IGCSE Additional Mathematics Formula List
Additional Mathematics assumes every 0580 formula and adds calculus, series, radians and identities on top. This sheet covers the material specific to 0606.
0606 expects fluency rather than recall alone, so the formulae below need to be usable without hesitation. Everything on the 0580 formula sheet is also assumed knowledge, so revise that alongside this one. Check which results are printed on your own paper.
Algebra, series and counting
| Result | Formula |
|---|---|
| Quadratic formula | x = (minus b plus or minus the square root of (b2 minus 4ac)) divided by 2a |
| Discriminant | b2 minus 4ac. Zero means equal roots, negative means no real roots |
| Binomial general term | n choose r, times an-r, times br |
| Arithmetic nth term | a + (n minus 1)d |
| Arithmetic sum | S = n over 2, times [2a + (n minus 1)d] |
| Geometric nth term | a rn-1 |
| Geometric sum | S = a(rn minus 1) divided by (r minus 1) |
| Sum to infinity | S = a divided by (1 minus r), valid when the size of r is less than 1 |
| Permutations | n permute r = n! divided by (n minus r)! |
| Combinations | n choose r = n! divided by [r! (n minus r)!] |
Circular measure and trigonometry
| Result | Formula |
|---|---|
| Radian conversion | 180 degrees = pi radians |
| Arc length | s = r theta, theta in radians |
| Sector area | A = half r2 theta, theta in radians |
| Segment area | A = half r2(theta minus sin theta), theta in radians |
| Pythagorean identity | sin2 theta + cos2 theta = 1 |
| Tangent identity | tan theta = sin theta divided by cos theta |
| Secant identity | 1 + tan2 theta = sec2 theta |
| Cosecant identity | 1 + cot2 theta = cosec2 theta |
Calculus and coordinate geometry
| Result | Formula |
|---|---|
| Power rule, differentiation | d over dx of xn = n xn-1 |
| Chain rule for a bracket | d over dx of (ax + b)n = n a (ax + b)n-1 |
| Second derivative test | positive means minimum, negative means maximum |
| Power rule, integration | integral of xn = xn+1 divided by (n + 1), plus c |
| Integrating a bracket | integral of (ax + b)n = (ax + b)n+1 divided by a(n + 1), plus c |
| Area under a curve | the definite integral between the two limits |
| Kinematics chain | displacement differentiates to velocity, which differentiates to acceleration |
| Equation of a circle | (x minus a)2 + (y minus b)2 = r2 |
| Perpendicular gradients | the product of the two gradients equals minus 1 |
How to use this sheet
- Set your calculator to radian mode for circular measure and to degree mode for trigonometric equations stated in degrees. Check before every question.
- Exact form means surds, fractions or logarithms left unevaluated. A decimal does not satisfy it.
- For any stationary point, quote the second derivative value, then state the conclusion.
- Sum to infinity requires the size of the common ratio to be less than 1. State the condition before applying the formula.
- Check an integration by differentiating the result. It should return the original expression.
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Frequently asked questions
What does Additional Mathematics add beyond 0580?
Calculus, logarithms and exponentials, series and the binomial theorem, radians and circular measure, trigonometric identities, permutations and combinations, and coordinate geometry of the circle. Every 0580 formula is also assumed knowledge throughout.
When do I work in radians rather than degrees?
Use radians for circular measure and for calculus involving trigonometric functions, since the arc, sector and segment formulas assume them. Use degrees when a question states a range in degrees. Checking the calculator mode is the single most valuable habit in this syllabus.
How do I integrate a bracket raised to a power?
Raise the index by one, divide by the new index, then divide again by the coefficient of x inside the bracket. This reverses the chain rule. Differentiating your answer should return the original expression exactly.
What does exact form mean in 0606?
An answer left as a surd, a fraction, a multiple of pi, or a logarithm, rather than evaluated as a decimal. A rounded decimal is an approximation, so it does not satisfy a request for an exact value however many figures are given.
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Other reference sheets
Written to the published Cambridge IGCSE syllabuses. Always check the formula list and data sheet issued with your own paper, since the material provided differs between subjects and syllabus versions. Last reviewed 2026-08-12.