Arithmetic Series Can you add the first 100 counting numbers in less than 30 seconds? Begin How did he do it so quickly? It is said that he
|
|
- Pierce Thomas
- 5 years ago
- Views:
Transcription
1
2 Little Freddie is said to have done the work in his head and written only the answer on his slate in less than 30 seconds. Can you do it in less than 30 seconds? Arithmetic Series An arithmetic series is the sum of the first n terms of an arithmetic sequence. As the story goes, little Freddie Gauss was 10 years old (some sources claim 7) in the late 1700s. There were no calculators or pencils. He worked with chalk on a slate. The teacher reportedly gave the class the task of adding the first 100 counting numbers. He expected the class to add Of course, he expected this to take a class of third-graders some time.
3 Arithmetic Series Can you add the first 100 counting numbers in less than 30 seconds? Begin How did he do it so quickly? It is said that he recognized this pattern (101) = 5050 Little Freddie Gauss was Carl Friedrich Gauss, one of history s most celebrated minds. He is credited with advancements in astronomy, physics, electromagnetism, math, and other fields. He is also largely responsible for developing the method of the sum of least squares.
4 Arithmetic Series Try the same technique on this problem: Find the sum of the first 60 positive even integers. 30(122) = 3660 S n means the sum of the first n terms of a series. Find S 10 for (-33) = -165 Write the formula for the sum of the first n terms in an arithmetic series.
5 Arithmetic Series Evaluate There is a difference between and = 3(2 + 12) = 42. = 41. Find S 10 for a 1 = 4, a 10 = 31, so S 10 = 175
6 Arithmetic Series Find S 34 for (-3) + To use we need the 34 th term. a 34 = 12 + (34 1)(-5) = -153 S 34 = 17( ) = Replace a n in with a n = a 1 + (n 1)d and simplify to get a new formula. Apply this new formula to S 34 above. Often, one can use a n = a 1 + (n 1)d to get the n th term and apply couple problems,. In some cases, like the next is needed.
7 Arithmetic Series A display in a supermarket is built with one can on top, two cans in the next row, and one more can in each succeeding row. If there are 171 cans in the display, how many cans are in the bottom row? 342 = n 2 + n 0 = n 2 + n n = 18 or cans in the bottom row
8 Arithmetic Series A portion of the wall of a log playhouse consists of 6 logs, each one 8 inches longer than the previous log. One 14-ft log is cut to create the 6 logs. Find the length of all 6 cut pieces. 168 = 3(2a 1 + (6-1)8) where a 1 is the shortest log and lengths are in inches. 168 = 3(2a ) 168 = 6a = 6a 1 a 1 = 8. Lengths are 8, 16, 24, 32, 40, and 48
9 Arithmetic Series In training for a marathon, an athlete plans to begin by running 2 miles each day the first week, and add a half-mile per day each week. How many miles will the runner have logged at the end of the 10 th week? S 10 = 5(4 + 9(0.5)) S 10 = 42.5 Recognize that this is the sum of the one-day distance from each of the 10 weeks This needs to be multiplied by 7 to include all days of the week. 42.5(7) = mi.
10
11 Geometric Series Find the sum of This series is geometric. It is made up of the terms of a geometric sequence. Each term is a fourth of the previous term. There are only two missing terms, 50 and The sum is But what if 50 terms were missing instead of two terms? There must be an easier method, right? There is. It is somewhat like Gauss method with arithmetic series, but with geometric series, it s a little more complicated. It s demonstrated here with the example of grains of corn on the worksheet.
12 Geometric Series S 64 = S 64 = S 64 2S 64 = ( ) S 64 = S 64 = What does this equal? kernels Now try this formula from p.530:
13 Geometric Series Find the sum of using Find S 7 for
14 Geometric Series On the day she was born, and on each birthday thereafter, Jesse s parents deposited $200 in an account earning 7% annual interest. If there are no other adjustments except interest, how much is in the account after the deposit on her 18 th birthday? Birthday Value How many terms are there in 18 th 200 this geometric series? What 17 th 200(1.07) is r? What is g 1? 16 th 200(1.07) 2 1 st 200(1.07) 17 Birthday 200(1.07) 18
15 Geometric Series Years ago, my youngest son and I dropped a superball from a height of 5 in our kitchen and measured the bounce at 3 9. To what percent of the original height did the ball rebound? If with each bounce, it rebounds to 75% of the previous height, how far has the ball traveled when it strikes the ground the fourth time?
