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Discussion – 

175

Discussion – 

175

STPM 2016 Mathematics (T) Term 1 Assignment

STPM 2016 Term 1 Mathematics (T) Assignment
 

Introduction

Parametric equations express a set of related quantities as explicit functions of an independent variable, known as a parameter. An equation, relating variables x and y in Cartesian coordinates, can be expressed by parametric equations which describe a position on the curve.
Find information about parametric equations yourself.  

Sample Question

Parametric equations express a set of related quantities as explicit functions of an independent variable, known as a parameter. An equation, relating variables x and y in Cartesian coordinates, can be expressed by parametric equations which describe a position on the curve. 1  The parametric equations of a plane curve are defined by x = e^t, y = t^2-1, -2 \leq t \leq 2. Tabulate the values t, x and y, and plot the curve. 2 (a)  Find three sets of parametric equations for the curve whose equation is (y - 1)^2 = x - 49. (b)  Is it possible to choose x =-t^2 as the parametric equation for x? Can you start with any choice for the parametric equation for x? (c)  Can you start with any choice for the parametric equation for y? 3  Suppose that the position of a particle at time t is given by

x_1 = 2 \sin t, y_1 = 3 \cos t, 0\leq t\leq 2\pi,

and the position of another particle is given by

x_2 = \cos t - 2, y_2 = 1 + \sin t, 0 \leq t \leq 2\pi,

(a)  Sketch the paths of the particles on the same coordinate axes. (b)  How many points of intersection are there? (c)  Determine whether there is any point where the particles collide.
Sample Solution
Scroll down for the sample solution 🙂 The solution below is sample solution and not the accurate answer. 🙂 Please refer to your school teacher if you want to get the correct answer.

Question 1

Question 1 Table
Question 1 Graph

Question 2

(a) Three sets of parametric equations.

x=t^2+49,y=t+1,t\in R

x=49\sec^2 \theta, y=7\tan\theta, \frac{\pi}{2}<\theta<\frac{\pi}{2}

x=4t^2+49, y=2t+1, t\in R

Let me know if you know more.
(b) x=-t^2 is impossible to be chosen as the parametric equation for x because x-49 must be always positive as (y-1)^2 \geq 0 for every values of y. We can start with any choice for the parametric equation for x as long as x-49 is not negative.
(c) Basically, we can start with any choice for the parametric equation for y because x=(y-1)^2+49.

Question 3

(a) The curve in pink is 2\sin t, y=3\cos t. And the curve in black is x=\cos t -2, y=1+\sin t.
Question 3a
(b) Based on the graph above, there are two points of intersection.
(c) To determine whether the particles collide, we need to solve the simultaneous equations from the parametric equations. Please remember the particles does not collide even you are able to solve the equations. You must verify the values. Collision happens only when positions are the same with same t.
Simultaneous equation for 3c

Verification

Question 3c Checking
Hence, the particles collide at t=\frac{3\pi}{2}.
Checking again
Hence, the particles do not collide. Please do yourself for y=0 and y=\frac{9}{5}.   The particles collide at only 1 point.

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KK LEE

KK LEE has been a STPM Mathematics tuition teacher since June 2006, but his love of Maths dates back to at least 1999 when he was Form 4. KK LEE started teaching in 2006 at Pusat Tuisyen Kasturi. He was known as "LK" when he was teaching in PTK. After teaching STPM Mathematics for 8 years in PTK, he joined Ai Tuition Centre in 2014. Over the years he has taught Mathematics (T), Mathematics (S), Mathematics (M), Additional Mathematics.

175 Comments

  1. Fahmida

    Teacher may I ask a question…

    Is number 2a) the equation for hyperbola or parabola…And if it’s hyperbola why is it so…
    Thank you very much

    Reply
    • KK LEE

      2a is parabola

    • Fahmida

      Thank you sir…I really appreciate it..

  2. syah

    Sir, I would like to ask on the equation x=e^t, did you eliminate the variable e or you just ignore it? If you eliminate it, how did you do it?

    Reply
    • KK LEE

      Substitute the values of t into the equation of x

    • WATUCARE

      HUH IF I DO SO. THEN GOT 2 UNKNOWNS LOR.

  3. jinnsern

    Teacher, how can i find the intersection points in 3(b)?

    Reply
    • KK LEE

      Question is asking “HOW MANY points of intersection”. So based on the graph, there are two points of intersection. DONE.

  4. Hor cindy

    Sir, may i to ask you. how to get the 3 equation? i have no idea about this.

    Reply
    • KK LEE

      Any equations that satisfy the Cartesian equation.

