IB Math AI HL | 20 Core Concept Questions

Before You Begin

Core Concepts & Key Formulae

📐 Number & Algebra

Arithmetic & geometric sequences, compound interest, exponents, logs, binomial theorem. IB Formula Booklet provides key series formulae.

📈 Functions

Linear, quadratic, exponential, logistic, sinusoidal models. Key: domain/range, transformations, inverse, half-life, asymptotes.

📏 Geometry & Trigonometry

Sine rule, cosine rule, area of triangle, 3D geometry, Voronoi diagrams, graph theory basics, arc length, sector area.

📊 Statistics & Probability

Normal distribution, binomial distribution, hypothesis testing, $\chi^2$ test, Spearman rank, PMCC, regression lines.

∫ Calculus

Differentiation rules (power, product, chain), integration, area under curves, optimisation, differential equations, kinematics.

🔗 HL Extensions

Logistic models, transition matrices, Markov chains, phase portraits, complex numbers basics, Bayes' theorem.

📌 Essential Formulae to Memorise

Arithmetic Series $S_n = \dfrac{n}{2}(2a_1 + (n-1)d)$

Compound Interest $A = P\!\left(1 + \dfrac{r}{n}\right)^{nt}$

Sine Rule $\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$

Area of Triangle $\text{Area} = \tfrac{1}{2}ab\sin C$

Normal Distribution $X \sim N(\mu, \sigma^2)$

Binomial Distribution $P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$

Derivative — Power Rule $\dfrac{d}{dx}[x^n] = nx^{n-1}$

Definite Integral $\displaystyle\int_a^b f(x)\,dx = F(b)-F(a)$

Logistic Model $\dfrac{dP}{dt} = kP\!\left(1-\dfrac{P}{L}\right)$

Conditional Probability $P(A|B) = \dfrac{P(A \cap B)}{P(B)}$

📝 Worked Example (Exam Style)

Question: The first term of an arithmetic sequence is $a_1 = 5$ and the common difference is $d = 3$. Find the sum of the first 10 terms.

Solution:
Use $S_n = \dfrac{n}{2}(2a_1 + (n-1)d)$

$S_{10} = \dfrac{10}{2}(2 \times 5 + (10-1) \times 3) = 5(10 + 27) = 5 \times 37 = \mathbf{185}$

✓ Answer: 185

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