Geometric Sequences. Geometric Sequences. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 1
|
|
|
- Scot Wilcox
- 5 years ago
- Views:
Transcription
1 Warm Up Lesson Presentation Lesson Quiz Algebra 1
2 Warm Up Find the value of each expression ( 3) (0.2) ( 4) ( 0.4)
3 Objectives Recognize and extend geometric sequences. Find the nth term of a geometric sequence.
4 geometric sequence common ratio Vocabulary
5 The table shows the heights of a bungee jumper s bounces. The height of the bounces shown in the table above form a geometric sequence. In a geometric sequence, the ratio of successive terms is the same number r, called the common ratio.
6 Geometric sequences can be thought of as functions. The term number, or position in the sequence, is the input, and the term itself is the output Position Term a 1 a 2 a 3 a 4 To find a term in a geometric sequence, multiply the previous term by r.
7
8 Writing Math The variable a is often used to represent terms in a sequence. The variable a 4 (read a sub 4 )is the fourth term in a sequence.
9 Example 1A: Extending Find the next three terms in the geometric sequence. 1, 4, 16, 64, Step 1 Find the value of r by dividing each term by the one before it The value of r is 4.
10 Example 1A Continued Find the next three terms in the geometric sequence. 1, 4, 16, 64, Step 2 Multiply each term by 4 to find the next three terms The next three terms are 256, 1024, and 4096.
11 Example 1B: Extending Find the next three terms in the geometric sequence. Step 1 Find the value of r by dividing each term by the one before it. The value of r is.
12 Helpful Hint When the terms in a geometric sequence alternate between positive and negative, the value of r is negative.
13 Example 1B Continued Find the next three terms in the geometric sequence. Step 2 Multiply each term by three terms. to find the next The next three terms are
14 Check It Out! Example 1a Find the next three terms in the geometric sequence. 5, 10, 20, 40, Step 1 Find the value of r by dividing each term by the one before it The value of r is 2.
15 Check It Out! Example 1a Continued Find the next three terms in the geometric sequence. 5, 10, 20, 40, Step 2 Multiply each term by 2 to find the next three terms ( 2) ( 2) ( 2) The next three terms are 80, 160, and 320.
16 Check It Out! Example 1b Find the next three terms in the geometric sequence. 512, 384, 288, Step 1 Find the value of r by dividing each term by the one before it The value of r is 0.75.
17 Check It Out! Example 1b Continued Find the next three terms in the geometric sequence. 512, 384, 288, Step 2 Multiply each term by 0.75 to find the next three terms The next three terms are 216, 162, and
18 To find the output a n of a geometric sequence when n is a large number, you need an equation, or function rule. The pattern in the table shows that to get the nth term, multiply the first term by the common ratio raised to the power n 1.
19 If the first term of a geometric sequence is a 1, the nth term is a n, and the common ratio is r, then a n = a 1 r n 1 nth term 1 st term Common ratio
20 Example 2A: Finding the nth Term of a Geometric Sequence The first term of a geometric sequence is 500, and the common ratio is 0.2. What is the 7th term of the sequence? a n = a 1 r n 1 Write the formula. a 7 = 500(0.2) 7 1 Substitute 500 for a 1,7 for n, and 0.2 for r. = 500(0.2) 6 Simplify the exponent. = Use a calculator. The 7th term of the sequence is
21 Example 2B: Finding the nth Term of a Geometric Sequence For a geometric sequence, a 1 = 5, and r = 2. Find the 6th term of the sequence. a n = a 1 r n 1 Write the formula. a 6 = 5(2) 6 1 Substitute 5 for a 1,6 for n, and 2 for r. = 5(2) 5 Simplify the exponent. = 160 The 6th term of the sequence is 160.
22 Example 2C: Finding the nth Term of a Geometric Sequence What is the 9th term of the geometric sequence 2, 6, 18, 54,? a n = a 1 r n 1 Write the formula. a 9 = 2( 3) 9 1 Substitute 2 for a 1,9 for n, and 3 for r. = 2( 3) 8 Simplify the exponent. = 13,122 Use a calculator. The 9th term of the sequence is 13,122. The value of r is 3.
