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


 Lionel McCarthy
 1 years ago
 Views:
Transcription
1 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 = 8. Find d. Find u 0. Find S 0. () () (). In an arithmetic sequence u 1 = 7, u 0 = 64 and u n = Find the value of the common difference. Find the value of n. () (Total 5 marks) 3. Consider the arithmetic sequence 3, 9, 15,..., Write down the common difference. Find the number of terms in the sequence. Find the sum of the sequence. () 4. An arithmetic sequence, u 1, u, u 3,..., has d = 11 and u 7 = 63. Find u 1. () (i) Given that u n = 516, find the value of n. For this value of n, find S n. 5. The first three terms of an infinite geometric sequence are 3, 16 and 8. Write down the value of r. Find u 6. () Find the sum to infinity of this sequence. () (Total 5 marks) IB Questionbank Maths SL 1
2 6. The n th term of an arithmetic sequence is given by u n = 5 + n. Write down the common difference. (i) Given that the n th term of this sequence is 115, find the value of n. For this value of n, find the sum of the sequence. (5) 7. In an arithmetic series, the first term is 7 and the sum of the first 0 terms is 60. Find the common difference. Find the value of the 78 th term. () (Total 5 marks) In a geometric series, u 1 = and u4 = Find the value of r. Find the smallest value of n for which S n > 40. (Total 7 marks) 9. Expand 7 r= 4 r as the sum of four terms. (i) 30 Find the value of r= 4 r. Explain why =4 r r cannot be evaluated. (6) (Total 7 marks) 10. In an arithmetic sequence, S 40 = 1900 and u 40 = 106. Find the value of u 1 and of d. 11. Consider the arithmetic sequence, 5, 8, 11,... Find u 101. Find the value of n so that u n = 15. IB Questionbank Maths SL
3 1. Consider the infinite geometric sequence 3000, 1800, 1080, 648,. Find the common ratio. Find the 10 th term. Find the exact sum of the infinite sequence. () () () 13. Consider the infinite geometric sequence 3, 3(0.9), 3(0.9), 3(0.9) 3,. Write down the 10 th term of the sequence. Do not simplify your answer. Find the sum of the infinite sequence. (Total 5 marks) 14. In an arithmetic sequence u 1 = 37 and u 4 = 3. Find (i) the common difference; the first term. Find S 10. (Total 7 marks) 15. Let u n = 3 n. Write down the value of u 1, u, and u 3. 0 Find (3 n ). n= A theatre has 0 rows of seats. There are 15 seats in the first row, 17 seats in the second row, and each successive row of seats has two more seats in it than the previous row. Calculate the number of seats in the 0th row. Calculate the total number of seats. () 17. A sum of $ 5000 is invested at a compound interest rate of 6.3 % per annum. Write down an expression for the value of the investment after n full years. What will be the value of the investment at the end of five years? IB Questionbank Maths SL 3
4 The value of the investment will exceed $ after n full years. (i) Write down an inequality to represent this information. Calculate the minimum value of n. 18. Consider the infinite geometric sequence 5, 5, 1, 0.,. Find the common ratio. Find (i) the 10 th term; an expression for the n th term. Find the sum of the infinite sequence. 19. The first four terms of a sequence are 18, 54, 16, 486. Use all four terms to show that this is a geometric sequence. () (i) Find an expression for the n th term of this geometric sequence. If the n th term of the sequence is , find the value of n. 0. Write down the first three terms of the sequence u n = 3n, for n 1. Find (i) 0 n= n= 1 3n ; 3n. (5) 1. Consider the infinite geometric series For this series, find the common ratio, giving your answer as a fraction in its simplest form. Find the fifteenth term of this series. Find the exact value of the sum of the infinite series.. Consider the geometric sequence 3, 6, 1, 4,. (i) Write down the common ratio. Find the 15 th term. IB Questionbank Maths SL 4
5 Consider the sequence x 3, x +1, x + 8,. When x = 5, the sequence is geometric. (i) Write down the first three terms. Find the common ratio. () (d) Find the other value of x for which the sequence is geometric. For this value of x, find (i) the common ratio; the sum of the infinite sequence. (Total 1 marks) 3. Let S n be the sum of the first n terms of the arithmetic series Find (i) S 4 ; S 100. (PARTS B D ARE OPTIONAL CHALLENGES!!!!!) Let M = 1. (i) Find M. Show that M =. (5) It may now be assumed that M n = 1 n, for n 4. The sum Tn is defined by 1 (i) Write down M 4. T n = M 1 + M + M M n. Find T 4. (d) Using your results from part, find T 100. (Total 16 marks) IB Questionbank Maths SL 5
