Formulario IGCSE Maths: cosa ti danno e cosa devi imparare a memoria

The IGCSE Maths formula sheet is a short list printed on the first inside page of every exam paper. Many students discover this for the first time in the exam room and panic, because most of the formulas they need are not on it. The sheet is deliberately minimal. It only lists items the board considers complex enough to give away. Everything else, from the area of a triangle to Pythagoras' theorem, must live in your head.

For Cambridge IGCSE Mathematics 0580 Extended, the formula list typically includes:

• The quadratic formula for ax² + bx + c = 0 - Area of a triangle = 1/2 ab sin C - The sine rule: a/sin A = b/sin B = c/sin C - The cosine rule: a² = b² + c² minus 2bc cos A - Volume of a cone = 1/3 πr²h - Curved surface area of a cone = πrl - Volume of a sphere = 4/3 πr³ - Surface area of a sphere = 4πr²

For Edexcel International GCSE Mathematics 4MA1 Higher Tier, the list is very similar. Edexcel usually adds the volume of a prism (area of cross section times length) and sometimes the volume of a pyramid (1/3 base area times height). On the Core tier of CIE 0580, and on Foundation 4MA1F, the list is much shorter. Sine rule, cosine rule and the triangle area formula are absent because those topics are simply not on the syllabus at that level.

If you are unsure which board and tier you are sitting, ask your school or check the front of any past paper. The exact wording is on every Cambridge or Edexcel question paper, in the same place each session. Do not assume one board's sheet matches the other.

This is where most marks are quietly lost. The formula sheet does not give you the everyday tools. If you sit the exam expecting them to appear, you will burn time and panic. Here is the working memory you need before walking in.

Number and algebra

- Pythagoras' theorem: a² + b² = c² - Trig ratios SOH CAH TOA (sin = opp/hyp, cos = adj/hyp, tan = opp/adj) - Simple interest: I = PRT/100 - Compound interest: final amount = P (1 + r/100)ⁿ - Percentage change: (new minus old)/old times 100 - Reverse percentages: original = final divided by (1 plus or minus rate) - Standard form rules and laws of indices - Difference of two squares, completing the square (for CIE Extended and Edexcel Higher)

Geometry and mensuration

- Area of rectangle, parallelogram, trapezium and triangle (1/2 base times height) - Circumference of a circle = πd, area of a circle = πr² - Arc length = (θ/360) times 2πr, sector area = (θ/360) times πr² - Volume of a prism = area of cross section times length - Volume and surface area of a cuboid and cylinder

Statistics, probability and rates

- Mean = sum divided by count, also for grouped data using midpoints - Probability of A or B (mutually exclusive): P(A) + P(B) - Probability of A and B (independent): P(A) times P(B) - Speed = distance / time, density = mass / volume, pressure = force / area - Sequence rules: nth term of an arithmetic sequence a + (n minus 1) d

For a topic-by-topic refresher of these, see [our IGCSE Maths preparation guide](/igcse-maths-preparation-guide). If you are unsure how the question paper structure interacts with the formula sheet, the article on [Paper 2 versus Paper 4](/igcse-maths-paper-2-vs-paper-4) explains why the non-calculator paper especially rewards memorised arithmetic.

Students at international schools in Milan, Dubai or Singapore often switch boards between mock exams and the real session. The formula sheet is one of the small but real differences.

Cambridge 0580 Extended

- Quadratic formula, sine rule, cosine rule, area = 1/2 ab sin C - Sphere volume and surface area, cone volume and curved surface area - No prism, no pyramid, no cylinder. You must know these - No circle formulas, no arc, no sector. You must know these

Edexcel International GCSE 4MA1 Higher

- Same quadratic, trigonometry and sphere or cone block - Often adds volume of a prism and volume of a pyramid - Still no circle formulas, no arc or sector, no cylinder volume

The practical consequence: a student moving from Edexcel mocks to CIE finals (or vice versa) sometimes assumes prism volume will be given because it was on the mock. It will not be. For a deeper comparison of question style, mark scheme behaviour and grade boundaries, read [CIE 0580 vs Edexcel 4MA1](/igcse-maths-cie-0580-vs-edexcel-4ma1).

Tier matters too.

On the Core paper for CIE, or Foundation for Edexcel, you will not see the sine rule, cosine rule or trigonometric area formula at all. They are not just absent from the sheet; they are absent from the syllabus. If your teacher is preparing you for Core but you are practising Extended past papers, you will think the sheet is wrong. Confirm the tier first.

