Math Studies

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Math Studies

• Exam Prep Facts

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Percent Error
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Amount in an account after t years, compounded n
times per year, at a yearly rate of r (r being
expressed as a decimal)
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Box and Whisker Plot
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Measures of Central Tendency

• Mean sum of the numbers divided by the total.
• Median (numbers must be in order) middle number,
  if odd sum of the middle 2 numbers divided by 2,
  if even.

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Measures of Central Tendency

• Mode most often occurring number
• Midrange (least greatest) / 2
• Range Highest value Lowest value

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Quartile Ranges

• Lower Quartile median of all the numbers below
  the middle median
• Upper Quartile median of all the numbers above
  the middle median
• Inner Quartile Range Quartile 3-Quartile 1

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Cumulative Frequency

• Definition The sum of the frequency in a given
  class plus the frequencies in all lower classes.

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Some Cumulative Frequency Rules
Medians, 1st quartiles, and 3rd quartiles have to
be taken from the cumulative frequency, not from
the data.
bad
good
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Chi- squared Test

• H0 null hypothesis, is statement that the two
  classifications being considered are independent
• H1 alternative hypothesis, is statement that
  the two classifications being considered are not
  independent

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Chi Square Results

• ?2calc gt ?2crit, then reject null.
• p-value lt significance level, reject null.

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Chi-squared Facts

• Degrees of Freedom
• (rows 1)(columns-1)
• Expected Value
• (row total)(column total)/(grand total)
• If chi-squared calculated value is GREATER than
  the chi-squared critical value, the reject the
  null hypotheses.

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Probability

• P(event) of ways to get desired effect
  Total of possibilities
• nCr combination of n things r at a time
• Order does not matter
• nPr permutation of n things r at a time
• Order does matter

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Probability

• The probability of event A is the number of ways
  event A can occur divided by the total number of
  possible outcomes.
• The sample space is an exhaustive list of all the
  possible outcomes of an experiment. Each possible
  result of such a study is represented by one and
  only one point in the sample space.
• Two events are independent if the occurrence of
  one of the events gives us no information about
  whether or not the other event will occur that
  is, the events have no influence on each other.
• Two events are mutually exclusive (or disjoint)
  if it is impossible for them to occur together.

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Probability cont.

• The addition rule is a result used to determine
  the probability that event A or event B occurs or
  both occur.
• The multiplication rule is a result used to
  determine the probability that two events, A and
  B, both occur.
• The usual notation for "event A occurs given that
  event B has occurred" is AB (A given B). The
  symbol is a vertical line and does not imply
  division. P(AB) denotes the probability that
  event A will occur given that event B has
  occurred already.
• P(AB) the (conditional) probability that event
  A will occur given that event B has occurred
  already
• P(AnB) the (unconditional) probability that
  event A and event B occur
• P(B) the (unconditional) probability that event
  B occurs

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Probability

• Probability of this and that, multiply both
  probabilities together.
• Probability of this or that, add both
  probabilities together.

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Q-Rational numbers

• rational number -is a number that can be
  expressed in the form a/b where a and b are
  integers and b does not equal 0. Irrational
  numbers cannot be written in this form.
• Examples are 4 (4 4/1) or 7/42 or
• _
• 10.333333

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N-Natural numbers

• The set of counting numbers including zero
• Example 0,1,2,3,4,5,6,

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Z-Integers

• The set of all natural numbers and their additive
  inverses, and zero
• Example -3,-2,-1, 0, 1, 2, 3,.

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R- Real numbers

• The set of all real numbers, I.e. all numbers
  which can be placed on the number line. These
  include rational and irrational numbers.
• Examples square root of 2

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Venn Diagram for Sets of Numbers
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Logic

• Statement
• If A then B
• A ? B
• Converse
• If B then A
• B ? A

• Inverse
• If not A then not B
• A ? B
• Contrapositive
• If not B then not A
• B ? A

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Logical Statements

• Converse switch hypothesis and conclusion
• Inverse negate both parts of statement
• Contrapositive negate the converse

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Converse

• Statement P ? Q
• If I eat cake, then I get fat.
• Converse Q ? P
• If I get fat, then I eat cake.

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Inverse

• Statement P ? Q
• If I eat cake, then I get fat.
• Inverse P ? Q
• If I dont eat cake, then I dont get fat.

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Contrapositive

• Statement P ? Q
• If I eat cake, then I get fat.
• Contrapositive Q ? P
• If I dont get fat, then I dont eat cake.

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• Tautology final column is all true
• Contradiction all false
• Proving an argument Valid- link all
  hypothesis together if a and b and c, then
  conclusion, create a truth table if it
  generates a tautology, the argument is Valid.

