PART II
a) y
x x
x
x
y
4x+2y=200y= 200-4xArea, A=xy 2 =x(100-2x) = 100-2x A = 100x-2x2
dA = 100-4x = 0 A= 25(100-50)dX = 1250 x= 25 d2A= -4 < 0 dx2
Therefore, the area is maximum
b)
V = (30-2h)(30-2h) = 900h-120h2+4h2 dv= 900-240h+12h2= 0 dh
12h2-240h+900= 0 h= 5 V(5)= 20x20x5 = 2000
d2v= -240+24h dh2 h= 5, d2v= -240+24(5) dh2 = -120 Therefore, V
is maximum
Part III i) iii) iv)
ii)
Further exploration
iii)
No.no of cabinet Xno of cabinet Yprice Xprice YTOTAL PRICEvolume
of cabinet Xvolume of cabinet YTOTAL VOLUME
1002000.81.2
145400100014003.269.2
254500800130044.88.8
36460080014004.84.89.6
47370060013005.63.69.2
58380060014006.43.610
69290040013007.22.49.6
i) two methods to determine the maximum storage volume:
The equation for the storage volume is, V = 0.8x + 1.2 y
Method 1 : methods of analyzing the vertices. Method 2 :
straight-line questionnaire.R(8, 3)
Inequalities 1 blue colourInequalities 2 red colourInequalities
3 yellow colour
Method 2 determine the maximum point straight-line
questionnaire. Form equation volume for cabinet , V = 0.8x + 1.2
y
Arrange the equation, y = The equation of tangent is - or - So,
construct the equation = x + 3, by placing any value C (intercept
at Y-axis ), in this case I put C = 3. Plot the equation, and we
can draw graph of orange colorOrange color graphs declined in
parallel to that is away from the point of origin , and the last
corner to be found was the point ( 8 , 3 ) . 8 cabinet cabinet A
and 3 B.
So , the maximum is 0.8 V ( 8 ) + 1.2 ( 3 ) = 10 cubic meters.b)
i-think map
Find the value of x Find dy dx Equate dy = 0 dx
+ Find dy dx
Determine max/min. Do the second differentiation d2y
dxSubstitute x and find the value of d2ydx2. If d2y > 0, dx2
Minimum point
Substitute x into y, to find the value of y.
2
OBJECTIVESWe students taking Additional Mathematics are required
to carry out a project work while we are in Form 5. This year the
Curriculum Development Division,Ministry of Education has prepared
four tasks for us. We are to chooseand completeonly ONE task based
on our area ofinterest. This project can be done in groups or
individually, but each of us are expected to submit an individually
written report. Upon completion of the Additional Mathematics
Project Work, we are to gain valuable experiences and able to:
Apply and adapt avariety of problemsolving strategies
tosolveroutineand non-routine problems; Experience
classroomenvironmentswhich arechallenging,interestingand meaningful
and hence improve their thinking skills. Experience
classroomenvironmentswhere knowledge and skills areappliedin
meaningfulways in solving real-life problems Experience
classroomenvironmentswhere expressing ones mathematical thinking,
reasoning andcommunicationarehighly encouraged andexpected
Experience classroom environmentsthat stimulates and enhances
effective learning. Acquire effective mathematical
communicationthrough oral and writing, andto use the language of
mathematics to express mathematical ideas correctly and precisely
Enhance acquisition of mathematical knowledge and skills through
problem-solving in ways that increase interest and confidence
Prepare ourselves for the demand of our future undertakings and in
workplace. Realize thatmathematicsis an importantand powerfultoolin
solving real-life problems and hence develop positive attitude
towards mathematics. Train ourselves not only to be independent
learners but also tocollaborate,to cooperate, and to share
knowledge in an engaging and healthy environment Use
technologyespecially the ICT appropriatelyand effectively Train
ourselves to appreciate the intrinsic values of mathematics and to
become more creative and innovative Realize the importanceand the
beauty of mathematics
Determine max/min. Do the second differentiation d2y dx