23 Caution When writing a function rule for a sequence with a negative common ratio, remember to enclose r in parentheses ( 2) 12
24 Check It Out! Example 2 What is the 8th term of the sequence 1000, 500, 250, 125,? The value of r is. a n = a 1 r n 1 a 8 = 1000( ) 8 1 Write the formula. Substitute 1000 for a 1,8 for n, and for r. Simplify the exponent. = Use a calculator. The 8th term of the sequence is
25 Example 3: Application A ball is dropped from a tower. The table shows the heights of the balls bounces, which form a geometric sequence. What is the height of the 6th bounce? Bounce Height (cm) The value of r is 0.5.
26 Example 3 Continued a n = a 1 r n 1 a 6 = 300(0.5) 6 1 Write the formula. Substitute 300 for a 1, 6 for n, and 0.5 for r. = 300(0.5) 5 Simplify the exponent. = Use a calculator. The height of the 6th bounce is cm.
27 Check It Out! Example 3 The table shows a car s value for 3 years after it is purchased. The values form a geometric sequence. How much will the car be worth in the 10th year? Year Value ($) 1 10, , ,400 10,000 8,000 6,400 The value of r is 0.8.
28 Check It Out! Example 3 a n = a 1 r n 1 Write the formula. a 6 = 10,000(0.8) 10 1 Substitute 10,000 for a 1, 10 for n, and 0.8 for r. = 10,000(0.8) 9 Simplify the exponent. = 1, Use a calculator. In the 10th year, the car will be worth $
29 Lesson Quiz: Part I Find the next three terms in each geometric sequence. 1. 3, 15, 75, 375, ; 9375; 46, The first term of a geometric sequence is 300 and the common ratio is 0.6. What is the 7th term of the sequence? What is the 15th term of the sequence 4, 8, 16, 32, 64? 65,536
30 Lesson Quiz: Part II Find the next three terms in each geometric sequence. 5. The table shows a car s value for three years after it is purchased. The values form a geometric sequence. How much will the car be worth after 8 years? $ Year Value ($) 1 18, , ,005
1-6 Order of Operations
1-6 Order of Operations Warm Up Lesson Presentation Lesson Quiz 2 pts 3 pts Bell Quiz 1-6 Find each square root. 1. 25 Write all classifications that apply to each real number. 3. -55 5 pts possible Questions
10-2 Circles. Warm Up Lesson Presentation Lesson Quiz. Holt Algebra2 2
10-2 Circles Warm Up Lesson Presentation Lesson Quiz Holt Algebra2 2 Warm Up Find the slope of the line that connects each pair of points. 1. (5, 7) and ( 1, 6) 1 6 2. (3, 4) and ( 4, 3) 1 Warm Up Find
1-3 Multiplying and Dividing Real Numbers
Multiplying and Dividing 1-3 Multiplying and Dividing Real Numbers Real Numbers Warm Up Lesson Presentation Lesson Quiz 1 2 pts Bell Quiz 1-3 Add or Subtract 1. 3 8 2 pts 2. - 8 + 12 2 pts 3. 4 (-4) 2
1Identify and generate
Then You related arithmetic sequences to linear functions. (Lesson -5) Now Geometric Sequences as Exponential Functions 1Identify and generate geometric sequences. 2Relate geometric sequences to exponential
Algebra II Chapter 6: Rational Exponents and Radical Functions
Algebra II Chapter 6: Rational Exponents and Radical Functions Chapter 6 Lesson 1 Evaluate nth Roots and Use Rational Exponents Vocabulary 1 Example 1: Find nth Roots Note: and Example 2: Evaluate Expressions
12-4 Geometric Sequences and Series. Lesson 12 3 quiz Battle of the CST s Lesson Presentation
12-4 Geometric Sequences and Series Lesson 12 3 quiz Battle of the CST s Lesson Presentation Objectives Find terms of a geometric sequence, including geometric means. Find the sums of geometric series.
3.8.2 Geometric Sequences. Warm Up
Name: # Honors Coordinate Algebra: Period Ms. Pierre Date: 3.8.2 Geometric Sequences Warm Up This time, Julian left his homework in the back pocket of his jeans, and his mom put his jeans through the washing
Algebra II Chapter 8 Part 2: Rational Functions
Algebra II Chapter 8 Part 2: Rational Functions Chapter 8 Lesson 4 Multiply and Divide Rational Functions Vocabulary Words to Review: Reciprocal The rules of fractions DO NOT change! *When adding and subtracting,
Algebraically Speaking Chalkdust Algebra 1 Fall Semester
Algebraically Speaking Chalkdust Algebra 1 Fall Semester Homework Assignments: Chapter 1 The Real Number System: Lesson 1.1 - Real Numbers: Order and Absolute Value Do the following problems: # 1 9 Odd,
Warm Up Simplify each expression. Assume all variables are nonzero.
