the first two terms in the parentheses)

O: Outside (multiply the outside terms in the parentheses)

I: Inside (multiply the terms inside the parentheses)

L: Last (multiply the last terms in the parentheses)

Combine the outside and inside terms by using addition.

Inequalities

Greater than >

Less than <

Less than or equal to

Greater than or equal to

Math: Calculating its Purpose in Life

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What is MATH?

Math is “the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations” (Merriam-Webster.com).

In other words, math is the language of the universe. Whether if you are aware of it or not, you use math more often than any other subject in your daily life. For instance, you use math to count the number of breaths you take, the words per minute your type, even the number of hours your teacher can linger on about one topic that no one really seems to care about. Numbers are EVERYWHERE. Without numbers, the world would be at a standstill.

So, why is math so important? CLICK HERE to find out.

ORDER OF OPERATIONS

PEMDAS, an acronym most students learn as early as the second grade. PEMDAS describes the order in which operations are organized.

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(    )Parentheses    2^x Exponents x, *, (    ) Multiplication

÷, / Division    + Addition    - Subtraction

These operations are to be used with you evaluate an expression.

Examples

4(3x +5) – 12 —-> 12x + 20 – 12 —–>  12x – 8 —->  12x/12 = -8/12 —>

x = -1/3

SOLVING FOR THE “UNKNOWN”

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So, you may hear this a lot from your algebra teachers “Solve for the unknown.” But is the unknown really unknown?

A variable is a letter that replaces a number in an expression or equation. For example, in the equation 2c + 1 = 13, the letter c is the unknown. Below, we will use this example to solve for the variable c.

2c + 1 = 13 —> translation: Two multiplied by c plus one equals thirteen.

Steps

1) 2c + 1 =13

2) 2c + 1 – 1 = 13

3) 2c = 13 – 1

4) 2c =12

5) 2c/2 = 12/2

6) c = 6

7) 2(6) + 1 = 13

8) 12 + 1 =13

9) 13 = 13

10) CHECK!