6 4. Clara organizes cans in triangular piles, where each row has one less can than the row below. For example, the pile of 15 cans shown has 5 cans in the bottom row and 4 cans in the row above it. A pile has 0 cans in the bottom row. Show that the pile contains 10 cans. There are 340 cans in a pile. How many cans are in the bottom row? (i) There are S cans and they are organized in a triangular pile with n cans in the bottom row. Show that n + n S = 0. Clara has 100 cans. Explain why she cannot organize them in a triangular pile. (6) (Total 14 marks) Worked Solutions 1. attempt to find d u3 u e.g. 1, 8 = + d d = 3 N correct substitution () e.g. u 0 = + (0 1)3, u 0 = u 0 = 59 N correct substitution () e.g. S 0 = 0 ( + 59), S0 = 0 ( ) S 0 = 610 N. evidence of choosing the formula for 0 th term e.g. u 0 = u d correct equation e.g = d, d = 19 d = 3 N 3 IB Questionbank Maths SL 6
7 correct substitution into formula for u n e.g = 7 + 3(n 1), 3709 = 3n + 4 n = 135 N1 [5] 3. common difference is 6 N1 evidence of appropriate approach e.g. u n = 1353 correct working e.g = 3 + (n 1)6, 6 n = 6 N evidence of correct substitution 6 ( ) 6 e.g. S 6 =, ( ) S 6 = (accept ) N1 4. evidence of equation for u 7 M1 e.g. 63 = u , u 7 = u 1 + (n 1) 11, 63 (11 6) u 1 = 3 N1 (i) correct equation e.g. 516 = 3 + (n 1) 11, 539 = (n 1) 11 n = 50 N1 correct substitution into sum formula 50( ) 50( ( 3) ) e.g. S 50 =, S 50 = S 50 = 135 (accept 1300) N r = = 3 N1 correct calculation or listing terms () e.g. 3,8, 3,... 4,, 1 u 6 = 1 N 3 evidence of correct substitution in S 3 3 e.g., S = 64 N1 [5] 6. d = N1 (i) 5 + n = 115 () n = 55 N IB Questionbank Maths SL 7
8 u 1 = 7 (may be seen in above) () correct substitution into formula for sum of arithmetic series e.g. S 55 = ( ), S 55 = ((7) + 54()), (5 + k) k = 1 S 55 = 3355 (accept 3360) N3 () 7. attempt to substitute into sum formula for AP (accept term formula) 0 0 e.g. S 0 = { ( 7) + 19d }, or ( 7 + u 0 ) setting up correct equation using sum formula 0 e.g. {( 7) + 19d} = 60 N correct substitution u 78 = () = 301 N [5] 8. evidence of substituting into formula for nth term of GP 1 3 e.g. u 4 = r setting up correct equation r 3 = 81 3 r = 3 N METHOD 1 setting up an inequality (accept an equation) 1 n 1 n (3 1) (1 3 ) e.g ; 81 n > > 40;3 > 6481 M1 evidence of solving e.g. graph, taking logs M1 n > () n = 8 N METHOD if n = 7, sum = ; if n = 8, sum = A n = 8 (is the smallest value) A N [7] 9. 7 r= 4 r 4 = (accept ) N1 (i) METHOD 1 recognizing a GP u 1 = 4, r =, n = 7 () correct substitution into formula for sum 4 7 ( 1) e.g. S 7 = 1 S 7 = N4 () IB Questionbank Maths SL 8
9 METHOD recognizing 30 = 30 3 r= 4 r= 1 r= 1 recognizing GP with u 1 =, r =, n = 30 correct substitution into formula for sum ( 30 1) S 30 = () 1 = r= 4 r = ( ) = N4 () valid reason (e.g. infinite GP, diverging series), and r 1 (accept r > 1) R1R1 N [7] 10. METHOD 1 substituting into formula for S 40 correct substitution 40( u 106) e.g = 1 + u 1 = 11 N substituting into formula for u 40 or S 40 correct substitution e.g. 106 = d, 1900 = 0( + 39d) d = 3 N METHOD substituting into formula for S 40 correct substitution e.g. 0(u d) = 1900 substituting into formula for u 40 correct substitution e.g. 106 = u d u 1 = 11, d = 3 NN 11. d = 3 () evidence of substitution into u n = a + (n 1) d e.g. u 101 = u 101 = 30 N3 correct approach e.g. 15 = + (n 1) 3 correct simplification () e.g. 150 = (n 1) 3, 50 = n 1, 15 = 1 + 3n n = 51 N 1. evidence of dividing two terms IB Questionbank Maths SL 9
10 e.g , r = 0.6 N evidence of substituting into the formula for the 10 th term e.g. u 10 = 3000( 0.6) 9 u 10 = 30. (accept the exact value ) N evidence of substituting into the formula for the infinite sum 3000 e. g. S = 1.6 S = 1875 N 13. u 10 = 3(0.9) 9 N1 recognizing r = 0.9 () correct substitution 3 e.g. S = S = 0.1 () S = 30 N3 14. (i) attempt to set up equations 37 = u 1 + 0d and 3 = u 1 + 3d 34 = 17d d = N [5] 3 = u 1 6 u 1 = 3 N1 u 10 = = 15 () 10 S 10 = (3 + ( 15)) M1 = 60 N [7] 15. u 1 = 1, u = 1, u 3 = 3 N3 Evidence of using appropriate formula M1 0 correct values S 0 = ( ) (= 10( 38)) S 0 = 360 N1 16. Recognizing an AP u 1 = 15 d = n = 0 () substituting into u 0 = 15 + (0 1) M1 = 53 (that is, 53 seats in the 0th row) N IB Questionbank Maths SL 10
