Determine whether the sequence is arithmetic, geometric, or neither. 18, 11, 4,

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Determine whether the sequence is arithmetic, geometric, or neither. 18, 11, 4,"

Transcription

1 Over Lesson 10 1 Determine whether the sequence is arithmetic, geometric, or neither. 18, 11, 4, A. arithmetic B. geometric C. neither

2 Over Lesson 10 1 Determine whether the sequence is arithmetic, geometric, or neither. 18, 11, 4, A. arithmetic B. geometric C. neither

3 Over Lesson 10 1 Determine whether the sequence is arithmetic, geometric, or neither. 1, 2, 4, 8, A. arithmetic B. geometric C. neither

4 Over Lesson 10 1 Determine whether the sequence is arithmetic, geometric, or neither. 1, 2, 4, 8, A. arithmetic B. geometric C. neither

5 Over Lesson 10 1 Determine whether the sequence is arithmetic, geometric, or neither. 5, 6, 8, 11, A. arithmetic B. geometric C. neither

6 Over Lesson 10 1 Determine whether the sequence is arithmetic, geometric, or neither. 5, 6, 8, 11, A. arithmetic B. geometric C. neither

7 Over Lesson 10 1 Find the next three terms of the sequence. 25, 50, 75, 100, A. 125, 150, 175 B. 125, 250, 500 C. 125, 145, 175 D. 150, 200, 225

8 Over Lesson 10 1 Find the next three terms of the sequence. 25, 50, 75, 100, A. 125, 150, 175 B. 125, 250, 500 C. 125, 145, 175 D. 150, 200, 225

9 Over Lesson 10 1 Find the next three terms of the sequence. 1, 6, 36, 216, A. 236, 266, 336 B. 306, 336, 416 C. 1296, 7776, 46,656 D. 1296, 3888, 11,664

10 Over Lesson 10 1 Find the next three terms of the sequence. 1, 6, 36, 216, A. 236, 266, 336 B. 306, 336, 416 C. 1296, 7776, 46,656 D. 1296, 3888, 11,664

11 Over Lesson 10 1 Find the first term and the ninth term of the arithmetic sequence., 4.5, 7, 9.5, 12, A. 2; 14.5 B. 2.5; 22 C. 2; 22 D. 2.5; 14.5

12 Over Lesson 10 1 Find the first term and the ninth term of the arithmetic sequence., 4.5, 7, 9.5, 12, A. 2; 14.5 B. 2.5; 22 C. 2; 22 D. 2.5; 14.5

13

14 arithmetic means series arithmetic series partial sum sigma notation

15

16 Find the nth Term Find the 20th term of the arithmetic sequence 3, 10, 17, 24,. Step 1 Find the common difference = = = 7 So, d = 7.

17 Find the nth Term Step 2 Find the 20th term. a n = a 1 + (n 1)d nth term of an arithmetic sequence a 20 = 3 + (20 1)7 a 1 = 3, d = 7, n = 20 = or 136 Simplify. Answer: The 20th term of the sequence is 136.

18 Find the 17th term of the arithmetic sequence 6, 14, 22, 30,. A. 134 B. 140 C. 146 D. 152

19 Write Equations for the nth Term A. Write an equation for the nth term of the arithmetic sequence below. 8, 6, 4, d = 6 ( 8) or 2; 8 is the first term. a n = a 1 + (n 1)d Answer: a n = 2n 10 nth term of an arithmetic sequence a n = 8 + (n 1)2 a 1 = 8 and d = 2 a n = 8 + (2n 2) a n = 2n 10 Distributive Property Simplify.

20 Write Equations for the nth Term B. Write an equation for the nth term of the arithmetic sequence below. a 6 = 11, d = 11 First, find a 1. a n = a 1 + (n 1)d nth term of an arithmetic sequence 11 = a 1 + (6 1)( 11) a 6 = 11, n = 6, and d = = a 1 55 Multiply. 66 = a 1 Add 55 to each side.

21 Then write the equation. a n = a 1 + (n 1)d Write Equations for the nth Term nth term of an arithmetic sequence a n = 66 + (n 1)( 11) a 1 = 66, and d = 11 a n = 66 + ( 11n + 11) a n = 11n + 77 Distributive Property Simplify. Answer: a n = 11n + 77

22 A. Write an equation for the nth term of the arithmetic sequence below. 12, 3, 6, A. a n = 9n 21 B. a n = 9n 21 C. a n = 9n + 21 D. a n = 9n + 21

23 B. Write an equation for the nth term of the arithmetic sequence below. a 4 = 45, d = 5 A. a n = 5n + 25 B. a n = 5n 20 C. a n = 5n + 40 D. a n = 5n + 30

24 Find Arithmetic Means Find the arithmetic means in the sequence 21,,,, 45,. Step 1 Step 2 Find d. a n = a 1 + (n 1)d Since there are three terms between the first and last terms given, there are or 5 total terms, so n = 5. Formula for the nth term 45 = 21 + (5 1)d n = 5, a 1 = 21, a 5 = = d Distributive Property 24 = 4d Subtract 21 from each side. 6 = d Divide each side by 4.

