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This practice book underscores the significance of algebraic calculus across various mathematical problem categories encountered in international competitions. Including non-standard mathematical systems and equations, algebraic identities, and elements of number theory, the book highlights the broad applicability of algebraic calculus in diverse contexts encountered in international competitions. The Upper School students solved highly challenging problems given at Olympiads and later created original problems that can be ingeniously solved using the tips and tricks presented in the book.