11 0 0 Substituting into S 0 = ((15) + (0 1)) (or into ( )) M1 = 680 (that is, 680 seats in total) N (1.063) n N1 Value = $ 5000(1.063) 5 (= $ ) = $ 6790 to 3 s.f. (accept $ 6786, or $ ) N1 (i) 5000(1.063) n > or (1.063) n > N1 Attempting to solve the inequality nlog(1.063) > log n > () 1 years N3 Note: Candidates are likely to use TABLE or LIST on a GDC to find n. A good way of communicating this is suggested below. Let y = x When x = 11, y = 1.958, when x = 1, y =.0816 x = 1 i.e. 1 years N3 () (0.) N1 5 (i) 9 1 u 10 = 5 5 = ,1.8 10, N n 1 1 u n = 5 N1 5 For attempting to use infinite sum formula for a GP = N 4 S = 31.5 ( = 31.3 to 3 s f ) 19. For taking three ratios of consecutive terms = = ( = 3) hence geometric AG N0 IB Questionbank Maths SL 11
12 (i) r = 3 () u n = 18 3 n 1 N For a valid attempt to solve 18 3 n 1 = eg trial and error, logs n = 11 N 0. 3, 6, 9 N1 (i) Evidence of using the sum of an AP M1 0 eg 3+ ( 0 1) 3 0 n = 1 3n = 630 N1 METHOD Correct calculation for 3n () 100 n = 1 eg ( ), Evidence of subtraction eg n = 1 3n = 1450 N METHOD Recognising that first term is 63, the number of terms is 80 ()() eg ( ), ( ) 100 n = 1 3n = 1450 N 1. For taking an appropriate ratio of consecutive terms r = 3 N For attempting to use the formula for the n th term of a GP u 15 = 1.39 N IB Questionbank Maths SL 1
13 For attempting to use infinite sum formula for a GP S = 115 N. (i) r = N1 u 15 = 3 ( ) 14 () = 4915 (accept 4900) N (i), 6, 18 N1 r = 3 N1 Setting up equation (or a sketch) M1 x + 1 x + 8 = x 3 x + 1 (or correct sketch with relevant information) x + x + 1 = x + x 4 () (d) (i) r = 1 x = 5 x = 5 or x = 5 x = 5 N Notes: If trial and error is used, work must be documented with several trials shown. Award full marks for a correct answer with this approach. If the work is not documented, award N for a correct answer. N1 For attempting to use infinite sum formula for a GP S = S = 16 N Note: Award M0A0 if candidates use a value of r where r > 1, or r < 1. [1] 3. (i) S 4 = 0 N1 u 1 =, d = () Attempting to use formula for S n M1 S 100 = N IB Questionbank Maths SL 13
14 (i) M 1 4 = A N For writing M 3 as M M or M M or M1 M 3 = A M 3 = 1 6 AG N0 (i) M = N1 T 4 1 = = 4 N3 (d) T 100 = = N3 [16] 4. Note: Throughout this question, the first and last terms are interchangeable. For recognizing the arithmetic sequence u 1 = 1, n = 0, u 0 = 0 (u 1 = 1, n = 0, d = 1) () Evidence of using sum of an AP M S S 0 = ( ) (or = ( )) S 0 = 10 AG N0 Let there be n cans in bottom row Evidence of using S n = n n n eg ( ) = 340, ( + ( n 1) ) = 340, ( n + ( n 1)( 1) ) = 340 n n + n 6480 = 0 n = 80 or n = 81 () n = 80 N IB Questionbank Maths SL 14
15 ( + n ) (i) Evidence of using S = 1 n S = n + n METHOD 1 n + n S = 0 AG N0 Substituting S = 100 ( eg n + n ) + n 400 = 0, 100 = 1 n EITHER n = 64.3, n = 65.3 Any valid reason which includes reference to integer being needed, R1 and pointing out that integer not possible here. R1 N1 eg n must be a (positive) integer, this equation does not have integer solutions. OR Discriminant = Valid reason which includes reference to integer being needed, R1 and pointing out that integer not possible here. R1 N1 eg this discriminant is not a perfect square, therefore no integer solution as needed. METHOD Trial and error S 64 = 080, S 65 = 145 Any valid reason which includes reference to integer being needed, R1 and pointing out that integer not possible here. R1 N1 [14] IB Questionbank Maths SL 15
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 information2010 Solutions. a + b. a + b 1. (a + b)2 + (b a) 2. (b2 + a 2 ) 2 (a 2 b 2 ) 2
00 Problem If a and b are nonzero real numbers such that a b, compute the value of the expression ( ) ( b a + a a + b b b a + b a ) ( + ) a b b a + b a +. b a a b Answer: 8. Solution: Let s simplify the
More informationCollege Algebra. Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGrawHill, 2008, ISBN: 9780072867381
College Algebra Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGrawHill, 2008, ISBN: 9780072867381 Course Description This course provides
More informationMATH 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 noncourse based remediation in developmental mathematics. This structure will
More informationMEP Pupil Text 12. A list of numbers which form a pattern is called a sequence. In this section, straightforward sequences are continued.
