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Quantitative Literacy
Level A-MATC 103
MyPath Brandman
University, Irvine, CA
Quantitative analysis - Answer: The use of mathematics to support the problem-solving and decision-making process fundamental counting principle - Answer: Visually representing the given information - Answer: Mark is trying to figure out all possible combinations for traveling between two locations using a dircted graph. Which activity of the quantitative problem solving process does this scenario represent? A compound statement that uses "and" - a conjunction, will be true ONLY if the given two statements are BOTH true. - Answer: Statement one: Sandra believes that her communication skills will improve after the customer orientation program. Statement to: the organizers of the customer orientation program certify that their program is very effective. If one of these statements is false and the other is true which of the following statements must be false Polya's Four Steps - Answer: 1. Understand the problem
- Devise a plan
- Carry out the plan
- Look back Understand the problem - Answer: First step in Polya's general problem solving strategy
Identified what is being asked and what the given information is Sometimes it is helpful to rephrase the question in your own words and make a sketch were constructed table to illustrate the given information. Make a plan for solving the problem - Answer: The 2nd step and Polya's problem-solving process Look for patterns in the information provided an estimate a reasonable answer or range of values. Approximating the answer and working backwards can often give insight to a solution path Try to think of a similar, less complicated version of the situation. Carry out the plan - Answer: Third step in Polya's general problem solving strategy Identify in assign variables to unknown quantities and expressed in words what they each represent. Give yourself plenty of space and time to proceed in an organized fashion, step-by-step. If the plan does not yield a viable solution, learned from it and go back and try an alternate method. Trying many different approaches and running in to "dead ends" is a normal part of the process. Look back on your solution - Answer: Fourth step in Polya's problem-solving process Check that your solution makes sense and answers the question. Think about whether you could have solved the problem in a different way. Obtaining an answer is not your only goal; communicating your solution is just as important.
How do I envision myself in 6 months as a result of solving this problem? Are my friends dealing with similar problems? If so, how are they coping? Set criteria for judging potential solutions - Answer: At the final step - used to evaluate or judge the ideas. Think about it and make a list of 3 to 5A valuation criteria. Then put the list aside. You will not need it for a while. Mr. Quick climbing the steps baby come here I'll take you I'll take you Are their budget limitations? Time frame for other restrictions that will affect whether or not you can go ahead with an idea? What were you want to have accomplished with the ideas? What do you wish to avoid when you implement these ideas? Second step CPS - Answer: Research the problem Thirds step in CPS - Answer: Formulate one or more creative challenges Basically I simple question framed to encourage suggestions or ideas. Typically starts with "in what ways might I?" or" how might I?" or" how could I?" Should be simple concise and focus on a single issue Should not include evaluation criteria Fourth step in CPA - Answer: Generate ideas
Take only one creative challenge Give yourself some quiet time and try to generate at least 50 ideas that may or may not solve the challenge. This can be done alone or you can invite some friends or family members to help you Document your ideas Write every idea down - no exceptions Fifth step CPS - Answer: Combine and evaluate ideas Use the criteria you made earlier and go through each idea carefully Consider how well it meets each criterion and given a rating of 0 to 5 points With complex ideas, a simple a valuation May not be enough. You may need to do an SWOT analysis Sixth step CPS - Answer: Draw up an action plan You simple steps you need to take in order to implement your ideas 7th step CPS - Answer: Implement your idea If the situation beers away from your action plan steps, rewrite your action plan What is the calculation for distance traveled? - Answer: average rate of speed x time
↔ - Answer: if and only if /\ - Answer: and (conjunction) / - Answer: or (disjunction) ➡ - Answer: if-then conditional statement - Answer: a statement that can be written in if-then form It is used to show that one statement is the consequence of another ex. If Jose is a businessman, then he is very busy. antecedent - Answer: a thing or event that existed before or logically precedes another ex. If Joe is a business man, then he is very busy ( "Joe is a business man", is the antecedent.) consequent - Answer: the "then" clause in a conditional statement ex. If Joe is a business man, then he is very busy ("then he is very busy", is the consequent.) converse (of an if...then statement) (The converse of a true conditional is not necessarily true.) - Answer: Obtained by reversing the roles of the antecedent and the consequent ex. Conditional: (A➡B) If Jose is a businessman, then he is very busy.
Converse: (B➡A) If Jose is very busy, then he is a businessman. Contrapositive:(~B➡~A) If Jose is not very busy, then he is not a business man. Contrapositive of an if...then statement (The contrapositive of a true conditional is necessarily true.) - Answer: It is obtained by reversing the roles of the antecedent and the consequent. It is the converse of it's negated antecedent and the negated consequent. ex. Contrapositive:(~B➡~A) If Jose is not very busy, then he is not a business man. In which case is a conditional statement false? - Answer: It only occurs when the antecedent is true and the consequent is false. ex. Joe is a businessman who is not very busy. (The opening statement would be false if Joe is a businessman who is not very busy.) if...then statement - Answer: It is often considered a promise. The promise is only broken when the antecedent is true and the consequent is false. When is an "if-then" conditional statement false? - Answer: When the antecedent is true and the consequence is false. tautology - Answer: When a statement is true for all possible truth values Represents valid arguments
syllogism-The company revenues are in decline valid - Answer: When an argument's conclusion follows logically from its premises sound - Answer: When all of the premises of a valid argument are true If any one of the premises is false then the conclusion is not sound What is a rule for inductively reasoned conclusions? - Answer: In general, even if all the premises are true,inductively reasoned conclusions may still be false. Rule for deductively reasoned conclusions - Answer: If all premises are true, then they are necessarily true. Axioms - Answer: Self-evident truths Widely accepted truths Used by scientists and mathematicians in ductive reasoning, to prove conjectures. Hindu-Arabic numeral system - Answer: The most common positional numeral system. Estimation - Answer: The process of finding an approximation to and answer. symbol for an approximation (rounded) - Answer: Combinatorics - Answer: The branch of mathematics that counts arrangements of objects
Fundamental Counting Principle - Answer: If there are 2 separate categories with (a)possible choices for one category and (b) possible choices for another, than there are (a) x (b) possible choices for both categories. Sometimes called the multiplication rule Requires the choices to be independent How is average speed calculated? - Answer: total distance covered divided by the time interval How is distance traveled calculated? - Answer: Average rate of speed multiplied by time unit analysis - Answer: Including units for each quantity in a calculation to determine the unit of the answer Qualitative - Answer: Data in the form of recorded descriptions rather than numerical measurements. what is the key to better decisions in the real-world? - Answer: Open mindedness to a wide range of information. When converting among measurement units when do you multiply? - Answer: When converting from a larger unit to a smaller unit. When converting among measurement units when do you divide? - Answer: When converting from a smaller unit to a larger unit. What are the rules for using unit fractions? - Answer: 1) Multiply by the unit fractions. Each unit for fractions you multiply by must be equal to one.
- The numerator should use the measurement unit you want in your answer.
denoted Z set - Answer: a collection of objects typically grouped within braces, where each object is called an element. subset - Answer: I set consisting of elements that belong to a given set. Empty set symbol - Answer: ∅ OR {} but NEVER those combined Natural Numbers (Counting Numbers) - Answer: 1,2,3, denoted N whole numbers - Answer: Natural numbers ( counting numbers) and zero; 0, 1, 2, 3... denoted W real number line - Answer: a line that pictures real numbers as points coordinate - Answer: the real number that corresponds to a point graph - Answer: A point on the real number line that is associated with a coordinate. point of origin - Answer: Any point on a number line that represents the number 0. double-negative property - Answer: -(-a)=a
