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From IGCSE to the IB Diploma: What Maths and Physics Carry Over
4 min readBy Renzo DiazLast reviewed October 7, 2026
Cambridge IGCSE Mathematics (0580) at Extended level covers nearly everything the IB Mathematics guides list as prior learning, including the items marked for Higher Level only; the one gap is quadratic inequalities. The real step comes in the first year of Analysis and Approaches (AA): logarithms, the number e, radians, the binomial theorem, series and calculus beyond simple polynomials, none of which 0580 teaches and all of which IGCSE Additional Mathematics (0606) does. For Physics, IGCSE 0625 maps onto most of the IB's themes A to E; the IB adds the equations of motion, simple harmonic motion and standing waves, at HL relativity, thermodynamics and quantum physics, and logarithms among its mathematical tools.
Most students arrive at the IB Diploma from IGCSE or an equivalent, and the first term is where the difference between the two shows. Some of it is new content, some is old content asked more abstractly, and some is content an IGCSE student never met because it sat in a separate course. This article compares the documents side by side, so that a student can see where the step is before September.
The comparison uses Cambridge's current syllabuses for IGCSE Mathematics (0580), Additional Mathematics (0606) and Physics (0625), and the IB guides for Mathematics (first assessment 2021) and Physics (first assessment 2025), read on 7 October 2026. The guides are paraphrased, with their page numbers in the notes.
The step from IGCSE to AA is less about harder questions than about topics IGCSE Mathematics never teaches.
Key takeaways
- 0580 Extended meets the IB's prior learning: everything listed except quadratic inequalities.
- Core is short for HL: quadratic equations, surds, fractional indices and algebraic fractions are Extended-only in 0580 and listed by the IB as HL prior learning.
- Additional Maths 0606 previews AA's first year: logarithms, e, radians, the binomial theorem, series and calculus.
- IB Physics SL assumes no science background; HL expects some formal science.
- New in IB Physics: the equations of motion, oscillations, standing waves, and logarithms in the data work.
What the IB expects before the first lesson
Both IB Mathematics guides expect most students to have studied mathematics for at least ten years, and both list the same prior learning: topics that exam questions assume. Five items on that list are marked for Higher Level only: highest common factor and lowest common multiple, rational exponents, rationalising the denominator, quadratic equations and inequalities, and algebraic fractions.
The Physics guide is more open. It states that a student can study Physics at Standard Level with no previous science, while most students taking Higher Level need some formal science education behind them.
| IB prior learning (HL only) | IGCSE Mathematics 0580 | IGCSE Additional Mathematics 0606 |
|---|---|---|
| Highest common factor and lowest common multiple | Core | — |
| Rational exponents | Extended only | — |
| Rationalising the denominator | Extended only | — |
| Quadratic equations | Extended only | Yes |
| Quadratic inequalities | Not covered (linear inequalities only) | Yes |
| Algebraic fractions | Extended only | — |
Sources: IB Mathematics: analysis and approaches guide, prior learning, pp. 26–27 (the same list is in the applications and interpretation guide); Cambridge IGCSE Mathematics 0580 syllabus for 2025–2027 and Additional Mathematics 0606 syllabus for 2025–2027. "—" means 0606 does not list it, as it assumes IGCSE Mathematics.
IGCSE Mathematics 0580: Core and Extended
0580 is taught at two tiers. Core targets grades C to G and has no quadratic equations at all; Extended contains all of Core and more, and opens grades A* to E. For the IB, the Extended-only content is what matters: surds, algebraic fractions, fractional indices, quadratic equations by three methods, functions with inverses and composites, the sine and cosine rules with the ambiguous case, two-dimensional vectors, conditional probability, and a first taste of calculus, the derivative of axⁿ for whole-number powers and turning points.
Three things 0580 leaves out on purpose: logarithms, the number e and radians. All three appear in AA's first year.
| Tier | Papers | Length and marks | Grades available |
|---|---|---|---|
| Core | Paper 1 (no calculator) and Paper 3 (calculator) | 1 hour 30 minutes and 80 marks each | C to G |
| Extended | Paper 2 (no calculator) and Paper 4 (calculator) | 2 hours and 100 marks each | A* to E |
Source: Cambridge IGCSE Mathematics 0580 syllabus for 2025–2027 (version 3). The 2028–2030 syllabus states no significant changes to teaching.
Where AA's first year goes beyond IGCSE
The AA Standard Level syllabus, which every AA student covers in some form, is where the gap shows. The table sets each topic against what 0580 Extended and Additional Mathematics 0606 teach. The pattern is clear: what 0580 does not teach, 0606 usually does, statistics apart.
| AA SL topic | 0580 Extended | 0606 Additional Mathematics |
|---|---|---|
| Arithmetic and geometric series, sigma notation, sum to infinity | The nth term only | Yes |
| Logarithms, the number e, eˣ and ln x | Not required | Yes |
| The binomial theorem | No | Yes, with permutations and combinations |
| Functions, inverses and composites | Yes, without the domain and range of composites | Yes, with domain restriction |
| Quadratics: discriminant and inequalities | Equations and completing the square only | Yes |
| Transformations of graphs | No | In part |
| Radians, arcs and sectors | Arcs and sectors in degrees | Yes, radians throughout |
| Trigonometric identities | No | sin²x + cos²x = 1 only |
| Correlation, binomial and normal distributions | Correlation described, not calculated | No statistics |
| Differentiation | axⁿ for whole-number powers | Any rational power, trigonometric, exponential and log functions, chain, product and quotient rules |
| Integration and kinematics with calculus | No | Yes |
Sources: IB Mathematics: analysis and approaches guide, SL topics 1–5, pp. 29–65; Cambridge 0580 and 0606 syllabuses for 2025–2027. My comparison of the documents; neither Cambridge nor the IB publishes a mapping.
