TITLE: [Insert Course Title.] Financial Algebra Advanced .
![TITLE: [Insert Course Title.] Financial Algebra Advanced .](/img2/143/ncaa-syllabus-desc-outline.webp)
TITLE: [Insert Course Title.][Tip: The course name should reflect the use of algebra (i.e. Financial Algebra orAdvanced Algebra with Financial Applications). A finance-based name is not an accuraterepresentation of the course.]LEVELREGULARGRADE10 – 12CREDIT1.0PREREQUISITE: Algebra 1DESCRIPTION: Financial Algebra is an algebra-based, applications-oriented, technologydependent course that requires Algebra 1 and Geometry as a prerequisite. The courseaddresses college preparatory mathematics topics from Advanced Algebra, Statistics,Probability, Precalculus, and Calculus under seven financial umbrellas: Banking, Investingand Modeling a Business, Employment and Income Taxes, Automobile Ownership,Independent Living, and Retirement Planning and Household Budgeting. Students use avariety of problem solving skills and strategies in real-world contexts. The mathematicstopics contained in this course are introduced, developed, and applied in an as-neededformat in the financial settings covered.Financial Algebra adheres to the following basic assumptions regarding mathematicseducation: All students will have access to calculators and computers. Classroom activities will be student-centered. All units will have increased emphasis on algebraic representations, graphicalrepresentations, and verbal representations, and the interrelationships of thesethree approaches. There is an emphasis on estimation, number sense, problem solving, and the rolethat reading comprehension plays in problem solving. Evaluation will include alternative methods of assessment.USE OF TECHNOLOGYSpreadsheetsInternet ResearchGraphing CalculatorTEXTBOOKGerver, R. and Sgroi, R. Financial Algebra. South-Western/CengageLearning Mason, Ohio 2011 ISBN -13: 978-0-538-44967-0 INSTRUCTOR RESOURCES [List additional reference materials that may beused throughout the year][Tip: Additional reference materials may include textbooks in the areas of Geometry,Algebra II, Precalculus, Calculus, and Statistics. This will help accurately reflect therigor of the course.][Insert Court Title]—NCAA OutlinePage 1
COURSE OUTLINEUNIT 1Banking(approximately 25 days)Mathematics Topics§ Using the simple interest formulaI PRTand its algebraic equivalents§ Understanding compounding via iteration§ Deriving the compound interest formula§ Computing compound interest with and without the formula§ Applying the compound interest formula§ Introduction to limit notationrB (1 ) ntnLim f ( x) bx a§ x Approximating e by examining the sequence 1 1 § x Defining the natural base e using the rational and exponential expression limitxnotation1 x x Lim 1 § Applying the natural base e in the continuous compounding formulabIdentifying y ax as exponential decay when x 1§ Identifying§ Modeling a geometric series of the type§ B Perty axb as exponential growth when x 1n 1 ax bb 0§ § Graphing exponential functions of the typeAnalyzing rational functions and their limits of the formn m, and n m§ y axbLimax n bx cxm dwhere n m,Using the compound interest formula to derive the present value of a single depositinvestment formulaP [Insert Court Title]—NCAA OutlineB r 1 n ntPage 2
§ Using the compound interest formula to derive the present value of a periodicdeposit investment formula§ r B n P nt r 1 1 n Using the future value of a periodic deposit investment formulant r P 1 1 n B r n § Adapting all banking formulas for input into a spreadsheetEssential Financial ApplicationsSavings accounts; compound interest; continuous compounding; future value of single andperiodic investments; present value of single and periodic investments; reconcile a bankstatement, annual percentage rate (APR); annual percentage yield (APY)[Insert Court Title]—NCAA OutlinePage 3
