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Natural Number
Whole Number
Integer
Rational Number
Irrational Number

Prime Number
Composite Number
 Prime number: 2 positive integer factors
 2,3,5,7...
 Composite number: other numbers
 4,6,8...
1 is neither


Which expression below is incorrectly written in scientific notation?
A. 58x10^{5
}B. 5.333x10^{9}
C. 1.8x10^{6}
D. 4.92x10^{10}
Scientific notation is the product of a number between 1 and 10 multiplied by a power of 10.
(a) should be 5.8x10^{6
5.8 is a number between 1 and 10 and 58 is not
}

Zero Rule
Any number to the zero power equals 1 and not zero. This is so because the base is multiplied the exponent number of times so you are left with is 1
2^{0} = 1

Rule of 1
any base raised to the power of 1 is itself
2^{1} = 2

Negative exponents
look at the inverse operation of multiplication, which is division:
2 ^{4} = =

Product rules for exponents
when multiplying exponents w/ the same base, add the exponents and keep the same base
2^{4} x 2^{3} = 2^{ (4+3)} = 2^{7} = 128

Quotient rules for exponents
when dividing exponents w/ the same base, subtract the exponents and keep the same base
= 2 ^{(43)} = 2 ^{1}

Power rules for exponents
When an exponent is raised to another power,multiply the exponents and keep the same base
(2^{4})^{3} = 2 ^{(4x3)} = 2 ^{12}

multiplicative identity
a number is multiplied by 1 equals itself
365 x 1 = 365

commutative property
addition n multiplication stating the order in which 2 numbers are added or multiplied does not change their sum or product
 a + b = b + a
 44 + 55 = 55 + 44
 a x b = b x a
 25 x 5 = 5 x 25

associate property
addition n multiplication stating the grp of 3 numbers does not change their sum or product
 (a + b) + c = a + (b+c)
 (a x b) x c = a x (b x c)

distributive property
addition n multiplication stating that when multiplying a number by a sum or difference, you may either add/subtract first and then multiply, or multiply first then add/subtract
 a x (b+c) =a(b) + a(c)
 a x (bc) =a(b)  a(c)

diving fractions w/ mixed numbers
 1) write in fraction form
 2) multiply first term by the reciprocal of the second term
 3) write in simplest form
divide = x = =

PERDMAS
please excuse my dear aunt sally PEMDAS
 left to right:
 Parentheses
 Exponents
 Roots
 Division
 Multiplication
 Addition
 Subtraction

Flipping the inequality sign
occurs only when multiplying or dividing each side by a negative number; add/subtraction of terms from each side of an inequality does not change the direction of the inequality sign.
 3x + 3 ≥ 12
 3x ≥ 9
 x ≥ 3 change to x ≤3

Linear equations and their properties pg 274

System of equations pge 276

Linear equation y=mx+b pg 274
makes lines

quadratic equation ax^{2}+bx+c=0 pg 280
finds a parabola that opens up and down (never sideways)
 x^{2} > 0 up
 x^{2} < 0 down
 x = b/2a axis of symmetry of a parabola
 input "x" into the equation to find "y" to get
 coordinates (x,y)


Steps to graphing quadratic equation
y=ax^{2} + bx + c
1. Determine where the parabola opens upward/downward
a > 0 (up) or a < 0 (down)
2. Use the axis of symmetry formula to find "x"
x = b/2a
3. Vertex of the parabola: substitute the xcoordinate into the equation to find the ycoordinate (x,y)
4. Determine the yintercept: substitute x=0 into the standard form of the quadratic equation (0,y)
5. Determine the xintercept: substitute y=0 into the standard form of the quadratic equation (x,0),(x,0) [zero property]
6. Draw the graph w/ the coordinates. Symmetric to the vertical axis

Pythagorean Theorem (right triangles only)
a^{2}+b^{2}=c^{2}
the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse

Isosceles Triangle
Scalene Triangle
 Isosceles  2 sides of the same length
 Scalene  no equal sides

Area: Parallogram = rectangle

mass and weight
 mass  amt of matter an object has
 weight  measure of how much gravitational pull is acting on it
proportional to each other

Temperature
C = 5/9 (F32)
F = 9/5C + 32

Metric system
 Metric Prefix Mathematical Value
 Mega Million
 Kilo Thousand
 Hecto Hundred
 Deka Ten
 Deci Onetenth
 Centi Onehundredth
 Milli Onethousandth
 Micro Onemillionth

Length (US to metric)
 Length
 1 in = 2.54 cm
 1 ft = 30 cm
 1 yd = .9 m
 1 mile = 1.6 km

Weight (US to metric)
 1 oz = 28 g
 1 lb = 45 kg
 1 T = .9 metric tonne (t)

Area (US to metric)
 1 in^{2} = 6.5 sq cm
 1 ft^{2} = .09 sq m
 1 m^{2} = 2.6 sq km

Volume (US to metric)
 1 fl oz = 30 mL
 1 qt = .95 L
 1 gal = 3.8 L
 1 ft^{3} =.03 m^{3}
 1 yd^{3} =.76 m^{3}

Metric Units
 Volume
 1000 mL = 1 L
 250 mL = 1 metric cup
 4 metric cups = 1 L
 1000 L = 1 kL
 Mass
 1000 mg = 1 g
 1000 g = 1 kg
 Linear Units
 10 mm = 1 cm
 100 cm = 1 m
 1000 m = 1 km

US Units
 Volume
 8 fl oz = 1 c
 2 c = 1 pt
 2 pt = 1 qt
 4 c = 1 qt
 4 qt = 1 gal
 Weight
 16 oz = 1 lb
 2000 lb = 1 T
 Linear Units
 12 in = 1 ft
 3 ft = 1 yd
 5280 ft = 1 mi
 1760 yd = 1 mi

Formulas
Perimeter
Area
 Perimeter (P) Area (A)
 Triangle = a+b+c =1/2bh
Trapezoid =s _{1}+s _{2}+b _{1}+b _{2 } =1/2h(b _{1}+b _{2})
Parallelogram =2(a+b) =bh
Rectangle =2(l+w) =lw
Square =4s =s ^{2}
Circle = d or 2 r = r ^{2}

Formulas
Surface Area
Prism =+ areas of each face
 Pyramid =+ areas of the base + each face
Cylinder = (1) area of the 2 bases r^{2}
 (2) length (circumference value r) x height (width)
 (3) add the two values

Formulas
Volume
Prism =Bh (area of the base x height)
Pyramid = Bh (area of the base x height)
Cylinder = r ^{2}h
Cone = r ^{2}h
Sphere = r ^{3}


Graphs
 Line  show change over time
 Circle  part to whole relationships
 Bar  compare amts between grps
 Tally tables  record amts in general way

Mean, median, mode, range
 mean  avg
 median  middle number
 mode  occurs frequently
 range  difference between high and low number

Probability
Probability of an event =

