# How to use MF26 like a Pro? The Complete Guide

##### Timothy Gan

As a H2 Math student, you only have 3 best friends in any H2 math examination,

2. Your Graphing Calculator (Scientific calculator too!)
3. The List MF26

To do well in any H2 math examination, you need to make sure that these friends are well prepared and in tip-top condition.

Make sure you get sufficient rest to ensure your brain can function optimally and that your calculators are fully charged the day before the exams. These steps will address points 1 and 2.

In this article, we will mainly talk and discuss the use of the MF26 which is less discussed or known amongst students. How do you use MF26 like a pro in the H2 Math Examinations?

### 1. Know the formulas that are given in the MF26

This point may seem trivial, but I have taught enough students to know that students don’t use the MF26 enough to know which formulas are given and which are not.

For example, some students don’t know that $\int{\text{cosec }x}\text{ d}x$ and $\int{\text{tan }x}\text{ d}x$ can be found in the MF26.

Where is the formula ${}_{n}{{C}_{r}}$ located? Is it located in the Statistics or Pure Mathematics section? Some students may not know that it’s located under the pure math section under the Binomial Series.

The formulas of $\left( \begin{matrix}n \\1 \\\end{matrix} \right)=n$ ,$\left( \begin{matrix}n \\2 \\\end{matrix} \right)=\frac{n\left( n-1 \right)}{2!}$ and $\left( \begin{matrix}n \\r \\\end{matrix} \right)=\frac{n\left( n-1 \right)…\left( n-r+1 \right)}{r!}{{x}^{r}}$ can be found in the MF26 too. With this, we can deduce the formulas such as $\left( \begin{matrix}n \\3 \\\end{matrix} \right)=\frac{n\left( n-1 \right)\left( n-2 \right)}{3!}$ like what we need to know from the secondary school Additional Mathematics syllabus. It can be found under the Maclaurin Expansion section:

### 2. Have a scribbled MF26 (to know what is not given in MF26)

Many JC students often go for math exams without knowing what formulas are not given in the MF 26. It’s common to think that important formulas such as ${{\tan }^{2}}x+1={{\sec }^{2}}x$ and ${{\cot }^{2}}x+1=\text{cose}{{\text{c}}^{2}}x$ are given when they are in fact not. These formulas can be derived by dividing the familiar ${{\sin }^{2}}x+{{\cos }^{2}}x=1$ (also not given in the MF26) by ${{\cos }^{2}}x$ and ${{\sin }^{2}}x$.

Although vectors can take up to 15% of the overall grade, there are only two lines of formulas given, i.e. Ratio theorem and the vector cross product. So, it’s important to know what is not in the MF26 before your examinations.

Some of the other important formulas that are not given are,

1. Arc Length, $s=r\theta$
2. Area of sector, $A=\frac{1}{2}{{r}^{2}}\theta$
3. Cosine rule: ${{c}^{2}}={{a}^{2}}+{{b}^{2}}-2ab\cos C$
4. Sine Rule: $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$
5. Most Vectors formulas as only cross product and ratio theorem are given.
6. The formulas of Arithmetic and Geometric Progression

Thus, I always advise my students to keep a copy of a scribbled MF26 to jot down the formulas and a brief note about how to derive them. You can have a look at my scribbled formula list here!

### 3. Know the formulas that can be shown in MF26

Although seemingly insignificant, having a thorough understanding of how to derive the formulas in MF26 is a quintessential step towards doing well in H2 Mathematics as many JC students fail to recognise that formulas stated in the formula list can be easily derived.

For example,

How to show the derivative of  $\frac{\text{d}}{\text{d}x}{{\sin }^{-1}}x=\frac{1}{\sqrt{1-{{x}^{2}}}}$.

Some of the other formulas that can be shown are $\frac{\text{d}}{\text{d}x}{{\cos }^{-1}}x=-\frac{1}{\sqrt{1-{{x}^{2}}}}$, integrals of $\int{\tan x\text{ d}x=\ln \left( \sec x \right)}+c$ , $\int{\frac{1}{{{x}^{2}}+{{a}^{2}}}\text{d}x=\frac{1}{a}{{\tan }^{-1}}\left( \frac{x}{a} \right)}+c$ and $\int{\frac{1}{\sqrt{{{a}^{2}}-{{x}^{2}}}}\text{d}x={{\sin }^{-1}}\left( \frac{x}{a} \right)}+c$.

### 4. Know how to apply the formulas in MF26 properly

Some of the common mistakes I saw that were done by students during applications of formulas are:

$\int{{{\sin }^{-1}}x}\text{ d}x=\frac{1}{\sqrt{1-{{x}^{2}}}}$ and $\frac{\text{d}}{\text{d}x}\sec x=\ln \left( \sec x+\tan x \right)$.

The derivatives and integrals sections of the MF26 are commonly confused by students. This can be easily overcome by practising more.

### 5. Look through your scribbled MF26 before exams

Before any examinations, please look through the scribbled MF26 to get familiarised with what formulas are given and what is not given. Additionally, review which formulas can be derived or shown.

### Conclusion

All in all, MF26 is an important tool during the H2 Math examinations and just like any other tool, you need consistent practice and familiarity to maximise its utility. If you need help with all these tips and tricks in scoring for your H2 Mathematics examinations, please do consider joining our H2 Math Tuition Classes. You can join a trial class first before you decide to sign up with us.

Published: 15th February 2023
Written by
Timothy Gan
This is Tim. Tim loves to teach math. Tim seeks to improve his teaching incessantly! Help Tim by telling him how he can do better.
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