20 Core Questions · All Units
IB Mathematics
AA Higher Level
Exam-style multiple choice covering every major topic. Verified solutions with step-by-step explanations.
Algebra
Functions
Trigonometry
Complex Numbers
Sequences & Series
Calculus
Vectors
Probability
Statistics
Logarithms
Matrices
Proof
📐 Key Concepts & Formulae to Memorise
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Binomial Theorem
$(a+b)^n = \sum_{r=0}^{n}\binom{n}{r}a^{n-r}b^r$
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Geometric Series Sum
$S_n = \dfrac{a(r^n-1)}{r-1}$, $S_\infty = \dfrac{a}{1-r}$ (|r|<1)
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Double Angle Identities
$\sin 2\theta = 2\sin\theta\cos\theta$
$\cos 2\theta = \cos^2\theta - \sin^2\theta$
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Derivative Rules
Chain: $\frac{d}{dx}[f(g(x))] = f'(g)\cdot g'$
Product: $(uv)'=u'v+uv'$
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Integration
$\int x^n dx = \dfrac{x^{n+1}}{n+1}+C$
$\int e^x dx = e^x+C$
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Complex Modulus
$|a+bi| = \sqrt{a^2+b^2}$
Arg: $\theta = \arctan(b/a)$
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Normal Distribution
$X \sim N(\mu, \sigma^2)$
$Z = \dfrac{X-\mu}{\sigma}$
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Logarithm Laws
$\log(ab)=\log a+\log b$
$\log_b a = \dfrac{\ln a}{\ln b}$
▶ Worked Example
Find the coefficient of $x^3$ in the expansion of $(2x-1)^5$.
Using the binomial theorem: $\binom{5}{3}(2x)^2(-1)^3 = 10 \cdot 4x^2 \cdot (-1) = -40x^2$… wait, for $x^3$: $\binom{5}{3}(2x)^3(-1)^2 = 10 \cdot 8x^3 \cdot 1 = \mathbf{80}$