MEP Pupil Text Number Patterns. Simple Number Patterns A list of numbers which form a pattern is called a sequence. In this section, straightforward sequences are continued. Worked Example Write down the
More informationFACTORING QUADRATIC EQUATIONS
FACTORING QUADRATIC EQUATIONS Summary 1. Difference of squares... 1 2. Mise en évidence simple... 2 3. compounded factorization... 3 4. Exercises... 7 The goal of this section is to summarize the methods
More informationAlgebra 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 informationALGEBRA 2 CRA 2 REVIEW  Chapters 16 Answer Section
ALGEBRA 2 CRA 2 REVIEW  Chapters 16 Answer Section MULTIPLE CHOICE 1. ANS: C 2. ANS: A 3. ANS: A OBJ: 53.1 Using Vertex Form SHORT ANSWER 4. ANS: (x + 6)(x 2 6x + 36) OBJ: 64.2 Solving Equations by
More informationDeterminants can be used to solve a linear system of equations using Cramer s Rule.
2.6.2 Cramer s Rule Determinants can be used to solve a linear system of equations using Cramer s Rule. Cramer s Rule for Two Equations in Two Variables Given the system This system has the unique solution
More informationLAKE ELSINORE UNIFIED SCHOOL DISTRICT
LAKE ELSINORE UNIFIED SCHOOL DISTRICT Title: PLATO Algebra 1Semester 2 Grade Level: 1012 Department: Mathematics Credit: 5 Prerequisite: Letter grade of F and/or N/C in Algebra 1, Semester 2 Course Description:
More informationACCUPLACER 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 informationExamples of Tasks from CCSS Edition Course 3, Unit 5
Examples of Tasks from CCSS Edition Course 3, Unit 5 Getting Started The tasks below are selected with the intent of presenting key ideas and skills. Not every answer is complete, so that teachers can
More informationCourse Outlines. 1. Name of the Course: Algebra I (Standard, College Prep, Honors) Course Description: ALGEBRA I STANDARD (1 Credit)
Course Outlines 1. Name of the Course: Algebra I (Standard, College Prep, Honors) Course Description: ALGEBRA I STANDARD (1 Credit) This course will cover Algebra I concepts such as algebra as a language,
More information2.1 The Present Value of an Annuity
2.1 The Present Value of an Annuity One example of a fixed annuity is an agreement to pay someone a fixed amount x for N periods (commonly months or years), e.g. a fixed pension It is assumed that the
More informationChapter 2 Factors: How Time and Interest Affect Money
Chapter 2 Factors: How Time and Interest Affect Money Session 456 Dr Abdelaziz Berrado 1 Topics to Be Covered in Today s Lecture Section 2: How Time and Interest Affect Money SinglePayment Factors (F/P
More informationCOLLEGE ALGEBRA LEARNING COMMUNITY
COLLEGE ALGEBRA LEARNING COMMUNITY Tulsa Community College, West Campus Presenter Lori Mayberry, B.S., M.S. Associate Professor of Mathematics and Physics lmayberr@tulsacc.edu NACEP National Conference
More informationProgressions: 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 informationPrerequisites: TSI Math Complete and high school Algebra II and geometry or MATH 0303.
Course Syllabus Math 1314 College Algebra Revision Date: 82115 Catalog Description: Indepth study and applications of polynomial, rational, radical, exponential and logarithmic functions, and systems
More information86 Radical Expressions and Rational Exponents. Warm Up Lesson Presentation Lesson Quiz
86 Radical Expressions and Rational Exponents Warm Up Lesson Presentation Lesson Quiz Holt Algebra ALgebra2 2 Warm Up Simplify each expression. 1. 7 3 7 2 16,807 2. 11 8 11 6 121 3. (3 2 ) 3 729 4. 5.
More informationFlorida Math for College Readiness
Core Florida Math for College Readiness Florida Math for College Readiness provides a fourthyear math curriculum focused on developing the mastery of skills identified as critical to postsecondary readiness
More informationAlgebra Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 201213 school year.