UNIT 2Investing and Modeling a Business (approximately 30 days)Mathematics Topics§ Constructing and interpreting scatterplots§ Operations with functions§ Evaluating functions and using them to model situations§ Translating verbal situations into algebraic linear functions§ Translating verbal situations into quadratic functions§ Creating rational functions of the form§ Translating verbal situations into linear and quadratic inequalities§ Solving linear systems of equations and inequalities such as:§ Solving systems of linear equations and inequalities in two variables§ Identifying domains for which f(x) g(x), f(x) g(x), and f(x) g(x)§ Identifying form, direction, and strength from a scatterplot§ Finding, interpreting, and graphing linear regression equations§ Determining domains for which prediction using a regression line is consideredextrapolating or interpolating§ Finding and interpreting the Pearson Product-Moment Coefficient of Correlation§ Finding the axis of symmetryx f ( x) mx bx b b b , vertex , f , roots, and the2a 2a 2a concavity of parabolic curves§ Using the quadratic formula[Insert Court Title]—NCAA Outline bb 2 4acif ax bx c 0 then x 2a2a2Page 4
§ Finding and interpreting quadratic regression equations§ Solving linear-quadratic systems of equations and inequalities such as:§ Finding absolute and relative extrema§ Causation vs. correlation for bivariate data§ Identifying explanatory and response variables§ Identifying and diagramming lurking variables such as:§ Using the slope-intercept form of a linear equation§ Interpreting slope as a rate of change§ Using the transitive property of dependence§ Determining the zero net difference§ Writing algebraic formulas for use in spreadsheets§ Rational Expressions§ § Algebraic fractions, ratios, and proportionsWriting literal equations§ Solving linear equations and inequalities[Insert Court Title]—NCAA OutlinePage 5ΔyΔxy mx b
§ Calculating moving averages§ Reading and interpreting data in pictorial representations§ Algebraic representations of percent, percent increase and percent decrease§ Expressing averages as rational functions§ Translating verbal expressions into algebraic formulas for use in a spreadsheetEssential Financial ApplicationsSupply and demand; fixed and variable expenses; graphs of expense and revenuefunctions; breakeven analysis; the profit equation; mathematically modeling a business,sole proprietorships, partnerships, candlestick charts, simple moving averages, readingand interpreting stock market ticker output, stockbroker commissions, net proceeds, grossprofit, stock splits, dividend Income, yield vs. bank interest, common and preferred stock,corporate bonds[Insert Court Title]—NCAA OutlinePage 6
UNIT 3Credit (approximately 25 days)Mathematics Topics§ Using algebraic proportions§ Finding and interpreting cubic regression equations of the form32y ax bx cx dy mx b§ Using slope-intercept form§ Using and interpreting exponential growth and decay equations§ Computing the average daily balance§ Applying the monthly payment formular r P 1 1212M 12t r 1 1 12 12tr r P 1 1212M 12t r 1 1 12 12t§ Using slope-intercept form y Mx b where§ 12 t r r P 1 12 12 x b R where FC financeUsing the formula FC 12 t r 1 1 12 charge and R retail price§ Using inverse functions to introduce the natural logarithm functiony ln x asy loge x and as the inverse of y e x§ Using the formular r P 1 1212M 12t r 1 1 12 [Insert Court Title]—NCAA OutlinePage 712tto solve for the exponent t where
t Mln p M r ln p 12 r 12 ln 1 12 ndni 1 n§ Modeling the average daily balance using the formula§ Calculating the finance charge using the formula§ Creating algebraic formulas and applying them for use in spreadsheets n d n APRFC i 1 n 12Essential Financial ApplicationsCredit; deferred payments; mark up, wholesale price; retail price; finance charge loans;loan calculations and regression; credit cards; credit card statement; average daily balance[Insert Court Title]—NCAA OutlinePage 8
UNIT 4Automobile Ownership (approximately 25 days)Mathematics Topics§ Systems of linear equations§ Modeling exponential depreciation asy Pxb where P is purchase price and x 1.§ Transforming raw data into a frequency distribution§ Creating and interpreting stem and leaf plots and side-by-side steam plots such as§ Creating and interpreting box and whisker plots and side-by-side boxplots§ Creating and interpreting modified box and whisker plots§ Computing measures of dispersion§ Computing Q1, Q2, Q3, and Q4 manually and with the graphing calculator§ Using the expressions§ Compute and interpret percentilesR x H x L and IQR Q3 Q1.Q1 1.5( IQR ) and Q3 1.5( IQR) to determine outliersn xi i 1n§ Measures of central tendency x§ Creating and interpreting piecewise (split) functions of the form§ Determining the domains of a piecewise function from verbal situations§ Graphing piecewise functions using mutually exclusive domains[Insert Court Title]—NCAA OutlinePage 9, median and mode
