MATH FINAL LONG QUIZ Flashcards
Two. Ancient mathematicians.
Euclid and Pappus
The study of the methods, and rules of discovery and
invention
HEURISTICS
RENE DESCARTES
1596-1650
Contributed to the field of heuristics
RenΓ© Descartes
Gottfried Wilhelm Leibnitz
(1646-1716)
ART OF INVENTION
Gottfried Wilhelm Leibnitz
βNothing is more important than to see the sources of invention which are, in my opinion, more interesting than the inventions themselves.β
GOTTFRIED WILHELM LEIBNITZ
George Polya
(1887-1985).
was born in Hungary and moved to the United States in 1940.
GEORGE POLYA
Polyaβs Four-Step Problem-Solving Strategy (UDCR)
- UNDERSTAND THE PROBLEM
- DEVISE A PLAN
- CARRY OUT THE PLAN
- REVIEW THE SOLUTION
This part of Polyaβs four step strategy is often overlooked. You must have a clear understanding of the problem.
UNDERSTAND THE PROBLEM
Successful problem solvers use a variety of techniques when they attempt to solve a problem. Here are some frequently-used procedures.
DEVISE A PLAN
Once you have devised a plan, you must carry it out.
CARRY OUT THE PLAN
Once you have found a solution, check the solution.
REVIEW THE SOLUTION
When you are not sure how to start, guess an answer and then check it. In the process of checking a guess, you me see a way of revising your quess to get closer to the answer or to get the exact answer.
GUESS AND CHECK
Some problem describe relationships that involve regular sequence of number or other things. To solve the problem you need to be able
to recognize and describe the pattern that gives the relationship for the numbers or things. One
way to recognize the information given is a make a table.
MAKE A TABLE AND LOOK FOR A PATTERN
Some problems can be solve without the use of numbers. They can be solved by the use of logical reasoning, given some information.
USE OF LOGICAL REASONING
To solve some problems you need to start with the end result and work backward to the beginning
WORKING BACKWARDS
Making an organized list will lead you to work logically and systematically.
MAKE AN ORGANIZED LIST
Algebraic expression are use to represent information and solve problems. We used a variable for the unknown quantity and express the given information in an equation.
WRITE AND SOLVE EQUATION
7 OTHER STRATEGIES GMSUWMW
β’Guess & Check
β’make a table & look for a pattern
β’Solving similar but simple problems
β’Use of logical reasoning
β’Working backwards
β’Make an organized list
write and solve the
Equation
a problem that can be solved, or a question that can be answered, with the tools of mathematics
MATH PROBLEM
defined as the process of using various graphical formats to visually represent the relationship between two or more data sets, so that an informed decision can be made based on them.
Data presentation
3 Methods Of Presenting Data TTG
- πππ₯π‘π’ππ πππ‘hππ - a narrative description of the data gathered
- ππππ’πππ πππ‘hππ - a systematic arrangement of information into columns and rows
- πΊπππhππππ πππ‘hππ - an illustrative description of the data
narrative description of the data gathered
πππ₯π‘π’ππ πππ‘hππ
systematic arrangement of information into columns and rows
TABULAR METHOD
illustrative description of the data
GRAPHICAL METHOD
FDT
Frequency Distribution Table
is a statistical table showing the frequency or number of observations contained in each of the de ined classes or categories
Frequency Distribution Table
4 Parts of a Statistical Table TBstC
- πππππ π»ππππππ β includes the table number and the title of the table
- π΅πππ¦ β main part of the table that contains the information or igures
- ππ‘π’ππ ππ πΆπππ π ππ β classi ication or categories describing the data and usually found
at the left most side of the table - πΆπππ‘πππ β designations or identi ications of the information contained in a column,
usually found at the top most of the column
includes the table number, and the title of the table
table heading
main part of the table that contains the information or figures
body
classification or categories, describing the data, and usually found at the left most side of the table
Stubs or classes
designations or identi ications of the information contained in a column,
usually found at the top most of the column
Caption
two types of FDT
qualitative or categorical FDT
quantitative FDT
a frequency distribution table where the data are grouped according to some qualitative characteristics, data are grouped into non numerical categories
qualitative or categorical FDT
a frequency distribution table where the data are grouped according to some numerical or quantitative characteristics
Quantitative FDT
4 qualities of a good graph
accurate, clear simple, has a good appearance
A graph used to present measurements are values that are thought to be related
Scatter graph
graphical presentation of data, especially useful for showing trends over a period of time
Line chart
A circular graph that is useful in showing how a total quantity is distributed among a group of categories
Pie chart
They should be used for discreet group, data, or ordinal or nominal scale
column and bar graph
A bar graph that displays the classes on the horizontal axis
frequency histogram
A graph that displays the classes on the horizontal axis
relative frequency histogram
A line chart that is constructed by blocking the frequencies at the class marks, and connecting the plotted points
Frequency polygon
graphs of the cumulative frequency distribution
Ogives
status
state
in ancient times, statistics was used
By state leaders to know how much tax to Levy their subjects
in statistics is always a result of experiment observation investigation, in other means
Data
two types of statistics
Descriptive, and inferential statistics
deals with the collection and presentation of data to describe its group characteristics
Descriptive statistics
deals with the predictions and inferences based on the analysis and interpretation of the results
Inferential statistics
A numerical, characteristic or attribute. They are further classified as categorical or qualitative in numerical or quantitative.
variable
subdivided into four categories, and up on drawing inferences on a random sample
scales of measurement
it is the sum of all values or the average or norm
Mean
The middle value
median
The most frequent value
Mode
