MF27 Formula List for H2 Maths (2026): Full Contents and How to Use It

By Mr Ian Ang, Math Academy · Updated 29 October 2026

MF27 is the official List of Formulae and Results for Mathematics and Further Mathematics, the 8-page booklet that candidates receive in the Singapore-Cambridge A-Level Mathematics papers. Its cover states that it is for use from 2025 in all papers for the H1, H2 and H3 Mathematics and H2 Further Mathematics syllabuses, so it is the list you sit with for H2 Mathematics (9758) in 2026 and 2027. Below you will find the link to the official SEAB PDF, every formula in MF27 typed out page by page, the sections H2 Maths actually uses, what changed from MF26, and the results MF27 leaves out.

MF27 at a glance

Full name: List MF27, List of Formulae and Results for Mathematics and Further Mathematics.
Syllabuses: H1 Mathematics (8865), H2 Mathematics (9758), H2 Further Mathematics (9649), and H3 Mathematics.
In use from: the 2025 A-Level examinations. It replaced MF26, which had been in use from 2017.
Length: 8 pages. It no longer contains the normal distribution table or the t and chi-squared tables that MF26 had.
In the exam: provided to you. The H2 Mathematics syllabus states that candidates will be provided with a list of formulae and results.

Download the official MF27 PDF (SEAB)

If the link above ever moves, the PDF is listed on SEAB’s A-Level syllabuses page, next to the Mathematics syllabuses.

Open MF27 formula sheet on an exam desk beside an H2 Mathematics paper and calculator

What is MF27 in A-Level Maths?

MF27 is a reference booklet, not a summary of the syllabus. One booklet serves four syllabuses, so it holds results that H2 Mathematics never uses (the Wilcoxon table, for example, belongs to Further Mathematics) and it leaves out many results that H2 Mathematics uses every week (the derivative of $\sin x$ , the sum of a geometric series). Knowing which page holds what, and which results you must carry in your head, is the whole skill.

The booklet runs in this order: algebraic series and partial fractions (page 2), trigonometry and derivatives (page 3), integrals, vectors, applications of definite integrals and functions of two variables (page 4), numerical methods and standard distributions (page 5), sampling, regression and the Wilcoxon table (page 6), and mathematical results such as the AM-GM inequality (page 7). Page 1 is the cover and page 8 is the back page.

If you would rather work through it with a teacher, our JC H2 Maths tuition classes with Mr Ian Ang (NUS, First Class Honours in Mathematics) run in groups of at most 9 students, onsite in Bukit Gombak or online.

MF27 formula list: full contents, page by page

Every formula below is typed from the official SEAB PDF and uses the booklet’s own headings, notation and conditions. If anything here ever differs from SEAB’s copy, the SEAB copy is the one that counts in the exam hall.

Algebraic series (page 2)

Binomial expansion:

\begin{aligned}(a+b)^n ={} & a^n + \binom{n}{1}a^{n-1}b + \binom{n}{2}a^{n-2}b^2 \\ & + \binom{n}{3}a^{n-3}b^3 + \dots + b^n\end{aligned}

where $n$ is a positive integer and

\binom{n}{r} = \frac{n!}{r!\,(n-r)!}

Maclaurin expansion:

\begin{aligned}\mathrm{f}(x) ={} & \mathrm{f}(0) + x\,\mathrm{f}'(0) + \frac{x^2}{2!}\mathrm{f}''(0) \\ & + \dots + \frac{x^n}{n!}\mathrm{f}^{(n)}(0) + \dots\end{aligned}

\begin{aligned}(1+x)^n ={} & 1 + nx + \frac{n(n-1)}{2!}x^2 \\ & + \dots \\ & + \frac{n(n-1)\dots(n-r+1)}{r!}x^r + \dots \\ & (|x| \lt 1)\end{aligned}

\begin{aligned}\mathrm{e}^x ={} & 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots + \frac{x^r}{r!} + \dots \\ & (\text{all } x)\end{aligned}

\begin{aligned}\sin x ={} & x – \frac{x^3}{3!} + \frac{x^5}{5!} – \dots \\ & + \frac{(-1)^r x^{2r+1}}{(2r+1)!} + \dots \\ & (\text{all } x)\end{aligned}

\begin{aligned}\cos x ={} & 1 – \frac{x^2}{2!} + \frac{x^4}{4!} – \dots \\ & + \frac{(-1)^r x^{2r}}{(2r)!} + \dots \\ & (\text{all } x)\end{aligned}

\begin{aligned}\ln(1+x) ={} & x – \frac{x^2}{2} + \frac{x^3}{3} – \dots \\ & + \frac{(-1)^{r+1}x^r}{r} + \dots \\ & (-1 \lt x \leqslant 1)\end{aligned}

