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STPM 2016 Mathematics (T) Term 2 Assignment


The concept of a limit plays a central role in calculus. For example, continuity, derivative and integral require this concept. In this assignment, you are required to explore the concept of a limit.

Sample Question

Question 1

(a) Draw an equilateral triangle inscribed in a circle of radius  x cm. Express the area of the triangle A_3 in term of x.

(b) Repeat 1(a) with square, regular pentagon, regular hexagon, …, regular polygon with n sides in the circle of radius x cm.

(c) Determine the value of \frac{A_n}{x^2} correct to three decimal places when n is large.

Question 2

A function  f_k  is defined by  f_k(x) =(1+kx)^{\frac{1}{x}}.

(a)(i) Tabulate the values x and f_1(x) when x equals to 0.1, 0.01, 0.001, …. Deduce value of \lim_{x\to 0} f_1(x).

(a)(ii) Tabulate the values x and  f_k(x) for k = 2, 3 and 4, when x equals to 0.1, 0.01, 0.001, ….  Deduce value of  \lim_{x\to 0}f_k(x).

(b) Show that \lim_{x\to\infty} \left(1+\frac{k}{x}\right)^x=\lim_{x\to 0}(1+kx)^\frac{1}{x}.

Question 3

A function g is defined by g(t) = \int_1^t \frac{1}{x(x+1)}dx, where t>1.

(a) Suppose t is an integer, estimate g(t) using the trapezium rule with

(i) t-1 strips,

(ii) 2(t-1) strips,

(iii) 4(t-1) strips.

In each case, express g(t) in terms of  t and determine $\lim_{t\to\infty} g(t)$.

(b) Suppose t is a real number, find g(t) using integration and determine $\lim_{t\to\infty} g(t)$.

(c) Comment on your findings.




Sample Solution
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STPM 2021 Term 2 Exam Timetable

STPM 2021 Term 2 Exam Timetable

View the exam timetable for STPM 2021 Term 2. Countdown to STPM 2021 Examination. Join my tuition to help you achieve better results in the exam. Contact (60) 018-2016992 or for more information.

STPM 2018 Term 1 Mathematics (T) Coursework Sample

STPM 2018 Term 1 Mathematics (T) Coursework Sample

Question A complex number is an extension of a real number and it can be represented in Cartesian and polar forms. In this assignment, you are required to explore the powers and roots of complex numbers. 1 (a) Let z =1+i. Find z^n, where n = 2, 3, 4, …, and represent...


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.


  1. ashley

    Sir! Thank you for guiding us all these semesters!!! I’ve learned a lot from your solutions!
    Sir, I do really appreciate your hard work! THANK YOU SIR!!

    • KK LEE


  2. jack

    sir can you post the sample answer already? sem 2 already over , i need it as reference . Thank you in advance

    • jack

      oh , if sir do not wish to post it yet then can you email me the sample answer , i really need it ,thanks!

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