16 gives the sum of the 4 heights shown in the picture. 2( ) 5 gives the distance the ball travels Geometric Series If a ball is dropped from 5, and with each bounce it rebounds to 75% of the previous height, how far has the ball traveled when it strikes the ground the fourth time? Apply the formula for S n.
17 Review At noon, 1000 mg of medicine is administered to a patient. At the end of each hour, the concentration in the blood stream is 60% of the amount present at the beginning of the hour. What portion of medication remains in the blood stream at 4 pm? g 4 = 1000(.6) 4 = mg. If a second dose is administered at 2 pm, how much is in the blood stream immediately after the injection? 1360 mg
18 Review A student saving for college put away $100 on the first month, and increased that by a constant amount each month. On the 12 th month, she saved $925. What was the increase each month? 925 = d Recursive d = $75 Write a recursive and explicit formula for the situation. Explicit a n = (n 1) 75 Find the amount saved over the 12-month period. S 12 = 6( ) = $6150
Sequences A sequence is a function, where the domain is a set of consecutive positive integers beginning with 1.
1 CA-Fall 2011-Jordan College Algebra, 4 th edition, Beecher/Penna/Bittinger, Pearson/Addison Wesley, 2012 Chapter 8: Sequences, Series, and Combinatorics Section 8.1 Sequences and Series Sequences A sequence
More informationSequences and Series
UNIT 11 Sequences and Series An integrated circuit can hold millions of microscopic components called transistors. How many transistors can fit in a chip on the tip of your finger? Moore s law predicts
More informationFall IM I Exam B
Fall 2011-2012 IM I Exam B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following equations is linear? a. y = 2x - 3 c. 2. What is the
More informationVocabulary. Term Page Definition Clarifying Example. arithmetic sequence. explicit formula. finite sequence. geometric mean. geometric sequence
CHAPTER 2 Vocabulary The table contains important vocabulary terms from Chapter 2. As you work through the chapter, fill in the page number, definition, and a clarifying example. arithmetic Term Page Definition
More informationJUST THE MATHS UNIT NUMBER 2.1. SERIES 1 (Elementary progressions and series) A.J.Hobson
JUST THE MATHS UNIT NUMBER.1 SERIES 1 (Elementary progressions and series) by A.J.Hobson.1.1 Arithmetic progressions.1. Arithmetic series.1.3 Geometric progressions.1.4 Geometric series.1.5 More general
More information? Describe the nth term of the series and the value of S n. . Step 6 Will the original square ever be entirely shaded? Explain why or why not.
Lesson 13-2 Geometric Series Vocabulary geometric series BIG IDEA There are several ways to fi nd the sum of the successive terms of a fi nite geometric sequence Activity Step 1 Draw a large square on
More informationArithmetic Series. How can a long sequence of numbers be added quickly? Mean of All Terms
6.6 Arithmetic Series Dar Robinson was a famous stuntman. In 1979, Dar was paid $100 000 to jump off the CN Tower in Toronto. During the first second of the jump, Dar fell 4.9 m; during the next second,
More information11.4 Partial Sums of Arithmetic and Geometric Sequences
Section.4 Partial Sums of Arithmetic and Geometric Sequences 653 Integrated Review SEQUENCES AND SERIES Write the first five terms of each sequence, whose general term is given. 7. a n = n - 3 2. a n =
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA II. Student Name:
ALGEBRA II The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA II Thursday, January 24, 2019 1:15 to 4:15 p.m., only Large-Type Edition Student Name: School Name: The possession
More informationName Class Date. Geometric Sequences and Series Going Deeper. Writing Rules for a Geometric Sequence
Name Class Date 5-3 Geometric Sequences and Series Going Deeper Essential question: How can you write a rule for a geometric sequence and find the sum of a finite geometric series? In a geometric sequence,
More informationEquations and Inequalities in One Variable
Name Date lass Equations and Inequalities in One Variable. Which of the following is ( r ) 5 + + s evaluated for r = 8 and s =? A 3 B 50 58. Solve 3x 9= for x. A B 7 3. What is the best first step for
More informationUnit 2 Modeling with Exponential and Logarithmic Functions
Name: Period: Unit 2 Modeling with Exponential and Logarithmic Functions 1 2 Investigation : Exponential Growth & Decay Materials Needed: Graphing Calculator (to serve as a random number generator) To
More informationLesson 5: Modeling from a Sequence
Student Outcomes Students recognize when a table of values represents an arithmetic or geometric sequence. Patterns are present in tables of values. They choose and define the parameter values for a function
More informationReady for TAKS? Benchmark Tests Benchmark Pre-Test (7.1)(A)
Benchmark Pre-Test (7.)(A). Which is between and 5? A C 5 B D. Which statement is true? F G H 5. Which list of numbers is in order from greatest to least? A, 7,, B,,, 7 C,, 7, D 6, 5,, 6. Barney used the
More informationMathematics Practice Test 2
Mathematics Practice Test 2 Complete 50 question practice test The questions in the Mathematics section require you to solve mathematical problems. Most of the questions are presented as word problems.