Partial fractions decomposition (page 2)

Non-repeated linear factors:

\frac{px+q}{(ax+b)(cx+d)} = \frac{A}{(ax+b)} + \frac{B}{(cx+d)}

Repeated linear factors:

\begin{aligned}\frac{px^2+qx+r}{(ax+b)(cx+d)^2} ={} & \frac{A}{(ax+b)} + \frac{B}{(cx+d)} \\ & + \frac{C}{(cx+d)^2}\end{aligned}

Non-repeated quadratic factor:

\frac{px^2+qx+r}{(ax+b)(x^2+c^2)} = \frac{A}{(ax+b)} + \frac{Bx+C}{(x^2+c^2)}

Trigonometry (page 3)

\sin(A \pm B) \equiv \sin A\cos B \pm \cos A\sin B

\cos(A \pm B) \equiv \cos A\cos B \mp \sin A\sin B

\tan(A \pm B) \equiv \frac{\tan A \pm \tan B}{1 \mp \tan A\tan B}

\sin 2A \equiv 2\sin A\cos A

\begin{aligned}\cos 2A & \equiv \cos^2 A – \sin^2 A \\ & \equiv 2\cos^2 A – 1 \equiv 1 – 2\sin^2 A\end{aligned}

\tan 2A \equiv \frac{2\tan A}{1 – \tan^2 A}

Principal values:

-\tfrac{1}{2}\pi \leqslant \sin^{-1}x \leqslant \tfrac{1}{2}\pi \qquad (|x| \leqslant 1)

0 \leqslant \cos^{-1}x \leqslant \pi \qquad (|x| \leqslant 1)

-\tfrac{1}{2}\pi \lt \tan^{-1}x \lt \tfrac{1}{2}\pi

Derivatives (page 3)

$\mathrm{f}(x)$	$\mathrm{f}'(x)$
$\sin^{-1}x$	$\dfrac{1}{\sqrt{1-x^2}}$
$\cos^{-1}x$	$-\dfrac{1}{\sqrt{1-x^2}}$
$\tan^{-1}x$	$\dfrac{1}{1+x^2}$
$\operatorname{cosec} x$	$-\operatorname{cosec} x\cot x$
$\sec x$	$\sec x\tan x$

Integrals (page 4)

(Arbitrary constants are omitted; $a$ denotes a positive constant.)

$\mathrm{f}(x)$	$\displaystyle\int \mathrm{f}(x)\,\mathrm{d}x$	Condition
$\dfrac{1}{x^2+a^2}$	$\dfrac{1}{a}\tan^{-1}\left(\dfrac{x}{a}\right)$
$\dfrac{1}{\sqrt{a^2-x^2}}$	$\sin^{-1}\left(\dfrac{x}{a}\right)$	$(\|x\| \lt a)$
$\dfrac{1}{x^2-a^2}$	$\dfrac{1}{2a}\ln\left(\dfrac{x-a}{x+a}\right)$	$(x \gt a)$
$\dfrac{1}{a^2-x^2}$	$\dfrac{1}{2a}\ln\left(\dfrac{a+x}{a-x}\right)$	$(\|x\| \lt a)$
$\tan x$	$\ln(\sec x)$	$(\|x\| \lt \tfrac{1}{2}\pi)$
$\cot x$	$\ln(\sin x)$	$(0 \lt x \lt \pi)$
$\operatorname{cosec} x$	$-\ln(\operatorname{cosec} x + \cot x)$	$(0 \lt x \lt \pi)$
$\sec x$	$\ln(\sec x + \tan x)$	$(\|x\| \lt \tfrac{1}{2}\pi)$

Vectors (page 4)