Warm Up Simplify each expression. Assume all variables are nonzero. 1. x 5 x 2 3. x 6 x 2 x 7 x 4 Factor each expression. 2. y 3 y 3 y 6 4. y 2 1 y 5 y 3 5. x 2 2x 8 (x 4)(x + 2) 6. x 2 5x x(x 5) 7. x
15.1 Understanding Geometric
Name Class Date 15.1 Understanding Geometric Sequences Essential Question: How are the terms of a geometric sequence related? Resource Locker Explore 1 Exploring Growth Patterns of Geometric Sequences
7th Grade Math Unit 1 Algebraic Reasoning
7th Grade Math Unit 1 Algebraic Reasoning Name: Period: Common Core State Standards CC.7.NS.1 - Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers;
Warm-up for Geometry
Summer Work Packet Warm-up for Geometry Who should complete this packet? Students who will be taking Geometry in the fall of 018. Due Date: The first day of school How many of the problems should I do?
1-3 Variables and Algebraic Expressions. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Warm Up Evaluate. 1. 5(7) 1 2. 7(18 11) 3. 22 + 17 8 + 3 4. 36 + 15(40 35) 5. 3 3 + 7(12 4) Problem of the Day If charged per cut, how much
Curve Fitting with Linear Models
1-4 1-4 Curve Fitting with Linear Models Warm Up Lesson Presentation Lesson Quiz Algebra 2 Warm Up Write the equation of the line passing through each pair of passing points in slope-intercept form. 1.
MATH Ms. Becker
MATH 1-23-17 Ms. Becker Warm-Up: Write down 2 goals you wish to complete in Unit 5. (Area and Volume) When finished, either prepare yourself to correct your test or prepare yourself for taking notes. Agenda:
The Absolute Value Symbol
Section 1 3: Absolute Value and Powers The Absolute Value Symbol The symbol for absolute value is a pair of vertical lines. These absolute value brackets act like the parenthesis that we use in order of
2-2 Adding Integers. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Warm Up Find each absolute value. 1. 8 2. 6 3. 9 4. 7 5. 12 6. 53 Problem of the Day Jan s yearly salary is $30,000, and it will be increased
Multiplying and Dividing Rational Expressions
Multiplying and Dividing Rational Expressions Warm Up Simplify each expression. Assume all variables are nonzero. 1. x 5 x 2 3. x 6 x 2 x 7 Factor each expression. 2. y 3 y 3 y 6 x 4 4. y 2 1 y 5 y 3 5.
Chapter 1: Foundations for Algebra
Chapter 1: Foundations for Algebra Dear Family, The student will follow the order of operations, a set of rules that standardize how to simplify expressions. Order of Operations 1. Perform operations within
8-4 Transforming Quadratic Functions
8-4 Transforming Quadratic Functions Warm Up Lesson Presentation Lesson Quiz Algebra 1 Warm Up For each quadratic function, find the axis of symmetry and vertex, and state whether the function opens upward
3-6 Lines in the Coordinate Plane
3-6 Lines in the Coordinate Plane Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Substitute the given values of m, x, and y into the equation y = mx + b and solve for b. 1. m = 2, x = 3, and
Working with Rational Expressions
Working with Rational Expressions Return to Table of Contents 4 Goals and Objectives Students will simplify rational expressions, as well as be able to add, subtract, multiply, and divide rational expressions.