More informationLesson 3.notebook May 17, Lesson 2 Problem Set Solutions
Lesson 2 Problem Set Solutions Student Outcomes Lesson 3: Analyzing a Verbal Description > Students make sense of a contextual situation that can be modeled with linear, quadratic, and exponential functions
More informationModeling with Exponential Functions
CHAPTER Modeling with Exponential Functions A nautilus is a sea creature that lives in a shell. The cross-section of a nautilus s shell, with its spiral of ever-smaller chambers, is a natural example of
More informationSequence Not Just Another Glittery Accessory
Lesson.1 Skills Practice Name Date Sequence Not Just Another Glittery Accessory Arithmetic and Geometric Sequences Vocabulary Choose the term from the box that best completes each statement. arithmetic
More informationWrite down the common difference. (1) Find the number of terms in the sequence. (3) Find the sum of the sequence. (2) (Total 6 marks)
Arithmetic Sequence and Series 1. Consider the arithmetic sequence 3, 9, 15,..., 1353. Write down the common difference. (1) Find the number of terms in the sequence. (c) Find the sum of the sequence.
More informationFree Pre-Algebra Lesson 59! page 1
Free Pre-Algebra Lesson 59! page 1 Lesson 59: Review for Final Exam Section VII. Proportions and Percents Comprehensive Practice Lessons 37-42 Lesson 37: Scale and Proportion Skill: Write ratios of sides
More informationMATH 081. Diagnostic Review Materials PART 2. Chapters 5 to 7 YOU WILL NOT BE GIVEN A DIAGNOSTIC TEST UNTIL THIS MATERIAL IS RETURNED.
MATH 08 Diagnostic Review Materials PART Chapters 5 to 7 YOU WILL NOT BE GIVEN A DIAGNOSTIC TEST UNTIL THIS MATERIAL IS RETURNED DO NOT WRITE IN THIS MATERIAL Revised Winter 0 PRACTICE TEST: Complete as
More informationUNIT #6 EXPONENTS, EXPONENTS, AND MORE EXPONENTS REVIEW QUESTIONS
Name: Date: UNIT #6 EXPONENTS, EXPONENTS, AND MORE EXPONENTS REVIEW QUESTIONS Part I Questions 1. The epression 9 5 10 can be simplified to (1) 6 () () 1 1 6 (4). Which of the following is equivalent to
More informationHonors Math 2 Unit 5 Exponential Functions. *Quiz* Common Logs Solving for Exponents Review and Practice
Honors Math 2 Unit 5 Exponential Functions Notes and Activities Name: Date: Pd: Unit Objectives: Objectives: N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of
More informationWillmar Public Schools Curriculum Map
Note: Problem Solving Algebra Prep is an elective credit. It is not a math credit at the high school as its intent is to help students prepare for Algebra by providing students with the opportunity to
More informationConvert the equation to the standard form for an ellipse by completing the square on x and y. 3) 16x y 2-32x - 150y = 0 3)
Math 370 Exam 5 Review Name Graph the ellipse and locate the foci. 1) x 6 + y = 1 1) foci: ( 15, 0) and (- 15, 0) Objective: (9.1) Graph Ellipses Not Centered at the Origin Graph the ellipse. ) (x + )
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA II. Wednesday, January 24, :15 to 4:15 p.m., only.
