KPMT Suggested Ans Selangor 2015
9
SELANGOR ADDITIONAL MATHEMATICS PROJECT WORK 2015 SUGGESTED ANWSER BY www.addmathsprojectwork2015.blogspot.com PART 1 (a) (i) Mathematical optimization deals with the problem of finding numerically minimums (or maximums or zeros) of a function. In this context, the function is called cost function, or objective function, or energy. [ADD MORE, FIND IT IN GOOGLE] (ii) In mathematical analysis, the maxima and minima (the plural of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function within the entire domain of a function (the global or absolute extrema). We say that f(x) has an absolute (or global) maximum at x=c if f(x) ≤ f (c) for every x in the domain we are working on. We say that f(x) has an absolute (or global) minimum at x=c if if f(x) ≥ f (c) for every x in the domain we are working on. (iii) In mathematical analysis, the maxima and minima (the plural of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, within a given range (the local or relative extrema) We say that f(x) has a relative (or local) maximum at x=c if f(x) ≤ f (c) for every x in some open interval around . We say that f(x) has a relative (or local) minimum at x=c if f(x) ≥ f (c) for every x in some open interval around . (b) Create you own thinking map. You may visit www.ithink.org.my to get more information about I- Think Map www.addmathsprojectwork.blogspot.com
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Transcript of KPMT Suggested Ans Selangor 2015
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SELANGOR ADDITIONAL MATHEMATICS PROJECT WORK 2015 SUGGESTED ANWSER BY www.addmathsprojectwork2015.blogspot.com
PART 1 (a)
(i) Mathematical optimization deals with the problem of finding numerically minimums (or maximums or zeros) of a function. In this context, the function is called cost function, or objective function, or energy. [ADD MORE, FIND IT IN GOOGLE]
(ii) In mathematical analysis, the maxima and minima (the plural of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function within the entire domain of a function (the global or absolute extrema). We say that f(x) has an absolute (or global) maximum at x=c if f(x) f (c) for every x in the domain we are working on. We say that f(x) has an absolute (or global) minimum at x=c if if f(x) f (c) for every x in the domain we are working on.
(iii) In mathematical analysis, the maxima and minima (the plural of maximum and minimum) of a
function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, within a given range (the local or relative extrema) We say that f(x) has a relative (or local) maximum at x=c if f(x) f (c) for every x in some open interval around . We say that f(x) has a relative (or local) minimum at x=c if f(x) f (c) for every x in some open interval around .
(b) Create you own thinking map. You may visit www.ithink.org.my to get more information about I-Think Map
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PART 2 (a)
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(b)
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PART 3 (i) Based on the equation, a table has been constructed where t represent the number of hours
starting from 0 hours to 23 hours and P represent the number of people.
t / hours P / number of people
0 3600.0
1 3358.8
2 2699.8
3 1799.6
4 899.6
5 240.8
6 0.0
7 241.6
8 900.8
9 1801.1
10 2701.1
11 3359.5
12 3600.0
13 3358.1
14 2698.5
15 1798.2
16 898.3
17 240.1
18 0.0
19 242.3
20 902.1
21 1802.6
22 2702.3
23 3360.2
Based on table above, graph is generated using Microsoft Excel application.
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(ii) By assuming that the mall opens during business hours (8 a.m. 10 p.m.), the peak hours is at 12 pm with the number of people approximately 3600 people.
(iii) Based on the formula, 18006
cos1800)(
ttP
, substitute the value of t to 7.3,
401.718003.76
cos1800
Approximately 402 people are at the mall.
(iv) Based on the graph, assuming that the malls open during business hours (8 a.m. 10 p.m.), the mall reaches 2570 people at 9:48 a.m., 2:12 p.m. and 9:48 p.m.
FURTHER EXPLORATION a) GOOGLE ON YOUR OWN
b)
(i) (a)I. Cost : 100x + 200y 1400 II. Space : 0.6x + 0.8y 7.2 III. Volume = 0.8x + 1.2y
(b) I. 72
1 xy
II. 94
3 xy
x 0 2 4 6 8 12 14
y 7 6 5 4 3 1 0
x 0 2 4 6 8 10 12
y 9 7.5 6 4.5 3 1.5 0
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(ii) Maximum storage volume
Method 1 Test using corner point of Linear Programming Graph (8, 3), (0, 7), and (12, 0)
Volume = 0.8x + 1.2y
Coordinate 1 - (8,3)
Volume = 0.8(8) + 1.2(3)
Volume = 10 cubic meter
Coordinate 2 - (0,7)
Volume = 0.8(0) + 1.2(7)
Volume = 8.4 cubic meter
Coordinate 3 - (12,0)
Volume = 0.8(12) + 1.2(0)
Volume = 9.6 cubic meter
Thus the maximum storage volume is 10 cubic meter.
Method 2 Using simultaneous equation
72
1 xy ----- 1
94
3 xy ----- 2
Substitute Equation 2 into 1
72
19
4
3 xx
x = 8
y = 3
Applying the value of x and y in formula, Volume = 0.8x + 1.2y
Thus, the maximum storage volume is 10 cubic meter.
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(iii)
(iv) State your own selection and justification.
HINT Cost & Volume
REFLECTION
STATE YOUR OWN REFLECTION
Carbinet x Carbinet y Total Cost (RM)
4 6 1600
5 5 1500
6 4 1400
7 3 1300
8 3 1400
9 2 1300
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