MESSAGE TO TEACHERS: NOTE TO EDUCATORS:

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1 MESSAGE TO TEACHERS: NOTE TO EDUCATORS:

4 Teacher reflectio LESSON PLAN:2 Lesso Pla: FUNCTIONS, INVERSES AND LOGARITHMS Number of Activities 3 Duratio: 4h30 Week 4-5 Date Cotext: Mathematical : FUNCTIONS, INVERSES AND LOGARITHMS Lik with previous lesso: Fuctios, sequeces ad series KNOWLEDGE (K): Logarithms, fuctios, iverse relatios SKILLS (S): Ivestigate, discover, demostrate, calculate, problem solvig, drawig VALUES (V):Appreciatio ACTIVITY 1 ACTIVITY 2 ACTIVITY 3 Activity Cotet Logarithms Types of fuctios Graphs of iverse relatios LO,s ad AS s LO1.AS LO2 AS12.1,2,3 LO2 AS12.1,2,3 Learers give worksheets to demostrate a uderstadig of the defiitio of a logarithm ad ay laws eeded to solve real-life problems (Defiitio of a logarithm uderstad that the logarithmic fuctio is the iverse of the expoetial fuctio. Learers eed to covert fluetly betwee logarithmic form ad expoetial form. Note: Solvig logarithm equatios ad iequalities must be see i the cotext of fuctios. Learers demostrate the ability to work with various types of fuctios ad relatios icludig the iverses listed i the followig Assessmet Stadard. Demostrate kowledge of the formal defiitio of a fuctio. Give the relatioship betwee x ad y i - a set of graphs - tables - words - algebraic formulae Determie whether the give iformatio represets a fuctio. Learers draw graphs of the iverse relatios, of fuctios, i particular the iverse of: y = ax + q ; y = ax 2 ; y = a x ; a > 0: Teachig Methods questio ad aswer Questio ad aswer Discussio, questio ad aswer Educator, idividual, peer Class work, home work, test Expaded Opportuities: Differet examples ad remedial work Use of differet equatios

5 Teacher reflectio LESSON PLAN: 3 Lesso Pla: Fuctios ad iverses Number of Activities 2 Duratio: 4h30 Week 6 Date Cotext: Mathematical : Fuctios ad iverses Lik with previous lesso: Logarithms, iverses KNOWLEDGE (K): Iverse Fuctios SKILLS (S):Drawig, determie, iterpretatio VALUES (V): Appreciatio, Respect ACTIVITY 1 ACTIVITY 2 Activity Cotet Iverse Fuctios Characteristics of graphs LO,s ad AS s LO2 AS12.1,2,3 LO2 AS12.1,2,3 Determie which iverses are fuctios ad how the domai of the Origial fuctio eeds to be restricted so that the iverse is also a fuctio. Use ad iterpret fuctioal otatio. I the teachig process learers must uderstad how f (x) has bee trasformed to geerate f ( x), f (x), f ( x + a), f ( x) + a, f (ax), af (x) ad x = f (y) Idetify characteristics as listed below ad hece use applicable characteristics to sketch graphs of the iverses of the fuctios listed above: (a) domai ad rage; (b) itercepts with the axes; (c) turig poits, miima ad maxima; (d) asymptotes; (e) shape ad symmetry; (f) Average gradiet (average rate of chage); itervals o which the fuctio icreases/decreases. Teachig Methods questio ad aswer Questio ad aswer Educator, idividual, peer Expaded Opportuities: Differet examples ad remedial work Differet examples ad remedial work Teacher reflectio

7 Teachig Methods Discussio, questio ad aswer Questio ad aswer Discussio, questio ad aswer Educator, idividual, peer Class work, home work, test Expaded Opportuities: Differet examples ad remedial work. Use of differet equatios

8 LESSON PLAN: 5 Lesso Pla: FINANCIAL MATHEMATICS Number of Activities 3 Duratio: 4h30 Week8-9 Date Cotext: Fiacial Lik with previous lesso: Number patters KNOWLEDGE (K): Calculatig the period of ivestmet, uderstadig differet types of loas, SKILLS (S): Ivestigate, Calculate VALUES (V): Team member, fiacial disciplie ACTIVITY 1 ACTIVITY 2 ACTIVITY 3 Activity Cotet Periods of ivestmet Auities Bod repaymet LO,s ad AS s LO 1 AS12.1.4,5 LO 1 AS12.1.4,5 LO 1 AS12.1.4,5 Educators hads out worksheet ad assess the learers work (ability to use calculators) to calculate the value of i the formula : A = P (1 ± i) Facilitates ad use a checklist to see if learers are able to calculate the value of usig a calculator ad later discuss the differet periods of ivestmets. Discussio-teacher explais the auity cocept ad how the geometric series is used for the calculatio of auities, givig examples. Apply kowledge of geometric series to solve auity, with or without the use of the formulae: x[ (1 + i) 1] F = I ad P = x [(1 (1 + i) ] i Timelies are a useful strategy to solve problems i Fiacial Mathematics. Discussio-teacher explais bod repaymet problems ad how the geometric series is used for the calculatio of bod repaymets, givig examples. Apply kowledge of geometric series to bod repaymet problems, with or without the use of the formulae: x[ (1 + i) 1] F = I ad P = x [(1 (1 + i) ] i Timelies are a useful strategy to solve problems i Fiacial Mathematics.

