Mathmod Reviewer (Midterms) PDF

**MATHMOD REVIEWER (MIDTERMS)** **MATHEMATICAL LOGIC** - study of the rules and criteria for legitimate inferences and examples. **STATEMENT OR PROPOSITION**- It is a declarative sentence that is true or false but not both. **PROPOSITIONAL VARIABLES**- such as p, q, r, s, t, etc. are used to repr...

**MATHMOD REVIEWER (MIDTERMS)** **MATHEMATICAL LOGIC** - study of the rules and criteria for legitimate inferences and examples. **STATEMENT OR PROPOSITION**- It is a declarative sentence that is true or false but not both. **PROPOSITIONAL VARIABLES**- such as p, q, r, s, t, etc. are used to represent propositions. **LOGICAL CONNECTIVES**- which are used to combine simple propositions to form compound statements. **TRUTH TABLE**- displays the relationships between the truth values of propositions. **NEGATION**- statement p is denoted by -p where is the symbol for \"not\". The truth value of the negation is always the reverse of the truth value of the original statement. **CONJUNCTION**- The conjunction of the propositions p and q is the compound statement \"p and q\" denoted as p q which is true only when both p and q are true, otherwise false. **DISJUNCTION** - The disjunction of the proposition p and q is the compound statement \"p or q\" denoted as p v q which is false only when both p and q are false, otherwise, it is true. **CONDITIONAL/IMPLICATION**- The implication of the propositions p and q is the compound statement \"If p, then q.\" denoted as p - q which is false only when p is true and q is false. **BICONDITIONAL/ DOUBLE IMPLICATION** - The bi-conditional of the propositions p and q is the compound statement \"p if and only if q.\" denoted by which is true only when both p and q have the same truth value. **CONDITIONAL PROPOSITION-** Also called implication, it is composed of two parts - antecedent or hypothesis and consequent or conclusion. It is usually written using the world if \... then or implies. **INVERSE** it is foímed by negating the antecedent and consequent. **CONVERSE** - it is foímed by inteíchanging the position of the antecedent and consequent. **CONTRAPOSITIVE** - it is foímed by getting the inveíse of the conveíse. **PROBLEM** In English, a problem is any question or matter involving doubt, uncertainty, or difficulty or a question proposed for solution or discussion. In Mathematics, a problem is a statement requiring a solution, usually by means of mathematical operation/geometric construction. **PROBLEM SOLVING**- is the art of identifying problems and implementing the best possible solutions. It is a mathematical process where one uses his skills creatively in new situations **SIMPLE EQUATION**- solution = method + answer \"method\"- answer ways or techniques used to get an \"answer\" - number, quantity, or some other entity that the problem is asking for \"solution\" - the whole process of solving a problem including the method of obtaining an answer and the answer itself **GEORGE POLYA**- is one of the foremost recent mathematicians to make a study of problem-solving. He is also known as "Father of Problem Solving" **Polya\'s Problem - Solving Framework** **STEP 1 UNDERSTAND THE PROBLEM-** The key task is to learn the necessary underlying mathematical concepts and principles, terminologies, and notations. **STEP 2 DEVISE A PLAN-** There are varieties of strategies for solving mathematical problems called heuristic methods. **STEP 3 CARRY OUT THE PLAN** A problem may have more than one solution. Sometimes the plan may not be workable or feasible to solve the problem, hence, the need to use another plan. **STEP 4 LOOK BACK-** Checking is necessary to determine if it is reasonable whether the conditions are satisfied.  **REASONING IN MATHEMATICS** **INDUCTIVE REASONING**- It is a type of reasoning that starts with a specific statement, or hypothesis to reach a general conclusion. **DEDUCTIVE REASONING-** It is a type of reasoning that starts with a general statement, or hypothesis to reach a specific and logical conclusion. **CONSUMER MATHEMATICS**- field of mathematics, which shows you how to use your basic math skills to real-life situations **HOURLY PAY**- It is the amount of money paid to an employee for every hour of work performed.**Straight-time pay** = hourly rate of pay times the hours worked. **OVERTIME PAY**- It is the compensation employers pay for any work beyond 8 hours a day or over 40 hours a week. **SALARY**- refers to a fixed amount of money that is paid to an employee regardless of the number of hours worked each week. **COMMISSIONS**- is the extra income an employee earns when they sell goods or services and is paid by a base salary plus commission **INTEREST-** It is the money earned when money is invested **SIMPLE INTEREST**- It is calculated on the principal, or original, amount of a loan.  **COMPOUND INTEREST**- It is calculated on the principal amount and the accumulated interest of previous periods and can therefore be referred to as "interest on interest." \> I = A -- P The values of "n" when specific compounding occurs: n = 1, annually, n = 2, semi-annually, n = 4, quarterly n = 6, bimonthly, n = 12, monthly