* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Lesson 1 - Purdue Math
Foundations of mathematics wikipedia , lookup
Ethnomathematics wikipedia , lookup
History of logarithms wikipedia , lookup
Law of large numbers wikipedia , lookup
Infinitesimal wikipedia , lookup
Bra–ket notation wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Georg Cantor's first set theory article wikipedia , lookup
Musical notation wikipedia , lookup
Location arithmetic wikipedia , lookup
Big O notation wikipedia , lookup
Bernoulli number wikipedia , lookup
History of mathematical notation wikipedia , lookup
Abuse of notation wikipedia , lookup
Surreal number wikipedia , lookup
Proofs of Fermat's little theorem wikipedia , lookup
Positional notation wikipedia , lookup
Real number wikipedia , lookup
Large numbers wikipedia , lookup
Lesson 1.1 (Part 1) Translating to Algebraic Expressions Key Words Subtraction Multiplication Division add subtract sum of difference of plus minus increased decreased by more lessbythan than Examples: multiply product of times twice of divide divided by quotient of ratio per Addition Let n = a number 1) twelve less than twice some number 2) eight more than the ratio of twice a number and five 3) the difference of 45% of a number and one Exponential Notation The expression an, in which n is a counting number means a a a a..... a n factors In a , a is called the base and n is called the exponent, or power. When no exponent appears, it is assumed to be 1. Thus a1 = a. n Rules for Order of Operations 1. Simplify within any grouping symbols. 2. Simplify all exponential expressions. 3. Perform all multiplication and division working from left to right. 4. Perform all addition and subtraction working from left to right. 1 Examples: 1) 4 2 6(7) 4(1 2) = 2) 2(12) 4(6 1) 2 4(3 1) = 3 1 To EVALUATE an expression or formula, substitute the given value(s) for the variable(s) and follow the order of operations. 8 xz y for x 2, y 7, z 3 3) 4) 2 x 3 12 x 2 for x 2. 5) 4 x 2 2 xy z for x 3, y 2, z 8 2 2 6) 3a 2 m 4am 2 for a 3, m 2 7) x 2 [2(a b) ab]2 for x 12, a 2, b 1 8) The base of a triangle is 10 feet and the height is 3.1 feet. Find the area of the triangle. 1 A bh 2 3.1 10 9) Find the area of a trapezoid if b1 12, b2 18, h 8 b1 A h 1 h(b1 b2 ) 2 b2 Sets of Numbers (Part 2 of lesson) 1. Natural Numbers: {1, 2, 3, ...} These are sometimes called the Counting Numbers. 2. Whole Numbers: {0, 1, 2, 3, ...} The Whole Numbers are the Natural Numbers plus zero. 3 3. Integers: {..., -3, -2, -1, 0, 1, 2, 3,...} The integers include all whole numbers and their opposites. The set notation used in the above number sets is called roster set notation. Roster notation simply lists the numbers included. p 4. Rational Numbers: | p is an integer, q is a non-zero integer This set of q numbers includes any type of number that can be represented as a fraction. These types of number include the following Fractions (proper, improper, or mixed) Integers (denominator of 1) Terminating Decimals Repeating Decimals 2,5,17, 0 (integers) 9 7 11 , , (fractions) 11 8 2 Examples include the following: 2.34, 0.0456 (terminating decimals) 1 1.2,3.4787878... (repeating decimals) The set notation used in the above number set is called Set-Builder Notation. The one above is read ‘all numbers of the form p over q such that p is an integer and q is a non-zero integer’. In this set notation a description is used. The vertical bar is read ‘such that’ or ‘where as’. There will be a variable or an expression with variables at the front. 5. Irrational Numbers: Irrational numbers include numbers that cannot be expressed as a fraction. Most of the irrational numbers you will encounter will be roots or the number pi (π). When written as a decimal, irrational numbers will not terminate or repeat. For example, an approximation for π is 3.14, but 3.14 does not exactly equal π. 6. Real Numbers: {x | x is rational or irrational} Use this list of numbers and identify which numbers are in the following sets. 5 3 10 6.2 5 2 3 2 4 5 0.457 0.234 16 0 400 9 Whole Numbers: 4 Integers: Rational Numbers: Irrational Numbers. There is a good diagram found on the course web page or in your textbook that shows the relationship among the sets of numbers. Roster Notation: {2, 4, 6,8} Set-Builder Notation: {x | x is an even number between 1 and 9} Ex) Write the following using roster notation. {x | x is an even number between 5 and 12} {x | x is a natural number no more than 7} 5 Ex) Write the following using set-builder notation. {9,11,13,15,17} {24, 28,32} Elements & Subsets B {1,3,5, 7} The elements of set B are 1, 3, 5, and 7 3 B read '3 is an element of B ' 4 B read '4 is not an element of B ' When all numbers of a first set A are members of a second set B, we can write A B , which is read ‘A is a subset of B’. A {1,3} A B B (1,3,5, 7} Use the following sets to determine if the statements below are true or false. N = Natural Numbers W = Whole Numbers Z = Integers Q = Rational Numbers H = Irrational Numbers R = Real Numbers 2.3 W 6 Q 4 H 5 QR H Z WN 6