25 Find Arithmetic Means Step 3 Use the value of d to find the three arithmetic means Answer:

26 Find the three arithmetic means between 13 and 25. A. 16, 19, 22 B. 17, 21, 25 C. 13, 17, 21 D. 15, 17, 19

27

28 Use the Sum Formulas Find the sum Step 1 a 1 = 8, a n = 80, and d = 12 8 or 4. We need to find n before we can use one of the formulas. a n = a 1 + (n 1)d nth term of an arithmetic sequence 80 = 8 + (n 1)(4) a n = 80, a 1 = 8, and d = 4 80 = 4n + 4 Simplify. 19 = n Solve for n.

29 Use the Sum Formulas Step 2 Use either formula to find S n. Sum formula a 1 = 8, n = 19, d = 4 Simplify. Answer: 836

30 Find the sum A. 318 B. 327 C. 340 D. 365

31 Find the First Three Terms Find the first three terms of an arithmetic series in which a 1 = 14, a n = 29, and S n = 129. Step 1 Since you know a 1, a n, and S n, use to find n. Sum formula S n = 129, a 1 = 14, a n = 29 Simplify. Divide each side by 43.

32 Step 2 Find d. Find the First Three Terms a n = a 1 + (n 1)d nth term of an arithmetic sequence 29 = 14 + (6 1)d a n = 29, a 1 = 14, n = 6 15 = 5d Subtract 14 from each side. 3 = d Divide each side by 5.

33 Find the First Three Terms Step 3 Use d to determine a 2 and a 3. a 2 = or 17 a 3 = or 20 Answer: The first three terms are 14, 17, and 20.

34 Find the first three terms of an arithmetic series in which a 1 = 11, a n = 31, and S n = 105. A. 16, 21, 26 B. 11, 16, 21 C. 11, 17, 23, 30 D. 17, 23, 30, 36

35

36 Use Sigma Notation Evaluate. A. 23 B. 70 C. 98 D. 112 Read the Test Item You need to find the sum of the series. Find a 1, a n, and n.

37 Use Sigma Notation Method 1 Since the sum is an arithmetic series, use the formula. There are 8 terms. a 1 = 2(3) + 1 or 7, and a 8 = 2(10) + 1 or 21

38 Solve the Test Item Method 2 Use Sigma Notation Find the terms by replacing k with 3, 4,..., 10. Then add.

39 Evaluate. A. 85 B. 95 C. 108 D. 133

40

AFM Ch.12 - Practice Test

AFM Ch.12 - Practice Test AFM Ch.2 - Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question.. Form a sequence that has two arithmetic means between 3 and 89. a. 3, 33, 43, 89

More information

Some sequences have a fixed length and have a last term, while others go on forever.

Some sequences have a fixed length and have a last term, while others go on forever. Sequences and series Sequences A sequence is a list of numbers (actually, they don t have to be numbers). Here is a sequence: 1, 4, 9, 16 The order makes a difference, so 16, 9, 4, 1 is a different sequence.

More information

#1-12: Write the first 4 terms of the sequence. (Assume n begins with 1.)

#1-12: Write the first 4 terms of the sequence. (Assume n begins with 1.) Section 9.1: Sequences #1-12: Write the first 4 terms of the sequence. (Assume n begins with 1.) 1) a n = 3n a 1 = 3*1 = 3 a 2 = 3*2 = 6 a 3 = 3*3 = 9 a 4 = 3*4 = 12 3) a n = 3n 5 Answer: 3,6,9,12 a 1

More information

4/1/2017. PS. Sequences and Series FROM 9.2 AND 9.3 IN THE BOOK AS WELL AS FROM OTHER SOURCES. TODAY IS NATIONAL MANATEE APPRECIATION DAY

4/1/2017. PS. Sequences and Series FROM 9.2 AND 9.3 IN THE BOOK AS WELL AS FROM OTHER SOURCES. TODAY IS NATIONAL MANATEE APPRECIATION DAY PS. Sequences and Series FROM 9.2 AND 9.3 IN THE BOOK AS WELL AS FROM OTHER SOURCES. TODAY IS NATIONAL MANATEE APPRECIATION DAY 1 Oh the things you should learn How to recognize and write arithmetic sequences

More information

Arithmetic Progression

Arithmetic Progression Worksheet 3.6 Arithmetic and Geometric Progressions Section 1 Arithmetic Progression An arithmetic progression is a list of numbers where the difference between successive numbers is constant. The terms

More information

10.2 Series and Convergence

10.2 Series and Convergence 10.2 Series and Convergence Write sums using sigma notation Find the partial sums of series and determine convergence or divergence of infinite series Find the N th partial sums of geometric series and

