IB Mathematics · AA HL · 2024 Style

Master Quiz
Analysis & Approaches HL

20 Core Concept Questions — All Topics · Exam-Style · Full Solutions

40:00
All Topics at a Glance
Core Concepts & Key Formulae
Topic 1

Number & Algebra

  • Arithmetic & Geometric sequences/series
  • Binomial theorem (general term)
  • Proof by induction
  • Complex numbers: Cartesian, polar, Euler
  • De Moivre's theorem
Topic 2

Functions

  • Rational functions, inverse, composite
  • Transformations of functions
  • Solving inequalities graphically
  • Polynomial remainders & factor theorem
  • Modulus equations
Topic 3

Geometry & Trig

  • Unit circle, exact values
  • Compound, double-angle formulae
  • Inverse trig, reciprocal trig
  • 3D vector geometry
  • Lines & planes in 3D
Topic 4

Statistics & Probability

  • Discrete & continuous distributions
  • Binomial, Poisson, Normal
  • Hypothesis testing (z, t, χ²)
  • Conditional probability, Bayes' theorem
  • Unbiased estimators
Topic 5

Calculus

  • Limits & L'Hôpital's rule
  • Chain / product / quotient rules
  • Related rates, optimisation
  • Integration by parts, substitution
  • Maclaurin series, Euler's method

📐 Must-Memorise Formulae

Geometric Series (finite)
\(S_n = \dfrac{a(1-r^n)}{1-r}\)
Binomial Theorem
\((a+b)^n = \displaystyle\sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^k\)
De Moivre
\((\cos\theta+i\sin\theta)^n = \cos n\theta+i\sin n\theta\)
Euler's Formula
\(e^{i\theta} = \cos\theta + i\sin\theta\)
Chain Rule
\(\dfrac{dy}{dx} = \dfrac{dy}{du}\cdot\dfrac{du}{dx}\)
Integration by Parts
\(\int u\,dv = uv - \int v\,du\)
Maclaurin \(e^x\)
\(e^x = 1 + x + \dfrac{x^2}{2!} + \dfrac{x^3}{3!}+\cdots\)
Double Angle
\(\cos 2\theta = 2\cos^2\theta - 1 = 1 - 2\sin^2\theta\)
Normal Distribution
\(X \sim N(\mu, \sigma^2)\)
Poisson Distribution
\(P(X=k)=\dfrac{e^{-\lambda}\lambda^k}{k!}\)
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Practice Examination
20 Exam-Style Questions
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