ALGEBRA II The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA II Wednesday, January 24, 2018 1:15 to 4:15 p.m., only Student Name: School Name: The possession or use of any
More informationloose-leaf paper Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Class: Date: Algebra 2 Trig Midterm Exam Review 2014 loose-leaf paper Do all work in a neat and organzied manner on Multiple Choice Identify the choice that best completes the statement or answers the
More informationVariable Expression: a collection of numbers, variables, and operations *Expressions DO NOT have signs. Ex: If x = 3 6x = Ex: if y = 9..
Algebra 1 Chapter 1 Note Packet Name Section 1.1: Variables in Algebra Variable: a letter that is used to represent one or more numbers Ex: x, y, t, etc. (*The most popular one is x ) Variable Values:
More informationSection 8 Topic 1 Comparing Linear, Quadratic, and Exponential Functions Part 1
Section 8: Summary of Functions Section 8 Topic 1 Comparing Linear, Quadratic, and Exponential Functions Part 1 Complete the table below to describe the characteristics of linear functions. Linear Functions
More informationNMC Sample Problems: Grade 7
NMC Sample Problems: Grade 7. If Amy runs 4 4 mph miles in every 8 4. mph hour, what is her unit speed per hour? mph. mph 6 mph. At a stationary store in a state, a dozen of pencils originally sold for
More informationSEVENTH GRADE MATH. Newspapers In Education
NOTE TO TEACHERS: Calculators may be used for questions unless indicated otherwise. Two formula sheets are provided on the last two pages for grades 6, 7, 8, 11 and the Grad. The learning standard addressed
More informationThe Quadratic Formula, the Discriminant, and Solving Quadratic Equations and Inequalities
CHAPTER The Quadratic Formula, the Discriminant, and Solving Quadratic Equations and Inequalities 009 Carnegie Learning, Inc. The Chinese invented rockets over 700 years ago. Since then rockets have been
More informationImportant: You must show your work on a separate sheet of paper. 1. There are 2 red balls and 5 green balls. Write the ratio of red to green balls.
Math Department Math Summer Packet: Incoming 8 th -Graders, 2018-2019 Student Name: Period: Math Teacher: Important: You must show your work on a separate sheet of paper. Remember: It is important to arrive
More informationS.3 Geometric Sequences and Series
68 section S S. Geometric In the previous section, we studied sequences where each term was obtained by adding a constant number to the previous term. In this section, we will take interest in sequences
More informationFUNCTIONS Families of Functions Common Core Standards F-LE.A.1 Distinguish between situations that can be
M Functions, Lesson 5, Families of Functions (r. 2018) FUNCTIONS Families of Functions Common Core Standards F-LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential
More informationMath 3 Proportion & Probability Part 2 Sequences, Patterns, Frequency Tables & Venn Diagrams
Math 3 Proportion & Probability Part 2 Sequences, Patterns, Frequency Tables & Venn Diagrams 1 MATH 2 REVIEW ARITHMETIC SEQUENCES In an Arithmetic Sequence the difference between one term and the next
More informationLESSON 3.1. Your Turn
MODULE Rational Numbers Are You Ready?. 9 7 = 9 7 =. 7 =. = =. 9 = 9 = or. = = = =. = = = 7. = = 7 = 7. 9 7 = 9 7 = 9 7 = 9. = =. = = =. = = = =. = = =. - - 9. + ( 7 - ) + + 9 7. + ( - ) + ( ) +. 9 + +
More informationDISTANCE, RATE, AND TIME 7.1.1
DISTANCE, RATE, AND TIME 7.1.1 Distance (d) equals the product of the rate of speed (r) and the time (t). This relationship is shown below in three forms: d = r!t!!!!!!!!!r = d t!!!!!!!!!t = d r It is
More informationMATH CIRCLE Session # 2, 9/29/2018
MATH CIRCLE Session # 2, 9/29/2018 SOLUTIONS 1. The n-queens Problem. You do NOT need to know how to play chess to work this problem! This is a classical problem; to look it up today on the internet would
More informationNote: This essay is extracted from a Lesson from the forthcoming textbook Mathematics: Building on Foundations.