  5. ling ling

    can i know how to get the third parametric equation for question 2a ?I tried so many times and still din get that ans….sir,can u give me some clues..

    Reply
    • KK LEE

      Refer the above comments, any parametric equations that satisfy the Cartesian equation given.

  6. siaw ker

    can i know for the 2Qb)for the choice is based on the equation on the question 2a? ? thanks ^^

    Reply
    • KK LEE

      No

    • siaw ker

      that means i can create my own parametric equation for x without links to the parabola equation for question2a) ?

    • KK LEE

      Question is asking can or not. And not asking what is the parametric equation. so if you are going to create your own. Ask your teacher and good luck.

  7. Will Shong

    Sir , can your kindly write the introduction , methodology and conclusion ? Thx a lot for your kindness

    Reply
    • KK LEE

      No

    • will Shong

      Can you show me some guidance on doing the introduction , methodology and conclusion of this assignment .

    • KK LEE

      Please ask your teacher. Different school teachers have different requirements

    • Will Shong

      but teachers of my school just leave us to deal with it …. So I hope to get some information from you sir …

    • KK LEE

      Hi. Sorry. Cant help on this. 🙂

  8. Crist Ong

    Sir…. for the parametric eqn right…. can this? :
    1. y=sinϑ +1 ; x=50-(cosϑ)2 &
    2. y=tanϑ +1 ; x=(secϑ)2-48……….

    Reply
    • KK LEE

      yes. any equations

    • Jack

      How you get that parametic eqn? steps?

    • KK LEE

      With the understanding of parametric equations, you can obtain the three equation easily.

  9. iluvMathT

    question 3C) on the verification part, after u sub the x value, why are they so many t value if use x=-6/5 but all prove it does not collide, but using x= -2 , many t value as well but only 1 prove it collide at that time. If t value we found prove it dont collide, then they are many t value outside which we dont find on the equation said it don collide.

    question 3b)u sub x1 and x2 into sin^2 t +cos ^2 t = 1 and y value as well, and u found the point of intersection, but referring to the point we found on the graph , one of the point which is x=-6/5 does not seem to be logic, based on the graph it should -1.5 something, which clearly shown on the graph. does that mean it is wrong?

    Reply
    • KK LEE

      For 3c. It is given that t lies between 0 and $latex 2\pi$.

      For 3b. I NEVER substitute any values in my calculation. Thanks

    • iluvMathT

      sry maybe i dont really understand, may i know for the first part of 3c), why do u sub x1/2 = sin t and x2 + 2 = cos t equation into sin^2 t + cos^2 t = 1?

    • KK LEE

      To solve the simultaneous equations. You can use any other ways to solve the simultaneous equations to find the points where the particles collide.

    • iluvMathT

      ok, so we found the point of intersection using simultaneous equations, which have two value for both x and y , but one of the x value which is x= -6/5 does not seem to be logic ,can u explain this?? because graphical method also can be used to find the point of intersection right? so if i use graphical method then my x coordinate for the point of intersection is not the same although y coordinate correct.

    • KK LEE

      To find points of intersection of the curve and to find the point where the particles collide are not the same. Please ask your teacher or attend my class. 😛

    • iluvMathT

      oic, then that makes clear that i dont really understand haha, cuz i thought u solve the simultaneous equation to find the point of intersection first, and assuming one of the particles be at that point then traces back t value and find coordinate of another particle.If x1=x2 and y1=y2 then it collide, So now your working is to find the point where particles collide? and may i know how to find point of intersection by using simultaneous equation?

    • KK LEE

      Ways to find the points of intersection will only be shown to my students. Thanks

    • iluvMathT

      haha alright then, tq so much for your time ! appreciate it !

  10. Anson lee

    Is that q2 c is using b^2-4ac to solve ? And then we need to list up the possible parametric equation ?

    Reply
    • KK LEE

      It depends on your teacher.

  11. jessie kok

    Is there any other way to find the collision of points for 3(c) ?

    Reply
    • KK LEE

      There are many methods to find the points.

  12. ng

    Question 2 how do start ? I don’t understand…

    Reply
    • KK LEE

      Write the answer directly.

  13. comfused

    Sir, are you sure that t= 3.785 & 5.690 when sin t= -0.6? When I use the calculator, I got a different answer.

    Reply
    • KK LEE

      Yes. It is correct. Change your calculator or change your hand.

    • MathsLover

      Its correct. When you press your calculator,you shouldnt insert the negative in. Just insert the 0.6. After that you will get 36.8698… The negative sign shows that it’s actually in the third and fourth quadrant.For the third quadrant, its (180+36.8698), after that change the ans in term of rad. Which means you should take [(180+36.87)xπ]/180 = 3.786
      Do the same thing for the fourth quadrant (360-36.87) and you will get 5.64

      You’re welcome 🙂

    • KK LEE

      Haha.. A long explanation. But, u dint utilise the power of your calculator. 🙁

    • yihui0225

      is 5.64 or 5.69?

