A-Math Formula Sheet: Singapore O-Level Formulas and Revision Guide
An A-Math formula sheet gives Singapore Secondary 3 and Secondary 4 students a handy place to review formulas for Additional Mathematics before tests and the Singapore-Cambridge O-Level examination. It can save revision time, especially when quadratic equations, trigonometry and calculus start to overlap in exam questions. But there’s one detail students shouldn’t overlook: a personal revision sheet is not necessarily the same as the mathematical formulae printed in the examination materials. The 2026 O-Level Additional Mathematics syllabus, code 4049, lists specific algebra and trigonometry formulas. Other topic rules still need to be learnt and practised.
SEAB The sections below cover key formulas, when to use them and how to revise without simply memorising symbols.
TL;DR: A-Math Formula Sheet
For Singapore O-Level A-Math, use a formula sheet to review quadratic equations, binomial expansion, trigonometric identities, differentiation, integration and other syllabus topics. SEAB’s 2026 syllabus lists the mathematical formulae supplied for Additional Mathematics 4049. Check the syllabus for your examination year, then practise applying each formula to exam-style questions.
A-Math Formula Sheet for Singapore O-Level Students
The formulae below are useful for revision. The quadratic formula, binomial expansion and listed trigonometric identities appear in the 2026 SEAB mathematical formulae section.
SEAB The examples show how to use them; they aren’t a replacement for the full syllabus.
Quadratic Formula and Binomial Expansion
| Topic | Formula | When to use it |
|---|---|---|
| Quadratic equation | \(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) | Solve \(ax^2+bx+c=0\), where \(a\ne0\). |
| Binomial expansion | \(\displaystyle (a+b)^n=\sum_{r=0}^{n}\binom nr a^{n-r}b^r\) | Expand a positive integer power of a binomial. |
| Binomial coefficient | \(\displaystyle \binom nr=\frac{n!}{r!(n-r)!}\) | Find the coefficient for a particular term. |
For the quadratic formula, substitute the values of \(a\), \(b\) and \(c\) carefully. The \(\pm\) sign gives two possible roots when the discriminant is positive. For binomial expansion, identify the required term before expanding everything — it can save time.
Trigonometric Identities and Double-Angle Formulas
| Formula | When to use it |
|---|---|
| \(\sin^2 A+\cos^2 A=1\) | Rewrite sine or cosine in terms of the other. |
| \(1+\tan^2 A=\sec^2 A\) | Simplify expressions involving tangent and secant. |
| \(\sin 2A=2\sin A\cos A\) | Replace a double-angle sine expression. |
| \(\cos 2A=\cos^2 A-\sin^2 A\) | Rewrite cosine of a double angle. |
| \(\displaystyle \tan 2A=\frac{2\tan A}{1-\tan^2 A}\) | Work with a double-angle tangent expression. |
The cosine double-angle identity also has two useful forms:
\[ \cos 2A=2\cos^2 A-1=1-2\sin^2 A \]
Choose the form that matches the information in the question. If the question gives \(\sin A\), the version using \(\sin^2 A\) may be more direct. The full formulae section also includes compound-angle identities for sine, cosine and tangent.
Sine Rule, Cosine Rule and Triangle Area
For a triangle with sides \(a,b,c\) opposite angles \(A,B,C\), the 2026 formulae section includes these relationships:
| Formula | When to use it |
|---|---|
| \(\displaystyle \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\) | Find a missing side or angle when a matching side-angle pair is known. |
| \(a^2=b^2+c^2-2bc\cos A\) | Find a side or angle when two sides and the included angle, or three sides, are known. |
| \(\displaystyle \text{Area}=\frac12 bc\sin A\) | Calculate triangle area using two sides and their included angle. |
Check which side lies opposite each angle before substituting. Mixing up the labels is a small mistake that can spoil an otherwise correct method.
Which A-Math Formulas Are Given in the O-Level Exam?
For the 2026 Singapore-Cambridge O-Level, the relevant syllabus is Additional Mathematics 4049. SEAB’s mathematical formulae section lists the quadratic equation formula, binomial expansion and selected trigonometric identities and triangle formulas. It does not serve as a complete formula sheet for every topic studied in A-Math.
SEAB Check the official 2026 Additional Mathematics syllabus (4049) and the SEAB list of 2026 O-Level syllabuses. Use the document for your own examination year, rather than assuming that a formula list from an older paper is unchanged.
| Formula or topic | 2026 syllabus reference status | What to revise |
|---|---|---|
| Quadratic equation | Listed in mathematical formulae | Substitution, signs and the discriminant. |
| Binomial expansion | Listed in mathematical formulae | Term selection and coefficients. |
| Trigonometric identities and triangle formulas | Selected formulas listed | Recognising which identity fits the question. |
| Differentiation and integration | Not listed in that mathematical formulae section | Rules and methods from the relevant syllabus topics. |
| Logarithms and coordinate geometry | Not listed as a separate formula group in that section | Laws, equations and applications taught in the syllabus. |
“Not listed in the formulae section” doesn’t mean a topic is excluded from the examination. It means students shouldn’t assume its rules will be supplied in that section. Check the syllabus and your school’s current exam instructions before making a final revision list.
A-Math Formulas to Revise Separately
Some formulas and rules need regular practice even when they aren’t included in the printed mathematical formulae section. The list below is a revision reference, not a claim that every line must be memorised in isolation. Match it to the topics in your examination-year syllabus.
