Download FINAL EXAM REVIEW NOTES:

FINAL EXAM REVIEW NOTES:
IRRATIONAL NUMBERS: Numbers that never end and never repeat. Example Pi never
ends and never repeats.
RATIONAL NUMBERS: numbers that end or repeat.
Examples: -1, -2.5, 2.55555, .76767676, 0, 3, 3000 1/10
INTEGERS: All Real numbers and 0 and their opposites.
Example: -2000, -2, 0, 2, 2000
WHOLE NUMBERS: All Real numbers and 0.
0, 1, 2, 3, 4,000,000 ect.
REAL NUMBERS: 1, 2, 3, 4, 5, 100, 50,000
LEAST TO GREATEST:
The larger the negative number appears the smaller it is.
EX. -500, -4, -220, -1
-500, -220, -4, -1 (Negative 1 is your largest number and Negative five-hundred is your
smallest)
When working with decimals start with the whole numbers and work your way to the
right.
Ex. 5.246, 5.426, 5.002, 4.526, 4.5
Line up your decimals and start with your whole numbers.
5.246
5.426
5.002
4.526
4.5
you know that your 4's are going to be the smallest whole numbers so you must compare
them first.
4.526
4.5
Since they both have a 5 in the tenths place move to the hundredths place. Since 2 is
larger than 0 4.5 is our smallest with 4.526 next.
Then compare your 5's
5.246
5.426
5.002
Compare your tenths place. You have a 2, 4, and a 0. The smallest is the 0 so 5.002 is the
next smallest, then you have a 2 which is smaller than 4 so your order will be...
5.002, 5.246, 5.426 and now put it with the first numbers you placed in order.
4.5, 4.526, 5.002, 5.246, 5.426
MULTIPLYING and DIVIDING INTEGERS
Negative x Negative = Positive
Negative x Positive = Negative
Negative / Positive = Negative
Negative / Negative = Positive
When you have more than two numbers work only two at a time left to right.
Ex.
-3(-3)(-3)
-3(-3)=9
9(-3)= -27
ADDING and SUBTRACTING INTEGERS
Negative minus a number is the same as a negative plus a negative
-9-2= -11
Negative plus negative
-9+-1= -10 just add
Negative plus a positive (When signs are different subtract and take the sign of the
number that appears to be largest.)
-10+ 20= 10
positive plus a negative(When signs are different subtract and take the sign of the number
that appears to be largest.)
10+-20= -10
SQAURE ROOTS and CUBE ROOTS
When finding the Square root of a number you are looking for a number times itself that
equals the number you are looking for the root of.
Example. square root of 81
2x2 does not equal 81
3x3 does not equal 81
4x4 does not equal 81
5x5 does not equal 81
6x6 does not equal 81
7x7 does not equal 81
8x8 does not equal 81
9x9 does equal 81!!! so 9 is my root of 81.
I go through a list of numbers until I find the correct answer.
Cube roots, you are looking for a number times itself times itself.
Example. Cube root of 27
2x2x2 does not equal 27
3x3x3 does equal 27!!!!!! so 3 is my cube root of 27.
FRACTIONS TO DECIMALS:
When Given a fraction and asked to change it to a decimal divide the bottom into the top.
Example 18/19 18 divided by 19. The top number goes under the Radical and the 19 on
the outside.
0.9473684
SCIENTIFIC NOTATION
GOING FROM STANDARD FORM TO SCIENTIFIC NOTATION:
When writing a number in Scientific Notation Remember the following:
There can only be one number in front of the decimal and it has to be larger than 0 and
less than 10 infront of the decimal.
5,000 = 5.x 10^3
You have to move the decimal until there is only one number infront of the decimal.
Numbers that start off less than 1 have negative exponents
0.00000457 4.57 x 10^-6
Numbers that start off larger than 1 have positive exponents
2,500,000 2.5 x 10^6
The exponent tells you how many places to move your decimal NOT HOW MANY
ZEROS
Numbers that do not change when written in Scientific Notation have an exponent of 0.
