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Further answers address geometric sequences, TVM solver outputs, matrix operations, and critical-path analysis with cost and time 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General Mathematics Exam 2 Solutions © itute 2023  \nData analysis  \nQ1a Two, they are ID and size.  \nQ1bi mean = 11.42 Q1bii median = 14.1 Q1ci volume  \nQ1cii 0.953×10 = 9.53  \nQ1d Volume = 0.002857 + 2.571× image size Q1e mean = 4.4 standard deviation = 0.1  \nQ2ai    \n Size  Frequency  %   small  7  35   medium  10  50   large  3  15   Total  20  100   \nQ2aii  \n44 + 46   \nQ2bi ≈ 0.1698 ≈ 17%  \n210 + 320  \nQ2bii Yes, the information in Table 3 supports the farmer’s believe.  44   \nFarm A: ≈ 21% large oysters  \n210  \n 46   \nFarm B: ≈ 14% large oysters  \n320  \nQ3a (−10, 0 . 1164) , (25, 0 .2004)  \nQ3b r = 0.7212 ≈ 0.849 Q3c Strong, positive, linear Q3d Intercept: (0, 0 . 1404)  \nAt temperature 0°C the ice cream consumption is 0.1404 L/person. Q3e consumption = 0.1404 + 0.0024× − 6 = 0.126 L/person Q3f Extrapolation  \nQ4a The occurrence of peak followed by trough is repeated annually.  \nQ4b Read from graph, actual consumption for month 4 = 0.18 0.18  \nDeseasonalised value = ≈ 0.17  \n1.05  \nsum of monthly averages   \nQ4c Average for the year = ≈ 0.167  \n12  \nJuly average   0.183  \nS.I. for July ≈ ≈ ≈ 1.10  \n0.167 0.167  \nRecursion and financial modelling  \nQ5a 24  \nQ5b A0 = 30000 , A1 = 1.016 × 30000 − 1515.18 = 28964.82 A1 = 1.016 × 28964.82 −1515.18 = 27913.08  \nQ5c Final payment ≈ 1515.18 − 0.14 = 1515.04 (0.14 by TVM Solver) Q6a I% = 0.42% ×12 = 5.04%  \nQ6b  \n\n| 3 | 3973.00 | 2507.77 | 1465.23 | 595622.67 |\n| --- | --- | --- | --- | --- |\n\nQ6c V0 = 600000 , Vn+1 = 1.0042×Vn − 3973.00 Q6d Perpetuity  \nQ7a (1 .0015 −1)× 52 = 0.078 = 7. 8%  \nQ7bi Weekly interest rate = 0.0015 , d = 60000 × 0.0015 = 90  \nQ7bii By TVM Solver $278.86 Q7c By TVM Solver $350.01 Q7d Without any repayment ( d = 0 ),  \nV0 = 60000 , V1 = 60000 ×1 .0015 , V2 = 60000×1 .00152 ,… is a geometric sequence.  \nMatrices  \nQ8a n31  \nQ8b [1 0 0]  \n􀀆204 0 0 􀀃  \n􀀄 􀀁  \nQ8c 􀀄 0 162 0 􀀁􀀄􀀅 0 0 176 􀀂􀀁  \nQ9a [2~~1~~0~~ ~~ ]× R = [48000 49525 47005 46040 45065] Q9b t = 1.25  \nQ9c IHEGF  \n1  \n2023 VCAA General Mathematics Exam 2 Solutions © itute 2023  \n\n|  | |  |\n| --- | --- | --- |\n\nQ9d  \n􀀆0 0 0 1 0 0􀀃  \n􀀄 􀀁  \n􀀄 0 0 1 0 0 0 􀀁  \n􀀄 0 0 0 0 0 1 􀀁􀀄 􀀁  \n􀀄 0 0 0 0 1 0 􀀁􀀄 0 1 0 0 0 0 􀀁􀀄􀀅1 0 0 0 0 0 􀀂􀀁  \nQ10a CSMD  \nQ10bi  \n􀀆1 2 1 2 2􀀃  \n􀀄 􀀁  \n􀀄 0 3 1 2 2 􀀁  \n􀀄 1 0 1 1 1 􀀁􀀄 􀀁  \n􀀄 1 0 1 2 1 􀀁􀀄􀀅0 1 0 0 1 􀀂􀀁  \nQ10bii The only way performers P and sales staff S can communicate with directors D is through managers M .  \nQ11a  \n􀀆0 .95 0􀀃  \nT = 􀀄 􀀁  \n􀀅0.05 1 􀀂  \nQ11b  \n􀀆9􀀃  \nB = 􀀄 􀀁  \n􀀅0 􀀂  \nNetworks and decision mathematics  \nQ12a 2 + 3 + 4 + 3 + 2 = 14  \nQ12bi 5 + 4 = 7 + 2  \nQ12bii planar  \nQ12c  \n\n| State | State number |\n| --- | --- |\n| B | 3 |\n| C | 2 |\n| D | 4 |\n| E | 1 |\n\nQ13a 1.5 + 1 .2 + 3 .2 = 5.9 km Q13b G HK IJ M O L N G  \nQ13c vertex N and vertex L; vertex M and vertex J Q14a C and G  \nQ14b 4 + 5 + 7 = 16  \nQ14c Five. Activities A, C, I, K and L are on the critical path. Q14d Two  \nQ14e  \n\n| Activity | Reduction in completion time |\n| --- | --- |\n| A | 2 |\n| B | 2 |\n| F | 0 |\n| H | 2 |\n| I | 2 |\n| K | 1 |\n\nIncrease in cost  \n= 2 ×1500 + 2 × 2000 + 2 ∗1000 + 2 ×1500 + 1× 3000 = 15000  \nPlease inform [mathline@itute.com](mathline@itute.com) re conceptual and/or mathematical errors  \n2  \n2023 VCAA General Mathematics Exam 2 Solutions © itute 2023","cbCaipgKp1d8iPMv","https://ap.wps.com/l/cbCaipgKp1d8iPMv","pdf",97902,"English","# Data analysis\n## Recursion and financial modelling\n## Matrices\n## Networks and decision mathematics\n## Critical path and cost calculation","[{\"question\":\"What key statistics are calculated in the data analysis section?\",\"answer\":\"The solutions compute the mean, median, and related quantities such as volume-based measures and standard deviation for the given datasets.\"},{\"question\":\"How are recursion and financial modelling problems approached?\",\"answer\":\"They use recurrence relations (e.g., updating values year to year or period to period) and TVM/solver methods to obtain final payments and values under different repayment assumptions.\"},{\"question\":\"What topics are covered in the matrices and networks sections?\",\"answer\":\"The document includes matrix constructions/operations and then network or decision mathematics questions such as state layouts, graph-related conclusions, and decision outcomes.\"}]","2023 VCAA General Mathematics Exam 2 Solutions | PDF",1789903560]