More information

College Algebra. Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1

College Algebra. Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1 College Algebra Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1 Course Description This course provides

More information

Major Work of the Grade

Major Work of the Grade Counting and Cardinality Know number names and the count sequence. Count to tell the number of objects. Compare numbers. Kindergarten Describe and compare measurable attributes. Classify objects and count

More information

IB Maths SL Sequence and Series Practice Problems Mr. W Name

IB Maths SL Sequence and Series Practice Problems Mr. W Name IB Maths SL Sequence and Series Practice Problems Mr. W Name Remember to show all necessary reasoning! Separate paper is probably best. 3b 3d is optional! 1. In an arithmetic sequence, u 1 = and u 3 =

More information

Thinkwell s Homeschool Algebra 2 Course Lesson Plan: 34 weeks

Thinkwell s Homeschool Algebra 2 Course Lesson Plan: 34 weeks Thinkwell s Homeschool Algebra 2 Course Lesson Plan: 34 weeks Welcome to Thinkwell s Homeschool Algebra 2! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson

More information

Math 1050 Khan Academy Extra Credit Algebra Assignment

Math 1050 Khan Academy Extra Credit Algebra Assignment Math 1050 Khan Academy Extra Credit Algebra Assignment KhanAcademy.org offers over 2,700 instructional videos, including hundreds of videos teaching algebra concepts, and corresponding problem sets. In

More information

Math 115 Spring 2011 Written Homework 5 Solutions

Math 115 Spring 2011 Written Homework 5 Solutions . Evaluate each series. a) 4 7 0... 55 Math 5 Spring 0 Written Homework 5 Solutions Solution: We note that the associated sequence, 4, 7, 0,..., 55 appears to be an arithmetic sequence. If the sequence

More information

9.2 Summation Notation

9.2 Summation Notation 9. Summation Notation 66 9. Summation Notation In the previous section, we introduced sequences and now we shall present notation and theorems concerning the sum of terms of a sequence. We begin with a

More information

Finding Rates and the Geometric Mean

Finding Rates and the Geometric Mean Finding Rates and the Geometric Mean So far, most of the situations we ve covered have assumed a known interest rate. If you save a certain amount of money and it earns a fixed interest rate for a period

More information

Algebra I Credit Recovery

Algebra I Credit Recovery Algebra I Credit Recovery COURSE DESCRIPTION: The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics,

More information

Arithmetic Sequence. Formula for the nth Term of an Arithmetic Sequence

Arithmetic Sequence. Formula for the nth Term of an Arithmetic Sequence 638 (1-1) Chapter 1 Sequences and Series In this section 1.3 ARITHMETIC SEQUENCES AND SERIES We defined sequences and series in Sections 1.1 and 1.. In this section you will study a special type of sequence

More information

1, 1 2, 1 3, 1 4,... 2 nd term. 1 st term

1, 1 2, 1 3, 1 4,... 2 nd term. 1 st term 1 Sequences 11 Overview A (numerical) sequence is a list of real numbers in which each entry is a function of its position in the list The entries in the list are called terms For example, 1, 1, 1 3, 1

More information

Overview. Essential Questions. Precalculus, Quarter 4, Unit 4.5 Build Arithmetic and Geometric Sequences and Series

Overview. Essential Questions. Precalculus, Quarter 4, Unit 4.5 Build Arithmetic and Geometric Sequences and Series Sequences and Series Overview Number of instruction days: 4 6 (1 day = 53 minutes) Content to Be Learned Write arithmetic and geometric sequences both recursively and with an explicit formula, use them

More information

Precalculus REVERSE CORRELATION. Content Expectations for. Precalculus. Michigan CONTENT EXPECTATIONS FOR PRECALCULUS CHAPTER/LESSON TITLES

Precalculus REVERSE CORRELATION. Content Expectations for. Precalculus. Michigan CONTENT EXPECTATIONS FOR PRECALCULUS CHAPTER/LESSON TITLES Content Expectations for Precalculus Michigan Precalculus 2011 REVERSE CORRELATION CHAPTER/LESSON TITLES Chapter 0 Preparing for Precalculus 0-1 Sets There are no state-mandated Precalculus 0-2 Operations

More information

Geometric Series and Annuities

Geometric Series and Annuities Geometric Series and Annuities Our goal here is to calculate annuities. For example, how much money do you need to have saved for retirement so that you can withdraw a fixed amount of money each year for

More information

Core Maths C1. Revision Notes

Core Maths C1. Revision Notes Core Maths C Revision Notes November 0 Core Maths C Algebra... Indices... Rules of indices... Surds... 4 Simplifying surds... 4 Rationalising the denominator... 4 Quadratic functions... 4 Completing the

More information

Maths Workshop for Parents 2. Fractions and Algebra

Maths Workshop for Parents 2. Fractions and Algebra Maths Workshop for Parents 2 Fractions and Algebra What is a fraction? A fraction is a part of a whole. There are two numbers to every fraction: 2 7 Numerator Denominator 2 7 This is a proper (or common)

More information

Step 1: Set the equation equal to zero if the function lacks. Step 2: Subtract the constant term from both sides:

Step 1: Set the equation equal to zero if the function lacks. Step 2: Subtract the constant term from both sides: In most situations the quadratic equations such as: x 2 + 8x + 5, can be solved (factored) through the quadratic formula if factoring it out seems too hard. However, some of these problems may be solved

More information

Since the ratios are constant, the sequence is geometric. The common ratio is.