Simplifying Algebraic Expressions Involving Exponents
Simplifying Algebraic Expressions Involving Exponents GOAL Simplify algebraic expressions involving powers and radicals. LEARN ABOUT the Math The ratio of the surface area to the volume of microorganisms
1-1 Sets of Numbers. Warm Up Lesson Presentation Lesson Quiz. Holt Algebra 2
1-1 Sets of Numbers Warm Up Lesson Presentation Lesson Quiz Warm Up Write in decimal form. 1. 4.5 2. 3. Write as a decimal approximation. 1.414 Order from least to greatest. 4. 10, 5, 10, 0, 5 10, 5, 0,
Math-2. Lesson 3-1. Equations of Lines
Math-2 Lesson 3-1 Equations of Lines How can an equation make a line? y = x + 1 x -4-3 -2-1 0 1 2 3 Fill in the rest of the table rule x + 1 f(x) -4 + 1-3 -3 + 1-2 -2 + 1-1 -1 + 1 0 0 + 1 1 1 + 1 2 2 +
Algebra II Chapter 4: Quadratic Functions and Factoring Part 1
Algebra II Chapter 4: Quadratic Functions and Factoring Part 1 Chapter 4 Lesson 1 Graph Quadratic Functions in Standard Form Vocabulary 1 Example 1: Graph a Function of the Form y = ax 2 Steps: 1. Make
ALGEBRA I Summer Packet
ALGEBRA I Summer Packet 2018-2019 Name 7 th Grade Math Teacher: Objectives for Algebra I Summer Packet I. Variables and translating (Problems #1 5) Write Algebraic Expressions Writing Algebraic Equations
2-9 Operations with Complex Numbers
2-9 Operations with Complex Numbers Warm Up Lesson Presentation Lesson Quiz Algebra 2 Warm Up Express each number in terms of i. 1. 9i 2. Find each complex conjugate. 3. 4. Find each product. 5. 6. Objective
Chapter 1: Variables, Expressions, and Integers
Name: Pre-Algebra Period: 8 Chapter 1: Variables, Expressions, and Integers Outline 1.1: p. 7 #12-15, 20-27, 32, 33, 34, 36 Date 1.2: p. 12 #16-20, 25-28, 30, 31, 36 1.3: p. 19 #10-18, 21-25, 31 1.4: p.
Linear, Quadratic, and Exponential Models Attendance Problems 1. Find the slope and y-intercept of the line that passes through (4, 20) and (20, 24).
Page 1 of 13 Linear, Quadratic, and Exponential Models Attendance Problems 1. Find the slope and y-intercept of the line that passes through (4, 20) and (20, 24). The population of a town is decreasing
Solving Algebraic Equations
Lesson 4. Solving Algebraic Equations 3 3 3 3 3 8 8 4 Add 3 to both sides. Divide both sides by. 4 gives the solution of the equation 3. Check: Substitute 4 for x into the original equation. 3 4 3 When
4-8 Similar Figures and Proportions. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Warm Up Find the cross products, and then tell whether the ratios are equal. 1. 16, 40 6 15 2. 3. 3 8, 18 46 8, 24 9 27 4. 28, 42 12 18 240
Lesson 1: Arithmetic Review
In this lesson we step back and review several key arithmetic topics that are extremely relevant to this course. Before we work with algebraic expressions and equations, it is important to have a good
NAME UNIT 4 ALGEBRA II. NOTES PACKET ON RADICALS, RATIONALS d COMPLEX NUMBERS
NAME UNIT 4 ALGEBRA II NOTES PACKET ON RADICALS, RATIONALS d COMPLEX NUMBERS Properties for Algebra II Name: PROPERTIES OF EQUALITY EXAMPLE/MEANING Reflexive a - a Any quantity is equal to itself. Symmetric
Welcome back! Sit down and work on the warm up!