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Truth Table Symbols

• ? and
• ? or
• ? either or, but not both
• ? if, then
• ? if and only if (iff)

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Truth Tables
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And Truth Table
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Or Truth Table
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Exclusive Or Truth Table
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If, Then Truth Table
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IFF Truth Table
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Set Language

• is an empty set contains no elements
• Union or P and Q combined
• Intersect and common in P and Q

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I WILL NOT FORGET THE MIDDLE TERM WHEN I SQUARE A
BINOMIAL

• (a b)2 a2 2ab b2 NOT a2 b2
• (a b)(a b) a2 b2
• Because
• a2 ab ab b2 a2 b2

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Powers reminders

• a0 1
• Anything to the power of 0 is equal to 1
• a1 a
• Anything to the power of 1 equals itself

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Interval reminders

• Domain is X
• Range is Y

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Perpendicular Bisector Survival Kit

• Distance formula
• sqrt(x1- x2)2 (y1 y2)2
• Midpoint Formula
• ((x1 x2)/2 , (y1 y2)/2)
• Finding the Slope a.k.a. Gradient
• (y1 y2)/(x1- x2)
• Point-Slope Formula
• (y-y1) m(x-x1)

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Equation of a Line

• Standard/General Form
• Ax By C
• Gradient/Slope Intercept Form
• y mx C

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Positive Correlation

• Generally an upward trend, and in this case an
  increase in the independent variable means that
  the dependent variable generally increases.

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Negative Correlation

• Generally downward trend, and in this case an
  increase in the independent variable means that
  the dependent variable generally decreases.

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No Correlation

• Randomly scattered points (with no upward or
  downward trend) there is usually no correlation.

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Significant Figures

• Rule To round off to n significant figures, look
  at the (n 1)th figure
• If it is 0, 1, 2, 3, or 4 do not change the nth
  figure,
• If it is 5, 6, 7, 8, or 9 increase the nth figure
  by 1
• And delete all figures after the nth figure,
  replacing by 0s if necessary.
• Leading zeros are not significant figures
• 0.00026 is only 2 significant figures
• Trailing zeros are not significant figures if
  there is no decimal
• 54,600 is only 3 significant figures
• 0.36700 is 5 significant figures
• 230. is 3 significant figures

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Conversion of Units

• Mass Units
• 1 t 1000 kg
• 1 kg 1000g
• 1 g 1000mg
• Length Units
• 1 m 100 cm 1 km 1000 m
• 1000 mm 100,000 cm
• 1/1000 km 1,000,000 mm
• 1 cm 10 mm 1 mm 1/10 cm
• 1/ 100 m 1/ 1000 m

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Graphing Sine and Cosine Equations
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yasinbxc

• Amplitude the distance between a max or min
  point and the principal axis (the a)
• Period the length of one repetition or cycle
  (360/b)
• Vertical shift entire graph moved up or down c
  units (line of oscillation)

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Unit Circle
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Sin-Cos-TanSOH-CAH-TOA

• Sin- Opposite Cos- Adjacent
• Hypotenuse
  Hypotenuse

Tan- Opposite Adjacent
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Derivatives

• F(x) the first derivative, multiply the
  coefficient by the exponent and lower the power
  by one for each term.
• F(x) the second derivative, do the same
  procedure on the first derivative.
• Note the derivative function is the slope at a
  given point.

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First Principles

• Finding the derivative by first principles is the
  same as finding it using the difference quotient
• f(xh) f(x)
• h
• Dont forget to plug everything in and carry the
  negatives through the function

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Find Minimum or Maximum

• Find the derivative, set it equal to zero and
  solve.
• Take the solutions x, and plug them back into
  the original function to find the corresponding y
  values.

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Solving Triangles(that are not right)

• Given a side-angle-side use cosine law to find
  third side, then either sine or cosine law to
  find another angle.
• Given 3 sides use cosine law to find an angle
  then either sine or cosine law to find another
  angle.
• Given 2 angles a side Subtract from 180 to
  find the 3rd angle then use sine law to find
  other sides.

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1 is not a prime number 1 in not a composite
number (it is the loneliest number)
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I will always compute slope by doing BOTH Ys
on top pf BOTH Xs
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I will always label the X and Y axis EVERY
time I draw a graph!
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I will always give money Answers to 2 decimal
places (This is an EXACT answer)
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I will NEVER compute with rounded off
answers. I will use 2nd-ans to compute with
the full answer.
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I will NOT Cancel across plus or minus
signs!!!! Cancellation may be done when
everything is expressed with multiplication!!!!!
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