Since the ratios are constant, the sequence is geometric. The common ratio is. Determine whether each sequence is arithmetic, geometric, or neither. Explain. 1. 200, 40, 8, Since the ratios are constant, the sequence is geometric. The common ratio is. 2. 2, 4, 16, The ratios are

More information

Sometimes it is easier to leave a number written as an exponent. For example, it is much easier to write

Sometimes it is easier to leave a number written as an exponent. For example, it is much easier to write 4.0 Exponent Property Review First let s start with a review of what exponents are. Recall that 3 means taking four 3 s and multiplying them together. So we know that 3 3 3 3 381. You might also recall

More information

Appendix F: Mathematical Induction

Appendix F: Mathematical Induction Appendix F: Mathematical Induction Introduction In this appendix, you will study a form of mathematical proof called mathematical induction. To see the logical need for mathematical induction, take another

More information

CE 314 Engineering Economy. Interest Formulas

CE 314 Engineering Economy. Interest Formulas METHODS OF COMPUTING INTEREST CE 314 Engineering Economy Interest Formulas 1) SIMPLE INTEREST - Interest is computed using the principal only. Only applicable to bonds and savings accounts. 2) COMPOUND

More information

Factor Diamond Practice Problems

Factor Diamond Practice Problems Factor Diamond Practice Problems 1. x 2 + 5x + 6 2. x 2 +7x + 12 3. x 2 + 9x + 8 4. x 2 + 9x +14 5. 2x 2 7x 4 6. 3x 2 x 4 7. 5x 2 + x -18 8. 2y 2 x 1 9. 6-13x + 6x 2 10. 15 + x -2x 2 Factor Diamond Practice

More information

1.2. Successive Differences

1.2. Successive Differences 1. An Application of Inductive Reasoning: Number Patterns In the previous section we introduced inductive reasoning, and we showed how it can be applied in predicting what comes next in a list of numbers

More information

Accuplacer Arithmetic Study Guide

Accuplacer Arithmetic Study Guide Testing Center Student Success Center Accuplacer Arithmetic Study Guide I. Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole

More information

MEP Y9 Practice Book A

MEP Y9 Practice Book A 1 Base Arithmetic 1.1 Binary Numbers We normally work with numbers in base 10. In this section we consider numbers in base 2, often called binary numbers. In base 10 we use the digits 0, 1, 2, 3, 4, 5,

More information

Math Common Core Sampler Test

Math Common Core Sampler Test High School Algebra Core Curriculum Math Test Math Common Core Sampler Test Our High School Algebra sampler covers the twenty most common questions that we see targeted for this level. For complete tests

More information

GEOMETRIC SEQUENCES AND SERIES

GEOMETRIC SEQUENCES AND SERIES 4.4 Geometric Sequences and Series (4 7) 757 of a novel and every day thereafter increase their daily reading by two pages. If his students follow this suggestion, then how many pages will they read during

More information

More on annuities with payments in arithmetic progression and yield rates for annuities

More on annuities with payments in arithmetic progression and yield rates for annuities More on annuities with payments in arithmetic progression and yield rates for annuities 1 Annuities-due with payments in arithmetic progression 2 Yield rate examples involving annuities More on annuities

More information

Free Pre-Algebra Lesson 55! page 1

Free Pre-Algebra Lesson 55! page 1 Free Pre-Algebra Lesson 55! page 1 Lesson 55 Perimeter Problems with Related Variables Take your skill at word problems to a new level in this section. All the problems are the same type, so that you can

More information

GCSE MATHEMATICS. 43602H Unit 2: Number and Algebra (Higher) Report on the Examination. Specification 4360 November 2014. Version: 1.

GCSE MATHEMATICS. 43602H Unit 2: Number and Algebra (Higher) Report on the Examination. Specification 4360 November 2014. Version: 1. GCSE MATHEMATICS 43602H Unit 2: Number and Algebra (Higher) Report on the Examination Specification 4360 November 2014 Version: 1.0 Further copies of this Report are available from aqa.org.uk Copyright

More information

LESSON 4 Missing Numbers in Multiplication Missing Numbers in Division LESSON 5 Order of Operations, Part 1 LESSON 6 Fractional Parts LESSON 7 Lines,

LESSON 4 Missing Numbers in Multiplication Missing Numbers in Division LESSON 5 Order of Operations, Part 1 LESSON 6 Fractional Parts LESSON 7 Lines, Saxon Math 7/6 Class Description: Saxon mathematics is based on the principle of developing math skills incrementally and reviewing past skills daily. It also incorporates regular and cumulative assessments.

