O-Level A-Math Formula Sheet: AMF Guide for Singapore Students

The AMF formula sheet includes key results from algebra and trigonometry. On the first page, students can see formulas such as:

• Quadratic equation formula
• Binomial expansion
• Basic trigonometric identities
• Compound angle formulas
• Double angle formulas
• Sine rule, cosine rule, and triangle area formula

For example, the sheet gives the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

It also gives the binomial expansion. If this topic is still shaky, revise the full Binomial Theorem study guide alongside the formula sheet. The most useful part to understand during practice is the general term:

${n \choose r}a^{n-r}b^r$

and common trigonometric identities such as:

$\sin^2 A + \cos^2 A = 1$

The sheet is useful because it reduces memory load. But it does not remove the need for understanding. A student still has to know which topic is being tested and which formula fits the question.

A common misconception is: "If the formula is given, I do not need to learn it properly." In our lessons, this is one of the first habits we try to correct.

In A Math, marks are often lost before the formula is even used. Students may choose the wrong identity, substitute the wrong value, miss a condition, or write unclear working.

So the goal is not just to "know where the formula is". The goal is to know why the formula applies.

The algebra section looks short, but it appears across many chapters. For algebra foundations behind these formulas, use the Indices, Surds, and Logarithms study guides as supporting practice.

Quadratic formula

For $ax^2 + bx + c = 0$:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Students should not use this blindly. If the quadratic factorises neatly, factorisation is usually faster. If the question is about the nature of roots, tangent conditions, or intersections, the discriminant $b^2 - 4ac$ may be the main idea.

Binomial expansion

The formula sheet gives the expansion, but students still need to handle the general term:

${n \choose r}a^{n-r}b^r$

This is where many mistakes happen. Students mix up the term number with the value of $r$, forget negative signs, or substitute the wrong expression for $a$ and $b$.

The trigonometry part of the sheet can feel crowded because many identities are printed together. Students should not wait until the exam to scan the whole page. For topic revision beyond the formula list, pair this section with the Trigonometric Functions study guide and the Sketching of Trigonometric Curves study guide.

Important identities include:

$\sin^2 A + \cos^2 A = 1$

$\sec^2 A = 1 + \tan^2 A$

$\sin(A \pm B) = \sin A\cos B \pm \cos A\sin B$

$\cos(A \pm B) = \cos A\cos B \mp \sin A\sin B$

For double angles, students should be comfortable moving between forms:

$\begin{aligned}\cos 2A &= \cos^2 A - \sin^2 A \\ &= 2\cos^2 A - 1 \\ &= 1 - 2\sin^2 A\end{aligned}$

The key question is not "Which formula did I memorise?" The better question is "What expression do I need to create?" That shift helps students choose identities more calmly.

The AMF formula sheet also includes formulas for a triangle $ABC$:

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

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

$\Delta = \frac{1}{2}bc\sin A$

A quick decision rule helps:

• Use sine rule when there is a matching side-angle pair.
• Use cosine rule when there are two sides and the included angle, or all three sides.
• Use area formula when there are two sides and the included angle.

If the angle is not between the two sides, pause. Many careless errors come from substituting a non-included angle into the area formula.

The AMF sheet does not replace topic mastery. It does not show every algebraic manipulation, proof step, or exam pattern.

Students still need to know how to:

• Factorise and simplify expressions accurately
• Complete the square when graph interpretation is required
• Solve inequalities and state ranges correctly
• Handle logarithmic and exponential equations
• Differentiate and integrate with correct notation
• Prove trigonometric identities step by step
• Check whether an answer satisfies the domain or context

When the gap is calculus rather than formula recall, revise the Differentiation, Techniques of Integration, and Applications of Integration guides before returning to exam questions.

This is why memorising math formulas alone is not enough. A Math rewards students who understand how formulas connect.

Use this practice loop:

1. Attempt with the formula sheet open. Focus on recognising the topic and selecting the correct formula.
2. Mark the question and label the mistake. Was it formula choice, substitution, algebra, sign error, or presentation?
3. Redo the same question without looking at the solution. This checks whether the correction actually stuck.
4. Attempt a similar question without opening the formula sheet immediately. Only check the sheet after deciding the method.
5. Write one sentence beside the formula. For example: "Use cosine rule when I know two sides and the included angle."

When a mistake points to a topic gap instead of formula recall, go back to the matching A-Math study guide and practise that skill directly. This turns the sheet from a crutch into a training tool. If A Math feels overwhelming beyond formulas, pair this with our guide on how to do well in Additional Mathematics.

A Math formula habits matter later. In A-Level H2 Math, students use the MF27 formula list, but the principle is the same: the booklet gives results, not strategy.

Students who learn the AMF sheet properly usually transition better because they have trained three habits:

• Identify the structure of the question before choosing a formula
• Understand the conditions behind each formula
• Present working clearly enough to earn method marks

This is why A Math is a useful foundation for students who intend to take H2 Math. The formulas matter, but the thinking habits matter more.