Document Sample

Lesson 1-1 #1 NOTES 1-1 VARIABLES AND EXPRESSIONS Variable: a letter or a symbol used to represent a value that can change Constant: a number that does not change Numerical Expression: contains only constants and/or operations Algebraic Expression: contains variables, constants, and/or operations + – Lesson 1-1 #2 x Lesson 1-1 #3 “2 times y” “2 divided by y” Give two ways to write each algebraic expression in words. A. 9 + r B. q – 3 C. 7m D. j 6 Lesson 1-1 #4 John types 62 words per minute. Write an expression for the number of words he types in m minutes. m = the number of minutes that John types Roberto is 4 years older than Emily, who is y years old. Write an expression for Roberto’s age. y = Emily’s age Lesson 1-1 #5 Evaluate: substitute numbers for the variables in the expression and simplify Replacement Set { }: a set of numbers that can be substituted for a variable Evaluate n for the replacement set {2, 3, 9}. n n n Lesson 1-1 #6 Eighty-five bottles must be recycled to produce a sleeping bag. Find the number of bottles needed to make 20, 50, and 325 sleeping bags. Lesson 1-2 #1 NOTES 1-2 ADDING AND SUBTRACTING REAL NUMBERS The set of all numbers that can be represented on a number line are called real numbers. Add or subtract using a number line. –4 + (–7) = –11 + (–7) –4 11 10 9 8 7 6 5 4 3 2 1 0 Lesson 1-2 #2 The absolute value of a number is the distance from zero on a number line. |–5| = 5 |5| = 5 5 units 5 units -6 -5 - 4 -3 -2 -1 0 1 2 3 4 5 6 Lesson 1-2 #3 ADDING #s with SAME SIGNS • Add their absolute values, keep the sign 3+6= –2 + (–9) = ADDING #s with DIFFERENT SIGNS • Subtract their absolute values, keep the sign of the more powerful # –8 + 12 = 3 + (–15) = Add. Lesson 1-2 #4 A. B. –6 + (–2) C. –13.5 + (–22.3) D. 52 + (–68) Lesson 1-2 #5 Two numbers are opposites if their sum is 0. 5 + (–5) = 0 Additive Inverses same distance from zero (same absolute value) Lesson 1-2 #6 To SUBTRACT a number, add its opposite. (Keep… Change… Change…) A. 3 – 8 B. 5 – (–4) C. –6.7 – 4.1 D. E. Lesson 1-2 #7 An iceberg extends 75 feet above the sea. The bottom of the iceberg is at an elevation of –247 feet. What is the height of the iceberg? elevation at top minus elevation at bottom The height of the iceberg is ____ feet. Lesson 1-3 #1 NOTES 1-3 MULTIPLYING AND DIVIDING REAL NUMBERS The product or quotient of two numbers with the… SAME sign is POSITIVE DIFFERENT sign is NEGATIVE Find the value of each expression. A. B. C. Lesson 1-3 #2 Two numbers are reciprocals if their product is 1. 4 ● 1=1 4 Multiplicative Inverses To divide fractions… multiply by its multiplicative inverse! Lesson 1-3 #3 Lesson 1-3 #4 0 has special properties for multiplication and division A. 0 The quotient of zero and any nonzero # is _______. 15 B. –22 0 Division by zero is _____________. C. –8.45(0) The product of any number and 0 is ______. Lesson 1-3 #5 The speed of a hot-air balloon is 3 3 mi/h. It 4 travels in a straight line for 1 1 hours before 3 landing. How many miles away from the liftoff site will the balloon land? Distance = Rate x Time The balloon lands _____ miles from the site. Lesson 1-4 #1 NOTES 1-4 POWERS AND EXPONENTS Exponent Base what you multiply 3 2 how many times you multiply the base Power base and exponent Lesson 1-4 #2 The Area of a Square s s s s = s2 or “s squared” s The Volume of a Cube s s sss= s3 or “s cubed” Lesson 1-4 #3 Write the power represented by the geometric models. 6 The factor 6 is used 2 times. 6 = _____ The factor 5 is used 3 times. 5 = _____ 5 5 Lesson 1-4 #4 Powers are Repeated Multiplication 31 = 32 = 33 = 34 = 35 = Lesson 1-4 #5 Write each number as a power of the given base. 64; base 8 81; base –3 –27; base –3 Remember, if the base is negative: Even Exp = Positive Answer Odd Exp = Negative Answer Lesson 1-4 #6 The exponent belongs to what is directly in front of it. (–6)3 Exp belongs to everything inside the ( ) –102 Means “the opposite of 10²” A. (–5)3 B. –62 C. Lesson 1-4 #7 The PTA president calls 3 families. Each family calls 3 other families, and so on. How many families will have been called in the 4th round of calls? 1 Understand the problem • The president calls 3 families. • Each family calls 3 more families. President 2 Make a Plan • Draw a diagram. 