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

GRAPHING OR SUBSTITUTION

Solve each system of equations by using the graphing or substitution method.

1. y= x + 3          x – 2y = 0

substitute your first equation for the y-value in the second equation.

x – 2(x + 3) = 0 —-> x- 2x – 6 = 0 —–> -x – 6 = 0 —–> -x -6 + 6 = 0 + 6 —-> -x/-1 = 6/-1 —-> x = -6

substitute your x-value into the first equation.

y= -6 + 3 —-> y = -3

write your solution

Solution (-6, -3)

GRAPHIING S.O.E. 2

x – 13 = 2y + x – 17          FIRST EQUATION

3x + y= 29                           SECOND EQUATION

Step 1: Take the 2nd equation and put it into y-intercept form.

3x – 3x + y = 29 – 3x——-> y  =-3x + 29

Step 2: Substitute the above equation for y in the 1st equation.

x – 13 = 2(-3x + 29) + x – 17 ——>     x- 13 = -6x + 58 + x -17 ——>  x – 13 = -5x + 41  ——> x + 5x – 13 = -5x + 5x + 41

6x – 13 = 41 —–> 6x = 54 —-> 6x/6 = 54/6 —–> x = 9

Step 3: Substitute your x-value into the second equation.

3(9) + y = 29 —–> 27 + y = 29 —–> 27- 27 + y = 29 – 27 ——> y = 2

Step 4: Write your solution.

Solution (9, 2)

GRAPHING S.O.E.

SYSTEM OF EQUATIONS

When the system of equations is already written in y-intercept form, the best method to use is graphing.

Y = 2x + 8             slope: rise 2, run 1           y-intercept: (0,8)

Y =-3x + 3             slope: rise 3, run 1           y-intercept: (0,3)

Solution ( -1, 6)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CHECK

Y= 2x + 8                              y = -3x + 3

6 = 2(-1) + 8                        6 = -3(-1) + 3

6= -2 + 8                               6 = 3 + 3

6 = 6                                       6 = 6

Check                                    check