Differentiation and Integration Formulas
| Rule | Formula | Quick example |
|---|---|---|
| Power rule for differentiation | \(\displaystyle \frac{d}{dx}(x^n)=nx^{n-1}\) | \(\frac{d}{dx}(x^3)=3x^2\) |
| Constant multiple | \(\displaystyle \frac{d}{dx}[kf(x)]=kf'(x)\) | \(\frac{d}{dx}(4x^2)=8x\) |
| Power rule for integration | \(\displaystyle \int x^n\,dx=\frac{x^{n+1}}{n+1}+C,\ n\ne-1\) | \(\int x^2\,dx=\frac{x^3}{3}+C\) |
The constant \(C\) appears in indefinite integration. For differentiation, reduce the power by one and multiply by the original power. For integration, increase the power by one and divide by the new power. Easy to mix up when you’re rushing.
Logarithm Laws and Coordinate Geometry
| Topic | Formula | Watch out for |
|---|---|---|
| Product law | \(\log_a x+\log_a y=\log_a(xy)\) | The logarithms must have the same base. |
| Quotient law | \(\log_a x-\log_a y=\log_a(x/y)\) | Subtraction becomes division inside the logarithm. |
| Power law | \(k\log_a x=\log_a(x^k)\) | The multiplier becomes an exponent. |
| Gradient | \(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\) | Keep the coordinate order consistent. |
| Circle with centre \((h,k)\) | \((x-h)^2+(y-k)^2=r^2\) | \(r\) is the radius, not the diameter. |
For logarithms, the arguments must be positive and the base must satisfy \(a>0\) and \(a\ne1\). In coordinate geometry, check whether the question asks for a gradient, equation of a line or equation of a circle. They’re related, but they don’t use the same formula.
How to Use an A-Math Formula Sheet in Exam Questions
A formula is useful only when you can recognise the right moment to apply it. Start by identifying what the question gives you and what it asks you to find.
Choose the Correct Formula
Look for clues in the wording. A quadratic equation set equal to zero may need the quadratic formula. A triangle question with two sides and the included angle may call for the cosine rule or the area formula. If an expression contains \(\sin 2A\), a double-angle identity may be the quickest route.
Apply the Formula Step by Step
Worked example: Solve \(x^2-5x+6=0\) using the quadratic formula. Here, \(a=1\), \(b=-5\) and \(c=6\).
\[ x=\frac{-(-5)\pm\sqrt{(-5)^2-4(1)(6)}}{2(1)} \]
\[ x=\frac{5\pm\sqrt{25-24}}{2} =\frac{5\pm1}{2} \]
So \(x=3\) or \(x=2\).
Check Signs, Substitutions and Final Answers
Notice that \(b=-5\), so \(-b=5\). A common slip is to copy the negative sign incorrectly. After solving, substitute each answer into the original equation:
- \(3^2-5(3)+6=0\)
- \(2^2-5(2)+6=0\) Both roots work. Practise the same steps with exam-style questions until you can select and apply a formula without guessing.
A-Math Formula Revision Checklist
Use this checklist during your weekly revision:
- Open the official SEAB syllabus for your examination year.
- Mark the formulas listed in the mathematical formulae section.
- Make separate notes for topic rules you need to practise.
- Group practice questions by algebra, trigonometry, calculus and other syllabus topics.
- Solve past-year questions without looking at your notes first.
- Record mistakes, such as sign errors or choosing the wrong identity.
- Revisit the questions you got wrong a few days later. A short, regular review is often easier to maintain than trying to relearn every formula the night before an exam.
Frequently Asked Questions
Is an A-Math formula sheet provided in the O-Level exam?
The 2026 SEAB Additional Mathematics 4049 syllabus contains a mathematical formulae section listing selected algebra and trigonometry formulas. Check the examination-year syllabus and exam instructions for the exact reference.
Which A-Math formulas do students need to memorise?
Start with the formulas listed by SEAB, then revise the rules and methods for the other topics in your syllabus. Your revision notes should help you recall how a formula works, not just what it looks like.
Are differentiation and integration formulas provided?
They are not listed in the 2026 syllabus’s mathematical formulae section in the same way as the quadratic formula and selected trigonometric identities. Revise the differentiation and integration methods required by your syllabus, and confirm the current exam arrangements.
Where can I find the official Singapore A-Math syllabus?
Use SEAB’s 2026 O-Level syllabus page and open Additional Mathematics, code 4049. The direct 4049 syllabus PDF contains the mathematical formulae section.
How can I revise A-Math formulas effectively?
Review one topic at a time, write down what each formula is used for and solve questions without checking your notes immediately. Then correct mistakes and try a similar question later. This tests recall and application together.
Conclusion
An A-Math formula sheet is a useful revision companion for Singapore O-Level Additional Mathematics, but it shouldn’t be the only resource you use. Check the SEAB syllabus for your examination year, separate supplied formulas from topic rules you must learn, and practise questions from each area. A little focused practice each week can make it easier to spot the right formula under exam pressure.
Global Arena is a Singapore-focused SEO and digital marketing brand with a network of 25+ publisher websites, helping businesses strengthen their online presence through guest posting, link building, content marketing, and digital PR.
For collaborations, publishing opportunities, or business inquiries:
Hamza@globalarena.org | WhatsApp: +971 52 399 4589