If you are deciding which tier to sit, the article on [Extended versus Core](/igcse-maths-extended-vs-core-decision) walks through grade ceilings, university implications and the kind of student who genuinely benefits from each route.

Here is a typical Extended question that mixes formulas from the sheet with formulas you must already know.

Problem.

A solid is made by attaching a hemisphere of radius 5 cm to the flat circular face of a cylinder of radius 5 cm and height 12 cm. Calculate the total surface area of the solid, to 3 significant figures.

Step 1. Identify which formulas come from the sheet.

The surface area of a full sphere, 4πr², is on the formula sheet. A hemisphere is half a sphere, so the curved part of the hemisphere is 1/2 times 4πr² = 2πr².

Step 2. Identify which formulas are NOT on the sheet.

The cylinder is not given. You must know two things from memory: - Curved surface area of a cylinder = 2πrh - Area of a circle = πr² (needed for the cylinder's bottom face)

Step 3. Decide which faces actually show.

- Hemisphere curved surface: 2π(5)² = 50π - Cylinder curved surface: 2π(5)(12) = 120π - The bottom of the cylinder is exposed: π(5)² = 25π - The top of the cylinder is COVERED by the hemisphere, so do not count it

Step 4. Add and evaluate.

Total = 50π + 120π + 25π = 195π = 612.6105... = 613 cm² to 3 s.f.

Notice what happened: the sheet gave you one piece (4πr²), but the question rewarded students who knew the cylinder formulas cold and who paused to think about which faces were actually visible. That second skill, deciding what to count, is where examiner reports flag the most marks lost on solids questions. To see how examiners word these in real papers, work through a few from [past paper practice](/igcse-maths-past-papers-how-to-use).

The formula sheet is not just a memory aid. It is also a hint sheet. The examiners are telling you, in advance, which formulas the harder questions on this paper will require. If a paper gives you the sine rule and cosine rule on the front, expect a non-right-angled triangle question, usually worth 4 to 6 marks. If it gives you the sphere volume, expect a composite solid or a rate-of-change problem involving spheres. Treat the sheet as a preview.

Three habits that turn the sheet into marks:

• Read the formula page before Question 1. Sixty seconds spent here orients your brain. You will spot the trigonometry question coming on page 7 before you turn the page. - Tear off the page if your board allows it. On Cambridge papers the formula list is part of the cover, so it stays attached, but you can fold it back. On Edexcel papers the formula sheet is sometimes a detachable insert. Keep it open next to your working hand. - Annotate the sheet. You are allowed to write on the question paper. As soon as you start a question that uses sine rule, draw a quick arrow from your working back to the formula. It stops you reproducing the formula incorrectly in the rush of part (c).

What the sheet will not save you from.

Mis-reading degrees vs radians on a calculator, confusing ab sin C with bc sin A (the labelling matters; the side opposite the named angle is excluded), and applying the cosine rule with the wrong angle position. None of those are sheet problems. They are practice problems. The fix is volume of past paper questions under timed conditions, marked against the official scheme.

After many years of marking IGCSE mock papers, the same handful of formula sheet mistakes recur every session. Here is the short list, with the fix in each case.

• Copying the quadratic formula wrong. The fraction bar must extend under both minus b and the discriminant. Writing x = minus b plus or minus √(b² minus 4ac) divided by 2a, with the 2a only under the root, is a guaranteed lost mark. The sheet has it correctly; just transcribe carefully. - Mislabelling sides in the sine rule. Side a is opposite angle A, side b opposite angle B. If your diagram does not label vertices, label them in pencil before you write anything. - Using the cone curved surface area as the full surface area. The sheet gives πrl, which is the curved part only. If the cone has a base, you must add πr² yourself. - Sphere vs hemisphere confusion. The 4πr² on the sheet is for a complete sphere. For a hemisphere, the curved part is 2πr², and if you need the total external surface including the flat circle, add πr². - Assuming the cylinder is on the sheet. It is not, on either board. 2πrh for the curve, πr² for each end. Memorise it as a fixed pair. - Forgetting that the sheet does not include circle formulas. Arc length and sector area are very common, very testable, and never given.

These are exactly the gaps a [structured exam-tips routine](/igcse-maths-exam-tips) is designed to close, especially in the final 6 weeks before the May or June session.