9 Teachig Methods Expaded Opportuities: Discussio, questio ad aswer Questio ad aswer Discussio, questio ad aswer Class work, home work, test Educator, idividual, peer Differet examples ad remedial work Learers are asked to go to the differet Bakig Istitutios to ivestigate differet types of ivestmet ad which oe gives better returs. Teacher brigs to class differet pamphlets from differet Bakig Istitutios ad let the learers ivestigate which bak will give a better retur.

10 LESSON PLAN: 6 Lesso Pla: Fiacial Matters Number of Activities 2 Duratio: 4h30 Week10 Date Cotext: Fiacial Lik with previous lesso: umber patters, logarithms KNOWLEDGE (K): Calculatig the period of ivestmet, uderstadig differet types of loas, SKILLS (S): Ivestigate, Calculate VALUES (V): Team member, fiacial disciplie ACTIVITY 1 ACTIVITY 2 Activity Cotet Sikig value Aalysis of ivestmet ad loas LO,s ad AS s LO 1 AS12.1.4,5 LO 1 AS12.1.4,5 Teacher explais the sikig fud cocept ad how it ca be calculated ad apply kowledge of geometric series to sikig fud problems, with or without the use of the formulae: x[ (1 + i) 1] F = i ad P = x [(1 (1 + i) ] i Timelies are a useful strategy to solve problems i Fiacial Mathematics. Critically aalyse ivestmet ad loa optios ad make iformed decisios as to the best optio(s) (icludig pyramid ad micro-leders schemes). Teachig Methods Questio ad aswer Questio ad aswer Discussio, questio ad aswer Educator, idividual, peer Class work, home work, test Expaded Opportuities: Differet examples ad remedial work Learers are asked to go to the differet Bakig Istitutios to ivestigate differet types of ivestmet ad which oe gives better returs. Teacher brigs to class differet pamphlets from differet Bakig Istitutios ad let the learers ivestigate which bak will give a better retur.

11 NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P EXEMPLAR 04 MARKS: 50 TIME: 3 hours This questio paper cosists of 8 pages ad iformatio sheet. Please tur over Mathematics/P DBE/04 NSC Grade Eemplar INSTRUCTIONS

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MATHEMATICS P1 COMMON TEST JUNE 2014 NATIONAL SENIOR CERTIFICATE GRADE 12 Mathematics/P1 1 Jue 014 Commo Test MATHEMATICS P1 COMMON TEST JUNE 014 NATIONAL SENIOR CERTIFICATE GRADE 1 Marks: 15 Time: ½ hours N.B: This questio paper cosists of 7 pages ad 1 iformatio sheet. Please NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P NOVEMBER 0 MARKS: 50 TIME: 3 hours This questio paper cosists of 8 pages, diagram sheet ad iformatio sheet. Please tur over Mathematics/P DBE/November 0

Institute of Actuaries of India Subject CT1 Financial Mathematics Istitute of Actuaries of Idia Subject CT1 Fiacial Mathematics For 2014 Examiatios Subject CT1 Fiacial Mathematics Core Techical Aim The aim of the Fiacial Mathematics subject is to provide a groudig i NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P NOVEMBER 007 MARKS: 50 TIME: 3 hours This questio paper cosists of 9 pages, diagram sheet ad a -page formula sheet. Please tur over Mathematics/P DoE/November NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P NOVEMBER 009() MARKS: 50 TIME: 3 hours This questio paper cosists of 0 pages, a iformatio sheet ad diagram sheet. Please tur over Mathematics/P DoE/November

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Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions Chapter 5 Uit Aual Amout ad Gradiet Fuctios IET 350 Egieerig Ecoomics Learig Objectives Chapter 5 Upo completio of this chapter you should uderstad: Calculatig future values from aual amouts. Calculatig

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where: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return EVALUATING ALTERNATIVE CAPITAL INVESTMENT PROGRAMS By Ke D. Duft, Extesio Ecoomist I the March 98 issue of this publicatio we reviewed the procedure by which a capital ivestmet project was assessed. The