    • unknown

      5.639 so it is 5.64

    • MathsLoL

      I have a different ans too..

  14. lasini

    can we use graph(method)to solve ques 2

    Reply
    • KK LEE

      Any methods. It depends on your teacher. 🙂

  15. Tay

    My teacher says that the answer for 2c is wrong.If you substitute your y equals to t² ,my graph will be limited to positive only.But according to the graph my y has negative values.

    Reply
    • KK LEE

      Then u can adjust the answer yourself.

  16. Aaron

    How to write a suitable title?

    Reply
    • KK LEE

      “Race between turtle and rabbit using parametric equation”

    • Wan Mai

      Race between turtle and rabbit? is tht real?

    • KK LEE

      Why not?

    • Wan Mai

      excuse me, but anybody here have intro, methodology and others for this assignment? idk how to do.

      or sir, can you please write an entry abt how to write all this stuffs? thank you

    • KK LEE

      Cant help you on this.

  17. nantha

    Sir it seems that there is more than 1 graph fr various valuess of t

    Reply
    • KK LEE

      What you mean?

  18. AH BENG

    Sir,Mat i know how to do the intro??

    Reply
    • KK LEE

      Please ask your school teacher.

  19. Kok

    Sir for the question 3c
    I think you made a mistake
    Its 5x^2 + 16x + 15
    Not 5x^2 + 16x + 12

    Reply
    • Kok

      Eh sorry correct already

    • yihui0225

      I think 5x^2+16x+12 is correct.

  20. yihui0225

    Hello sir. How to calculate the position of both particles collide in Q3 c)when t=3.785 and 5.640?

    Reply
    • KK LEE

      Subs into the equation of x and y

    • yihui0225

      Which equation of x and y?

    • KK LEE

      Please refer to the question. It is stated there

  21. Ivan

    Sir, how do i explain the part for 3(c) in my methodology, whereby i change the sin^-1(-0.6) to 3.785 and 5.64?

    Reply
    • KK LEE

      “By calculator”

  22. Yong Sheng

    Sir….. Regarding no.2(a) … If I let x=t^2 , y=+-(surd t^2-49)+1…. In this case, I’ll have 3 parametric equations. One x and two y. So which of the y parametric eqn should I choose to get a set??

    Reply
    • KK LEE

      Please change to others. Unless this is your teacher’s requirement

  23. Ain canti

    Sir , how to find three sets of parametric equation like question 2a ?

    Reply
    • KK LEE

      Any equations that satisfy the Cartesian equation

  24. KHZ

    Sir,may i ask y did u chg the ans to rad when using x=-6/5 in verification step…thx in advance

    Reply
    • KK LEE

      It is in radian from the beginning. I dint change anything.

    • KHZ

      ops, sry my bad

  25. Catherine

    Sir,at verification step, if i substitute x=-2 into x=cos t – 2, then cos t would be 0 and i will get 2 answers, so i just have to conclude that the particles would not collide when t=pi or is it that i am only supposed to use x=2sin t

    Reply
    • KK LEE

      Use ALL equations to verify.

  26. unknown

    sir, do you have any example or tips on how to do the methodology and conclusion?

    Reply
    • KK LEE

      Nope

  27. WRN

    Sir, why the 2nd parametric equation in 2(a)is y=7tanθ, but not y=7tanθ+1? I thought it should be y=7tanθ+1…

    Reply
    • KK LEE

      Yes. Please edit yourself.

    • MathsLoL

      May I know How do you find the parametric eqn for y=7tan + 1 ??

    • KK LEE

      Make sure you can get all the points.

  28. nabilah

    sir…may i ask you one quest…for the answer of Q2 n Q3…should i write on methodology or results?

    Reply
    • KK LEE

      result

  29. nabilah

    another quest,,,,,where did you get t=3/2 pi….for Q3(c) verification,,,,when i press on the calculator,,,the answer is diffrence from yours
    waiting for your explanation

    Reply
    • KK LEE

      Make sure you are using the rad mode. Else change your calculator.

  30. MICHAEL

    sir, i notice sumthing…… according to u….
    when x=-6/5 the 2nd t= 5.690
    but t=5.640 when u are relating the t to both curves……
    i already tried using calculator…. t=5.640 is more reasonable……

    Reply
    • KK LEE

      I cannot understand what you asking. I hope you have solved your question.

