Define $ f(x) = ax^2 + bx + c , a,b,c \in \mathbb{R}$ and $ f^n(x) = f(f^{n-1}(x)), n>1 $. Prove that the real roots of $ f^n(x) $ are symmetric about the vertical line passing through vertex i.e. $ x = \frac{-b}{2a} $

This seems like …

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Evaluate the integral $$\int_0^1 \frac{\log(x)}{x-1}dx$$

There are a few methods of doing this: the first one uses the taylor series expansion of \( \log(1-x) \): $$I = -\int_0^1 \frac{\log(1-x)}{x}dx$$ $$I = \int_0^1 \frac 1x \left( x + \frac{x^2}{2} + \frac{x …

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A speculative format for the 2018 ICSE Mathematics paper, created by analysis of the mathematics question papers of the past 23 years.

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