IGCSE Maths Formula Sheet: What You Actually Get

Before opening any past paper, you need to know exactly what the formula sheet hands you and what it expects you to carry in your head. The IGCSE Maths formula sheet is printed inside the question paper itself, usually on page 2, and it is the same sheet for every paper in that exam series at that tier. You do not request it, you do not lose it, and you cannot bring your own copy.

For CIE 0580 Extended and Edexcel International GCSE 4MA1 Higher Tier, the sheet gives you a tightly chosen set of formulas:

• The quadratic formula for solving ax² + bx + c = 0 - The sine rule and the cosine rule for non right angled triangles - The area of a triangle using ½ ab sin C - Volume and surface area of a sphere (4/3 πr³ and 4πr²) - Volume and curved surface area of a cone (1/3 πr²h and πrl)

Edexcel 4MA1 Higher additionally tends to give you the volume of a prism (area of cross section × length) and the volume of a pyramid (1/3 × area of base × height), which CIE leaves to memory. This is not a printing accident, it is a deliberate syllabus difference and it shows up in the exam.

For CIE 0580 Core and Edexcel 4MA1 Foundation, the sheet is stripped down. The trigonometric formulas (sine rule, cosine rule, area = ½ ab sin C) disappear, because non right angled trigonometry is not assessed at the lower tier. The basic mensuration formulas stay. If you are sitting Core, you should already have asked whether [Extended is the right tier for you](/igcse-maths-extended-vs-core-decision) before exam season starts.

Two formulas that students always expect on the sheet and that simply are not there:

• Pythagoras' theorem (a² + b² = c²) - Area and circumference of a circle (πr², 2πr)

These are treated as foundational. The sheet assumes you know them cold.

Most students never sit both boards, but the formula sheet differences are worth understanding because they reveal what each board treats as core knowledge. If you have changed school, or you tutor across both, this matters.

CIE 0580 (Cambridge)

prints a single page with seven boxed formulas at Extended tier:

• Quadratic formula - Sine rule - Cosine rule (in the form a² = b² + c² minus 2bc cos A) - Area of triangle = ½ ab sin C - Sphere: V = 4/3 πr³, A = 4πr² - Cone: V = 1/3 πr²h, curved surface A = πrl - Nothing else (no prism, no pyramid, no cylinder)

Edexcel International GCSE 4MA1 (Pearson)

gives a slightly fuller sheet at Higher tier. You get the same trig and 3D shapes, and in addition:

• Volume of a prism = area of cross section × length - Volume of a pyramid = 1/3 × area of base × height

This Edexcel generosity bites students in two ways. First, if you switch from Edexcel to CIE between Year 10 and Year 11, you must commit pyramid volume to memory or you will lose those marks. Second, CIE students sometimes substitute 4/3 πr³ for a hemisphere question and forget to halve, because the sheet only gives the full sphere. The board hands you the bare formula and trusts you to adapt it.

For a deeper look at how the two boards differ across the whole syllabus, not just the sheet, see [CIE 0580 vs Edexcel 4MA1](/igcse-maths-cie-0580-vs-edexcel-4ma1).

This is where most students lose marks. The formula sheet is short on purpose. Anything not printed is assumed knowledge, and examiners will not award method marks for a half remembered version. Here is the working memory list you must carry into the exam, regardless of board:

Number and algebra

• Laws of indices, including negative and fractional indices - Compound interest: final amount = P(1 + r/100)ⁿ - Recurring decimal to fraction conversion technique - Difference of two squares, and the completed square form

Geometry and mensuration

• Pythagoras' theorem - Right angled trigonometry (SOH CAH TOA) - Circle: area = πr², circumference = 2πr - Arc length = (θ/360) × 2πr, sector area = (θ/360) × πr² - Cylinder: volume = πr²h, curved surface area = 2πrh - Angle facts: parallel line angles, polygon interior and exterior angle sums

Statistics and probability

• Mean from a frequency table - Estimated mean from grouped data using midpoints - Probability of independent and mutually exclusive events - Reading cumulative frequency curves: median, quartiles, IQR

Vectors and transformations

• Column vector arithmetic - Magnitude of a vector - Standard matrix transformations (CIE 0580 only)

The list looks long, but most of it appears in early topics and becomes second nature with practice. The trick is to revise the list explicitly. Do not assume that doing past papers will catch every gap, it will not. For a structured way to drill this material, see [how to revise for IGCSE Maths](/how-to-revise-for-igcse-maths).