  31. aaron

    sir,how to do the methodology for those question?

    Reply
    • KK LEE

      Please refer to your school teacher. Thanks

  32. nabilah

    sir,,,why did you used sin^2t-cos^2t=1 for quest 3 C).
    why did you used alphbet t??can we use any aplphbets other than t?

    Reply
    • KK LEE

      Because there is t in the question.

    • nabilah

      thanks a lot sir

  33. nabilah

    sir,may i know,,where did you get the coordinates for question 3 C)?did you subsitute the values of t in the equation of x=2sint,x=cost-2,y=3cost,y=1+sint?

    Reply
    • KK LEE

      yes

  34. Mariani

    Sry sir…it’s tht can,if I just gv the definition of parametric equ n some example for intro.^^

    Reply
    • KK LEE

      Ya. It depends on your teacher.

  35. ila

    sir can i know how to do the conclusion. what point must we put in the conclusion

    Reply
    • KK LEE

      Hi. Please ask your teacher. I am not going to help in this part.

    • Ila

      Thank you sir. Sir why x-49 must be in positive?

    • KK LEE

      Because $latex \sqrt(x-49)$ is defined only if $latex x-49>=0$.

  36. Nantini

    Sir , can i know how to draw the graph using computer

    Reply
    • KK LEE

      Sorry. I cant teach here. Please youtube yourself.

  37. KHZ

    Sir, does t represent the time when the particles collide?

    Reply
    • KK LEE

      t represents the time, any time when the particle is moving

    • KHZ

      kk, tq sir

  38. James

    Sir, can give me some idea how to write the title

    Reply
  39. a

    Sir can i know how to find the range of the second for question 2(a)?

    Reply
    • KK LEE

      You have to test one by one to get the complete curve.

  40. Cukudut

    Sir what means of this “$latex \sqrt(x-49)$ is defined only if $latex x-49>=0$.”

    Reply
    • KK LEE

      x-49 must be positive, else the square root function cannot be defined.

  41. BKHong

    For question 3c, x=-6/5 and -2,then to find t,I have to use equation x=2sin t right?Should I use another equation of x ,(x=cos t-2)to find t?

    Reply
    • KK LEE

      You can use any equations.

  42. Jason Chin

    For the 2a) question right, x= 4t^2+49 y= 4t+1
    Sir am i right?

    Reply
    • KK LEE

      x= 4t^2+49 y= 2t+1

    • Jason Chin

      NO sir. i mean x= (4t)^2+49 y= 4t+1
      So sir. am i right?

    • KK LEE

      can

  43. dayang

    sir, for the question 2a) can i just substitute the x=e^t into the eq 2a as my parametric equation?

    Reply
    • KK LEE

      Can. If you can find the corresponding y

  44. rickywong

    Teacher,can you tell me how to get 3 parametric equation in 2a.please?

    Reply
  45. chalester

    Teacher,can you give me same tips on how to write methology and conclusion because our maths t teacher already retire and want to wait until next year new teacher come and we don’t have any teacher guide us.Thanks you for your reply~

    Reply
    • KK LEE

      For methodology, try to write about the methods/theorem/ways you used to solve the questions.

      For conclusion, you can rewrite again all your important result from each part and write one or two example that related.

  46. rickywong

    Sir,can you tell me how to get 3 parametric equation in Q2a,thx.

    Reply
    • KK LEE

      It can be obtained directly if you know what is parametric equation. I can’t explain further here.

  47. xxxxxxxxx

    Hi ?I want to ask that the questions 2)a) are we need to form 3 parametric equation form that cartesian equation or just sub the x or y value that you give into that cartesian equation??? Thank you ?

    Reply
    • KK LEE

      You need to form 3 equations.

    • xxxxxxxxx

      Ok, thank you very much.

  48. Chalester

    thank you for your reply(^_^)

    Reply
  49. Sharon

    Sir, for question 2 a) can I let x=t, x=2t and x=t^2 and in each case express y in terms of t. [x=t, y=+/- square root(x-49)-1] is a set?

    Reply
    • KK LEE

      For me, No. For your teacher, i don’t know.

  50. Hedarus

    Can i use y=t,y=(t^2)-1 and y=-t^2 to prove that it can used for y in 2(c)?
    As my teacher want us to show the equation….

    Reply
    • KK LEE

      Can. If your teacher accept.

  51. Hi

    Sir,what should i write for an introduction for parametric equation?

    Reply
    • KK LEE

      Hi. It depends on your teacher. Please google for some related info and use it.

  52. ying

    Sir, is it 2(a) need to plot the curve??because the question have say “….the curve whose equation is…..” so need to sketh a parabola graph or not??