Welcome back! Sit down and work on the warm up! 1 Rewrite 4 4 4 4 4 4 4 4 4 using exponents 2 Circle the coefficient and square the constant of the function y=3x+7 3 Rewrite the expression using multiplication:
Specific Objectives Students will understand that that the family of equation corresponds with the shape of the graph. Students will be able to create a graph of an equation by plotting points. In lesson
ACCELERATED MATH 6/7 Plans QUARTER
ACCELERATED MATH 6/7 Plans QUARTER 1 2017-2018 DATES (A & B) ASSESSMENT UNIT SOL LESSON 8/24 & 8/25 Class expectations; Getting-to-know-you activities 8/28 & 8/29 UNIT 1 - Integers 6.3, 7.3a, 7.1e Identify
Unit 3: Multiplication and Division Reference Guide pages x 7 = 392 factors: 56, 7 product 392
Lesson 1: Multiplying Integers and Decimals, part 1 factor: any two or more numbers multiplied to form a product 56 x 7 = 392 factors: 56, 7 product 392 Integers: all positive and negative whole numbers
ALGEBRA 2 W/ TRIGONOMETRY MIDTERM REVIEW
Name: Block: ALGEBRA W/ TRIGONOMETRY MIDTERM REVIEW Algebra 1 Review Find Slope and Rate of Change Graph Equations of Lines Write Equations of Lines Absolute Value Functions Transformations Piecewise Functions
QUADRATICS Geometric Applications of Quadratics Common Core Standard
H Quadratics, Lesson 4, Geometric Applications of Quadratics (r. 018) QUADRATICS Geometric Applications of Quadratics Common Core Standard Next Generation Standard A-CED.1 Create equations and inequalities
SEQUENCES AND SERIES Sequences CC Standard
N Sequences and Series, Lesson 1, Sequences (r. 2018) SEQUENCES AND SERIES Sequences CC Standard NG Standard F-IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain
SUMMER REVIEW PACKET 2 FOR STUDENTS ENTERING ALGEBRA 1
SUMMER REVIEW PACKET FOR STUDENTS ENTERING ALGEBRA Dear Students, Welcome to Ma ayanot. We are very happy that you will be with us in the Fall. The Math department is looking forward to working with you
Exponents. Reteach. Write each expression in exponential form (0.4)
9-1 Exponents You can write a number in exponential form to show repeated multiplication. A number written in exponential form has a base and an exponent. The exponent tells you how many times a number,
Objective. 9-4 Transforming Quadratic Functions. Graph and transform quadratic functions.
Warm Up Lesson Presentation Lesson Quiz Warm Up For each quadratic function, find the axis of symmetry and vertex, and state whether the function opens upward or downward. 1. y = x 2 + 3 2. y = 2x 2 x
A B C 1 Number of Squares Number of Nickels Total Number of Nickels =A2+1 =B2*2 =B3+C2
6.7 Geometric Series The Canadian Open is an outdoor tennis tournament. The tournament started in 1881, and the men s and women s events alternate between Toronto and Montreal every other year. In the
or 5.00 or 5.000, and so on You can expand the decimal places of a number that already has digits to the right of the decimal point.
1 LESSON Understanding Rational and Irrational Numbers UNDERSTAND All numbers can be written with a For example, you can rewrite 22 and 5 with decimal points without changing their values. 22 5 22.0 or
QUADRATIC FUNCTIONS TEST REVIEW NAME: SECTION 1: FACTORING Factor each expression completely. 1. 3x p 2 16p. 3. 6x 2 13x 5 4.
QUADRATIC FUNCTIONS TEST REVIEW NAME: SECTION 1: FACTORING Factor each expression completely. 1. 3x 2 48 2. 25p 2 16p 3. 6x 2 13x 5 4. 9x 2 30x + 25 5. 4x 2 + 81 6. 6x 2 14x + 4 7. 4x 2 + 20x 24 8. 4x
This assignment is due the first day of school. Name:
This assignment will help you to prepare for Geometry A by reviewing some of the topics you learned in Algebra 1. This assignment is due the first day of school. You will receive homework grades for completion
Learning Log Title: CHAPTER 3: ARITHMETIC PROPERTIES. Date: Lesson: Chapter 3: Arithmetic Properties
Chapter 3: Arithmetic Properties CHAPTER 3: ARITHMETIC PROPERTIES Date: Lesson: Learning Log Title: Date: Lesson: Learning Log Title: Chapter 3: Arithmetic Properties Date: Lesson: Learning Log Title:
1.1 evaluating expressions 2017 ink.notebook. August 18, page 7 page 8 Unit 1 Basic Equations and Inequalities. 1.1 Order of Operations.
1.1 evaluating expressions 2017 ink.notebook page 7 page 8 Unit 1 Basic Equations and Inequalities 1.1 Order of Operations page 9 page 10 Lesson Objectives Standards 1.1 Order of Operations Press the tabs
Measures of Dispersion
Lesson 7.6 Objectives Find the variance of a set of data. Calculate standard deviation for a set of data. Read data from a normal curve. Estimate the area under a curve. Variance Measures of Dispersion
Working with Algebraic Expressions
2 Working with Algebraic Expressions This chapter contains 25 algebraic expressions; each can contain up to five variables. Remember that a variable is just a letter that represents a number in a mathematical
10-2. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry
Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Find the unknown side lengths in each special right triangle. 1. a 30-60 -90 triangle with hypotenuse 2 ft 2. a 45-45 -90 triangle with leg length
Writing and Graphing Linear Equations. Linear equations can be used to represent relationships.
