IB Maths AA formula booklet explained
The Mathematics: analysis and approaches formula booklet is one booklet for SL and HL. You need a clean copy in every Maths AA exam paper. It follows the five syllabus topics, and each topic has an SL and HL part and an HL only part.
This page explains what each part gives you and, just as useful, what it leaves out. It does not reproduce the booklet; your school downloads the official copy from the IB.
What each part of the booklet gives you
The number beside each formula in the booklet is its syllabus section (1.2, 3.4 and so on), so you can find the matching notes quickly. HL only formulas are marked AHL.
| Part | SL and HL | HL only |
|---|---|---|
| Prior learning | Areas of a parallelogram, triangle, trapezoid and circle; circumference; volumes of a cuboid, cylinder and prism; curved surface of a cylinder; distance between two points; midpoint. | Nothing extra |
| Topic 1: Number and algebra | Arithmetic and geometric sequences and series, including ; compound interest; logarithm laws and change of base; the binomial theorem. | Combinations and permutations; complex numbers in Cartesian, polar and Euler form; De Moivre’s theorem. |
| Topic 2: Functions | Equations of a straight line and the gradient formula; the axis of symmetry of a quadratic; the quadratic formula and discriminant; . | Sum and product of the roots of a polynomial. |
| Topic 3: Geometry and trigonometry | 3D distance and midpoint; volumes and surface areas of pyramids, cones and spheres; sine and cosine rules; area of a triangle; arc length and sector area in radians; the identity for tan; Pythagorean and double angle identities. | Reciprocal trig functions and their identities; compound angle identities; vectors: magnitude, scalar and vector products, equations of lines and planes. |
| Topic 4: Statistics and probability | Interquartile range; mean of grouped data; probability rules for combined, mutually exclusive, conditional and independent events; expected value; binomial mean and variance; the standardized normal variable. | Bayes’ theorem; variance and standard deviation formulas; continuous random variables; linear transformations of a random variable. |
| Topic 5: Calculus | Derivatives of , , , and ; chain, product and quotient rules; standard integrals; area under a curve; kinematics. | Differentiation from first principles; further standard derivatives and integrals; integration by parts; volumes of revolution; Euler’s method; the integrating factor; Maclaurin series. |
What you still need to know
The laws of indices, such as , and the exact values of , and at 0, , , and are not in the booklet. You need the exact values without a calculator in Paper 1.
Methods are not in the booklet either: finding the equation of a tangent or normal, classifying stationary points, or integration by substitution. The booklet gives you the derivative of a function, not what to do with it.
SL students get the mean of a data set but no variance or standard deviation formula; those are calculated on the GDC in Paper 2.
How to use it in the exam
Write the formula from the booklet before you substitute. Markschemes award method marks for a correct substitution into the right formula.
Watch the conditions printed next to formulas, such as for the sum to infinity of a geometric series, and angles in radians for arc length and sector area. Questions often test whether you checked them.