More information

Algebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions.

Algebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions. Page 1 of 13 Review of Linear Expressions and Equations Skills involving linear equations can be divided into the following groups: Simplifying algebraic expressions. Linear expressions. Solving linear

More information

Lesson 4 Annuities: The Mathematics of Regular Payments

Lesson 4 Annuities: The Mathematics of Regular Payments Lesson 4 Annuities: The Mathematics of Regular Payments Introduction An annuity is a sequence of equal, periodic payments where each payment receives compound interest. One example of an annuity is a Christmas

More information

Rational Exponents. Squaring both sides of the equation yields. and to be consistent, we must have

Rational Exponents. Squaring both sides of the equation yields. and to be consistent, we must have 8.6 Rational Exponents 8.6 OBJECTIVES 1. Define rational exponents 2. Simplify expressions containing rational exponents 3. Use a calculator to estimate the value of an expression containing rational exponents

More information

2.3. Finding polynomial functions. An Introduction:

2.3. Finding polynomial functions. An Introduction: 2.3. Finding polynomial functions. An Introduction: As is usually the case when learning a new concept in mathematics, the new concept is the reverse of the previous one. Remember how you first learned

More information

Addition and Multiplication of Polynomials

Addition and Multiplication of Polynomials LESSON 0 addition and multiplication of polynomials LESSON 0 Addition and Multiplication of Polynomials Base 0 and Base - Recall the factors of each of the pieces in base 0. The unit block (green) is x.

More information

HFCC Math Lab Arithmetic - 4. Addition, Subtraction, Multiplication and Division of Mixed Numbers

HFCC Math Lab Arithmetic - 4. Addition, Subtraction, Multiplication and Division of Mixed Numbers HFCC Math Lab Arithmetic - Addition, Subtraction, Multiplication and Division of Mixed Numbers Part I: Addition and Subtraction of Mixed Numbers There are two ways of adding and subtracting mixed numbers.

More information

To discuss this topic fully, let us define some terms used in this and the following sets of supplemental notes.

To discuss this topic fully, let us define some terms used in this and the following sets of supplemental notes. INFINITE SERIES SERIES AND PARTIAL SUMS What if we wanted to sum up the terms of this sequence, how many terms would I have to use? 1, 2, 3,... 10,...? Well, we could start creating sums of a finite number

More information

Algebra 1 Course Objectives

Algebra 1 Course Objectives Course Objectives The Duke TIP course corresponds to a high school course and is designed for gifted students in grades seven through nine who want to build their algebra skills before taking algebra in

More information

Click on the links below to jump directly to the relevant section

Click on the links below to jump directly to the relevant section Click on the links below to jump directly to the relevant section Basic review Writing fractions in simplest form Comparing fractions Converting between Improper fractions and whole/mixed numbers Operations

More information

6-3 Solving Systems by Elimination

6-3 Solving Systems by Elimination Warm Up Simplify each expression. 1. 2y 4x 2(4y 2x) 2. 5(x y) + 2x + 5y Write the least common multiple. 3. 3 and 6 4. 4 and 10 5. 6 and 8 Objectives Solve systems of linear equations in two variables

More information

Summer Assignment for incoming Fairhope Middle School 7 th grade Advanced Math Students

Summer Assignment for incoming Fairhope Middle School 7 th grade Advanced Math Students Summer Assignment for incoming Fairhope Middle School 7 th grade Advanced Math Students Studies show that most students lose about two months of math abilities over the summer when they do not engage in

More information

Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks

Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks Welcome to Thinkwell s Homeschool Precalculus! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson

More information

Developmental Math Course Outcomes and Objectives

Developmental Math Course Outcomes and Objectives Developmental Math Course Outcomes and Objectives I. Math 0910 Basic Arithmetic/Pre-Algebra Upon satisfactory completion of this course, the student should be able to perform the following outcomes and

More information

8-1 Adding and Subtracting Polynomials

8-1 Adding and Subtracting Polynomials Determine whether each expression is a polynomial. If it is a polynomial, find the degree and determine whether it is a monomial, binomial, or trinomial. 1. 7ab + 6b 2 2a 3 yes; 3; trinomial 2. 2y 5 +

More information

I remember that when I

I remember that when I 8. Airthmetic and Geometric Sequences 45 8. ARITHMETIC AND GEOMETRIC SEQUENCES Whenever you tell me that mathematics is just a human invention like the game of chess I would like to believe you. But I