Writing and Graphing Linear Equations Linear equations can be used to represent relationships. Linear equation An equation whose solutions form a straight line on a coordinate plane. Collinear Points that
Marcy Mathworks Answers Punchline Radical Expressions
Marcy Mathworks Answers Punchline Free PDF ebook Download: Marcy Mathworks Answers Punchline Download or Read Online ebook marcy mathworks answers punchline radical expressions in PDF Format From The Best
I can position figures in the coordinate plane for use in coordinate proofs. I can prove geometric concepts by using coordinate proof.
Page 1 of 14 Attendance Problems. 1. Find the midpoint between (0, x) and (y, z).. One leg of a right triangle has length 1, and the hypotenuse has length 13. What is the length of the other leg? 3. Find
Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 2 Section 12 Variables and Expressions
Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 2 Please watch Section 12 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item67.cfm
TI-84+ GC 3: Order of Operations, Additional Parentheses, Roots and Absolute Value
Rev 6--11 Name Date TI-84+ GC : Order of Operations, Additional Parentheses, Roots and Absolute Value Objectives: Review the order of operations Observe that the GC uses the order of operations Use parentheses
Ready To Go On? Skills Intervention 4-1 Graphing Relationships
Read To Go On? Skills Intervention -1 Graphing Relationships Find these vocabular words in Lesson -1 and the Multilingual Glossar. Vocabular continuous graph discrete graph Relating Graphs to Situations
Summer Math Assignments for Students Entering Integrated Math
Summer Math Assignments for Students Entering Integrated Math Purpose: The purpose of this packet is to review pre-requisite skills necessary for the student to be successful in Integrated Math. You are
Properties of Graphs of Quadratic Functions
H e i g h t (f t ) Lesson 2 Goal: Properties of Graphs of Quadratic Functions Identify the characteristics of graphs of quadratic functions: Vertex Intercepts Domain and Range Axis of Symmetry and use
5 th Grade Math Curriculum
Aug./May Problem of the Day Solve grade appropriate problem on a daily basis -Individual solving of problems -Group discussion Math vocabulary Define terminology used in daily lessons -Chapter review Problem
Section 6.2: Properties of Graphs of Quadratic Functions. Vertex:
Section 6.2: Properties of Graphs of Quadratic Functions determine the vertex of a quadratic in standard form sketch the graph determine the y intercept, x intercept(s), the equation of the axis of symmetry,
Think: 5 5 5, or 25. Think: Think: Evaluate Multiply. So, when s 2, the value of. 5(s 3) is 125. Then divide.
7 Multiply first. Think: 9 8 Then divide. Think: 8 Finally, subtract. Think: Replace a with 9. o, when a 9, the value of a is. 8 9 a ubtract.. Replace a with 5. The value of a is a a 5 b Add. is Divide.
2.) = 7.) Find the unit rate of 6 miles in 20 minutes. 4.) 6 8 = 8.) Put in simplified exponential form (8 3 )(8 6 )
Warm Up Do you remember how to... 1.) 3 + 9 = Wobble Chairs: Braden, Weston, & Avalon 6.) Put 3,400,000 in scientific notation? 2.) 2 + 8 = 7.) Find the unit rate of 6 miles in 20 minutes. 3.) 2 17 = 4.)
To find the surface area and volume of a sphere
To find the surface area and volume of a sphere Sphere set of all points in space equidistant from a given point called the center. Surface Area Formula: S.A. = 4πr 2 r Volume Formula: V = 4 πr 3 3 Great
Geometry Unit 5 Geometric and Algebraic Connections. Table of Contents
Geometry Unit 5 Geometric and Algebraic Connections Table of Contents Lesson 5 1 Lesson 5 2 Distance.p. 2-3 Midpoint p. 3-4 Partitioning a Directed Line. p. 5-6 Slope. p.7-8 Lesson 5 3 Revisit: Graphing
Maths Assessment Framework Year 10 Foundation
Success Criteria for all assessments: Foundation Tier 80% 5 70% 4 60% 3 50% 2 40% 1 Please note the GCSE Mathematics is one of the first GCSEs which will be graded by number rather than A*, A, B, C etc.