2.56 2.56 x 10^0
DIVISION and MULTIPLICATION of EXPONENTS WITH LIKE BASES.
DIVISION:
If the Bases are the same subtract the exponents and keep the base the same.
MULTIPLICATION:
IF the Bases are the same add the exponents and keep the base the same.
WHEN BASES ARE DIFFERENT YOU MUST WORK THEM OUT COMPLETELY!
NAMING POLYGONS:
3 sides- triangle
4 sides- quadrilateral
5 sides- pentagon
6 sides- hexagon
7 sides- heptagon
8 sides- octagon
9 sides- Nano-gon
10 sides- decagon
12 sides- do-decagon
AREA FORMULA:
Square: Side x Side
Rectangle: Length x Width
Trapezoid: 1/2 height x(base 1 + base 2)
Triangle: height x base then divide answer by 2
Circle: Radius x Radius x 3.14
Perimeter:
Add up all sides make sure you have found the missing sides first.
Circumference: Diameter x 3.14 or radius x 2 x 3.14
CONVERTING WITH CUSTOMARY:
Little to Big divide
Big to Little Multiply
12 inches= 1 foot
3 feet = 1 yard
1 mile = 5280 feet
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 ounces
1 pound = 16 ounces
1 ton = 2000 lbs
CONVERTING WITH METRIC:
KILO HECTO DEKA BASE DECI CENTI MILLI
Base = Grams, Meters, Liters
Example: 4 Kilograms = _____ Decigrams
Move your finger from kilo to deci.
you moved your finger 4 places to the right now do the same with your decimal.
40000.
4 kilograms= 40,000 decigrams
ANGLES:
ACUTE ANGLES- angle that is smaller than 90 degrees
RIGHT ANGLES- angles that measure exactly 90 degrees
OBTUSE ANGLES- angles that are larger than 90 degrees and smaller than 180
STRAIGHT ANGLES- angles that are exactly 180 degrees
COMPLEMETARY ANGLES- angles that measures add to 90 degrees
SUPPLEMENTARY ANGLES- angles that measures add to 180 degrees.
MISSING ANGLES OF TRIANGLES:
add the two angles you know and subtract the sum from 180.
Example if I have a triangle with a 90 degree angle and a 45 degree angle I add 90 and 45
and get 135 and then subtract 135 from 180 and get 45 degrees.
MISSING ANGLES OF A TRANSVERSAL:
Remember the following cluesVertical angles are congruent (same size)
vertical angles form an x or across from each other.
Adjacent angles add to 180 on a transversal.
Corresponding Angles- are congruent and sit in the same spot of you cut the transversal
in half and slid one picture down on top of the other picture.
Alternate Interior Angles are congruent. These angles form a z on the inside of the
parallel lines.
Take the angle measurement you know and subtract from 180 to find the angle next to it.
Your other missing angles will either be the measure of the angle measurement given to
you or the one you got by subtracting the known measurement from 180.
ORDER OF OPERATIONS
1 Parenthesis
2 Exponents
3 Multiply or Divide depending on which comes first moving left to right.
4 Add or Subtract depeding on which comes first moving left to right.
Remember if it has paranthesis around 1 number it is multiplication not considered
parenthesis.
PYTHAGOREAN THEOREM:
A(A) + B(B) = C(C)
LEG(LEG) + LEG(LEG) = HYP.(HYP)
Example if you are looking for the length of the hypotenuse:
Leg= 4
Leg= 4
hyp= ?
4(4)+ 4(4)= h(h)
16 + 16 = h(h)
32 = h(h)
now take the square root of 32 for the final step.
5.6568542
Example if you are looking for the length of a leg:
Leg=?
Leg= 10
Hyp.=12
Hyp(hyp)- Leg(leg)= other leg(other leg)
12(12) - 10(10) = l(l)
144 - 100 = l(l)
44 = l(l)
now take the square root of 44 to find the final answer.
6.6332495