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STPM PBS Assignment

STPM 2017 Mathematics (T) Term 1 Assignment

By KK LEE

July 3, 2016
STPM 2017 Term 1 MT Coursework Explained
03
JULY, 2016
Polynomial
Trigonometry
Transformation
I will start posting Mathematics (T) and Mathematics (M) coursework sample answer again this term. Only sample solution for mathematical part will be posted. Different school teacher have different requirement on the non-mathematical part (Introduction, methodology, and conclusion). That’s why i am not going to write it and post it here. Thanks.
Assignment A: Function (Investigation)
A function is a relation whereby every input gives a unique (exactly one) output. There are four
possible ways to represent a function; verbally, numerically, visually and algebraically.
Numbers
Photograph via Wikipedia
1. Discuss, with examples, the differences between a relation and a function.
2. Give at least five different representations of a simple discrete function.
3. Give at least three different representations of a continuous function.
“Please ask your school teacher for introduction, methodology, and conclusion.”
4. Consider the algebraic function f:x\rightarrow a(x-b)^n+c
Describe, with sketch graphs, the function f for different values of a, b and c for n = 1,2 and 3.
5 Repeat task 4 with the trigonometric function g:x\rightarrow a\sin[n(x-b)]+c.
6 Repeat task 4 with an exponential or logarithmic function of your own choice.
“Please submit your introduction/methodology/conclusions if you wish to share with others by submit a comment below.”
Sample solution for the mathematical part.

For question 1. Please google for the definition.

For question 2. You can assign any functions but make sure your range is “integer”.

For question 3. You also can assign any functions but make sure your range is “any numbers”.

Question 1 2 3
For question 4

For n=1. Some ideas for you. You can try a>0, a=0, a<0, b>0, b=0, b<0, c>0, c=0, c<0. So you will get many combinations. For the total number of combinations, please refer to your school teacher.

For n=2. Same.

For n=3. Same.

I am not going to sketch the graph for n=3. Please do it yourself. Thanks.

For question 5

For n=1. Some ideas for you. You can try a>0, a<0, a>c, c>a, b>0, b<0, b in first/2nd/3rd/4th quadrant. So you will get many combinations. For the total number of combinations, please refer to your school teacher.

In short. a is amplitude. b translation (left/right). c is translation (up/down).

For n=2. Same.

For n=3. Same.

I am not going to sketch the graph for n=2(frequency=2) and 3(frequency=3). Please do it yourself. Thanks.

5a

a=1, b=pi/6, c=2

5b

a=3, b=pi/6, c=2

5c

a=3, b=-pi/6, c=2

5d

a=2, b=-pi/6, c=3

5e

a=2, b=-pi/6, c=-3

5f

a=-2, b=-pi/6, c=-3

5g

a=-2, b=-pi/6, c=1

5h

a=3, b=5pi/3, c=1

For question 6

You can consider h(x)=ae^{n(x-b)}+c

For n=1. Some ideas for you. You can try a>0, a<0, b>0, b<0, b>0, c<0, c>0. So you will get many combinations. For the total number of combinations, please refer to your school teacher.

In short. a is scale factor(vertical). n is scale factor(horizontal). b translation (left/right). c is translation (up/down).

6a

a=1, b=0, c=0

6b

a=2, b=2, c=2

6c

a=-2, b=2, c=2

6d

a=-2, b=2, c=-2

Knowledge.
Photograph by jarmoluk via Pixabay
All solutions are updated now. I am not going to discuss the questions in class. Please Whatsapp me or comment below if you need my guidance.

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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.

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