The point dividing $AB$ in the ratio $\lambda : \mu$ has position vector

\frac{\mu\mathbf{a} + \lambda\mathbf{b}}{\lambda + \mu}

Vector product:

\mathbf{a}\times\mathbf{b} = \begin{pmatrix} a_1 \\ a_2 \\ a_3 \end{pmatrix} \times \begin{pmatrix} b_1 \\ b_2 \\ b_3 \end{pmatrix} = \begin{pmatrix} a_2b_3 – a_3b_2 \\ a_3b_1 – a_1b_3 \\ a_1b_2 – a_2b_1 \end{pmatrix}

Applications of definite integrals (page 4)

Arc length of a curve defined in cartesian form:

\int_a^b \sqrt{1 + \left(\frac{\mathrm{d}y}{\mathrm{d}x}\right)^2}\,\mathrm{d}x

Surface area of revolution about the $x$ -axis for a curve defined in cartesian form:

\int_a^b 2\pi y\sqrt{1 + \left(\frac{\mathrm{d}y}{\mathrm{d}x}\right)^2}\,\mathrm{d}x

Functions of two variables (page 4)

Quadratic approximation of $\mathrm{f}$ at $(a, b)$ :

\begin{aligned}\mathrm{f}(x, y) \approx{} & \mathrm{f}(a, b) + \mathrm{f}_x(a, b)(x-a) \\ & + \mathrm{f}_y(a, b)(y-b) \\ & + \tfrac{1}{2}\mathrm{f}_{xx}(a, b)(x-a)^2 \\ & + \mathrm{f}_{xy}(a, b)(x-a)(y-b) \\ & + \tfrac{1}{2}\mathrm{f}_{yy}(a, b)(y-b)^2\end{aligned}

Numerical methods (page 5)

Trapezium rule (for single strip):

\int_a^b \mathrm{f}(x)\,\mathrm{d}x \approx \tfrac{1}{2}(b-a)\left[\mathrm{f}(a) + \mathrm{f}(b)\right]

Simpson’s rule (for two strips):

\begin{aligned}\int_a^b \mathrm{f}(x)\,\mathrm{d}x \approx{} & \tfrac{1}{6}(b-a)\Bigl[\mathrm{f}(a) \\ & + 4\,\mathrm{f}\left(\frac{a+b}{2}\right) + \mathrm{f}(b)\Bigr]\end{aligned}

The Newton-Raphson iteration for approximating a root of $\mathrm{f}(x) = 0$ :

x_2 = x_1 – \frac{\mathrm{f}(x_1)}{\mathrm{f}'(x_1)}

where $x_1$ is a first approximation.

Euler Method with step size $h$ :

y_2 = y_1 + h\,\mathrm{f}(x_1, y_1)

Improved Euler Method with step size $h$ :

u_2 = y_1 + h\,\mathrm{f}(x_1, y_1)

y_2 = y_1 + \frac{h}{2}\left[\mathrm{f}(x_1, y_1) + \mathrm{f}(x_2, u_2)\right]

Standard discrete distributions (page 5)

Distribution of $X$	$\mathrm{P}(X = x)$	Mean	Variance
Binomial $\mathrm{B}(n, p)$	$\dbinom{n}{x}p^x(1-p)^{n-x}$	$np$	$np(1-p)$
Poisson $\mathrm{Po}(\lambda)$	$\mathrm{e}^{-\lambda}\dfrac{\lambda^x}{x!}$	$\lambda$	$\lambda$
Geometric $\mathrm{Geo}(p)$	$(1-p)^{x-1}p$	$\dfrac{1}{p}$	$\dfrac{1-p}{p^2}$

Standard continuous distribution (page 5)

Distribution of $X$	p.d.f.	Mean	Variance
Exponential	$\lambda\mathrm{e}^{-\lambda x}$	$\dfrac{1}{\lambda}$	$\dfrac{1}{\lambda^2}$

Sampling and testing (page 6)

Unbiased estimate of population variance:

\begin{aligned}s^2 & = \frac{n}{n-1}\left(\frac{\Sigma(x-\bar{x})^2}{n}\right) \\ & = \frac{1}{n-1}\left(\Sigma x^2 – \frac{(\Sigma x)^2}{n}\right)\end{aligned}