Let us see how the formula sheet plays out in a typical Paper 4 question on a composite solid, the kind that appears in roughly every CIE 0580 Extended paper.

Question.

A solid is made of a hemisphere of radius 5 cm joined to the flat circular face of a cone. The cone has the same radius and a slant height of 13 cm. Find the total surface area of the solid, in terms of π.

Step 1. Identify the formulas you need.

• Surface area of a sphere (on the sheet): A = 4πr² - Curved surface area of a cone (on the sheet): A = πrl - Area of a circle (NOT on the sheet): A = πr²

The trap: you need the area of a circle, and the sheet does not give it. If you cannot recall πr², you cannot finish the question.

Step 2. Hemisphere surface area.

Full sphere = 4π(5)² = 100π. Hemisphere curved surface = half of that = 50π. Do not include the flat circular face here, because that face is joined to the cone and is internal to the solid.

Step 3. Cone curved surface area.

A = πrl = π × 5 × 13 = 65π. Again, do not include the flat circular base, it is the same face shared with the hemisphere.

Step 4. Add and present.

Total surface area = 50π + 65π = 115π cm².

Three marks. Most students who lose marks here either forget to halve the sphere (the sheet gives the full sphere), include the shared circular face twice, or panic and write a numerical decimal when the question said 'in terms of π'. The formula sheet does its job. The thinking is on you.

For more on how examiners reward partial work, see [IGCSE Maths mark schemes explained](/igcse-maths-mark-schemes-explained).

The formula sheet itself is rarely the cause of lost marks. Misuse of the sheet is. The patterns below repeat across hundreds of past papers.

Mistake 1: using the cosine rule when the sine rule is faster.

The sheet gives you both. If you have a triangle with two sides and an angle, decide whether the angle is between the two sides (cosine rule) or opposite one of them (sine rule). Picking the wrong tool costs you time even when you eventually reach the right answer.

Mistake 2: forgetting the second solution in the sine rule.

The sine rule gives sin x = 0.6, say, which means x can be 36.87° or 143.13°. The sheet does not warn you. The question wording or a diagram will tell you which is wanted, but you must remember the ambiguity exists.

Mistake 3: misreading the cone formula.

The sheet gives πrl, not πrh. l is the slant height. Students substitute the perpendicular height by reflex when the question gives both, and the formula sheet will not save them.

Mistake 4: quadratic formula sign errors.

The sheet prints x = [-b ± √(b² - 4ac)] / 2a clearly, but when b is negative the substitution becomes -(-3) ± ..., and a sign drops. Slow down by half a second when you copy the formula across.

Mistake 5: not reading the sheet during the exam.

Many students never look at page 2 once the exam begins, because they have memorised the formulas anyway. Use the sheet as a check. If your answer to a sphere question looks wrong, glance back. The sheet costs nothing to consult.

The formula sheet should shape how you revise. Here is the approach I use with students sitting CIE 0580 or Edexcel 4MA1 in May/June.

Two months out.

Print the formula sheet for your specific paper, stick it above your desk, and write the unprinted list (Pythagoras, circle, cylinder, arc, sector, indices, compound interest, mean from frequency tables) next to it on a different colour paper. Two lists, one wall.

Six weeks out.

Do one past paper per week under timed conditions. After marking, classify every lost mark into one of three buckets: formula sheet correctly used, formula sheet misused, or formula not on sheet (had to recall, failed). The third bucket is your priority for the following week.

Four weeks out.

Start topic specific drills on the formulas you keep getting wrong. Most students discover here that sector area and compound interest are their biggest leaks, neither of which is on the sheet.

Two weeks out.

Stop opening the sheet. Try to reproduce it on a blank page. Then check. If you can write the sheet correctly from memory, you have understood what the board expects you to know and what they will hand you.

Exam day.

Read the sheet once before you start, just to anchor where it is and confirm it is the version you expect. Then forget about it until you need it. Do not flip back constantly, it breaks your rhythm.

For the longer plan, [a 3 month IGCSE Maths revision plan](/igcse-maths-revision-plan-3-months) builds the same logic into a full timetable.