\textbf{A Level Maths Formula Sheet}
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\textbf{1. Quadratic Formula} \
x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}
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\textbf{2. Laws of Indices} \
a^m \cdot a^n = a^{m+n} \quad \frac{a^m}{a^n} = a^{m-n} \quad (a^m)^n = a^{mn}
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\textbf{3. Surds Rules} \
\sqrt{a} \cdot \sqrt{b} = \sqrt{ab} \quad \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}
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\textbf{4. Trigonometric Identities} \
\sin^2\theta + \cos^2\theta = 1 \quad 1 + \tan^2\theta = \sec^2\theta
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\textbf{5. Sine Rule} \
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
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\textbf{6. Cosine Rule} \
c^2 = a^2 + b^2 – 2ab\cos C
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\textbf{7. Area of Triangle (Trig)} \
A = \frac{1}{2} ab \sin C
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\textbf{8. Differentiation Rules} \
\frac{d}{dx}(x^n) = nx^{n-1} \quad \frac{d}{dx}[\sin x] = \cos x \quad \frac{d}{dx}[\cos x] = -\sin x
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\textbf{9. Integration Rules} \
\int x^n dx = \frac{x^{n+1}}{n+1} + C \quad \text{(for } n \ne -1 \text{)}
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\textbf{10. Arithmetic Series} \
S_n = \frac{n}{2} \left(2a + (n – 1)d\right)
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\textbf{11. Geometric Series} \
S_n = a \cdot \frac{1 – r^n}{1 – r} \quad (r \ne 1)
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\textbf{12. Binomial Expansion (for } |x| < 1 \text{)} \
(1 + x)^n = 1 + nx + \frac{n(n – 1)}{2!}x^2 + \frac{n(n – 1)(n – 2)}{3!}x^3 + \cdots
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\textbf{13. Logarithm Laws} \
\log(ab) = \log a + \log b \quad \log\left(\frac{a}{b}\right) = \log a – \log b \quad \log(a^n) = n \log a
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