    Reply
  53. OnnGusta

    hi sir , 🙂 can i ask about question 2(b) why cannnot ?

    Reply
    • KK LEE

      Hi. Reason is stated there.

  54. MTPhobia

    Sir,for question 2(a),How to find the other 2 sets of parametric equations?For set 1,I used the formula x=at^2 and y=2at…but how about the other 2 sets?How can i get the other 2 sets?I have no idea…Just use back the same formula or there is another way to solve this?

    Reply
    • MTPhobia

      Does it mean any parametric equations of curve as long as it satisfy the Cartesian equation?So,If that is true,can I use the parametric equation of hyperbola?

    • KK LEE

      You can use any equation that satisfy the original equation.

    • MTPhobia

      How to meant by satisfy the original equation?

    • MTPhobia

      Ohh…I think maybe i get what you mean…Thanks a lot!

  55. Zoe

    Hi Sir, to find if the particles collide in 3c, can I do a table of t(0, pi/2, pi, 3pi/2, 2pi values), x1, x2, y1 & y2? and subs t values into the original equations in the questions to find the (x,y)coordinates that are the same? The answer will still be 3pi/2 as point where they collide.

    Reply
    • KK LEE

      For me, NO. For your teacher, i don’t know.

  56. Alexa A.

    Can you explain more from 3.C Verification? Only subs the value of x on x= 2 sin t?

    Reply
    • KK LEE

      Substitute into all the original equations to verify

  57. Drake

    Hi sir, may i know that for the question 3, should i use the same value as you had used for the simultaneous equation and verification or should i use a different set of values?

    Reply
    • KK LEE

      Same

  58. Lim

    Hello, sir. How do I get the values of t for Q3?

    Reply
    • KK LEE

      Solve the simultaneous equations

  59. yyee

    2a can use standard form of parabola to create the equation?

    Reply
    • KK LEE

      For me NO. For your teacher i dont know

  60. everyone

    that helps alot.thanks

    Reply
  61. .....

    Sir, can you please give me some example of the application of parametric equation in our daily life??? Because I cannot find it in the internet……..

    Reply
  62. random

    Hi sir
    For 2a
    Can I use x=50-sin^2€ and y=cos€+1 and the range of € is between 0 and pi?
    I have calculated the values using the range but it seems to be a graph with y-axis as major axis but the other two equations above are graphs with x-axis as major axis..

    Reply
    • KK LEE

      You can try to switch the x and y

  63. Smaster

    Sir,may I know how to get 3.785 and 5.640 when x=-1.2

    Reply
    • KK LEE

      Using calculator

  64. Wei

    Sir , for x=-2 and y=0 , I’ve got the value of t that is (3π/2) , so is it that the coordinates of the ellipse and circle for x=-2 AND y=0 are the same ?
    Your student here hahahahaha

    Reply
    • KK LEE

      Yes

  65. Alex

    Sir,how to write the conclusion and methodology?

    Reply
  66. Josephine

    Excuse me teacher? I would like to ask about what should i write for any comment or statement after i plot the curve(question 1)?Can you guide me some suggestions?

    Reply
    • KK LEE

      You can explain the shape.

  67. Kim

    sir for question 2a ,may i make the original equation into this form ? x²/36² – y²/6² = 1 ? thn my parametric eqaution will be like this,x = 36 sec ,y = 6 tan

    Reply
    • KK LEE

      For 2a. It is a parabola, which means it cant be x²/36² – y²/6² = 1

  68. Damn

    u know what , u r rude, n i read all your replies to all the comments.. u kinda reply in a sarcastic way.. just chill on , cause we r new to this kinda no guide assignment.. we need some help bcoz all of our school teacher dont give a damn.. so the point is have some courtesy to share knowledge… hope u get me, stingy 🙂

    Reply
    • KK LEE

      All right. Thanks of your comment.

      1. I am not a school teacher. And i never attend any meeting regarding the assignment. So do not expect me to know all the school teachers requirement. I have tried my best to give the information that i know. I have students from different schools. That’s why i know different school teachers have different requirement on the particular questions. This is also the reason i never answer all the questions that are not related to maths.

      2. I am posting all maths related solutions for your reference and please do not expect me to post 100% answers.

      3. I have tried my best to help and this will be my last posting on solutions of assignments. Thanks.

    • Rx

      U r so disgusting u know?people give u a sample to refer,u never say tanks, determine, but u still complain that the ans is not acceptable in your school?so ridiculous,no one is a must to provide amethyst is needed by your teacher,ok???I feel pity on u….

  69. Jack

    sir, do you have math (T) TERM 2 assignment solution?

    Reply

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