The 9709 Formula Sheet (MF19): What You Are Given, and What You Must Memorise
Get the Sheet
MF19 is the list of formulae and statistical tables supplied to you in the exam. You do not bring it. It is provided. It is also reproduced inside the 9709 syllabus document, so you may have had a copy all year without knowing.
- Our hosted copy of MF19: https://papers.exampilot.io/cie/mathematics/formula-sheet/9709/mf19.pdf
- The same list appears as a section of the official 9709 syllabus on cambridgeinternational.org
For Pure 1 and Pure 3, everything you can use sits in the Pure Mathematics section at the front, under six headings: mensuration, algebra, trigonometry, differentiation, integration, and vectors.
Pure 1: Given Versus Memorise
Paper 1 draws on quadratics, functions, coordinate geometry, circular measure, trigonometry, series, differentiation, and integration. Here is how MF19 covers those.
| Topic | On MF19 | You must memorise |
|---|---|---|
| Quadratics | The quadratic formula | Completing the square. The discriminant and what its sign tells you about the number of roots. Solving quadratics in disguise, for example in a squared or exponential variable. |
| Functions | Nothing | Domain and range. Composite function notation and order. Finding an inverse and its domain. The reflection of a graph in the line y = x. Graph transformations and how they combine. |
| Coordinate geometry | Nothing | Distance between two points. Midpoint. Gradient. Equation of a straight line. The perpendicular gradient condition. Equation of a circle in centre-radius form, and completing the square to get there. |
| Circular measure | Arc length and sector area, both in radian form | That MF19 gives you the radian form only, so working in degrees means taking a fraction of the whole circle instead. Segment area, which is the sector minus the triangle. Triangle area using two sides and the included angle. Converting between radians and degrees. |
| Trigonometry | The identity linking tan to sin and cos, and the Pythagorean identities | Exact values at 30, 45, and 60 degrees, and their radian equivalents. The shape and period of the sine, cosine, and tangent graphs. Finding every solution in a given interval, not just the one your calculator returns. The sine rule and the cosine rule. |
| Series | Arithmetic term and sum. Geometric term, sum, and sum to infinity with its condition. The binomial expansion for a positive integer power, with the binomial coefficient | Recognising which series you are looking at. When the sum to infinity is valid. Reading off a, d, and r from a worded problem. Extracting a single specified term or coefficient without expanding everything. |
| Differentiation | The derivative of a power of x. Product rule, quotient rule, and the parametric form | The chain rule, which is not on the list in its standard form. Stationary points and how to classify them. Increasing and decreasing intervals. Tangent and normal equations. Connected rates of change. |
| Integration | The integral of a power of x, with its exclusion | Integrating a linear-argument bracket, the reverse of the chain rule. Definite integrals and limits. Area between a curve and an axis, and area between two curves. Volume of revolution, which is not on MF19. Finding the constant of integration from a point. |
Pure 3: Given Versus Memorise
Paper 3 covers algebra, logarithmic and exponential functions, trigonometry, differentiation, integration, numerical solution of equations, vectors, differential equations, and complex numbers. MF19 is more generous here, but the gaps are sharper.