More information

Utah Core Curriculum for Mathematics

Utah Core Curriculum for Mathematics Core Curriculum for Mathematics correlated to correlated to 2005 Chapter 1 (pp. 2 57) Variables, Expressions, and Integers Lesson 1.1 (pp. 5 9) Expressions and Variables 2.2.1 Evaluate algebraic expressions

More information

APPLICATIONS AND MODELING WITH QUADRATIC EQUATIONS

APPLICATIONS AND MODELING WITH QUADRATIC EQUATIONS APPLICATIONS AND MODELING WITH QUADRATIC EQUATIONS Now that we are starting to feel comfortable with the factoring process, the question becomes what do we use factoring to do? There are a variety of classic

More information

Algebra Unit 6 Syllabus revised 2/27/13 Exponents and Polynomials

Algebra Unit 6 Syllabus revised 2/27/13 Exponents and Polynomials Algebra Unit 6 Syllabus revised /7/13 1 Objective: Multiply monomials. Simplify expressions involving powers of monomials. Pre-assessment: Exponents, Fractions, and Polynomial Expressions Lesson: Pages

More information

Fractions and Linear Equations

Fractions and Linear Equations Fractions and Linear Equations Fraction Operations While you can perform operations on fractions using the calculator, for this worksheet you must perform the operations by hand. You must show all steps

More information

EC3070 FINANCIAL DERIVATIVES. Exercise 1

EC3070 FINANCIAL DERIVATIVES. Exercise 1 EC3070 FINANCIAL DERIVATIVES Exercise 1 1. A credit card company charges an annual interest rate of 15%, which is effective only if the interest on the outstanding debts is paid in monthly instalments.

More information

Alum Rock Elementary Union School District Algebra I Study Guide for Benchmark III

Alum Rock Elementary Union School District Algebra I Study Guide for Benchmark III Alum Rock Elementary Union School District Algebra I Study Guide for Benchmark III Name Date Adding and Subtracting Polynomials Algebra Standard 10.0 A polynomial is a sum of one ore more monomials. Polynomial

More information

Sums & Series. a i. i=1

Sums & Series. a i. i=1 Sums & Series Suppose a,a,... is a sequence. Sometimes we ll want to sum the first k numbers (also known as terms) that appear in a sequence. A shorter way to write a + a + a 3 + + a k is as There are

More information

Perpetuities and Annuities: Derivation of shortcut formulas

Perpetuities and Annuities: Derivation of shortcut formulas Perpetuities and Annuities: Derivation of shortcut formulas Outline Perpetuity formula... 2 The mathematical derivation of the PV formula... 2 Derivation of the perpetuity formula using the Law of One

More information

0018 DATA ANALYSIS, PROBABILITY and STATISTICS

0018 DATA ANALYSIS, PROBABILITY and STATISTICS 008 DATA ANALYSIS, PROBABILITY and STATISTICS A permutation tells us the number of ways we can combine a set where {a, b, c} is different from {c, b, a} and without repetition. r is the size of of the

More information

Norwalk La Mirada Unified School District. Algebra Scope and Sequence of Instruction

Norwalk La Mirada Unified School District. Algebra Scope and Sequence of Instruction 1 Algebra Scope and Sequence of Instruction Instructional Suggestions: Instructional strategies at this level should include connections back to prior learning activities from K-7. Students must demonstrate

More information

Systems of Equations Involving Circles and Lines

Systems of Equations Involving Circles and Lines Name: Systems of Equations Involving Circles and Lines Date: In this lesson, we will be solving two new types of Systems of Equations. Systems of Equations Involving a Circle and a Line Solving a system

More information

Pre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems

Pre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems Academic Content Standards Grade Eight Ohio Pre-Algebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small

More information

Chapter 2: Systems of Linear Equations and Matrices:

Chapter 2: Systems of Linear Equations and Matrices: At the end of the lesson, you should be able to: Chapter 2: Systems of Linear Equations and Matrices: 2.1: Solutions of Linear Systems by the Echelon Method Define linear systems, unique solution, inconsistent,

More information

Arithmetic Sequences & Series

Arithmetic Sequences & Series About the Lesson Students use formulas to find the differences of the consecutive terms, plot a scatter plot of each sequence, and determine that sequences with common differences (called arithmetic sequences)

More information

Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question

Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question What is the difference between an arithmetic and a geometric sequence? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question

More information

Definition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.

Definition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality. 8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent

More information

ASA Angle Side Angle SAA Side Angle Angle SSA Side Side Angle. B a C

ASA Angle Side Angle SAA Side Angle Angle SSA Side Side Angle. B a C 8.2 The Law of Sines Section 8.2 Notes Page 1 The law of sines is used to solve for missing sides or angles of triangles when we have the following three cases: S ngle Side ngle S Side ngle ngle SS Side

More information

Simplifying Numerical Expressions Grade Five

Simplifying Numerical Expressions Grade Five Ohio Standards Connection Number, Number Sense and Operations Benchmark E Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the

More information

FRACTIONS OPERATIONS

FRACTIONS OPERATIONS FRACTIONS OPERATIONS Summary 1. Elements of a fraction... 1. Equivalent fractions... 1. Simplification of a fraction... 4. Rules for adding and subtracting fractions... 5. Multiplication rule for two fractions...