Regression and correlation (page 6)

Estimated product moment correlation coefficient:

r = \frac{\Sigma(x-\bar{x})(y-\bar{y})}{\sqrt{\left\{\Sigma(x-\bar{x})^2\right\}\left\{\Sigma(y-\bar{y})^2\right\}}}

= \frac{\Sigma xy – \dfrac{\Sigma x\,\Sigma y}{n}}{\sqrt{\left(\Sigma x^2 – \dfrac{(\Sigma x)^2}{n}\right)\left(\Sigma y^2 – \dfrac{(\Sigma y)^2}{n}\right)}}

Estimated regression line of $y$ on $x$ :

y – \bar{y} = b(x – \bar{x}),

\text{where } b = \frac{\Sigma(x-\bar{x})(y-\bar{y})}{\Sigma(x-\bar{x})^2}

Wilcoxon signed rank test (page 6)

$P$ is the sum of the ranks corresponding to the positive differences, $Q$ is the sum of the ranks corresponding to the negative differences, and $T$ is the smaller of $P$ and $Q$ . For each value of $n$ the table gives the largest value of $T$ which will lead to rejection of the null hypothesis at the level of significance indicated.

Critical values of $T$
One-tail level	0.05	0.025	0.01	0.005
Two-tail level	0.1	0.05	0.02	0.01
$n = 6$	2	0
7	3	2	0
8	5	3	1	0
9	8	5	3	1
10	10	8	5	3
11	13	10	7	5
12	17	13	9	7
13	21	17	12	9
14	25	21	15	12
15	30	25	19	15
16	35	29	23	19
17	41	34	27	23
18	47	40	32	27
19	53	46	37	32
20	60	52	43	37

Mathematical results (page 7)

AM-GM inequality: for any nonnegative real numbers $x_1, x_2, \dots, x_n$ ,

\frac{x_1 + x_2 + \dots + x_n}{n} \geqslant \sqrt[n]{x_1x_2\dots x_n},

where the equality holds if and only if $x_1 = x_2 = \dots = x_n$ .

Cauchy-Schwarz inequality: for any real numbers $u_1, u_2, \dots, u_n$ and $v_1, v_2, \dots, v_n$ ,

\left(\sum_{i=1}^{n} u_iv_i\right)^2 \leqslant \left(\sum_{i=1}^{n} u_i^2\right)\left(\sum_{i=1}^{n} v_i^2\right),

where the equality holds if and only if there exists a nonzero constant $k$ such that $u_i = kv_i$ for all $i = 1, 2, \dots, n$ .

Triangle inequality: for any real numbers $x_1, x_2, \dots, x_n$ ,

\begin{aligned}& |x_1 + x_2 + \dots + x_n| \\ & \leqslant |x_1| + |x_2| + \dots + |x_n|,\end{aligned}

where the equality holds if $x_1, x_2, \dots, x_n$ are all nonnegative.

Inclusion-Exclusion Principle: for any subsets $A_1, A_2, \dots, A_n$ of a set,

\begin{aligned} & |A_1 \cup A_2 \cup \dots \cup A_n| \\ & = |A_1| + |A_2| + \dots + |A_n| \\ & – [\,|A_1 \cap A_2| + |A_1 \cap A_3| + \dots \\ & \qquad + |A_{n-1} \cap A_n|\,] \\ & + [\,|A_1 \cap A_2 \cap A_3| + |A_1 \cap A_2 \cap A_4| + \dots \\ & \qquad + |A_{n-2} \cap A_{n-1} \cap A_n|\,] \\ & \;\;\vdots \\ & + (-1)^{n-1}\,|A_1 \cap A_2 \cap \dots \cap A_{n-1} \cap A_n|\end{aligned}

Which MF27 sections H2 Maths (9758) uses

Because one booklet serves four syllabuses, a good part of MF27 is outside H2 Mathematics. The table below matches each section to the 9758 syllabus content. Sections marked “No” cover topics that do not appear in the 9758 content outline, so you can skip them when you revise.

