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MATHEMATICS APPLIED 30 Revised Course of Studies This document contains only the specific outcomes for Applied Mathematics 30. The program rationale and philosophy and general outcomes can be found on pages 1 to 6 ofthe Applied Mathematics 10-20 program of studies, Interim 1998. /dibcrra QA 14 LEARNING C2 3rim 2000 Curriculum Standards Branch 1A735 2000 I gr.l2 C.6 CURRGDHIST Digitized by the Internet Archive in 2012 with funding from University of Alberta Libraries http://archive.org/details/appliedmath30revise00albe APPLIED MATHEMATICS 30 Revised Course of Studies This document contains only the specific outcomes for AppUed Mathematics 30. The program rationale and philosophy and general outcomes can be found on pages 1 to 6 of the Applied Mathematics 10-20 program of studies, Interim 1998. /dlbca-ra QA 14 LEARNING C2 3rim 2000 Curriculum Standards Branch A735 ! 2000 gr.l2 C.6 CURRGDHIST UNIVERSITY LIBRARY UNIVERSITY OF ALBERTS APPLIED MATHEMATICS 30 Strand: Number (Number Operations) [C] Conununication [PS] ProblemSolving 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 oroperations can be used to solve aproblem and then solve the problem. General and Specific Outcomes Illustrative Examples General Outcome Describe and apply operations on matrices to solve problems, using technology as required. Specific Outcomes A6-1. Model and solve problems, 1.1 CFL Western Division Standings (23'^'^ August) including those solved Against Eastern teWams previously, using technology T L Points BC to perform matrix operations 1 2 2 Calgary 2 4 ofaddition, subtraction and Saskatchewan 1 1 2 scalar multipUcation as Edmonton 2 2 1 required. [CN, PS, R, T, V] Against Western teams W T L Points BC 4 8 Calgary 3 2 6 Saskatchewan 1 4 2 Edmonton 1 3 2 a) Create a combined table using matrix addition. b) What condition is necessary for there to be a matrix sum A + B, given original matricesA and B7 1.2 A store sells items that are tax free, items that have a 7% GST charge on the base price, and items that have both a 7% GST and a 9% PST charge on the base price. A weekend's sales, before tax, is represented in the table: Weekend Sales Summary Sales byTax Category Saturday Sales ($) Sunday Sales ($) Tax free 500 700 GST only 1250 400 GST and PST 800 700 a) Determine each amount oftax (GST and PST) collected by the store on this weekend, using any method. b) Model and solve the problem, using appropriate matrices derived from the table given. c) How would you change your matrix model for a new GST rate of5% and a new PST rate of 12%? Applied Mathematics 30 /59 ©AlbertaLearning, Alberta, Canada (Interim 2000) Strand: Number (NumberOperations) [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 theproblem. General and Specific Outcomes Illustrative Examples 1.3 An arctic expedition outfitter has the following price list for tours ofvarying lengths and starting points. The prices are quoted in Canadian dollars. Starting Length ofTour and Cost Point 4 days 7 days 10 days 15 days Yellowknife $740 $1145 $1550 $2225 Edmonton $1640 $2045 $2540 $3125 Toronto $2240 $2645 $3050 $3725 Vancouver $1940 $2345 $2750 $3425 a) Research to find a table that compares the Canadian dollar to other currencies. b) Write a row matrix that represents the cost, in US dollars, of the four tours froma Toronto starting point. c) Write a matrix, in Japanese yen, for the entire price list. A6-2. Model and solve consumer 2.1 Singh's Grocery sells several different kinds ofbreakfast cereal, and networkproblems, using each at a different price. technology to perform matrix Cereal A is 2.65/box. multiplication, as required. Cereal B is 3.73/box. [CN, PS, T, V] Cereal C is 3.15/box. D Cereal is 2.99^ox. On Wednesday, they sold the following: 5 boxes ofCereal A 8 boxes ofCereal B 7 boxes ofCereal C 10 boxes ofCereal D. a) Model and solve this problem, using an appropriate row matrix, and an appropriate column matrix, then use matrix multiplication to determine Wednesday's total revenues. b) Can the total revenue be calculated, ifsix boxes ofCereal E (price unknown) were sold? Justify your response. 60/ Applied Mathematics 30 (Interim 2000) ©AlbertaLearning, Alberta, Canada Strand: Number (NumberOperations) [C] Communication [PS] Problem Solving Students will: [CN] Connections [R] Reasoning • demonstrate an understanding ofandproficiency witii [E] Estimation and [T] Technology calculations Mental Mathematics [V] Visualization • decide which arithmetic operation oroperations can be used to solve a problem and then solve theproblem. J General and Specific Outcomes Illustrative Examples 2.2 Sales ofeconomy cars were 200 in 1998 and fell by 4% in 1999. Sales of midsize cars were 300 in 1998 and rose by 10% in 1999. Sales ofluxury cars were 40 in 1998 and rose by 30% in 1999. a) Represent the 1998 and 1999 sales by appropriate column matrices. b) Represent the changes from 1998 to 1999 by an appropriate matrix multiplication. 2.3 Soccer's administrators have been experimenting with using league standings to discourage tie games, especially those in which no goals are scored. The traditional scheme of 2 points for a win and 1 point for any tie has been replaced by a new scheme that awards 3 points for a win and 1 point for all ties. Two other proposed schemes are 3 points for a win, 1 point for ties that'have goals scored and points for ties with no goals; and a scheme with 5 points for a win, 3 points for a tie with goals scored and points for a tie with no goals. In a local soccer league the top four team records after 42 games are: Ties with Ties with Wins Goals No Goals Losses Tigers 30 2 8 2 Irish 24 9 2 7 Colts 25 7 10 Jets 26 1 10 5 a) Determine the points for each team, using the traditional scheme. b) Model this solution, using matrix multiplication. c) Using matrices, model and determine the points for each team, using the new scheme. Repeat for the other two proposed schemes. d) Which ofthe alternative scoring systems can make the Irish second in the standings? e) Which ofthe alternative scoring systems can make the Colts second in the standings? f) Which ofthe alternative scoring systems can make the Jets second in the standings? g) Design a system that would drop the Tigers out of first place. Applied Mathematics 30 /61 ©AlbertaLearning, Alberta, Canada (Interim 2000)