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Research on use of internet ressources in teaching. Can undergraduate students learn mathematics with the internet? Ca udergraduate studets lear mathematics with the iteret? Research o use of iteret ressources i teachig Geeral Mathematics School Lots of stuff Some Uiversity Quite a lot Much less (~100) Carl Wisløw wislow@id.ku.dk

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when n = 1, 2, 3, 4, 5, 6, This list represents the amount of dollars you have after n days. Note: The use of is read as and so on. Geometric eries Before we defie what is meat by a series, we eed to itroduce a related topic, that of sequeces. Formally, a sequece is a fuctio that computes a ordered list. uppose that o day 1, you have

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Savings and Retirement Benefits 60 Baltimore Couty Public Schools offers you several ways to begi savig moey through payroll deductios. Defied Beefit Pesio Pla Tax Sheltered Auities ad Custodial Accouts Defied Beefit Pesio Pla Did you

Biology 171L Environment and Ecology Lab Lab 2: Descriptive Statistics, Presenting Data and Graphing Relationships Biology 171L Eviromet ad Ecology Lab Lab : Descriptive Statistics, Presetig Data ad Graphig Relatioships Itroductio Log lists of data are ofte ot very useful for idetifyig geeral treds i the data or the

Chapter Eleven. Taylor Series. (x a) k. c k. k= 0 Chapter Eleve Taylor Series 111 Power Series Now that we are kowledgeable about series, we ca retur to the problem of ivestigatig the approximatio of fuctios by Taylor polyomials of higher ad higher degree

Intro to Sequences / Arithmetic Sequences and Series Levels Itro to Sequeces / Arithmetic Sequeces ad Series Levels Level : pg. 569: #7, 0, 33 Pg. 575: #, 7, 8 Pg. 584: #8, 9, 34, 36 Levels, 3, ad 4(Fiboacci Sequece Extesio) See Hadout Check for Uderstadig Level

Definition. A variable X that takes on values X 1, X 2, X 3,...X k with respective frequencies f 1, f 2, f 3,...f k has mean 1 Social Studies 201 October 13, 2004 Note: The examples i these otes may be differet tha used i class. However, the examples are similar ad the methods used are idetical to what was preseted i class.

Mocks.ie Maths LC HL Further Calculus mocks.ie Page 1 Maths Leavig Cert Higher Level Further Calculus Questio Paper By Cillia Fahy ad Darro Higgis Mocks.ie Maths LC HL Further Calculus mocks.ie Page Further Calculus ad Series, Paper II Q8 Table of Cotets:.

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008 I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces

A GUIDE TO LEVEL 3 VALUE ADDED IN 2013 SCHOOL AND COLLEGE PERFORMANCE TABLES A GUIDE TO LEVEL 3 VALUE ADDED IN 2013 SCHOOL AND COLLEGE PERFORMANCE TABLES Cotets Page No. Summary Iterpretig School ad College Value Added Scores 2 What is Value Added? 3 The Learer Achievemet Tracker

UNIT 3 SUMMARY STATIONS THROUGHOUT THE NEXT 2 DAYS, WE WILL BE SUMMARIZING THE CONCEPT OF EXPONENTIAL FUNCTIONS AND THEIR VARIOUS APPLICATIONS. Name: Group Members: UNIT 3 SUMMARY STATIONS THROUGHOUT THE NEXT DAYS, WE WILL BE SUMMARIZING THE CONCEPT OF EXPONENTIAL FUNCTIONS AND THEIR VARIOUS APPLICATIONS. EACH ACTIVITY HAS A COLOR THAT CORRESPONDS

Estimating the Mean and Variance of a Normal Distribution Estimatig the Mea ad Variace of a Normal Distributio Learig Objectives After completig this module, the studet will be able to eplai the value of repeatig eperimets eplai the role of the law of large umbers

Learning outcomes. Algorithms and Data Structures. Time Complexity Analysis. Time Complexity Analysis How fast is the algorithm? Prof. Dr. Algorithms ad Data Structures Algorithm efficiecy Learig outcomes Able to carry out simple asymptotic aalysisof algorithms Prof. Dr. Qi Xi 2 Time Complexity Aalysis How fast is the algorithm? Code the

CDs Bought at a Bank verses CD s Bought from a Brokerage. Floyd Vest CDs Bought at a Bak verses CD s Bought from a Brokerage Floyd Vest CDs bought at a bak. CD stads for Certificate of Deposit with the CD origiatig i a FDIC isured bak so that the CD is isured by the Uited LINEST i Excel The Excel spreadsheet fuctio "liest" is a complete liear least squares curve fittig routie that produces ucertaity estimates for the fit values. There are two ways to access the "liest" Measures of Spread ad Boxplots Discrete Math, Sectio 9.4 We start with a example: Example 1: Comparig Mea ad Media Compute the mea ad media of each data set: S 1 = {4, 6, 8, 10, 1, 14, 16} S = {4, 7, 9,