This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these tools to better serve teachers. Algebra
More informationThe Ideal Class Group
Chapter 5 The Ideal Class Group We will use Minkowski theory, which belongs to the general area of geometry of numbers, to gain insight into the ideal class group of a number field. We have already mentioned
More informationTeaching and Learning Guide 5: Finance and Growth
Guide 5: Finance and Growth Table of Contents Teaching and Learning Section 1: Introduction to the guide... 3 Section 2: Arithmetic & Geometric Sequences and Series... 4 1. The concept of Arithmetic &
More informationJacobi s four squares identity Martin Klazar
Jacobi s four squares identity Martin Klazar (lecture on the 7th PhD conference) Ostrava, September 10, 013 C. Jacobi [] in 189 proved that for any integer n 1, r (n) = #{(x 1, x, x 3, x ) Z ( i=1 x i
More informationNumbers 101: Growth Rates and Interest Rates
The Anderson School at UCLA POL 200006 Numbers 101: Growth Rates and Interest Rates Copyright 2000 by Richard P. Rumelt. A growth rate is a numerical measure of the rate of expansion or contraction of
More informationTo define function and introduce operations on the set of functions. To investigate which of the field properties hold in the set of functions
Chapter 7 Functions This unit defines and investigates functions as algebraic objects. First, we define functions and discuss various means of representing them. Then we introduce operations on functions
More informationEssential 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, plus the present value of the $1,000 received in 15 years, which is 1, 000(1 + i) 30. Hence the present value of the bond is = 1000 ;
2 Bond Prices A bond is a security which offers semiannual* interest payments, at a rate r, for a fixed period of time, followed by a return of capital Suppose you purchase a $,000 utility bond, freshly
More informationMATH1510 Financial Mathematics I. Jitse Niesen University of Leeds
MATH1510 Financial Mathematics I Jitse Niesen University of Leeds January May 2012 Description of the module This is the description of the module as it appears in the module catalogue. Objectives Introduction
More informationSECTION 2.5: FINDING ZEROS OF POLYNOMIAL FUNCTIONS
SECTION 2.5: FINDING ZEROS OF POLYNOMIAL FUNCTIONS Assume f ( x) is a nonconstant polynomial with real coefficients written in standard form. PART A: TECHNIQUES WE HAVE ALREADY SEEN Refer to: Notes 1.31
More informationAlgebra 2: Q1 & Q2 Review
Name: Class: Date: ID: A Algebra 2: Q1 & Q2 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which is the graph of y = 2(x 2) 2 4? a. c. b. d. Short
More informationPolynomial Operations and Factoring
Algebra 1, Quarter 4, Unit 4.1 Polynomial Operations and Factoring Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Identify terms, coefficients, and degree of polynomials.
More informationChapter 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 informationReducing balance loans
Reducing balance loans 5 VCEcoverage Area of study Units 3 & 4 Business related mathematics In this chapter 5A Loan schedules 5B The annuities formula 5C Number of repayments 5D Effects of changing the
More informationDecember 4, 2013 MATH 171 BASIC LINEAR ALGEBRA B. KITCHENS
December 4, 2013 MATH 171 BASIC LINEAR ALGEBRA B KITCHENS The equation 1 Lines in twodimensional space (1) 2x y = 3 describes a line in twodimensional space The coefficients of x and y in the equation
More informationIntroduction to Real Estate Investment Appraisal
Introduction to Real Estate Investment Appraisal Maths of Finance Present and Future Values Pat McAllister INVESTMENT APPRAISAL: INTEREST Interest is a reward or rent paid to a lender or investor who has
More informationPossible Stage Two Mathematics Test Topics
Possible Stage Two Mathematics Test Topics The Stage Two Mathematics Test questions are designed to be answerable by a good problemsolver with a strong mathematics background. It is based mainly on material
More informationIntermediate Algebra Math 0305 Course Syllabus: Spring 2013
Intermediate Algebra Math 0305 Course Syllabus: Spring 2013 Northeast Texas Community College exists to provide responsible, exemplary learning opportunities. Jerry Stoermer Office: Math /Science 104 Phone:
More informationEL CAMINO COLLEGE COURSE OUTLINE OF RECORD. Grading Method: Letter Credit/No Credit Both No Grade
EL CAMINO COLLEGE COURSE OUTLINE OF RECORD I. COURSE DESCRIPTION Course Title and Number: Mathematics 43 Descriptive Title: Extended Elementary Algebra, Part II Discipline: Mathematics Division: Mathematical
More informationCOLLEGE ALGEBRA. Paul Dawkins
COLLEGE ALGEBRA Paul Dawkins Table of Contents Preface... iii Outline... iv Preliminaries... Introduction... Integer Exponents... Rational Exponents... 9 Real Exponents...5 Radicals...6 Polynomials...5
More informationHIBBING COMMUNITY COLLEGE COURSE OUTLINE
HIBBING COMMUNITY COLLEGE COURSE OUTLINE COURSE NUMBER & TITLE:  Beginning Algebra CREDITS: 4 (Lec 4 / Lab 0) PREREQUISITES: MATH 0920: Fundamental Mathematics with a grade of C or better, Placement Exam,
More informationAdministrative  Master Syllabus COVER SHEET
Administrative  Master Syllabus COVER SHEET Purpose: It is the intention of this to provide a general description of the course, outline the required elements of the course and to lay the foundation for
More informationMTH124: Honors Algebra I
MTH124: Honors Algebra I This course prepares students for more advanced courses while they develop algebraic fluency, learn the skills needed to solve equations, and perform manipulations with numbers,
More informationMarch 2013 Mathcrnatics MATH 92 College Algebra Kerin Keys. Dcnnis. David Yec' Lscture: 5 we ekly (87.5 total)
City College of San Irrancisco Course Outline of Itecord I. GENERAI DESCRIPI'ION A. Approval Date B. Departrnent C. Course Number D. Course Title E. Course Outline Preparer(s) March 2013 Mathcrnatics
More informationPURSUITS IN MATHEMATICS often produce elementary functions as solutions that need to be
Fast Approximation of the Tangent, Hyperbolic Tangent, Exponential and Logarithmic Functions 2007 Ron Doerfler http://www.myreckonings.com June 27, 2007 Abstract There are some of us who enjoy using our
More informationCopy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any.
