Review For Math Final

Solving Linear Equations

• 3x-5=19
• +5=+5
• 3x=24
• Divide by 3 on both sides
• X=8

Solving Rational Equations

• (4)x+3/4=3(4)
• x+3=12
• Subtract 3 from both sides
• x=9

Graphing inequalities on a number line

• Graphing an inequality on a number line, is very similar to graphing a number. For instance, look at the top number line x = 3. We just put a little dot where the '3' is, right? Now an inequality uses a greater than, less than symbol, and all that we have to do to graph an inequality is find the the number, '3' in this case and color in everything above or below it. Just remember if the symbol is (≥ or ≤) then you fill in the dot, like the top two examples in the graph below if the symbol is (> or

Finding Slope

• (2,4) and (3,-7)
• Y2-Y1/X2-X1
• -7-4/-3-2=-3/5
• Rise/Run=Y2-Y1/X2-X1

Pythagorean Theorem

• A2+B2=C2
• 9(9)+12(12)=C2
• 81+24=C2
• 105=C2
• 15=C

Writing Linear Expressions

• The product of 3 and a number (3n)
• The sum of b and h (b+h)
• The difference between 4 and a number (4-n or n-4)

Area and Volume Equations

• The base of a triangle is 4 units. The total area is 20 units, Find the height of the triangle
• bh/2=20
• 4h/2=4(10)/2=20

Simplifying Exponents

• Y^6Y^3=Y^9
• X^5X^3/X^4=X^8/X^4=X^4
• multiply - Add exponents

Greatest Common Factor

• The greatest common factor, or GCF, is the greatest factor that divides two numbers. To find the GCF of two numbers: List the prime factors of each number. Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1.

Least Common Multiple

• The least common multiple (LCM) of 2 numbers is the smallest number that they both divide evenly into. One good way to find the least common multiple of 2 numbers is to multiply both numbers by 1,2,3,4,5... and then find the first multiple that appears in both lists.

Writing Algebraic Expressions

• Read and write an algebraic expression containing a variable. ...
• Use alternative notation for multiplication and division in algebraic expressions. ...
• Read and write algebraic expressions using parentheses.
• Evaluate one-step algebraic expressions by substitution.
• Evaluate multiple step algebraic expressions by substitution.

Simplifying Fractions

• 66/12
• GCF=6
• 11/2=5/1/2

Scientific Notation

• Where a number is written in two parts: First: just the digits (with the decimal point placed after the first digit), Followed by: ×10 to a power that will put the decimal point back where it should be.
• 32=3.2*10^1

Order of Operations

• The rules that say which calculation comes first in an expression They are: • do everything inside parentheses first: () • then do exponents, like x2 • then do multiplies and divides from left to right • then do the adds and subtracts from left to right
• Example: 5 × (3 + 4) − 2 × 8 = 5 × 7 − 2 × 8 = 35 − 16 = 19

Mean,Median and Mode

• To find the mean, add up the values in the data set and then divide by the number of values that you added. To find the median, list the values of the data set in numerical order and identify which value appears in the middle of the list. To find the mode, identify which value in the data set occurs most often.

Simplifying Expressions

• By “simplifying” an algebraic expression, we mean writing it in the most compact or efficient manner, without changing the value of the expression. This mainly involves collecting like terms, which means that we add together anything that can be added together. The rule here is that only like terms can be added together.
• Examples: 3x, x, and –2x are like terms. 2x2, –5x2, and are like terms. xy2, 3y2 x, and 3xy2 are like terms. xy2 and x2 y are NOT like terms, because the same variable is not raised to the same power.