How to Use MF27: Complete H2 Math Formula Walkthrough (2025)

Watch Mr Tim Gan's comprehensive 1-hour 19-minute walkthrough where he explains every section of MF27 with practical examples and exam tips.

🎥 Watch: MF27 Explained — H2 Math Formula List 2025 Edition

What You'll Learn:

• Complete page-by-page walkthrough of MF27
• Binomial expansion vs. power series
• Trigonometric identities and small-angle approximations
• The R-Formula (Amplitude–Phase Form)
• Essential integration techniques not in MF27
• Vector geometry and 3D coordinate systems
• Formulas you must memorize (not found in MF27)

Get the complete annotated MF27 walkthrough PDF with handwritten notes, derivations, and examples used in the video lesson.

What's Inside:

✅ Handwritten annotations on MF27 formulas

✅ Step-by-step derivations for missing formulas

✅ Exam tips and common mistake warnings

✅ Cross-references between related topics

✅ Quick lookup guide for formula locations

From 2025, all A-Level H1, H2, and H3 Mathematics students in Singapore will use the updated MF27 Formula Booklet. Issued by SEAB and Cambridge International, it lists the official formulas and results allowed in the A-Level exams.

However, not every formula you need appears inside MF27 — and that's where students often lose marks. In our latest YouTube video, Mr. Tim Gan walks you through exactly how to use MF27 efficiently for H2 Math, covering formulas, derivations, and the tricks examiners expect you to know.

What Makes MF27 Essential:

✅ Official reference for all A-Level Math exams from 2025

✅ Published by SEAB and Cambridge International Education

✅ Contains formulas for Pure Math, Statistics, and Mechanics

❌ BUT — Critical formulas like Cosine Rule, Sine Rule, and key integrations are NOT included

The Strategy:

MF27 isn't just a list — it's a tool. Knowing what's in it (and what's missing) helps you revise smarter and save time during exams. Tim shows you how to annotate your MF27, derive missing results, and cross-link concepts between calculus, trigonometry, and vectors.

View and download the full MF27 Formula List →

Understand the difference between finite and infinite expansions:

$(a + bx)^n \quad \text{vs.} \quad (1 + x)^n$

Finite binomial expansion applies when $n$ is a positive integer. Power series (Maclaurin series) applies when $n$ is non-integer or negative.

Tim explains when to make the expression "1 + something" so that you can safely expand it as a power series:

$(1 + 3x)^{\frac{1}{2}} = 1 + \frac{1}{2}(3x) - \frac{1}{8}(3x)^2 + \dots$

Learn why:

$\tan x \approx x, \quad \sin x \approx x, \quad \cos x \approx 1 - \frac{x^2}{2}$

for small $x$.

These are used in Maclaurin Series and small-angle approximation questions.

Tim also discusses principal values — the restricted domains for inverse trigonometric functions that make them one-to-one:

$\sin^{-1}x \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right], \quad \cos^{-1}x \in [0, \pi], \quad \tan^{-1}x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$

A common A-Level question type. Learn to express:

$a\cos x + b\sin x = R\cos(x - \alpha)$

where:

$R = \sqrt{a^2 + b^2}, \quad \tan\alpha = \frac{b}{a}$

This makes it easy to find maximum and minimum values in trigonometric functions.

These are not fully listed in MF27, but are crucial to know:

$\int \frac{dx}{a^2 + x^2} = \frac{1}{a}\tan^{-1}\!\left(\frac{x}{a}\right) + C$

$\int \sec^2 x \, dx = \tan x + C$

$\int \csc x \, dx = \ln|\csc x - \cot x| + C$

$\int \tan x \, dx = \ln|\sec x| + C$

Tim also explains how to apply partial fractions and substitution to handle more complex rational forms such as:

$\int \frac{1}{x^2 - a^2} \, dx = \frac{1}{2a}\ln\left|\frac{x - a}{x + a}\right| + C$

Even though these are examinable, you'll need to memorise or derive them during the exam:

Cosine Rule:

$a^2 = b^2 + c^2 - 2bc\cos A$

Sine Rule:

$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

Arc Length:

$s = r\theta$

Area of a Sector:

$A = \frac{1}{2}r^2\theta$

Key results for A-Level Paper 1:

Ratio Theorem:

If point $P$ divides $AB$ in the ratio $\lambda : \mu$, then:

$\vec{OP} = \frac{\mu \vec{A} + \lambda \vec{B}}{\lambda + \mu}$

Line Equation:

$\mathbf{r} = \mathbf{a} + \lambda\mathbf{d}$

Plane Equation:

$\mathbf{r} \cdot \mathbf{n} = a$

Angle between two lines:

$\cos\theta = \frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{a}||\mathbf{b}|}$

MF27 isn't just a list — it's a tool. Knowing what's in it (and what's missing) helps you revise smarter and save time during exams.

Tim shows you how to annotate your MF27, derive missing results, and cross-link concepts between calculus, trigonometry, and vectors.

By the end of the walkthrough, you'll:

• Know which results to memorise
• Recognise derivations quickly during the paper
• Feel confident handling unexpected exam questions