Algebra 2  Chapter Prerequisites Vocabulary Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any. P1 p. 1 1. counting(natural) numbers  {1,2,3,4,...}
More informationA Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions
A Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions Marcel B. Finan Arkansas Tech University c All Rights Reserved First Draft February 8, 2006 1 Contents 25
More informationIf A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C?
Problem 3 If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C? Suggested Questions to ask students about Problem 3 The key to this question
More informationThe Australian Curriculum Mathematics
The Australian Curriculum Mathematics Mathematics ACARA The Australian Curriculum Number Algebra Number place value Fractions decimals Real numbers Foundation Year Year 1 Year 2 Year 3 Year 4 Year 5 Year
More informationMATH APPLICATIONS CURRICULUM
MATH APPLICATIONS CURRICULUM NEWTOWN SCHOOLS NEWTOWN, CT. August, 1997 MATHEMATICS PHILOSOPHY We believe mathematics instruction should develop students' ability to solve problems. We believe that the
More informationSECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS
(Section 0.6: Polynomial, Rational, and Algebraic Expressions) 0.6.1 SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS LEARNING OBJECTIVES Be able to identify polynomial, rational, and algebraic
More informationJust What Do You Mean? Expository Paper Myrna L. Bornemeier
Just What Do You Mean? Expository Paper Myrna L. Bornemeier In partial fulfillment of the requirements for the Master of Arts in Teaching with a Specialization in the Teaching of Middle Level Mathematics
More informationMath Course Descriptions & Student Learning Outcomes
Math Course Descriptions & Student Learning Outcomes Table of Contents MAC 100: Business Math... 1 MAC 101: Technical Math... 3 MA 090: Basic Math... 4 MA 095: Introductory Algebra... 5 MA 098: Intermediate
More informationFACTORING POLYNOMIALS
296 (540) Chapter 5 Exponents and Polynomials where a 2 is the area of the square base, b 2 is the area of the square top, and H is the distance from the base to the top. Find the volume of a truncated
More informationMath at a Glance for April
Audience: School Leaders, Regional Teams Math at a Glance for April The Math at a Glance tool has been developed to support school leaders and region teams as they look for evidence of alignment to Common
More informationACCUPLACER. Testing & Study Guide. Prepared by the Admissions Office Staff and General Education Faculty Draft: January 2011
ACCUPLACER Testing & Study Guide Prepared by the Admissions Office Staff and General Education Faculty Draft: January 2011 Thank you to Johnston Community College staff for giving permission to revise
More informationMajor 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( ) ( ) Math 0310 Final Exam Review. # Problem Section Answer. 1. Factor completely: 2. 2. Factor completely: 3. Factor completely:
Math 00 Final Eam Review # Problem Section Answer. Factor completely: 6y+. ( y+ ). Factor completely: y+ + y+ ( ) ( ). ( + )( y+ ). Factor completely: a b 6ay + by. ( a b)( y). Factor completely: 6. (
More informationPayment streams and variable interest rates
Chapter 4 Payment streams and variable interest rates In this chapter we consider two extensions of the theory Firstly, we look at payment streams A payment stream is a payment that occurs continuously,
More informationHigh School Functions Interpreting Functions Understand the concept of a function and use function notation.
Performance Assessment Task Printing Tickets Grade 9 The task challenges a student to demonstrate understanding of the concepts representing and analyzing mathematical situations and structures using algebra.