The 19 th century mathematician Carl Friedrich Gauss (1777-1855) was known both for his mathematical trait of curiosity and his renowned ability to calculate. His ability to calculate can be illustrated
More informationMath 0240 Final Exam Review Questions 11 ( 9) 6(10 4)
11 ( 9) 6(10 4) 1. Simplif: 4 8 3 + 8 ( 7). Simplif: 34 3. Simplif ( 5 7) 3( ) 8 6 4. Simplif: (4 3 ) 9 5. Simplif: 4 7 3 6. Evaluate 3 4 5 when and 3 Write each of the values below in decimal or standard
More informationEureka Math. Grade, Module. Student _B Contains Sprint and Fluency, Exit Ticket, and Assessment Materials
A Story of Eureka Math Grade, Module Student _B Contains Sprint and Fluency,, and Assessment Materials Published by the non-profit Great Minds. Copyright 2015 Great Minds. All rights reserved. No part
More informationARITHMETIC PROGRESSIONS
ARITHMETIC PROGRESSIONS 93 ARITHMETIC PROGRESSIONS 5 5.1 Introduction You must have observed that in nature, many things follow a certain pattern, such as the petals of a sunflower, the holes of a honeycomb,
More informationAlgebra 1 Honors EOC Review #4 Calculator Portion
Algebra 1 Honors EOC Review #4 Calculator Portion 1. Given the data set : 9, 16, 35, 7, 1, 3, 11, 4, 6, 0, 8, 415, 30,, 18, 3, Find the following values : a) Mean b) Median c) Lower Quartile d) Upper Quartile
More informationB-10. If a ball is dropped from 160 cm and rebounds to 120 cm on the first bounce, how high will the ball be:
ALGEBRA 2 APPENDIX B HOMEWORK PROBLEMS Below is a list of the vocabulary used in this chapter. Make sure that you are familiar with all of these words and know what they mean. Refer to the glossary or
More informationGrade 6 - SBA Claim 1 Example Stems
Grade 6 - SBA Claim 1 Example Stems This document takes publicly available information about the Smarter Balanced Assessment (SBA) in Mathematics, namely the Claim 1 Item Specifications, and combines and
More informationContent Standard Geometric Series. What number 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
9-5 Content Standard Geometric Series A.SSE.4 Derive the formula for the sum of a geometric series (when the common ratio is not 1), and use the formula to solve problems. Objective To define geometric
More information{ }. The dots mean they continue in that pattern.
INTEGERS Integers are positive and negative whole numbers, that is they are;... 3, 2, 1,0,1,2,3... { }. The dots mean they continue in that pattern. Like all number sets, integers were invented to describe
More informationALGEBRA 1 SUMMER ASSIGNMENT
Pablo Muñoz Superintendent of Schools Amira Presto Mathematics Instructional Chair Summer Math Assignment: The Passaic High School Mathematics Department requests all students to complete the summer assignment.
More informationName: Class: Date: Describe a pattern in each sequence. What are the next two terms of each sequence?
Class: Date: Unit 3 Practice Test Describe a pattern in each sequence. What are the next two terms of each sequence? 1. 24, 22, 20, 18,... Tell whether the sequence is arithmetic. If it is, what is the
More information7) 24% of the lawyers in a firm are female. If there are 150 lawyers altogether, how many lawyers are female?
Math 110 Sample Final Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the perimeter (or circumference) and area of the figure. 1) Give the exact
More informationIntegrated Math 1 - Chapter 5 Homework Scoring Guide
Integrated Math 1 - Chapter 5 Homework Scoring Guide Integrated Math 1 - Chapter 5 Homework Scoring Guide Lesson Lesson Title Homework Problems Score 5.1.1 How does the pattern grow? 5-6 to 5-15 5.1.2
More informationMath 80a exam 1 review (Part I)
Math 80a exam 1 review (Part I) This is a preview of the test. Any questions from the homework are possible on the exam. i) Please practice every problem on this review two or three times, ii) Find problems
More informationTransMath Third Edition Correlated to the South Carolina High School Credential Courses: Essentials of Math I, II, and III
TransMath Third Edition Correlated to the South Carolina High School Credential Courses: Essentials of Math I, II, and III TransMath correlated to the South Carolina High School Credential Courses: Essentials
More informationMath 0240 Final Exam Review Questions 11 ( 9) 6(10 4)
Math 040 Final Eam Review Questions 11 ( 9) 6(10 4) 1. Simplif: 4 8 3 + 8 ( 7). Simplif: 34 3. Simplif ( 5 7) 3( ) 8 6 4. Simplif: (4 3 ) 9 5. Simplif: 6. Evaluate 4 7 3 3 4 5 when and 3 Write each of
More informationAlgebra 1 Semester 2 Final Exam Part 2
Algebra 1 Semester 2 Final Eam Part 2 Don t forget to study the first portion of the review and your recent warm-ups. 1. Michael s teacher gave him an assignment: Use an initial term of 5 and a generator
More informationUnit 3: Linear and Exponential Functions
Unit 3: Linear and Exponential Functions In Unit 3, students will learn function notation and develop the concepts of domain and range. They will discover that functions can be combined in ways similar
More information8. 2 3x 1 = 16 is an example of a(n). SOLUTION: An equation in which the variable occurs as exponent is an exponential equation.