More information

Algebra 1-2. A. Identify and translate variables and expressions.

Algebra 1-2. A. Identify and translate variables and expressions. St. Mary's College High School Algebra 1-2 The Language of Algebra What is a variable? A. Identify and translate variables and expressions. The following apply to all the skills How is a variable used

More information

MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab

MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab MATH 0110 is established to accommodate students desiring non-course based remediation in developmental mathematics. This structure will

More information

Mathematics. Curriculum Content for Elementary School Mathematics. Fulton County Schools Curriculum Guide for Elementary Schools

Mathematics. Curriculum Content for Elementary School Mathematics. Fulton County Schools Curriculum Guide for Elementary Schools Mathematics Philosophy Mathematics permeates all sectors of life and occupies a well-established position in curriculum and instruction. Schools must assume responsibility for empowering students with

More information

1.4. Arithmetic of Algebraic Fractions. Introduction. Prerequisites. Learning Outcomes

1.4. Arithmetic of Algebraic Fractions. Introduction. Prerequisites. Learning Outcomes Arithmetic of Algebraic Fractions 1.4 Introduction Just as one whole number divided by another is called a numerical fraction, so one algebraic expression divided by another is known as an algebraic fraction.

More information

4.1. COMPLEX NUMBERS

4.1. COMPLEX NUMBERS 4.1. COMPLEX NUMBERS What You Should Learn Use the imaginary unit i to write complex numbers. Add, subtract, and multiply complex numbers. Use complex conjugates to write the quotient of two complex numbers

More information

4. Life Insurance Payments

4. Life Insurance Payments 4. Life Insurance Payments A life insurance premium must take into account the following factors 1. The amount to be paid upon the death of the insured person and its present value. 2. The distribution

More information

Linear Equations and Inequalities

Linear Equations and Inequalities Linear Equations and Inequalities Section 1.1 Prof. Wodarz Math 109 - Fall 2008 Contents 1 Linear Equations 2 1.1 Standard Form of a Linear Equation................ 2 1.2 Solving Linear Equations......................

More information

Derivative Approximation by Finite Differences

Derivative Approximation by Finite Differences Derivative Approximation by Finite Differences David Eberly Geometric Tools, LLC http://wwwgeometrictoolscom/ Copyright c 998-26 All Rights Reserved Created: May 3, 2 Last Modified: April 25, 25 Contents

More information

ACCUPLACER Arithmetic & Elementary Algebra Study Guide

ACCUPLACER Arithmetic & Elementary Algebra Study Guide ACCUPLACER Arithmetic & Elementary Algebra Study Guide Acknowledgments We would like to thank Aims Community College for allowing us to use their ACCUPLACER Study Guides as well as Aims Community College

More information

7. Solving Linear Inequalities and Compound Inequalities

7. Solving Linear Inequalities and Compound Inequalities 7. Solving Linear Inequalities and Compound Inequalities Steps for solving linear inequalities are very similar to the steps for solving linear equations. The big differences are multiplying and dividing

More information

South Carolina College- and Career-Ready (SCCCR) Algebra 1

South Carolina College- and Career-Ready (SCCCR) Algebra 1 South Carolina College- and Career-Ready (SCCCR) Algebra 1 South Carolina College- and Career-Ready Mathematical Process Standards The South Carolina College- and Career-Ready (SCCCR) Mathematical Process

More information

Progressions: Arithmetic and Geometry progressions 3º E.S.O.

Progressions: Arithmetic and Geometry progressions 3º E.S.O. Progressions: Arithmetic and Geometry progressions 3º E.S.O. Octavio Pacheco Ortuño I.E.S. El Palmar INDEX Introduction.. 3 Objectives 3 Topics..3 Timing...3 Activities Lesson...4 Lesson 2.......4 Lesson

More information

A vector is a directed line segment used to represent a vector quantity.

A vector is a directed line segment used to represent a vector quantity. Chapters and 6 Introduction to Vectors A vector quantity has direction and magnitude. There are many examples of vector quantities in the natural world, such as force, velocity, and acceleration. A vector

More information

Course Name: College Algebra Course Number: Math 1513 Semester: Fall 2015

Course Name: College Algebra Course Number: Math 1513 Semester: Fall 2015 Course Name: College Algebra Course Number: Math 1513 Semester: Fall 2015 Instructor s Name: Ricky Streight Hours Credit: 3 Office Phone: 945-6794 Office Hours: Check http://www.osuokc.edu/rickyws/ for

More information

Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum

Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum UNIT I: The Hyperbolic Functions basic calculus concepts, including techniques for curve sketching, exponential and logarithmic

More information

Prerequisites: TSI Math Complete and high school Algebra II and geometry or MATH 0303.

