Math Notes

Odd & Even Numbers:

• Numbers divisible by 2 are even and if not odd, but 0 is considered even

Prime Number – whole numbers that can be divided evenly by only themselves and 1. The exception is: 1, 0. Whats the smallest prime? 2; example: 2, 3, 5, 7, 11, 13, 17, 19, 23

Divisibility, Factors, Multiples:

• dividend/divisor = quotient
• “divide evenly” a division of 1 integer by another yeilding a remainder of 0
• If a number can be divided evenly by another number than dividend, or fist number, is said to be divisble by the divisor, the second number.
• a number that can divide another number( divisor) evenly is said to be a factor of the divisor
• product is a result of a multiplication or an expression that identifies the factors to be multiplied. product = factor * factor; 2,7 are factors of 14, 14 is a multiple of 2,7
• multiple of a number is product of that number with any integer; every number is a multiple of itself

Fractions

• Every fraction is quotient of numbers , the quantity obtained when the numerator is divided by the denominator
• We deal with base 10 number system so 82.537 = 8*10 + 2*1 + 5*1/10 + 3*1/100 + 7*1/1000
• conversion of decimal to fraction, look at how many places after the decimal and that tells you the denominator examples: 84.1 = 841/10, 9.17 = 917/100, .612 = 612/1000
• When adding or subtracting decimals, line up the decimals when you write the numbers in a vertical column
• when multiplying decimals, multiply numbers as usual, then place the decimal point in the answer according to the total number of decimal places in the numbers; example 45.1 * .3 = 13.53, because there is 1 number behind the decimal in each of the two factors( terminology goes multiplicand and multiplier )
• dividing decimals move the decimal in the divisor till it shows no decimal then move the dividend’s decimal the same number of places, adding 0’s if nessary

Averages, Ratios, Porpotions, Percentages

• average = sum of all numbers / # of elements in the set
• average is same as mean
• median the middle value in a set containing an odd number of data items, in a set containing an even number of items median is the average of the 2 middle values
• Mode is the value that appears most often in a data set.
• Ratio is a comparison of 2 numbers, can be written as a fraction like 2/3 or as 2 numbers side-by-side seperated only by a colon like 2:3
• porportions describe 2 ratios that are equal, example 5 is to 6 as 10 is to 12, 5/6=10/12
• Percent means “part of 100″, so 5% means 5 parts of 100
• 
• What percent of 80 is 5?
• Percentage Problem:
  • Quality Increases from 600 to 750, then Percent Increase is found by dividing the amount of the increase by the base quantity number and then multiply it by 100: $latex\frac{increase}{base}\times 100=?\%increase&s=4$

Rules for Power and Roots

Some Examples to be aware of, simplify the following:

Geometry

• A line can be named by a single letter or 2 points on a line
• Bisector divides a line segment into 2 equal parts
• An Angle can be named 3 ways:
  1. 
  2. 
  3. 
• A bisector of an angle divides the angle into 2 equal parts, example:
  • 
  • Which is the bisector? line C
• Acute angle > 0 degrees but less than 90 degrees
• Obtuse angle > 90 degrees but less than 180 degrees
• Straight Line is 180 degrees
• 2 angles that form a straight line are called Supplementary, the sum of 2 supplementary angles is 180 degrees
• 2 angles that form a right angle are Complementary, the sum of two complementary angles is 90 degrees
• Vertical angles are formed when 2 lines intersect, vertical angles are equal. Example:

• if 2 lines are parrallel to 3rd line then they are all parallel to eachother
• travesal line is a line that passes thru 2 or more parallel lines
• Parrallel lines cut by a traversal line form equal angles:
  1. Corresponding angles are equal
  2. Alternate interior angles are equal
  3. Same side interior & exterior angles are supplementary

• 2 lines that intersect at right angles are perpendicular
• 2 lines that are perpendicular to the same line are parallel

Triangles

• Equilateral triangles: 3 equal: sides & angles
• Isosceles triangle: has 2 equal sides , the angles opposite to the equal sides are equal.
• Right triangle: has 1 right angle, longest side is opposite the right angle called the hypotenuse, other 2 sides called legs
• The sum of the angles in a triangle is 180 degrees
• The sum of the length of any 2 sides must be greater than the length of the 3rd side
• Area = (1/2)*b*h, drawn perpendicular to the base
• Pythagoream Theorem: for right triangls only

Parallelograms and Rectangles

• parallelogram 4 sided figure in which opposite sides are parallel
• parallelogram: opposite sides & angles are equal
• rectangle: a parallelogram with right angles, diagonals of a rectangle are equal
• square: a rectangle with 4 equal sides
• A=l*w
• P=2l+2w

Circles

• tangent is a line that intersects a circle( a set of points equidistant from 1 point) at 1 point
• circumferance: distance around the circle
• arc is a portion of the circle and named for it 2 endpoints
  • the measure of the arc is the measure of its central angle, an angle whose vertex is at the center of the circle.
  • measure of the arc is done in degrees
  • length of the arc is a porportion to the circle’s circumference
• Area of circle =
• Circumference of a circle,
• Length of an Arc: where x is the measure of the arc AB, r=radius
• Approx value of is 3.14 or

Inscribed Figures

• an angle drawn inside a circle with its vertex lying on the circle is called an inscribed angle
  • the meausure of inscribed angle is half the measure of its intercepted arc, remeber that an arc is measured by its central angle( an angle whose vertex is at the center of the circle)

Solids

• A solid is a 3 dimensional figure
• Rectangular solid has 6 faces that are rectangles
• cube:
  • rectangular solid in which all edges are equal b/ all faces are squares
  • surface area of a cube of edge length “a” is latex d\ =\ \sqrt{{(x_{1}-x_{2}})^{2}\ +\ {(y_{1}-y_{2}})^{2}}&s=4$
  • Midpoint