MATH 110 All Modules Exam 110 Final Exam Portage Learning Latest Verified Questions and Answers 100 Correct Answers Verified A Graded
Portage Learning's All Modules Exam 110 Final Exam MATH 110 | Verified Correct Answer Key 5 NCTM Process Standards - answer - -problem solving -connections -communication -reasoning & proof -representation What does NCTM stand for and when was it made/updated? - answer - National Council of Teachers of Mathematics (1989) (2000) Problem Solving - answer - Have students try multiple different strategies; open ended problems, non-routine problems Connections - answer - Show why it's useful in the real world. Why do they need to know this? -connections within math -connections with other subjects -connections to the real world Communication - answer - Student discussion, have students write sentences; How would you explain today's concept to a student that was absent? (students answer) Reasoning & Proof - answer - WHY we do problems the way we do; have students make conjectures; have students discover something; have students support what they say Representation - answer - Represent ideas in as many different ways that you can think of Inductive Reasoning - answer - specific - general ex. eyeglasses some people wear eyeglasses, everyone wears eyeglasses (conjecture is false) Deductive Reasoning - answer - general - specific ex. if right triangle, then a2+b2=c2 (general proven fact) 5^2+12^2=c2 - 13=c Conjecturing - answer - Inferring or predicting from incomplete evidence; making a statement Investigation - answer - uses reasoning to find answers ex. odd+odd=even even+even=even even+odd=odd Counterexample - answer - an example that disproves a statement Negation - answer - ~A; NOT; S: Today is Thursday; N: Today is NOT Thursday conditional statement - answer - If A, then B (-_) (double bar arrow means implies) converse - answer - If B, then A ex. S- If today is TH, then tomorrow is F. Converse- If tomorrow is F, then today is TH. Inverse - answer - If not A, then not B ex. S- If today is TH, then tomorrow is F. Inverse- If today is not TH, then tomorrow is not F. Contrapositive - answer - If not B, then not A ex. S-If today is TH, then tomorrow is F. Contrapositive- If tomorrow is not F, then today is not TH. everyday language to conditional language - answer - Every dog is a mammal - If it is a dog, then it is a mammal not all vs. all not - answer - S- All Americans are Pennsylvanians Negation- Not all Americans are Pennsylvanians WRONG negation- all Americans are not Pennsylvanians Roster method - answer - Listing each item in a set within braces {0,1,2,3,4} Informal word description - answer - {whole #s less than 5} set builder notation - answer - {x| xEW, x5} set - answer - a collection of objects called elements element - answer - an object in the set E (symbol not really an E) - answer - is an element of cardinality - answer - the number of objects in a set shown as n(A)=4 Empty set - answer - set with no objects; {} ; always a subset of a set; zero with the line- null equal sets - answer - {q,r,s}={q,r,s}={r,q,s} SAME SET Equivalent sets - answer - sets with the same cardinality (same # of elements) ex. {a,b,c} ~ {dog, cat, fish} One to One correspondance - answer - same cardinality sets, shown with lines finite v. infinite - answer - set number of elements v. infinite elements Venn Diagrams - answer - Universe, A, B subsets - answer - usually a smaller part of a usually bigger set; a set is a subset of itself; symbol- sideways u with line under it proper subset - answer - it's missing something; nothing can be a proper subset of itself; symbol- sideways u complement of a set - answer - stuff in the universe that's not in the set; symbol- A with line over union of sets - answer - everything that's in A or B or BOTH (AuB) Intersection of sets - answer - everything that's in BOTH A and B (overlap) (AnB) disjoint sets - answer - nothing in common (AnB= { }) one-to-one correspondence -
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