| Topic | On MF19 | You must memorise |
|---|---|---|
| Algebra | The binomial expansion for a rational power, with its validity condition | Modulus equations and inequalities, and the squaring technique. Polynomial division. The factor theorem and the remainder theorem. Every partial fraction form, including a repeated factor and an irreducible quadratic factor. |
| Logs and exponentials | Nothing | All three log laws. Change of base. The inverse relationship between the exponential function and the natural logarithm. Reducing a power law or an exponential model to a straight line, and reading the constants off the gradient and intercept. |
| Trigonometry | The Pythagorean identities in all three forms. Compound angle formulae. Double angle formulae. Principal value ranges for the inverse functions | The harmonic form, expressing a sine plus a cosine as a single trigonometric function, and how to get its two constants. That is not on MF19. Also the half-angle substitutions if your teaching route uses them, and rearranging a double angle formula to integrate a squared sine or cosine. |
| Differentiation | Derivatives of the natural logarithm, the exponential, sine, cosine, tangent, secant, cosecant, cotangent, and the inverse tangent. Product rule, quotient rule, and the parametric form | The chain rule. Implicit differentiation. Getting a tangent or normal from a parametric or implicit curve. Which of the three rules a messy expression actually needs, which is the real Paper 3 skill. |
| Integration | Standard integrals for a power of x, the reciprocal, the exponential, sine, cosine, and secant squared. Three inverse-trigonometric and logarithmic results with a constant a. Integration by parts. The integral of a derivative over its own function | Integration by substitution, which is not given as a formula. Handling a linear argument inside any standard integral, since the list gives the plain form only. Choosing which part is u in integration by parts. Splitting into partial fractions before integrating. Using a double angle identity to integrate a squared trigonometric function. |
| Numerical solution | Nothing | Locating a root by a change of sign. Running a given iterative formula and knowing when it has converged. Rearranging an equation into an iterative form. Stating the root to the accuracy the question demands. |
| Vectors | The scalar product, in component form and in the form with the angle | The magnitude of a vector and the unit vector. The vector equation of a line. Testing whether two lines meet, are parallel, or are skew. The angle between two lines. The perpendicular condition. |
| Differential equations | Nothing | Separating the variables. Applying the initial condition to find the constant, rather than leaving a general solution. Forming the equation from a described rate of change, which is usually the hardest mark on the question. |
| Complex numbers | Nothing | Arithmetic with complex numbers, including division by the conjugate. Modulus and argument, and the argument's range convention. Converting between the two forms. What multiplication and division do to modulus and argument. Argand diagram loci for a circle, a perpendicular bisector, and a half line. |
How to Use MF19 Before the Exam
- Print the Pure Mathematics pages. Ignore the rest until you also sit Cambridge 9231 (Cambridge International AS & A Level Further Mathematics).
- Sit a full paper with it open on the desk, the way it will be. You need to know where each heading is by feel.
- Every time you look something up during practice, mark it. Those are the formulae you are one look away from not knowing, and the list will not always save you, because many of them are not on it.
- Build a one-page sheet of your own for the memorise column above. That sheet, not MF19, is what your revision has to close.
Two Pages You Want Next
The 9709 syllabus page sets out which papers you sit, what each is worth, and what changed for 2026 and 2027. The grade thresholds page explains how your raw marks become a grade.
Closing the Memorise Column
The right-hand column of those two tables is a revision plan. It is also the exact thing that decays fastest, because it is recall, and recall fades on a schedule.
ExamPilot uses spaced repetition to resurface a technique just before you would have forgotten it, and tracks your accuracy on each 9709 topic so you can see which entries in that column are actually secure. Learning science, applied to one specific syllabus.
Reviewed by
Teresa González is co-founder of ExamPilot, an adaptive learning platform for Cambridge and Edexcel A-Level students. She holds Law and Marketing degrees from ICADE, and an MBA from ICEX-CECO, Spain's leading international trade institution.
Her career spans international trade and investment across Spain, Nigeria, and the United Kingdom. She subsequently became an entrepreneur and trading coach and educator at an internationally recognised trading education firm, before co-founding ExamPilot.
Her direct experience with A-Level preparation comes from supporting her children through the Edexcel and Cambridge examination systems. At ExamPilot, she leads educational content strategy, syllabus alignment, and quality review.
The 9709 Formula Sheet (MF19): What You Are Given, and What You Must Memorise: frequently asked questions
No. MF19 gives the derivative of a power of x, the product rule, the quotient rule and the parametric form, but not the chain rule in its standard form. Almost every real integration and differentiation question needs it, so it has to be memorised.
No. MF19 gives the identity linking tan to sin and cos, and the Pythagorean identities, but neither the sine rule nor the cosine rule appears anywhere in it. Both must be memorised.
No. It is supplied to you in the exam room. It is also reproduced as a section inside the official 9709 syllabus document, so you can practise with it all year.
MF19 is a combined list for Cambridge 9709 Mathematics and Cambridge 9231 Further Mathematics. The sections headed Further Pure Mathematics, Further Mechanics and Further Probability and Statistics are for 9231 only. If you sit Pure 1 and Pure 3, the only section you can use is Pure Mathematics.
No. It is not on MF19 at all, and it is a standard Pure 1 integration question, so it has to be memorised.