1st round 2nd round Lesson 1-4 #8 3 Solve 1st round: 1 3 = 3 or 31 2nd round: 3 3 = 9 or 32 3rd round: 9 3 = 27 or 33 4th round: 27 3 = 81 or 34 families Or 3 3 3 3 = 34 = 81 families Lesson 1-5 #1 NOTES 1-5 ROOTS AND IRRATIONAL NUMBERS Square Root: a number multiplied by itself to form a product = “radical sign”, used to represent square roots 49 = 7 or -7 **Positive numbers have two square roots Lesson 1-5 #2 Principal Square Root: Always Positive 36 = 25 = Negative Square Root: – Always Negative – 81 = – 121 = Lesson 1-5 #3 Squaring and taking the square root are opposite operations… they undo each other. Perfect Squares: a number whose positive square root is a whole number 1 4 9 16 25 36 49 1² 2² 3² 4² 5² 6² 7² Lesson 1-5 #4 Index: tells you how many times to multiply the root What # do you multiply by itself 3 times to get 8? What # do you multiply by itself 4 times to get 16? Lesson 1-5 #5 Find each root. Lesson 1-5 #6 Irrational Numbers: any number that cannot be written as a fraction, “wacky numbers” Non-terminating non-repeating decimals (pi) Irrational square roots ( ) REAL NUMBERS include all rational and irrational #s. (All numbers you have learned about so far…) Lesson 1-5 #7 Rational Numbers: any number that can be written as a fraction, includes all numbers that “make sense” Natural Numbers: counting numbers {1, 2, 3, 4 . . . } Whole Numbers: counting numbers plus 0 {0, 1, 2, 3, 4 . . .} Integers: Whole numbers and their opposites { . . . -3, -2, -1, 0, 1, 2, 3 . . . } Also fractions and decimals (terminating and repeating) Lesson 1-5 #8 Note the symbols for the sets of numbers… R: real #s Q: rational #s Z: integers W: whole #s N: natural #s Lesson 1-5 #9 Write all classifications that apply to each real #. A. –32 B. C. 7 D. Lesson 1-6 #1 NOTES 1-6 PROPERTIES OF REAL NUMBERS Properties of Addition and Multiplication ComMUtative Property – (Mixed Up) You can add or multiply real #s in any order. a+b=b+a ab = ba AsSOciative Property – (Same Order) Changing the grouping does not change the sum (a + b) + c = a + (b + c) (ab)c = a(bc) Lesson 1-6 #2 Name the property that is illustrated in each equation. A. 7(mn) = (7m)n B. (a + 3) + b = a + (3 + b) C. x + (y + z) = x + (z + y) Lesson 1-6 #3 Distributive Property: also works with subtraction because subtracting is “adding the opposite” a(b + c) = ab + ac a(b – c) = ab – ac Write and simplify each product using the Distributive Property: 5(71) 4(38) Lesson 1-6 #4 Counterexample - example that disproves a statement, or shows that it is false. Statement Counterexample No month has fewer than February has fewer than 30 30 days. days, so the statement is false. Every integer that is 18 is divisible by 2 but not divisible by 2 is also by 4, so the statement is divisible by 4. false. Lesson 1-6 #5 Closure Property: Real numbers are “closed” if the result of the operation on any two numbers in the set is also in the set The set of even numbers is closed under addition. 4 + 6 = 10 (When you add any two even #s, the result must be even) Even #s Lesson 1-6 #6 Find a counterexample to show that the statement is false. The prime numbers are closed under addition. Find two prime #s such that their sum is not prime. Since ___ is not a prime number, the statement is _____. Lesson 1-6 #7 Find a counterexample to show that the statement is false. The set of odd numbers is closed under subtraction. Find two odd #s such that the difference is not odd. ___ and ___ are odd numbers, but __________, which is not an odd number, so the statement is ________. Lesson 1-7 #1 NOTES 1-7 SIMPLIFYING EXPRESSIONS Order of Operations tells you which operation to perform first in an expression. Order of Operations G Grouping Symbols - ( ), [ ], { }, fraction bar, , E Exponents M/D Mult. and Div. from left to right A/S Add. and Sub. from left to right Goodbye PEMDAS and hello GEMDAS!!! Lesson 1-7 #2 Simplify each expression. 15 – 2 3 + 1 12 + 32 + 10 ÷ 2 Lesson 1-7 #3 Start with the innermost grouping symbol and work outward… 100 – [(3+4)² – 6] Lesson 1-7 #4 Terms: the parts that are added or subtracted Terms 4x – 3x + 2 Constant: numerical term Like Terms Constant with no variable Like Terms: terms that have the same variables and exponents Lesson 1-7 #5 Coefficient: a number multiplied by a variable Coefficients 1x2 + 3x Combining Like Terms – • Add or subtract the coefficients • Keep the variables and exponents the same Alphabetical order with constants last! Lesson 1-7 #6 A. 72p – 25p B. C. 0.5m + 2.5n D. 14x + 4(2 + x) E. 2a + 4b + 6(a – 3) – 5b

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 0 |

posted: | 10/4/2012 |

language: | Unknown |

pages: | 48 |

OTHER DOCS BY tuKkt86

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.