Mat 105 exam 1 questions and guaranteed correct answer| solutions guaranteed.

mathematics - correct answers the deeper understanding will lead to increased confidence and comfortable level useful tools - correct answers drawing a picture, using algebra, using concrete materials, solving a simpler problem, making a table, guess-check-revise, looking for patterns, visualization tools George Polya's Four Steps - correct answers - understanding the problem: questions/actions that can be useful - devising a plan - carrying out the plan - looking back Sets - correct answers a group of repetitions Describing sets - correct answers - individual objects in a given set known as members or elements - symbol: Ɛ - "is a member of" - braces: {} - 3 dots: ellipsis (...): set continues Natural numbers - correct answers The set of counting numbers; (1,2,3...) whole numbers - correct answers the set of natural numbers and zero (0,1,2,3...) integers - correct answers set of positive and negative whole number (-3,-2,-1,0,1,2,3...) Rational number - correct answers - symbol: Q - set of all numbers can be represented as the ratio of 2 integers, denominator is not 0 set-builder notation - correct answers Q= {a/b | a Ɛ／and b Ɛ ／ b ≠ 0} finite - correct answers number of elements in set is a whole number - set of Nobel prize winners infinite - correct answers unlimited number of members - grains of sand at a beach subset - correct answers - Symbol: ⊆ "is a subset of" - a set is a subset of another set is all elements in the subset are also in the set empty set - correct answers - set with no elements - known as a null set - represent as {}, nothing inside the brackets - symbol: ∅ mathematical statements - correct answers - every set is a subset of itself - the empty set is a subset of every set equal/equivalent - correct answers - sets contain the same elements - same number of elements - symbol: - one-to-one correspondence intersections - correct answers Set builder: B n S = {x| x Ɛ B and x Ɛ Union - correct answers B U S = {x| x Ɛ B and / or x Ɛ S} complement - correct answers line over the variable subtraction - correct answers B - S = {x| x Ɛ B and x ∉ S} disjoint sets - correct answers nothing in common base 10 - correct answers groups of 10 base 5 - correct answers groups of 5 Egyptian numeration system - correct answers - Astonished person :1,000,000 - Polliwog or burbot fish: 100,000 - Pointing finger: 10,000 - Lotus flower: 1,000 - Scroll: 100 - Heel Bone: 10 - Staff: 1 - no symbol for zero, no whole numbers, only natural numbers Roman number system - correct answers I - 1 V - 5 X - 10 L - 50 C - 100 D - 500 M - 1,000 Babylonian numeration system - correct answers -upright wedge: one - sideways wedge: ten decimal system - correct answers - base 10 system, based on groupings of ten - deci: ten expanding form - correct answers represent a number by decomposing it into the sum of values from each place concept of 0 - correct answers - works like any other digit - acts like a placeholder fractions - correct answers - comes from latin word fractio meaning break - number that can be represented as a quotient rational number - correct answers - ratio of two number a & b - a/b - a number whose value can be expressed as the quotient fractions as a quotient - correct answers area model fractions as a measure - correct answers linear model fractions as an operator - correct answers set model fraction as a ratio - correct answers set model Greatest common factor - correct answers The largest factor that two or more numbers have in common - notation: GCF(a,b) ways to find GCF - correct answers - concrete/ pictorially - use factorization repeatedly divide by prime numbers - prime factorization - factor houses Notation - correct answers Whole numbers: capital letters Decimals: lowercase fractions to decimals - correct answers - use equivalent fractions - power of ten - multiply to get a denominator of 10 decimals to fractions - correct answers - divide - repeating decimals tells repeating number 9 Strategies to write decimals from smallest to largest - correct answers 1: use equivalent fractions with common denominator 2. line up the decimal points and add zeros 3. represent them on a number line strategies for decimal to whole numbers - correct answers 1. connect decimals to fractions 2. connect decimals to expanded form 3. connect decimals to place value integers - correct answers the union set of positive integers, the set of negative integers and zero - (...-4,-3,-2,-1,0,1,2,3,4...) use of negative numbers - correct answers - Businesses use negative numbers to indicate a business loss or "negative profit" - We often use negative numbers when describing change - We use negative numbers to indicate temperature - Elevations below sea level - A golfer uses negative to indicate a score - Physicists use negative numbers to indicate negatively charged particles - We use a coordinate system to indicate the position of an object representation of integers - correct answers - number lines - two sided coins irrational numbers - correct answers - there is no rational number (that is a number that is expressed as the quotient of two integers) that will produce a product of exactly 2 - x=√2 real numbers - correct answers - the union of the sets of rational and irrational numbers