Choose the word or term that best completes each sentence. 1. 7xy 4 is an example of a(n). A product of a number and variables is a monomial. 2. The of 95,234 is 10 5. 95,234 is almost 100,000 or 10 5,
More informationChapter 3. Q1. Show that x = 2, if = 1 is a solution of the system of simultaneous linear equations.
Chapter 3 Q1. Show that x = 2, if = 1 is a solution of the system of simultaneous linear equations. Q2. Show that x = 2, Y = 1 is not a solution of the system of simultaneous linear equations. Q3. Show
More informationUnit 6: Exponential and Logarithmic Functions
Unit 6: Exponential and Logarithmic Functions DAY TOPIC ASSIGNMENT 1 Exponential Functions p. 55-56 2 Applications p. 57-58 3 Derivatives of Exponential Functions 4 Derivatives of Exponential Functions
More informationSERIES
SERIES.... This chapter revisits sequences arithmetic then geometric to see how these ideas can be extended, and how they occur in other contexts. A sequence is a list of ordered numbers, whereas a series
More informationMath Final Exam PRACTICE BOOKLET
Math Final Exam PRACTICE BOOKLET KEEP CALM AND SHOW YOUR WORK! Name: Period: EXPONENT REVIEW: Multiple Choice: 1. What is the value of 12 0? A 0 B 12 C 1 D neither 5. Simplify: 18r5 t 6 30r 6 t 3 A 3t3
More informationFirst Name: Last Name:
5 Entering 6 th Grade Summer Math Packet First Name: Last Name: 6 th Grade Teacher: I have checked the work completed: Parent Signature 1. Find the products. This page should be completed in 3 minutes
More informationComplete Week 18 Package
Complete Week 18 Package Jeanette Stein Table of Contents Unit 4 Pacing Chart -------------------------------------------------------------------------------------------- 1 Day 86 Bellringer --------------------------------------------------------------------------------------------
More informationFind an expression, in terms of n, for the number of sticks required to make a similar arrangement of n squares in the nth row.
8. Ann has some sticks that are all of the same length. She arranges them in squares and has made the following 3 rows of patterns: Row 1 Row Row 3 She notices that 4 sticks are required to make the single
More informationALGEBRA I SEMESTER EXAMS PRACTICE MATERIALS SEMESTER Use the diagram below. 9.3 cm. A = (9.3 cm) (6.2 cm) = cm 2. 6.
1. Use the diagram below. 9.3 cm A = (9.3 cm) (6.2 cm) = 57.66 cm 2 6.2 cm A rectangle s sides are measured to be 6.2 cm and 9.3 cm. What is the rectangle s area rounded to the correct number of significant
More informationHonors Physics. Summer Assignments Teacher Information. Summer Assignment Goals
Honors Physics Summer Assignments 2017 Teacher Information Mr. Michael Wichart (Rm. 109) wichart.m@woodstown.org Summer Assignment Goals The main goals of summer assignment in physics are to provide a
More informationLesson 26: Problem Set Sample Solutions
Problem Set Sample Solutions Problems and 2 provide students with more practice converting arithmetic and geometric sequences between explicit and recursive forms. Fluency with geometric sequences is required
More informationMATH 153 FIRST MIDTERM EXAM
NAME: Solutions MATH 53 FIRST MIDTERM EXAM October 2, 2005. Do not open this exam until you are told to begin. 2. This exam has pages including this cover. There are 8 questions. 3. Write your name on
More informationMathematics Background
For a more robust teacher experience, please visit Teacher Place at mathdashboard.com/cmp3 Patterns of Change Through their work in Variables and Patterns, your students will learn that a variable is a
More information1. Consider the following graphs and choose the correct name of each function.