Intro to Rational Expressions
Intro to Rational Expressions Fractions and Exponents Review Fractions Review Adding and Subtracting Fractions Always find a common denominator when adding or subtracting fractions! a) b) Multiplying and
Project 2: How Parentheses and the Order of Operations Impose Structure on Expressions
MAT 51 Wladis Project 2: How Parentheses and the Order of Operations Impose Structure on Expressions Parentheses show us how things should be grouped together. The sole purpose of parentheses in algebraic
ACCELERATED MATH 6/7 Plans QUARTER
ACCELERATED MATH 6/7 Plans QUARTER 1 2017-2018 DATES (A & B) ASSESSMENT UNIT SOL LESSON 8/24 & 8/25 Class expectations; Getting-to-know-you activities 8/28 & 8/29 UNIT 1 - Integers 6.3, 7.3a, 7.1e Identify
Unit Title Key Concepts Vocabulary CCS
Unit Title Key Concepts Vocabulary CCS Unit 1 Writing and Evaluating s Unit 2 Writing and Solving Equations s and Equations Write numerical expressions Evaluate numerical expressions Write algebraic expressions
In math, the rate of change is called the slope and is often described by the ratio rise
Chapter 3 Equations of Lines Sec. Slope The idea of slope is used quite often in our lives, however outside of school, it goes by different names. People involved in home construction might talk about
Due Date: Friday, September 9 th Attached is your summer review packet for the Algebra 1 course.
Due Date: Friday, September 9 th Attached is your summer review packet for the Algebra 1 course. This is your first Graded HW grade. You MUST SHOW WORK in order to receive credit. This means if you typed
In this lesson, we will use the order of operations to evaluate and simplify expressions that contain numbers and variables.
Show Me: Expressions M8081 Could we sit in a classroom on the other side of the world and still make sense of the mathematics? The answer is yes! Of course, we might not understand exactly what the teacher
Modesto City Schools. Secondary Math I. Module 1 Extra Help & Examples. Compiled by: Rubalcava, Christina
Modesto City Schools Secondary Math I Module 1 Extra Help & Examples Compiled by: Rubalcava, Christina 1.1 Ready, Set, Go! Ready Topic: Recognizing a solution to an equation. The solution to an equation
MathMammoth Grade 6. Supplemental Curriculum: Learning Goals/Performance Objectives:
MathMammoth Grade 6 Class Description: In sixth grade, students encounter the beginnings of algebra, learning about algebraic expressions, one-variable equations and inequalities, integers, and ratios.
Which explicit formula can be used to model the sequence?
1. A sequence is defined by the equations and. What is the fifth term in the sequence? 30 48 60 96 2. An arithmetic sequence is defined by the equations a1= 10 and an= an-1+ 6. What is third term of an=
9-1. Warm Up Lesson Presentation Lesson Quiz. Holt Geometry
9-1 9-1 Warm Up Lesson Presentation Lesson Quiz Warm Up Find the unknown side length in each right triangle with legs a and b and hypotenuse c. 1. a = 20, b = 21 2. b = 21, c = 35 3. a = 20, c = 52 c =
Lesson 8: Graphs and Graphing Linear Equations
In this chapter, we will begin looking at the relationships between two variables. Typically one variable is considered to be the input, and the other is called the output. The input is the value that
SPIRE MATHS Stimulating, Practical, Interesting, Relevant, Enjoyable Maths For All
Proportion TYPE: OBJECTIVE(S): DESCRIPTION: OVERVIEW: EQUIPMENT: Main Direct proportion using algebraic methods, relating algebraic solutions to graphical representations of the equations. 1 lets you investigating
College Prep Algebra II Summer Packet
Name: College Prep Algebra II Summer Packet This packet is an optional review which is highly recommended before entering CP Algebra II. It provides practice for necessary Algebra I topics. Remember: When
Unit 1: Module 1 Quantitative Reasoning. Unit 1: Module 2 Algebraic Models. Unit 2: Module 3 Functions and Models. Unit 3: Module 5 Linear Functions
Fall Unit : Module Quantitative Reasoning Unit : Module 2 Algebraic Models Unit 2: Module 3 and Models Unit 3: Module 5 Linear Unit 3: Module 6 Forms of Linear Equations Unit 5: Module Solving Systems
6-8 Math Adding and Subtracting Polynomials Lesson Objective: Subobjective 1: Subobjective 2:
6-8 Math Adding and Subtracting Polynomials Lesson Objective: The student will add and subtract polynomials. Subobjective 1: The student will add polynomials. Subobjective 2: The student will subtract
Gateway Regional School District VERTICAL ALIGNMENT OF MATHEMATICS STANDARDS Grades 3-6
NUMBER SENSE & OPERATIONS 3.N.1 Exhibit an understanding of the values of the digits in the base ten number system by reading, modeling, writing, comparing, and ordering whole numbers through 9,999. Our
Evaluating And Simplifying Algebraic Expressions
And Free PDF ebook Download: And Download or Read Online ebook evaluating and simplifying algebraic expressions in PDF Format From The Best User Guide Database and. Reporting Category and Operations. Topic.