MF27 section	Page	Used in H2 Maths?
Algebraic series	2	Yes: binomial expansion and the five standard Maclaurin series
Partial fractions decomposition	2	Yes: the three forms match the assumed A Math knowledge
Trigonometry, principal values	3	Yes
Derivatives	3	Yes
Integrals	4	Yes: the four $a^2 \pm x^2$ forms are named in the syllabus
Vectors	4	Yes: ratio theorem and vector product
Applications of definite integrals	4	No: arc length and surface area are not in 9758
Functions of two variables	4	No
Numerical methods	5	No: H2 approximates definite integrals with a graphing calculator
Standard discrete distributions	5	Binomial row only
Standard continuous distribution	5	No
Sampling and testing	6	Yes: unbiased estimate of population variance
Regression and correlation	6	Yes
Wilcoxon signed rank test	6	No
Mathematical results	7	No

In practice, an H2 Mathematics candidate uses pages 2 to 4 for Paper 1 and Section A of Paper 2, and a few lines of pages 5 and 6 for the statistics section.

MF26 vs MF27: what changed

MF26 was the list for papers from 2017 to 2024. Comparing the two booklets line by line, the pure mathematics formulae that H2 students use are almost unchanged, but the statistics tables are gone. These are the differences:

New name and length. MF26 was the “List of Formulae and Statistical Tables” (11 printed pages). MF27 is the “List of Formulae and Results” (8 pages).
Tables removed. The normal distribution function table, the critical values for the normal distribution, and the critical values for the t-distribution and the chi-squared distribution are no longer printed. The Wilcoxon signed rank table stays.
Factor formulae removed. MF26 printed the four sum-to-product formulae, such as $\sin P + \sin Q \equiv 2\sin\tfrac{1}{2}(P+Q)\cos\tfrac{1}{2}(P-Q)$ . MF27 does not.
Two-sample variance removed. The unbiased estimate of common population variance from two samples is no longer listed.
New sections added. Applications of definite integrals (arc length and surface area of revolution), the quadratic approximation for functions of two variables, and a page of mathematical results: the AM-GM, Cauchy-Schwarz and triangle inequalities and the Inclusion-Exclusion Principle.
Unchanged. Algebraic series, partial fractions, the compound and double angle formulae, principal values, derivatives, integrals, vectors, numerical methods, the standard distributions, the unbiased estimate of population variance, and regression and correlation.

Papers set in 2024 or earlier were written for MF26. The pure mathematics results they rely on are mostly the same, but if a solution uses a factor formula or a statistical table, remember that MF27 will not give it to you. Our page on the MF26 formula sheet has the older booklet if you need it for those papers.

What MF27 leaves out for H2 Maths

MF27 is a reference list, not a method list. A great deal of routine H2 Mathematics is absent, and you are expected to carry it in your head. None of the following is printed in MF27:

Basic derivatives and integrals: the derivatives of $x^n$ , $\sin x$ , $\cos x$ , $\tan x$ , $\mathrm{e}^x$ and $\ln x$ , the integrals of $x^n$ , $\sin x$ , $\cos x$ , $\sec^2 x$ and $\mathrm{e}^x$ , the product, quotient and chain rules, and integration by parts.
Core trigonometric identities: $\sin^2 x + \cos^2 x \equiv 1$ , $1 + \tan^2 x \equiv \sec^2 x$ , the factor formulae, and the $R\sin(\theta \pm \alpha)$ and $R\cos(\theta \pm \alpha)$ forms.
Arithmetic and geometric series: the $n$ th term, the sum to $n$ terms and the sum to infinity $\dfrac{a}{1-r}$ for $|r| \lt 1$ .
Small angle approximations: $\sin x \approx x$ , $\cos x \approx 1 – \tfrac{1}{2}x^2$ and $\tan x \approx x$ .
Vectors and complex numbers: the scalar product, the equations of lines and planes, and every complex number result.
Area and volume: the formulae for area under a curve and volume of revolution.
Probability and statistics: $\mathrm{P}(A \cup B)$ , conditional probability, $\mathrm{E}(aX+b)$ and $\mathrm{Var}(aX+b)$ , $\mathrm{E}(\bar{X}) = \mu$ and $\mathrm{Var}(\bar{X}) = \dfrac{\sigma^2}{n}$ , standardising to $Z$ , and any normal distribution table. The H2 syllabus states that papers are set on the assumption that you have a graphing calculator, and that is where normal probabilities come from.