Name Date Summary of Functions Comparing Linear, Quadratic, and Exponential Functions - Part 1 Independent Practice 1. Consider the following graphs and choose the correct name of each function. Part A:
More informationSECTION 9.2: ARITHMETIC SEQUENCES and PARTIAL SUMS
(Chapter 9: Discrete Math) 9.11 SECTION 9.2: ARITHMETIC SEQUENCES and PARTIAL SUMS PART A: WHAT IS AN ARITHMETIC SEQUENCE? The following appears to be an example of an arithmetic (stress on the me ) sequence:
More informationAlpha Sequences and Series FAMAT State Convention 2017
Alpha Sequences and Series FAMAT State Convention 017 For all questions, E NOTA means none of the above answers is correct. 1. We say that a number is arithmetically sequenced if the digits, in order,
More informationMathematics (Project Maths Phase 2)
2012. S234S Coimisiún na Scrúduithe Stáit State Examinations Commission Junior Certificate Examination 2012 Sample Paper Mathematics (Project Maths Phase 2) Paper 1 Higher Level Time: 2 hours, 30 minutes
More informationName: Linear and Exponential Functions 4.1H
TE-18 Name: Linear and Exponential Functions 4.1H Ready, Set, Go! Ready Topic: Recognizing arithmetic and geometric sequences Predict the next 2 terms in the sequence. State whether the sequence is arithmetic,
More informationArithmetic Testing OnLine (ATOL) SM Assessment Framework
Arithmetic Testing OnLine (ATOL) SM Assessment Framework Overview Assessment Objectives (AOs) are used to describe the arithmetic knowledge and skills that should be mastered by the end of each year in
More informationAlgebra I EOC Review (Part 2)
1. Let x = total miles the car can travel Answer: x 22 = 18 or x 18 = 22 2. A = 1 2 ah 1 2 bh A = 1 h(a b) 2 2A = h(a b) 2A = h a b Note that when solving for a variable that appears more than once, consider
More informationALGEBRA I EOC REVIEW PACKET Name 16 8, 12
Objective 1.01 ALGEBRA I EOC REVIEW PACKET Name 1. Circle which number is irrational? 49,. Which statement is false? A. a a a = bc b c B. 6 = C. ( n) = n D. ( c d) = c d. Subtract ( + 4) ( 4 + 6). 4. Simplify
More informationAdmission-Tests GMAT GMAT.
Admission-Tests GMAT GMAT https://killexams.com/pass4sure/exam-detail/gmat Question: 1491 For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value
More informationTEACHER GUIDE VOLUME 1. Larry Bradsby. Chapter 3, Objective 2
TEACHER GUIDE VOLUME Larry Bradsby Chapter 3, Objective 2 Solving Linear Equations In this chapter, students begin to solve basic linear equations using addition, subtraction, multiplication, division,
More information{ }. The dots mean they continue in that pattern to both
INTEGERS Integers are positive and negative whole numbers, that is they are;... 3, 2, 1,0,1,2,3... { }. The dots mean they continue in that pattern to both positive and negative infinity. Before starting
More informationMath Final Examination Fall 2013
Department of Mathematics The City College of New York Math 18000 Final Examination Fall 2013 Instructions: Please Read Carefully. You must show all your work to receive credit, and explain clearly and
More informationRead 4:30:12 as 4:30 and 12 seconds, or 30 minutes and 12 seconds after 4.
Name Units of Time Essential Question How can you use models to compare units of time? Lesson. Measurement and Data.MD.A. Also.MD.A. MATHEMATICAL PRACTICES MP, MP5, MP7 Unlock the Problem The analog clock
More information1.1 The Language of Algebra 1. What does the term variable mean?
Advanced Algebra Chapter 1 - Note Taking Guidelines Complete each Now try problem after studying the corresponding example from the reading 1.1 The Language of Algebra 1. What does the term variable mean?
More informationChapter 8: Recursion. March 10, 2008
Chapter 8: Recursion March 10, 2008 Outline 1 8.1 Recursively Defined Sequences 2 8.2 Solving Recurrence Relations by Iteration 3 8.4 General Recursive Definitions Recursively Defined Sequences As mentioned
More informationPart 1 will be selected response. Each selected response item will have 3 or 4 choices.
