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Discussion –

46

Discussion –

46

# STPM 2017 Mathematics (M) Term 1 Assignment

STPM 2017 Term 1 MM Coursework Explained.
##### —00
The lower sum and upper sum are defined as follows: Lower Sum = $\sum_{i=1}^n f(m_i)\triangle x$ Lower Sum = $\sum_{i=1}^n f(M_i)\triangle x$ You are required to investigate the area of the region bounded by the curve $y=f(x)=x^2+1$, the x-axis, and the lines x=0 and x=2.
“Only sample solution for mathematical part will be posted. Please ask your school teacher for introduction, methodology, and conclusion.”
##### —01
(a) (i) Sketch the curve with 5 inscribed rectangles and evaluate the lower sum. (ii) Sketch the curve with 5 circumscribed rectangles and evaluate the upper sum. (iii) Comment on your results. (b) (i) Tabulate the lower sums and upper sums for n=10, 20, 40. (ii) What do you observe about the lower sums and upper sums as n increases?
##### —02

Let $A_n=\sum_{i=1}^n f(c_i)\triangle x$. (a) (i) Show that $A_n=\frac{4}{3}\left[\frac{(n+1)(2n+1)}{n^2}\right]+2$ if $c_i=a+i\triangle x$, (ii) Tabulate the values of $A_i$ for n=1000, 5000, 10000, 50000, 100000, 500000. (iii) Evaluate $\lim_{n\to \infty}A_n$. (b) It is given that $A_n=\frac{4}{3}\left[\frac{(n-1)(2n-1)}{n^2}\right]+2$ if $c_i=a+(i-1)\triangle x$. Repeat steps (a)(ii) and (a)(iii). (c) What happens to the value of $\lim_{n\to\infty} A_n$ if $a+(i-1)\triangle x < c_i < a+i\triangle x$?

##### —03
(a) Use the Fundamental Theorem of Calculus to evaluate $\int_0^2 f(x) dx$. (b) Suggest a definition of a definite integral.
“Scroll down for the sample solution!”
##### 1 (a) (i)
Lower sum can be calculated by calculate the total area of the inscribed rectangles (refer the diagram). For n=5, △ x=2/n=2/5=0.4. Area of rectangle is given by f(x) multiply △ x or f(x) multiply 0.4.
##### 1 (a) (ii)
Lower sum can be calculated by calculate the total area of the circumscribed rectangles (refer the diagram). For n=5, △ x=2/n=2/5=0.4. Area of rectangle is given by f(x) multiply △ x or f(x) multiply 0.4.
##### 1 (a) (iii)
The upper sum is 40.8% larger than the lower sum. The exact area should be between 5.520 and 3.920.
##### 1 (b) (i)
For n=10, △ x=2/n=2/10=0.2. Area of rectangle is given by f(x) multiply △ x or f(x) multiply 0.2.
##### 1 (b) (i)
For n=20, △ x=2/n=2/20=0.1. Area of rectangle is given by f(x) multiply △ x or f(x) multiply 0.1.
##### 1 (b) (i)
For n=40, △ x=2/n=2/40=0.05. Area of rectangle is given by f(x) multiply △ x or f(x) multiply 0.05.
##### 1 (b) (ii)
As n increases the gap between the lower sum and upper sum is getting smaller.
##### 2 (a) (i)
You need to find the proof for the sum $\sum_{i=1}^n r^2=\frac{n(n+1)(2n+1)}{6}$.
##### 2 (a) (ii)
Prepare the table using the formula provided in part (i)
Find the limit.
##### 2 (b) (ii)
Prepare the table using the formula provided in part (i)
Find the limit.
Same value.
##### 3 (a)
Normal integration.

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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.

# 46 Comments

1. how to find f(mi) and the lower sum ?
and the comment for my results how to write?

Reply
• Sample solution will be posted once they are available or after i discuss the solution in class.

• okay,thanks

• may i kw u gt 2018 sem 1 assignment answer

• No. I din write it.

2. Hi. I’m Aries. I’m not your student. But I really need explanation. Because I’m so confused and I really dont know how to start my coursework. I hope that you can help me out. Thanks Sir.

Reply
• Hi. If you read properly. I have mentioned there. I will post the solution asap when they are available. I will write it after my holiday. 🙂

• Aries Christie Lawrence , do you mind to send me a sample of introduction? or anyone here can share v me? thanks and appreciate a lot

• @ywlai how you do your introduction ? what are the important point need to mentions ? Can you share with me ? thank you

• I’ve difficult to understand the project question sir, can you briefly explain what i should do from beginning coz my tutor left hand and ask me to do own. I was worried coz still left several day to past my assigment.

• Hi. Try to get help from other teacher from your school. I will only help on the maths part.

3. Ok.thanks sir.?

Reply
4. Hi sir..our school just startd our coursework..but I’m still confuse on finding the lower sum and upper sum..looking forwrd for ur rply.. tq..

Reply
• Solution will be updated soon

5. Teacher , may i know what are the important point need to mentions in introduction ?

Reply
• Provides sufficient description to the given problem. (Upper sum. Lower sum) including the title.

• teacher can i have some example ? thank you

• Please check with your school teacher for details

6. hi mr.lee,our school have just started our maths M coursework.Thank you for the guidance eventhough i am not one of your students.

Reply
• can u help me how to do it? becoz I don’t have any guideline to do it.
tpaavitthira@gmail.com its my email. I hope u guys help me.

7. sir, I’m your student. I’m taking Maths M as my extra subject. So, I’m really confused how to coursework. can u help me?

Reply
• Which part? Did you get the handout in class?

• no I didn’t get any handout. they asked to me to it by own.

• You can get the handout from me in class tomorrow

• okey sir. thank you.

8. Hi Sir, can you please help me on introduction? I can’t find any example or description for it. What I got is only the definition of integration

Reply
• thank you sir 😀

9. hi, can u pls tell me what is the software u use to draw the graph??
thx a lot~

Reply
• Graph.

10. sir can i know to do the introduction and methodology??thx

Reply
• As mentioned above. Please refer to your teacher.

11. sir, may i know the title of this assignment?

Reply
12. sir,I know how to do introduction and methology can you help me please

Reply
13. How the 2(b) same with 2(a)(i) as 2(b) ci = a+(i-1) delta x?? Can you show me the step pls tq

Reply
• Which part of 2b? I cant find the “same” part that u mentioned.

14. Sir, may I know what do we need to write for the methodology?

Reply
15. hai sir, may i know for term 2 assigment dont have ka?

Reply
• Ya. Not yet posted.

16. Hi sir,may i know when do you post the asignment M term 2?

Reply
17. Hello sir can I know when sem 2 assignment will be posted..?

Reply
• Hi there. I am not going to post it soon. Whatsapp me if you really need some help.

18. Hey , do you have math M stpm 2018 assignment? :))

Reply
• No

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