This is why H2 Mathematics leans on A Math so heavily. The syllabus lists O-Level Additional Mathematics as assumed knowledge, including the derivatives and integrals above. If that base is shaky, MF27 cannot rescue you, because the booklet only helps a candidate who already knows which result to look for. Our guide to the hardest H2 Math topics shows where these gaps usually surface.

How to use MF27 in the H2 Maths exam

Use MF27 as a check and a time-saver, not as a substitute for understanding. These habits are worth building well before the paper.

Revise with the official copy open. Print the SEAB PDF and keep it beside you for every practice paper, so the layout becomes familiar.
Know your three pages. For Pure Mathematics, nearly everything you will look up sits on pages 2 to 4: series and partial fractions, then trigonometry and derivatives, then integrals and vectors. For statistics, page 5 has the binomial mean and variance and page 6 has $s^2$ , $r$ and the regression line.
Confirm, then write. Recall a result yourself first, then glance at MF27 to check signs, conditions and the order of terms. The $\mp$ in $\cos(A \pm B)$ and the $\dfrac{1}{2a}$ in the logarithmic integrals are the usual slips.
Read the conditions. MF27 prints the range of validity next to each series and integral, such as $|x| \lt 1$ for $(1+x)^n$ and $-1 \lt x \leqslant 1$ for $\ln(1+x)$ . The syllabus includes the range of values of $x$ for which a standard series converges, so read these carefully.
Do not over-search. If a result is not on pages 2 to 6 within a few seconds, it is almost certainly one you are expected to know. Stop hunting and recall it.

For a fuller revision plan that puts MF27 alongside timed practice and topic review, see our guide on how to study H2 Math.

MF27 FAQs

What is MF27?

MF27 is the List of Formulae and Results for Mathematics and Further Mathematics published for the Singapore-Cambridge A-Level. Its cover states that it is for use from 2025 in all papers for the H1, H2 and H3 Mathematics and H2 Further Mathematics syllabuses, so H2 Mathematics (9758) candidates use it in 2026 and 2027.

Where can I download the official MF27 PDF?

SEAB publishes MF27 as a PDF on its A-Level syllabuses page, listed beside the Mathematics syllabuses. Use that copy rather than a re-typed version, because it is the booklet you will see in the exam.

Do I need to bring my own MF27 to the exam?

No. The H2 Mathematics syllabus states that candidates will be provided in the examination with a list of formulae and results. That list is MF27, so you do not bring your own copy.

Is MF27 the same for H1 and H2 Math?

Yes. One MF27 booklet covers H1 Mathematics, H2 Mathematics, H3 Mathematics and H2 Further Mathematics. Each syllabus uses only the sections that match its own content, so H2 Mathematics candidates can ignore sections such as numerical methods and the Wilcoxon table.

Does MF27 have normal distribution tables?

No. MF26 printed the normal distribution table and the t and chi-squared tables, but MF27 does not. H2 Mathematics papers are set on the assumption that candidates have a graphing calculator, which is where normal probabilities come from.

Does MF27 include basic differentiation and integration formulae?

No. The derivatives of x^n, sin x, cos x, tan x, e^x and ln x, and the basic integrals, are assumed knowledge and are not printed. MF27 lists only the derivatives of the inverse trigonometric functions, cosec x and sec x, and a short table of less common integrals.

What is the difference between MF26 and MF27?

MF27 replaced MF26 from 2025. It drops the statistical tables except the Wilcoxon table, the factor formulae and the two-sample common variance estimate. It adds arc length, surface area of revolution, a quadratic approximation for functions of two variables, and a page of results including the AM-GM and Cauchy-Schwarz inequalities.

Using the MF27 formula list well

MF27 gives an H2 Mathematics candidate about three pages of genuinely useful results: the series, the trigonometric and calculus tables, the vector results, and a handful of statistics formulae. Everything else on the list belongs to other syllabuses, and much of what H2 needs is not on the list at all. Know which is which, revise with the official copy open, and the booklet becomes a quick check instead of a search. If you would like that built into weekly practice, our JC H2 Maths tuition classes with Mr Ian Ang have at most 9 students, onsite in Bukit Gombak or online.

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