Items on this review are grouped by Unit and Topic. A calculator is permitted on the Algebra 1 A Semester Exam. The Algebra 1 A Semester Exam will consist of two parts. Part 1 will be selected response.
More informationF.LE.A.2: Sequences 1a
F.LE.A.2: Sequences 1a 1 The diagrams below represent the first three terms of a sequence. 4 A theater has 35 seats in the first row. Each row has four more seats than the row before it. Which expression
More information1617 GSE Alg. I Reasoning w/linear Equalities & Inequalities Touchstone
High School HS Algebra 1 1617 GSE Alg. I Reasoning w/linear Equalities & Inequalities Touchstone 1. A number of apples were shared evenly among 4 students. Each student was also given 2 pears. Each student
More informationWinter Break Packet Math I. Standardized Test Practice. is exponential has an absolute minimum
1.Which characteristics best describe the graph? Winter Break Packet Math I Standardized Test Practice is a function has an absolute minimum is a function is linear has an absolute minimum is a function
More informationPrinciples of Math 12 - Geometric Series Practice Exam 1
Principles of Math 2 - Geometric Series Practice Exam www.math2.com Principles of Math 2 - Geometric Series Practice Exam Use this sheet to record your answers. 0. 8. 26. NR ). 9. 27. 2. 2. 20. 28. 3.
More information0118AII Common Core State Standards
0118AII Common Core State Standards 1 The operator of the local mall wants to find out how many of the mall's employees make purchases in the food court when they are working. She hopes to use these data
More informationUNIT 2: REASONING WITH LINEAR EQUATIONS AND INEQUALITIES. Solving Equations and Inequalities in One Variable
UNIT 2: REASONING WITH LINEAR EQUATIONS AND INEQUALITIES This unit investigates linear equations and inequalities. Students create linear equations and inequalities and use them to solve problems. They
More informationExamples of Finite Sequences (finite terms) Examples of Infinite Sequences (infinite terms)
Math 120 Intermediate Algebra Sec 10.1: Sequences Defn A sequence is a function whose domain is the set of positive integers. The formula for the nth term of a sequence is called the general term. Examples
More informationMCR3U Unit 7 Lesson Notes
7.1 Arithmetic Sequences Sequence: An ordered list of numbers identified by a pattern or rule that may stop at some number or continue indefinitely. Ex. 1, 2, 4, 8,... Ex. 3, 7, 11, 15 Term (of a sequence):
More informationEvery subset of {1, 2,...,n 1} can be extended to a subset of {1, 2, 3,...,n} by either adding or not adding the element n.
11 Recurrences A recurrence equation or recurrence counts things using recursion. 11.1 Recurrence Equations We start with an example. Example 11.1. Find a recurrence for S(n), the number of subsets of
More informationWheels Radius / Distance Traveled
Mechanics Teacher Note to the teacher On these pages, students will learn about the relationships between wheel radius, diameter, circumference, revolutions and distance. Students will use formulas relating
More informationName Period Date DRAFT
Name Period Date Equations and Inequalities Student Packet 4: Inequalities EQ4.1 EQ4.2 EQ4.3 Linear Inequalities in One Variable Add, subtract, multiply, and divide integers. Write expressions, equations,
More informationUnit 3: Linear and Exponential Functions
Unit 3: Linear and Exponential Functions In Unit 3, students will learn function notation and develop the concepts of domain and range. They will discover that functions can be combined in ways similar
More informationLesson 1. Problem 1. Solution. Problem 2. Solution. Problem 3
Lesson 1 Tyler reads of a book on Monday, of it on Tuesday, of it on Wednesday, and of the remainder on Thursday. If he still has 14 pages left to read on Friday, how many pages are there in the book?
More informationALGEBRA 1. Workbook Common Core Standards Edition. Published by TOPICAL REVIEW BOOK COMPANY. P. O. Box 328 Onsted, MI
Workbook Common Core Standards Edition Published by TOPICAL REVIEW BOOK COMPANY P. O. Box 328 Onsted, MI 49265-0328 www.topicalrbc.com EXAM PAGE Reference Sheet...i January 2017...1 June 2017...11 August
More information