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MwJ I h of Vllnrtal.ihrar> HI III I I I I I I IIII ! ... " "(j 1620 1603 07S3 APPLIED MATHEMATICS 10b-20b Program of Studies /dlbcrra EDUCATION QCAURRGDHT_nt_er_im__1 9_98_ Curriculum Standards Branch 14 C2 A738 1998 gr. 10-11 Digitized by the Internet Archive in 2012 with funding from University of Alberta Libraries http://archive.org/details/appliedmath10b20b98albe — 1 APPLIED MATHEMATICS 10b-20b Program of Studies /dlbota EDUCATION QCAURRGDHT=nte=ri=m=19=98==:=====-^—-————--—Curr—ic—ul—um—S—tan—da^rd=s B^ran—ch 14 C2 A738 1998 ar. n-1 1 [ [ Ex LIBRIS UNIVERSITATIS ALBERTENSIS 1 APPLIED MATHEMATICS 10b-20b RATIONALE AND PHILOSOPHY A. Students, for a variety of reasons, may want to transfer after meeting the acceptable standard in transfer from the pure mathematics course Pure Mathematics 10, the prerequisite is Applied sequence to the applied mathematics course Mathematics 10b, a 3-credit course. For those sequence. In this case, students must satisfy the students who want to transfer after meeting the prerequisites that cover the outcomes exclusive to acceptable standard in Pure Mathematics 20 or applied mathematics. The outcomes common to Pure Mathematics 30, the prerequisite is Applied pure mathematics and applied mathematics need Mathematics 20b, a 5-credit course. The two not be repeated. For those students who want to bridging courses are shown in the diagram below. Pure Pure Pure Mathematics Mathematics Mathematics 10(5) 20(5) 30 (5) Applied Applied Applied Mathematics Mathematics Mathematics 10(5) 20(5) 30(5) Rationale and Philosophy Applied Mathematics 10b-20b /l ©Albena Education. Alberta.Canada (Interim 1998) — LEARNER OUTCOMES B. The general outcomes for the Applied Mathematics 10b—20b program are shown first. For each of the two courses, the learner outcomes follow the format of general outcome, specific outcomes and illustrative examples. The illustrative examples are for discretionary use only. The outcomes are arranged in order of strand and substrand, following the order Number, Patterns and Relations, Shape and — Space, Statistics and Probability established in the Grade 10 to Grade 12 common curriculum framework. This listing is not intended as a sequence for instruction, and the number of outcomes is not an indication of the relative times to be spent on each ofthe strands. All the specific outcomes have an A prefix, such as A1-3, and they refer to those outcomes that are exclusive to applied mathematics. The learner outcomes listing for Applied Mathematics 10b includes all those outcomes that are exclusive to Applied Mathematics 10. The learner outcomes listing for Applied Mathematics 20b includes all those outcomes that are exclusive to Applied Mathematics 10 and Applied Mathematics 20. Outcomes that are exclusive to Applied Mathematics 10 are printed twice, once as Applied Mathematics 10b and once as part of Applied Mathematics 20b. 2/ Applied Mathematics 10b-20b Learner Outcomes (Interim 1998) UNIVERSITY LIBRARY ©Alberta Education. Alberta.Canada UNIVERSITY OF ALBERTA GENERAL OUTCOMES—Number Strand Substrand Applied Mathematics 10b-20b Number Operations Students will: • demonstrate an Describe and apply arithmetic operations on tables to solve problems, understanding ofand using technology as required. [Applied Mathematics 10b and 20b] proficienc> with calculations • decide which arithmetic operation or operations can be used to solve a problem and then solve the problem. GENERAL OUTCOMES—Patterns and Relations Strand Substrand Applied Mathematics 10b-20b Variables and Equations Students will: • represent algebraic Use linear programming to solve optimization problems. expressions in multiple [Applied Mathematics 20b] ways. GENERAL OUTCOMES—Shape and Space Strand Substrand Applied Mathematics 10b-20b Measurement Students will: • describe and compare Use measuring devices to make estimates and to perform calculations everyday phenomena, in solving problems. [Applied Mathematics 10b and 20b] using either direct or Demonstrate an understanding of scale factors, and their indirect measurement. interrelationship with the dimensions ofsimilar shapes and objects. [Applied Mathematics 20b] 3-D Objects and 2-D Shapes Students will: • describe the Develop and apply the geometric properties ofcircles and polygons to characteristics of3-D solve problems. [Applied Mathematics 20b] objects and 2-D shapes, and analyze the relationships among them. General Outcomes Applied Mathematics 