§ Identifying the cusp of a piecewise function at a change in slope such as§ Using multi-variable square root functions such as the skid length S§ Using§ § § § 30 Dfn . 5280 s RD 0.75 to determine reaction distance2 60 2Using BD 5(.1s) to compute the breaking distance 5280 s 2Using TSD 0.75 to compute total stopping distance 5(0.1s) 2 60 DDManipulating D RT , R , and T to determine distance, rate, and timeTRUsing D MPG(G) to compute miles per gallon§ Using geometry theorems involving chords intersecting in a circle and radiiperpendicular to chords to determine yaw mark arc lengthC2 MFinding radius r where C is chord length and M is middle ordinate§ Computing arc lengths§ Using dilations Dk to transform formulas between the English Standard and Metricmeasurement systems§ Applying all algebraic formulas from the chapter for use in spreadsheets§ 8M2Essential Financial ApplicationsClassified ads, negotiating auto purchases and sales, automobile insurance, linearautomobile depreciation, historical and exponential depreciation, driving data, drivingsafety data, accident investigation data[Insert Court Title]—NCAA OutlinePage 10
Unit 5Employment and Income Taxes (approximately 28 days)Mathematics Topics§ Identifying continuous and discontinuous functions by their graphs§ Interpreting jump discontinuities§ Writing an interpreting domains and piecewise functions of the formsand§ Graphing exponential pay schedules such as§ Graphing piecewise functions with cusps such as§ Using measures of central tendency and rational functions such asa ( x) 40r 1.5trt ra n xr n with common ratio r§ Geometric sequences such as§ Expressing percent increases and decreases as rational functions§ Reading and interpreting data§ Introducing point-slope form y y1 m( x x1 ) and convertingit to slope-intercept form y[Insert Court Title]—NCAA Outline mx bPage 11
§ Graphing continuous polygonal functions with multiple slopes and cusps§ Translating verbal expressions into literal rational, exponential, and linearequations.§ Expressing domains using compound inequality notation of the formt t1 and t t2§ Expressing domains using compound inequality notation of the formt t1 and t t2 , interval notation of the form t1 x t2 , and tax schedulenotation of the form “over t1 but not over t 2 ”§ Given a compound inequality statement, modeling a tax bracket to determine thetax using a linear equation of the form y a p( x t1 ) where y is the tax, a isthe base tax, p is the tax percentage expressed as a decimal, t1 is the lowerboundary of the domain, and x is the taxable income§ Converting point-slope form to slope-intercept form of a linear equation§ Writing equations in point-slope form§ Modeling algebraically a tax schedule of the form[Insert Court Title]—NCAA OutlinePage 12
§ Using a piecewise function of the formwhere f(x) represents the tax liability function for taxpayers using a given tax schedulewith taxable incomes on a given domain§ Graphing piecewise functions of the formon the coordinate plane.§ Identifying the cusps of piecewise functions from the function notation§ Interpreting the graphs, slopes, and cusps of continuous polygonal functions withmultiple slopes and cusps§ Translating verbal expressions into literal equations§ Adapting all algebraic formulas in the unit for use in spreadsheetsEssential Financial ApplicationsTax credits and tax deductions, tax evasion vs. tax avoidance, filing long form 1040, filingSchedules A and B, filing Forms 1040A and 1040EZ, looking for employment, pay periodsand rates, commissions, royalties, piecework pay, employee benefits, Social Security andMedicare, tax tables, worksheets, and schedules, modeling Tax Schedules[Insert Court Title]—NCAA OutlinePage 13
UNIT 6Independent Living (approximately 22 days)Mathematics Topics§ Using rational functions to compute back-end ratios of the formb § Using rational functions to compute front-end ratios of the formf § § § § m p / 12 h / 3 c d.a / 12m p / 12 h / 12.x / 12Using the monthly payment formula12t r r P 1 12 12 M 12t r 1 1 12 12t r r P 1 12 12 C where C is original costComputing interest I 12 t r 1 1 12 1Using the apothem to compute the area of a regular polygon A ap2Using probability to find the area of irregular plane region (The Monte Carlo Method)number of points inside regionarea of irregular region number of random points generated area of framing rectangle§ Using factors of dilations to draw to scale§ Finding areas of irregular and shaded regions§ Using rational functions to compute BTU’s, such as§ Solving proportions§ Creating multi-variable tax assessment equations§ Using exponential equations to model rent increases such asD 1B R A 1 100 [Insert Court Title]—NCAA OutlinePage 14BTU rating while60
