MF19 Formula Sheet: What You Get in the 9709 Exam and What to Memorise

MF19 is the “List of formulae and statistical tables” that Cambridge gives you in every 9709 paper. Knowing exactly what is on it saves you from memorising things you will be handed, and, more importantly, stops you assuming a formula is there when it is not.

What is MF19?

MF19 is one booklet for two syllabuses: AS & A Level Mathematics (9709) and Further Mathematics (9231), for use from 2020. The 9709 syllabus says it is supplied in examinations and prints a copy in section 5.

Because it is shared, some pages are not for you. Skip the sections headed Further Pure Mathematics, Further Mechanics and Further Probability & Statistics, plus the t-distribution and Wilcoxon tables. Everything else is fair game for 9709.

Which formulas are on the MF19 formula sheet?

Section	What is on it
Mensuration	Volume and surface area of a sphere, volume of a cone or pyramid, curved surface of a cone, arc length rθ and sector area ½r²θ (θ in radians)
Algebra	Quadratic formula; nth term and sum of an arithmetic series; nth term, sum and sum to infinity of a geometric series; binomial expansion for positive integer n and for rational n with |x| < 1
Trigonometry	tan θ = sin θ / cos θ; the three Pythagorean identities; compound angle formulas for sin, cos and tan; double angle formulas; principal values of sin⁻¹, cos⁻¹ and tan⁻¹
Differentiation	Derivatives of xⁿ, ln x, eˣ, sin x, cos x, tan x, sec x, cosec x, cot x and tan⁻¹ x; product rule; quotient rule; parametric differentiation
Integration	Integrals of xⁿ, 1/x, eˣ, sin x, cos x, sec² x, 1/(x² + a²), 1/(x² − a²) and 1/(a² − x²); integration by parts; ∫ f′(x)/f(x) dx = ln |f(x)|
Vectors	The scalar product a·b = a₁b₁ + a₂b₂ + a₃b₃ = |a||b| cos θ
Mechanics	The four constant acceleration equations: v = u + at, s = ½(u + v)t, s = ut + ½at², v² = u² + 2as
Probability & Statistics	Mean and standard deviation for ungrouped and grouped data; E(X) and Var(X) for discrete and continuous variables; binomial, geometric and Poisson probabilities with their means and variances; unbiased estimators; the normal distribution function table and critical values

Which formulas are not on MF19?

These come up all the time in 9709 and are not on the list. Learn them until you can write them without thinking.

Pure Mathematics 1

• The discriminant b² − 4ac and what its sign tells you.
• Gradient, midpoint and distance between two points; y − y₁ = m(x − x₁); perpendicular gradients multiply to −1.
• The equation of a circle, (x − a)² + (y − b)² = r².
• Exact values of sin, cos and tan for 30°, 45° and 60°.
• The sine rule, the cosine rule and area = ½ab sin C (they are prior knowledge, not on MF19).
• The chain rule, and that stationary points have dy/dx = 0.
• Area under a curve and volume of revolution: V = π∫y² dx.

Pure Mathematics 3

• Laws of logarithms and how to use them to linearise y = axⁿ or y = abˣ.
• The modulus function and how to solve modulus equations and inequalities.
• The form R cos(θ ± α) and R sin(θ ± α).
• Implicit differentiation.
• Partial fractions, and complex number results such as |z₁z₂| = |z₁||z₂| and arg(z₁z₂) = arg z₁ + arg z₂.
• The vector equation of a line, r = a + λb.

Mechanics (Paper 4)

• Newton’s second law F = ma, and weight W = mg.
• Friction F ≤ μR, with F = μR when sliding or about to slide.
• Momentum mv and conservation of momentum.
• Work done = force × distance, kinetic energy ½mv², potential energy mgh, power P = Fv.
• Using calculus when acceleration is not constant (the suvat equations on MF19 only work for constant acceleration).

Probability & Statistics 1 (Paper 5)

• nPr and nCr counting rules, and when to use each.
• P(A ∪ B) = P(A) + P(B) − P(A ∩ B), and conditional probability P(A | B) = P(A ∩ B) / P(B).
• Standardising: Z = (X − μ) / σ.
• The conditions for a normal approximation to a binomial and the continuity correction.

How should you use MF19 in the exam?

1. Practise with it from day one. Print it and keep it next to you for every past paper, so you know where each formula sits on the page.
2. Copy, then substitute. Write the formula you are using, then the values. Examiners need to see the substitution: in the June 2024 report on Paper 11 they noted that quoting a formula alone is not enough.
3. Watch the conditions. The binomial expansion for rational n needs |x| < 1, the GP sum to infinity needs |r| < 1, and the arc and sector formulas need θ in radians.
4. Know the list of what is missing. Turn the “not given” lists above into flashcards.

Back to the Cambridge A Level Maths 9709 guide, or see the mistakes examiners report most.