More informationSPECIAL PRODUCTS AND FACTORS
CHAPTER 442 11 CHAPTER TABLE OF CONTENTS 111 Factors and Factoring 112 Common Monomial Factors 113 The Square of a Monomial 114 Multiplying the Sum and the Difference of Two Terms 115 Factoring the
More information1 TRIGONOMETRY. 1.0 Introduction. 1.1 Sum and product formulae. Objectives
TRIGONOMETRY Chapter Trigonometry Objectives After studying this chapter you should be able to handle with confidence a wide range of trigonometric identities; be able to express linear combinations of
More informationEntry Level College Mathematics: Algebra or Modeling
Entry Level College Mathematics: Algebra or Modeling Dan Kalman Dan Kalman is Associate Professor in Mathematics and Statistics at American University. His interests include matrix theory, curriculum development,
More informationThe Basics of Interest Theory
Contents Preface 3 The Basics of Interest Theory 9 1 The Meaning of Interest................................... 10 2 Accumulation and Amount Functions............................ 14 3 Effective Interest
More informationAlgebra and Geometry Review (61 topics, no due date)
Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties
More informationHigher. Polynomials and Quadratics 64
hsn.uk.net Higher Mathematics UNIT OUTCOME 1 Polnomials and Quadratics Contents Polnomials and Quadratics 64 1 Quadratics 64 The Discriminant 66 3 Completing the Square 67 4 Sketching Parabolas 70 5 Determining
More informationBond Price Arithmetic
1 Bond Price Arithmetic The purpose of this chapter is: To review the basics of the time value of money. This involves reviewing discounting guaranteed future cash flows at annual, semiannual and continuously
More information2. Annuities. 1. Basic Annuities 1.1 Introduction. Annuity: A series of payments made at equal intervals of time.
2. Annuities 1. Basic Annuities 1.1 Introduction Annuity: A series of payments made at equal intervals of time. Examples: House rents, mortgage payments, installment payments on automobiles, and interest
More informationMohawk Valley Community College MVCC MA115 Mr. Bauer
Mohawk Valley Community College MVCC MA115 Course description: This is a dual credit course. Successful completion of the course will give students 1 VVS Credit and 3 MVCC Credit. College credits do have
More informationTaylor 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 information88 Differences of Squares. Factor each polynomial. 1. x 9 SOLUTION: 2. 4a 25 SOLUTION: 3. 9m 144 SOLUTION: 4. 2p 162p SOLUTION: 5.
Factor each polynomial. 1.x 9 SOLUTION:.a 5 SOLUTION:.9m 1 SOLUTION:.p 16p SOLUTION: 5.u 81 SOLUTION: Page 1 5.u 81 SOLUTION: 6.d f SOLUTION: 7.0r 5n SOLUTION: 8.56n c SOLUTION: Page 8.56n c SOLUTION:
More informationZeros of Polynomial Functions
Review: Synthetic Division Find (x 25x  5x 3 + x 4 ) (5 + x). Factor Theorem Solve 2x 35x 2 + x + 2 =0 given that 2 is a zero of f(x) = 2x 35x 2 + x + 2. Zeros of Polynomial Functions Introduction
More informationGREEN CHICKEN EXAM  NOVEMBER 2012
GREEN CHICKEN EXAM  NOVEMBER 2012 GREEN CHICKEN AND STEVEN J. MILLER Question 1: The Green Chicken is planning a surprise party for his grandfather and grandmother. The sum of the ages of the grandmother
More informationMATH 90 CHAPTER 1 Name:.
MATH 90 CHAPTER 1 Name:. 1.1 Introduction to Algebra Need To Know What are Algebraic Expressions? Translating Expressions Equations What is Algebra? They say the only thing that stays the same is change.
More informationGrade 11 PreCalculus Mathematics (30S)
Grade 11 PreCalculus Mathematics (30S) A Course for Independent Study Field Validation Version G r a d e 1 1 P r e  C a l c u l u s M a t h e m a t i c s ( 3 0 S ) A Course for Independent Study Field
More informationSection 1.5 Linear Models
Section 1.5 Linear Models Some reallife problems can be modeled using linear equations. Now that we know how to find the slope of a line, the equation of a line, and the point of intersection of two lines,
More informationPennies and Blood. Mike Bomar
Pennies and Blood Mike Bomar In partial fulfillment of the requirements for the Master of Arts in Teaching with a Specialization in the Teaching of Middle Level Mathematics in the Department of Mathematics.
