In this question, part (a) tests us on basic concepts of Maclaurin’s Series Expansion by making use of the formula in the MF15/26. Part (b) is the interesting one which require us to make some observations and manipulations so that you can answer the question using answers from earlier part. Many students would struggle to answer part (b) as they do not see the links. I hope I have presented the solutions clearly for your understanding.

# 9758 Syllabus

## Differentiation Application: Rate of Change

In this interesting question, it is highly recommended that students draw a diagram to show the depth of water and volume of water. This question is set to be slightly tricky as students must realize that **volume of water is the difference between total volume and volume of air. **Students must also be able to use similar triangles to make radius the subject formula since question is asking for rate of change of depth.

## Periodic Functions

In one of the years, students were asked a question on **periodic functions** which were not exactly covered in the syllabus. But information given were sufficiently clear to allow us to figure out how to work out the sum. I have always advise my students to expect the unexpected and be flexible during examinations.

One of my students ask me on how to approach the question using a shorter method. In this post, I share with you one way you can analyse this question.

## Integers Grouped into Sets (AP and GP)

In this question, students are tested on their understanding of mainly Arithmetic Progression but information is presented in a ‘twisted’ manner.

This is what we mean by application. We must have firm foundation in the concepts and flexibility to apply the concepts correctly in this question.

I hope you will find my thought process beneficial.

## Can a Graph Cross An Asymptote?

In this post, I define the meaning of asymptote, vertical and horizontal.

Asymptote is an important feature of rational function. Students learn this concept under the topic of Graphing Technique and they should aware though Graphing Calculator is a useful tool but asymptotes are not shown on the screen.

I also use an example to discuss this question on: **Can a Graph Cross An Asymptote?**

## Solving a System of Linear Equations with No Unique Solutions

In system of linear equations, we can solve them and conclude with the following:

- One unique solution
- No unique solutions
- No solutions

In this application problem, we investigate and understand the meaning of no unique solutions when we solve two linear equations with three unknowns using our GC (Graphing Calculator). Therefore, I hope through this question, you can gain a deeper understanding of the solutions presented in the GC, rather than viewing it as a mere number.