§ Modeling rent increases using exponential regression§ Reading and interpreting data§ Using the future value of a periodic deposit formula r nt P 1 1 n B r n tomake comparisons to mortgage payments and increasing resale value of a home§ Writing all algebraic formulas from the chapter for use in spreadsheets§ Translating verbal expressions into literal equationsEssential Financial ApplicationsCondominiums, cooperative rentals, private residences, reading a floor plan, the mortgageapplication process, purchasing a home, renter’s and homeowner’s insurance, liability andumbrella insurance, personal floater insurance[Insert Court Title]—NCAA OutlinePage 15
UNIT 7Retirement Planning and Budgeting (approximately 25 days)Mathematics Topics§ Using the future value of a periodic investment formula of the formto predict balances after t years when given a periodic deposit amount, aninvestment return rate, and compounding information§ Using the present value of a periodic investment formula of the formto determine the principal when given a future value, a timein years, an investment return rate, and compounding information§ Writing rational expressions as a combination of rational and polynomialexpressions§ Using inequalities to define domains when creating algebraic expressions§ Analyzing the effect that a change in multipliers has to the value of an algebraicexpression§ Writing rational expressions to represent increase over time§ Using and interpreting the greatest integer function of the form§ § Determining and interpreting the expected value of a probability distribution wherenthe expected value is of the form xi f ( xi )i 1Reading and interpreting data presented in multiple formats§ Creating, interpreting, and graphing greatest integer functions of the form[x ]y [x a]§ Creating, interpreting, and graphing greatest integer functions of the formy [x a] 1§ Understanding the algebraic and contextual differences betweeny [x a] 1[Insert Court Title]—NCAA OutlinePage 16y [x a] and
§ Incorporating the greatest integer function into a piecewise function of the formc(x) aa c(x – d)a c([x – d] 1)when x bwhen x b and x is an integerwhen x b and x is not an integer§ Evaluating a piecewise function that includes a greatest integer function for variousvalues on the domain of the piecewise function§ Creating, interpreting, and graphing a system of a linear and a piecewise functionand determining the point of intersection as shown in the following graph:§ Using sectors and central angles of a circle to depict proportional categories on apie chart when given categorical information§ Creating and interpreting budget line equations of the typeC x represents the cost of the first of two items and C yC x x C y y Bwhererepresents the cost of thesecond of two items, x and y represent quantities under consideration and Brepresents an amount budgeted§ Interpreting points on a budget line graphs in the context of their relationship to thebudget line as shown in the following display:[Insert Court Title]—NCAA OutlinePage 17
§ Comparing budget line graphs and interpreting them as transformations in the planeas shown here:§ Using inequalities to interpret regions and points in the plane in relation to a budgetline graph§ Using multiple representations to chart data such as§ Using algebraic rational expressions to model ratios in context§ Writing algebraic formulas for use in spreadsheetsEssential Financial ApplicationsRetirement income from savings; social security benefits; pensions; life insurance; utilityexpenses; electronic utilities; charting a budget; cash flow; budgeting[Insert Court Title]—NCAA OutlinePage 18
DESCRIPTION: Financial Algebra is an algebra-based, applications-oriented, technology dependent course that requires Algebra 1 and Geometry as a prerequisite. The course addresses college preparatory mathematics topics from Advanced Algebra, Statistics, Probability, Precalculus, and Calculus under seven financial umbrellas: Banking, Investing
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