EXAMPLE A {(1, 2), (2, 4), (3, 6), (4, 8)}
Name class date Understanding Relations and Functions A relation shows how one set of things is related to, or corresponds to, another set. For instance, the equation A 5 s shows how the area of a square
Writing Linear Functions
2- Writing Linear Functions Objectives Use slope-intercept form and point-slope form to write linear functions. Write linear functions to solve problems. Vocabulary Point-slope form Why learn this? When
The designer should construct a can with the height of 2 centimeters and the radius of centimeters in order to minimize cost.
1. A 2 liter oil can is being designed in the shape of a right circular cylinder. What dimensions, in terms of centimeters, should the designer use in order to use the least amount of material? Hint: Recall
Algebra 2 Semester 2 Final Exam Study Outline Semester 2 Final Exam Study Tips and Information
Algebra 2 Semester 2 Final Exam Study Outline 2013 Semester 2 Final Exam Study Tips and Information The final exam is CUMULATIVE and will include all concepts taught from Chapter 1 through Chapter 13.
Section 1.1 Definitions and Properties
Section 1.1 Definitions and Properties Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Abbreviate repeated addition using Exponents and Square
Algebra 2 Common Core Summer Skills Packet
Algebra 2 Common Core Summer Skills Packet Our Purpose: Completion of this packet over the summer before beginning Algebra 2 will be of great value to helping students successfully meet the academic challenges
Find the distance between each pair of points. Write your answer in simplest radical form.
Warm Up Simplify each radical. 1. 2. 3. Find the distance between each pair of points. Write your answer in simplest radical form. 4. C (1, 6) and D ( 2, 0) 5. E( 7, 1) and F( 1, 5) Objectives EQ: How
Algebra 1 Review. Properties of Real Numbers. Algebraic Expressions
Algebra 1 Review Properties of Real Numbers Algebraic Expressions Real Numbers Natural Numbers: 1, 2, 3, 4,.. Numbers used for counting Whole Numbers: 0, 1, 2, 3, 4,.. Natural Numbers and 0 Integers:,
Watkins Mill High School. Algebra 2. Math Challenge
Watkins Mill High School Algebra 2 Math Challenge "This packet will help you prepare for Algebra 2 next fall. It will be collected the first week of school. It will count as a grade in the first marking
6 3 Practice Binomial Radical Expressions Answers
6 3 Practice Binomial Answers Free PDF ebook Download: 6 3 Practice Binomial Answers Download or Read Online ebook 6 3 practice binomial radical expressions answers in PDF Format From The Best User Guide
MATH 021 UNIT 2 HOMEWORK ASSIGNMENTS
MATH 021 UNIT 2 HOMEWORK ASSIGNMENTS General Instructions You will notice that most of the homework assignments for a section have more than one part. Usually, the part (A) questions ask for explanations,
6 th Grade Math in Focus
6 th Grade Math in Focus Chapter 1: Positive Numbers the Number Line The Number Line Prime Factorization Common Factors Multiples Squares Square Roots Lesson 5 Cubes Cube Roots Represent whole numbers,
Chapter 3 Practice Test
1. Complete parts a c for each quadratic function. a. Find the y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex. b. Make a table of values that includes the vertex.