MATHEMATICS (T)COURSEWORK

SEMESTER 1 VIVANAME: R MAHALETCHUMY A/P RAMAN

CLASS: LOWER SIX SCIENCE BIOLOGY

I.C NO: 970414-38-5072

INTRODUCTION Definition of mathematical modelling, parametric equation, explicit function, independent

variable, parameter, Cartesian coordinate, point of intersection, and point of collision

Aim: To study the parametric equation which modelled by mathematical modelling.

I)To investigate the parametric equation using a plane curve.

II)To study the 3 sets of parabola, identify x and y values using variety of parametric equation.

III)To explore the movement of particles using parametric equation with trigonometry function.

History (Professor Daniel Davis and James Dana’s 1837 paper)

Application: I)Projectile motion

II)Motion of golf ball

III)Motion of base ball

METHODOLOGY I have used several methods to solve the coursework: For question 1, question 2 (part 1), and question 3 (part 2):

I) manual graph

II) Microsoft excel 2013

III) online graph generator(plotly) For question 2(part 2 and part 3) solved using calculation and justification. For question 3(part 2 and part 3) solved based on graph.

PARAMETRIC EQUATION FOR PLANE CURVET x y-2.00 0.14 3.00-1.80 0.17 2.24-1.60 0.20 1.56-1.40 0.25 0.96-1.20 0.30 0.44-1.00 0.37 0.00-0.80 0.45 -0.36-0.60 0.55 -0.64-0.40 0.67 -0.84-0.20 0.82 -0.960.00 1.00 -1.000.20 1.22 -0.960.40 1.49 -0.840.60 1.82 -0.640.80 2.23 -0.361.00 2.72 0.001.20 3.32 0.441.40 4.06 0.961.60 4.95 1.561.80 6.05 2.242.00 7.39 3.00

Q 2: 1ST SET OF(Y-1)²=X-49 t x y-10.00 74.00 -4.00-9.00 69.25 -3.50-8.00 65.00 -3.00-7.00 61.25 -2.50-6.00 58.00 -2.00-5.00 55.25 -1.50-4.00 53.00 -1.00-3.00 51.25 -0.50-2.00 50.00 0.00-1.00 49.25 0.500.00 49.00 1.001.00 49.25 1.502.00 50.00 2.003.00 51.25 2.504.00 53.00 3.005.00 55.25 3.506.00 58.00 4.007.00 61.25 4.508.00 65.00 5.009.00 69.25 5.5010.00 74.00 6.00

Q 2: 2ND SET OF (Y-1)²=X-49x y1 y249.00 1.00 1.0050.00 2.00 0.0051.00 2.41 -0.4152.00 2.73 -0.7353.00 3.00 -1.0054.00 3.24 -1.2455.00 3.45 -1.4556.00 3.65 -1.6557.00 3.83 -1.8358.00 4.00 -2.0059.00 4.16 -2.1660.00 4.32 -2.3261.00 4.46 -2.4662.00 4.61 -2.6163.00 4.74 -2.7464.00 4.87 -2.8765.00 5.00 -3.0066.00 5.12 -3.1267.00 5.24 -3.2468.00 5.36 -3.3669.00 5.47 -3.47

Q 2: 3RD SET OF (Y-1)²=X-49t x y-10 149 -9-9 130 -8-8 113 -7-7 98 -6-6 85 -5-5 74 -4-4 65 -3-3 58 -2-2 53 -1-1 50 00 49 11 50 22 53 33 58 44 65 55 74 66 85 77 98 88 113 99 130 10

10 149 11

Q 2: 4TH SET OF (Y-1)²=X-49t x y-5 149 -9

-4.5 130 -8

-4 113 -7

-3.5 98 -6

-3 85 -5-2.5 74 -4

-2 65 -3-1.5 58 -2

-1 53 -1-0.5 50 0

0 49 10.5 50 21 53 31.5 58 42 65 52.5 74 63 85 73.5 98 84 113 9

4.5 130 10

5 149 11

40 50 60 70 80 90 100 110 120 130 140 150 160

-10

-6

-2

2

6

10

14 Graph of (y-1)²=x-49

y ordi

nat

e

x ordinate

Q 3: PARTICLE 1(X=2SIN T, Y=3COS T) AND PARTICLE 2(X=COS T-2, Y=1+SIN T)

t x1 y1 x2 y20.00 0.00 3.00 -1.00 1.000.31 0.62 2.85 -1.05 1.310.63 1.18 2.43 -1.19 1.590.94 1.62 1.76 -1.41 1.811.26 1.90 0.93 -1.69 1.951.57 2.00 0.00 -2.00 2.001.88 1.90 -0.93 -2.31 1.952.20 1.62 -1.76 -2.59 1.812.51 1.18 -2.43 -2.81 1.592.83 0.62 -2.85 -2.95 1.313.14 0.00 -3.00 -3.00 1.003.46 -0.62 -2.85 -2.95 0.693.77 -1.18 -2.43 -2.81 0.414.08 -1.62 -1.76 -2.59 0.194.40 -1.90 -0.93 -2.31 0.054.71 -2.00 0.00 -2.00 0.005.03 -1.90 0.93 -1.69 0.055.34 -1.62 1.76 -1.41 0.195.65 -1.18 2.43 -1.19 0.415.97 -0.62 2.85 -1.05 0.696.28 0.00 3.00 -1.00 1.00

For question 2, x-49 must be always positive as (y-1)² ≥ 0. So, x=-t² is impossible to be chosen as parametric equation

For y value, I can choose any value because the value of y is positive as x=(y-1)² +49

CONCLUSION

In conclusion, I understand about parametric equation through mathematical modeling. I have also learnt on how to set the t limits and realize that not every point or values can be insert into the parametric equation to plot for an ideal graph. This coursework had thought me to sketch, plot, analyse and solve problem using the graphs. I have also learnt to determine the point of intersection and the point of collision using parametric equation. I found that the question given were quite challenging and require a deep thinking to solve the question.

When I’m doing this coursework, I faced some problems that were insufficient of time, formatting the axis of online and excel graph and finding solution for question. I found that I need a good time management, and more guidance from teachers and friends. In this coursework, I found that Microsoft excel method is easier way to use compared to manual and online generator graph because it is more accurate, easy to use, and just need to put the formula and the graph automatically generate.