Prerequisites: TSI Math Complete and high school Algebra II and geometry or MATH 0303. Course Syllabus Math 1314 College Algebra Revision Date: 8-21-15 Catalog Description: In-depth study and applications of polynomial, rational, radical, exponential and logarithmic functions, and systems

More information

Discrete Mathematics. Chapter 11 Sequences and Series. Chapter 12 Probability and Statistics

Discrete Mathematics. Chapter 11 Sequences and Series. Chapter 12 Probability and Statistics Discrete Mathematics Discrete mathematics is the branch of mathematics that involves finite or discontinuous quantities. In this unit, you will learn about sequences, series, probability, and statistics.

More information

SEQUENCES ARITHMETIC SEQUENCES. Examples

SEQUENCES ARITHMETIC SEQUENCES. Examples SEQUENCES ARITHMETIC SEQUENCES An ordered list of numbers such as: 4, 9, 6, 25, 36 is a sequence. Each number in the sequence is a term. Usually variables with subscripts are used to label terms. For example,

More information

IV. ALGEBRAIC CONCEPTS

IV. ALGEBRAIC CONCEPTS IV. ALGEBRAIC CONCEPTS Algebra is the language of mathematics. Much of the observable world can be characterized as having patterned regularity where a change in one quantity results in changes in other

More information

Introduction. Appendix D Mathematical Induction D1

Introduction. Appendix D Mathematical Induction D1 Appendix D Mathematical Induction D D Mathematical Induction Use mathematical induction to prove a formula. Find a sum of powers of integers. Find a formula for a finite sum. Use finite differences to

More information

Factoring Quadratic Trinomials

Factoring Quadratic Trinomials Factoring Quadratic Trinomials Student Probe Factor Answer: Lesson Description This lesson uses the area model of multiplication to factor quadratic trinomials Part 1 of the lesson consists of circle puzzles

More information

Simple Examples. This is the information that we are given. To find the answer we are to solve an equation in one variable, x.

Simple Examples. This is the information that we are given. To find the answer we are to solve an equation in one variable, x. Worksheet. Solving Equations in One Variable Section 1 Simple Examples You are on your way to Brisbane from Sydney, and you know that the trip is 1100 km. You pass a sign that says that Brisbane is now

More information

Addition with Unlike Denominators

Addition with Unlike Denominators Lesson. Addition with Unlike Denominators Karen is stringing a necklace with beads. She puts green beads on _ of the string and purple beads on of the string. How much of the string does Karen cover with

More information

Acquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A3d,e Time allotted for this Lesson: 4 Hours

Acquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A3d,e Time allotted for this Lesson: 4 Hours Acquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A3d,e Time allotted for this Lesson: 4 Hours Essential Question: LESSON 4 FINITE ARITHMETIC SERIES AND RELATIONSHIP TO QUADRATIC

More information

9.3 OPERATIONS WITH RADICALS

9.3 OPERATIONS WITH RADICALS 9. Operations with Radicals (9 1) 87 9. OPERATIONS WITH RADICALS In this section Adding and Subtracting Radicals Multiplying Radicals Conjugates In this section we will use the ideas of Section 9.1 in

More information

Estimated Pre Calculus Pacing Timeline

Estimated Pre Calculus Pacing Timeline Estimated Pre Calculus Pacing Timeline 2010-2011 School Year The timeframes listed on this calendar are estimates based on a fifty-minute class period. You may need to adjust some of them from time to

More information

Section 1.3 P 1 = 1 2. = 1 4 2 8. P n = 1 P 3 = Continuing in this fashion, it should seem reasonable that, for any n = 1, 2, 3,..., = 1 2 4.

Section 1.3 P 1 = 1 2. = 1 4 2 8. P n = 1 P 3 = Continuing in this fashion, it should seem reasonable that, for any n = 1, 2, 3,..., = 1 2 4. Difference Equations to Differential Equations Section. The Sum of a Sequence This section considers the problem of adding together the terms of a sequence. Of course, this is a problem only if more than

More information

Taylor and Maclaurin Series

Taylor and Maclaurin Series Taylor and Maclaurin Series In the preceding section we were able to find power series representations for a certain restricted class of functions. Here we investigate more general problems: Which functions

More information

El Paso Community College Syllabus Instructor s Course Requirements Summer 2015

El Paso Community College Syllabus Instructor s Course Requirements Summer 2015 Syllabus, Part I Math 1324, Revised Summer 2015 El Paso Community College Syllabus Instructor s Course Requirements Summer 2015 I. Course Number and Instructor Information Mathematics 1324-31403, From

More information