More information2009 Chicago Area AllStar Math Team Tryouts Solutions
1. 2009 Chicago Area AllStar Math Team Tryouts Solutions If a car sells for q 1000 and the salesman earns q% = q/100, he earns 10q 2. He earns an additional 100 per car, and he sells p cars, so his total
More informationThe Relation between Two Present Value Formulae
James Ciecka, Gary Skoog, and Gerald Martin. 009. The Relation between Two Present Value Formulae. Journal of Legal Economics 15(): pp. 6174. The Relation between Two Present Value Formulae James E. Ciecka,
More informationSyllabus MAT0020 College Preparatory Math (Selfpaced Modular Course)
Syllabus MAT0020 College Preparatory Math (Selfpaced Modular Course) Term: SPRING 20092 Reference #: Instructor s Name: Email: Office: Math Lab, Room # 2223 Mailbox: Math Lab, Room # 2223 Office Hours:
More informationUndergraduate Notes in Mathematics. Arkansas Tech University Department of Mathematics
Undergraduate Notes in Mathematics Arkansas Tech University Department of Mathematics A Semester Course in Finite Mathematics for Business and Economics Marcel B. Finan c All Rights Reserved August 10,
More informationMathematics Placement Packet Colorado College Department of Mathematics and Computer Science
Mathematics Placement Packet Colorado College Department of Mathematics and Computer Science Colorado College has two all college requirements (QR and SI) which can be satisfied in full, or part, b taking
More informationCENTRAL TEXAS COLLEGE SYLLABUS FOR DSMA 0306 INTRODUCTORY ALGEBRA. Semester Hours Credit: 3
CENTRAL TEXAS COLLEGE SYLLABUS FOR DSMA 0306 INTRODUCTORY ALGEBRA Semester Hours Credit: 3 (This course is equivalent to DSMA 0301. The difference being that this course is offered only on those campuses
More informationA.3. Polynomials and Factoring. Polynomials. What you should learn. Definition of a Polynomial in x. Why you should learn it
Appendi A.3 Polynomials and Factoring A23 A.3 Polynomials and Factoring What you should learn Write polynomials in standard form. Add,subtract,and multiply polynomials. Use special products to multiply
More informationLesson 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 informationMath 046 Online Course Syllabus Elementary Algebra and Geometry
Math 046 Online Course Syllabus Elementary Algebra and Geometry THIS IS AN 8 WEEK CLASS Carol Murphy, Professor CRN # 08391 Online office hours: Tuesdays from 8 9 pm Office Phone: 6193887691 Fall Other
More informationInformation Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay
Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture  17 ShannonFanoElias Coding and Introduction to Arithmetic Coding
More informationU.C. Berkeley CS276: Cryptography Handout 0.1 Luca Trevisan January, 2009. Notes on Algebra
U.C. Berkeley CS276: Cryptography Handout 0.1 Luca Trevisan January, 2009 Notes on Algebra These notes contain as little theory as possible, and most results are stated without proof. Any introductory
More informationTHE SAULT COLLEGE OF APPLIED ARTS AND TECHNOLOGY SAULT STE. MARIE, ON COURSE OUTLINE
THE SAULT COLLEGE OF APPLIED ARTS AND TECHNOLOGY SAULT STE. MARIE, ON COURSE OUTLINE Course Title: College Preparatory Mathematics Code No.: Mth 925 Semester: Two Program: College Entrance  Native Author:
More informationAnnuities: Present Value
8.5 nnuities: Present Value GOL Determine the present value of an annuity earning compound interest. INVESTIGTE the Math Kew wants to invest some money at 5.5%/a compounded annually. He would like the
More informationSolving Quadratic Equations by Factoring
4.7 Solving Quadratic Equations by Factoring 4.7 OBJECTIVE 1. Solve quadratic equations by factoring The factoring techniques you have learned provide us with tools for solving equations that can be written
More informationAlgebra 1 Advanced Mrs. Crocker. Final Exam Review Spring 2014
Name: Mod: Algebra 1 Advanced Mrs. Crocker Final Exam Review Spring 2014 The exam will cover Chapters 6 10 You must bring a pencil, calculator, eraser, and exam review flip book to your exam. You may bring
More informationGeometric 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 informationDick Schwanke Finite Math 111 Harford Community College Fall 2013
Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of
More informationCORE Assessment Module Module Overview
CORE Assessment Module Module Overview Content Area Mathematics Title Speedy Texting Grade Level Grade 7 Problem Type Performance Task Learning Goal Students will solve reallife and mathematical problems
More informationSection A3 Polynomials: Factoring APPLICATIONS. A22 Appendix A A BASIC ALGEBRA REVIEW
A Appendi A A BASIC ALGEBRA REVIEW C In Problems 53 56, perform the indicated operations and simplify. 53. ( ) 3 ( ) 3( ) 4 54. ( ) 3 ( ) 3( ) 7 55. 3{[ ( )] ( )( 3)} 56. {( 3)( ) [3 ( )]} 57. Show by
More informationAlgebra 1 Course Information
Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through
More informationIn this section, you will develop a method to change a quadratic equation written as a sum into its product form (also called its factored form).
CHAPTER 8 In Chapter 4, you used a web to organize the connections you found between each of the different representations of lines. These connections enabled you to use any representation (such as a graph,
More informationCopyrighted Material. Chapter 1 DEGREE OF A CURVE
Chapter 1 DEGREE OF A CURVE Road Map The idea of degree is a fundamental concept, which will take us several chapters to explore in depth. We begin by explaining what an algebraic curve is, and offer two
More informationAlgebra 1 If you are okay with that placement then you have no further action to take Algebra 1 Portion of the Math Placement Test
Dear Parents, Based on the results of the High School Placement Test (HSPT), your child should forecast to take Algebra 1 this fall. If you are okay with that placement then you have no further action
More information