A quirk worth knowing
Vectors leave and come back
IGCSE 0580 Extended teaches two-dimensional vectors, but AA Standard Level has none: vectors return only in AA Higher Level, in two and three dimensions. A student moving from IGCSE to AA SL sets them aside for two years.
AI starts closer to IGCSE
Applications and Interpretation shares its Standard Level core with AA, but it spends more of its hours on statistics and works in degrees at Standard Level: the AI guide states that radians are not required at SL. Its Standard Level hours give statistics and probability 36 of 120 topic hours, against 27 in AA. For an IGCSE student, the new ground in AI is mostly statistical, the correlation coefficient and the binomial and normal distributions, which neither 0580 nor 0606 calculates. What the AA-or-AI choice means for university entry is set out in IB Math AA or AI: what universities require.
Physics: IGCSE 0625 against IB Physics 2025
IGCSE Physics 0625 covers six topics; the IB's current course is organised in five themes, A to E. Most of 0625 has a clear place in the IB, usually as its starting point.
| IGCSE Physics 0625 | IB Physics 2025 |
|---|---|
| Motion | A.1 Kinematics, which adds the equations of motion and projectiles |
| Forces, momentum, energy, work and power | A.2 Forces and momentum, A.3 Work, energy and power |
| Moments and centre of gravity | A.4 Rigid body mechanics, HL only |
| Density, thermal physics, the gas law pV = constant | B.1 Thermal energy transfers, B.3 Gas laws |
| Electrical quantities and circuits | B.5 Current and circuits; alternating current is not required |
| Waves, the electromagnetic spectrum, sound, refraction | C.2 Wave model, C.3 Wave phenomena |
| Magnetism, electric fields, the motor effect | D.2 Electric and magnetic fields, D.3 Motion in electromagnetic fields |
| Induction, generators, transformers | D.4 Induction, HL only |
| The nuclear atom, radioactivity, half-life | E.1 Structure of the atom, E.3 Radioactive decay; the decay constant is HL |
| Fission, fusion, the Sun and stars | E.4 Fission, E.5 Fusion and stars |
Sources: Cambridge IGCSE Physics 0625 syllabus for 2026–2028 (version 2) and the IB Physics guide (first assessment 2025), syllabus content pp. 33–59. My mapping; neither body publishes one.
What is new in IB Physics
Three kinds of content are new to an IGCSE student. Topics 0625 does not teach: simple harmonic motion, standing waves and the greenhouse effect for every student, and relativity, thermodynamics and quantum physics at Higher Level. Mathematics 0625 leaves out: the equations of motion, which IGCSE replaces with speed–time graphs, and logarithms and logarithmic scales, which the IB lists among its mathematical tools. And quantitative versions of qualitative ideas, such as centripetal force, which 0625 describes without its formula.
A few 0625 topics do not continue: thin lenses, the Hubble constant and the cosmic microwave background have no place in the IB's current syllabus. How the IB's themes weigh in the exams is counted in IB Physics 2025 exams, marks by theme.
Using the summer before the Diploma
Four things to do before DP1
Close the Extended gap if you took Core
Quadratic equations, surds, fractional indices and algebraic fractions are assumed at HL and are Extended-only in 0580.
Meet logarithms and radians before AA does
They arrive early in AA and are absent from 0580; 0606 covers both.
Learn quadratic inequalities
The one item on the IB's prior-learning list that 0580 does not teach.
For Physics, practise the equations of motion
IGCSE works from graphs; IB kinematics uses the equations from the first topic, and the data booklet prints them.
Terms used in this article
- Core and Extended
- The two tiers of Cambridge IGCSE Mathematics and Physics; Extended contains all of Core and more, and opens the top grades.
- Additional Mathematics (0606)
- A separate Cambridge IGCSE course for students going on to advanced mathematics, covering algebra, trigonometry and calculus beyond 0580.
- Prior learning
- The content an IB guide expects students to know before the course, which exam questions may assume.
- AA and AI
- The two IB Mathematics courses, Analysis and Approaches and Applications and Interpretation.
- Equations of motion
- The four equations for motion with constant acceleration, used from the first topic of IB Physics.
Questions about moving from IGCSE to the IB
Is IGCSE Core Maths enough for IB Math AA HL?
It leaves gaps. The IB lists quadratic equations, surds, rational exponents and algebraic fractions as HL prior learning, and in IGCSE 0580 they are taught only at Extended.
Is IGCSE Additional Maths useful for the IB?
Yes, for AA. 0606 teaches logarithms, radians, the binomial theorem, series and calculus that AA covers in its first year; the IB does not require it.
Can I take IB Physics HL without IGCSE Physics?
The IB guide expects some formal science for HL. It states that SL needs no previous science, while most HL students need some formal science education.
Does IGCSE Maths include calculus?
A little, at Extended. 0580 Extended teaches the derivative of axⁿ for whole-number powers and turning points; 0606 goes much further.
Which IGCSE Physics topics are not in the IB?
Thin lenses, the Hubble constant and the cosmic microwave background. The IB's current syllabus has no place for them.
Written by
Teaching IB since 2016. Seven years of IB reviews you can check on Google — and named results with the documents behind them.
Last reviewed October 7, 2026
Sources
The Cambridge syllabuses are public documents; the IB guides are made available to schools and are paraphrased here with page numbers. The topic comparisons and the Physics mapping are my own reading of the documents side by side, read on 7 October 2026.