10b-20b /3 ©Alberta Education. Alberta. Canada (Interim 1998) GENERAL OUTCOMES—Statistics and Probability Strand Substrand Applied Mathematics 10b-20b Data Analysis Students will: • collect, display and Apply line-fitting and correlation techniques to analyze experimental analyze data to make results. [Applied Mathematics 10b and 20b] predictions about a population. Analyze graphs or charts ofgiven situations to derive specific information. [Applied Mathematics 20b] 9 4/ Applied Mathematics l()b-20b General Outcomes (Interim 1998) ©Alberta Education. Alberta. Canada P . APPLIED MATHEMATICS 10b Strand: Number (Number Operations) [CI Communication [PS] Problem Solving Students will: |CN] Connections |R] Reasoning • demonstrate an understanding ofand proficiency with [E] Estimation and [T] Technology calculations Mental Mathematics [V] Visualization • decide which arithmetic operation or operations can be used to solve a problem and then solve the problem. General and Specific Outcomes Illustrative Examples [Discretionary General Outcome Describe and apply arithmetic operations on tables to solve problems, using technology as required. Specific Outcomes A2-1. Solve problems involving The following is an income and expenses report for a business combinations oftables, using: for the vear ending December 3 1 • addition or subtraction of two tables Sales Year 1 Year2 Year3 Year4 Year5 • multiplication ofa table by a Laundrv $135000 $148000 $150000 $148000 $140000 DryCleaning 45000 47000 48000 45000 45000 real number RepairsandSundrv iniwrfi II 000 11 000 10000 9000 • spreadsheet functions and loialSales S190000 $206000 $209000 S203000 $194000 templates. OperatingExpenses [PS.T, V] SalariesandWages $ 94000 $ 99000 $101 000 $101 000 $ 96000 OperatingSupplies 22000 24000 25000 24000 23000 RepairsandMisc 4000 5000 6000 8000 5000 AccountingandLegal 2000 2000 2000 2000 2000 Advertising 2000 2000 2000 2000 2000 Sundrv 4000 5000 5000 4500 4000 TotalOperatingExpenses $128000 $137000 $141 000 $141 500 $132000 ProfitBeforeOverhead $ 62000 $ 69000 $ 68000 $ 61 500 $ 62000 OverheadExpenses Rent $ 12000 $ 14000 $ 16000 $ 18000 $ 18000 Utilities 6000 7000 8000 9000 10000 Insurance 3000 3000 3000 3000 3000 TaxesandLicenses 3000 3000 4000 4000 5000 Depreciation-Equip 10000 8000 7000 6000 5000 TotalOverheadExp. % 34000 S 35000 $ 38000 $ 40000 $ 41 000 ProfitBeforeTax $ 28000 $ 34000 $ 30000 $ 21 500 $ 21 000 IncomeTax $ 7000 $ 8500 $ 7500 $ 5375 $ 5250 NetProfit $ 21000 $ 25500 $ 22500 * 1612S $ \£.W Enter the data above onto a spreadsheet template provided to students. a) Calculate the dollar change in total sales, total operating expenses and total overhead expenses, between each year in the table. b) Which is the greatest dollar change? Applied Mathematics 10b /5 ©Alberta Education. Alberta. Canada (Interim 1998) Strand: Number (Number Operations) [C] Communication [PS] Problem Solving Students will: [CN] Connections [R] Reasoning • demonstrate an understanding ofand proficiency with [E] Estimation and [T] Technology calculations Mental Mathematics [V] Visualization • decide which arithmetic operation or operations can be used to solve a problem and then solve the problem. General and Specific Outcomes Illustrative Examples [Discretionary] 1.1.2 a) Calculate the percentage change in total sales, total operating expenses and total overhead expenses, between each year in the table, b) Which is the greatest percentage change? 1.1.3 a) Determine the percentage change foreach item for each year, b) Predict the figures for each type ofincome and expense for year 6. and predict the net profit for year 6. 1.1.4 Prepare a line graph showing the annual sales, operating expenses and overhead expenses for the five year period. Use the graph to determine which item has the greatest rate of increase, and which item has the greatest rate ofdecrease. 1.1.5 For the five year period, use a line ofbest fit procedure to determine equations oflines ofbest fit for total sales, total operating expenses and total overhead expenses. Use these equations to predict the values in year 6. From these values, predict the net profit in year 6. 1.1.6 Calculate the net profit as a percentage of sales for each ofthe five years. In which year did the net profit represent the highest proportion of sales? 1.1.7 Derive a formula relating total sales, total operating expenses, total overhead expenses, income tax and net profit. 6/ Applied Mathematics 10b (Interim 1W8) cAlberta Education. Alberta.Canada