How a trigonometric integral is evaluated incorrectly — and how to fix it.
How to evaluate the least positive residue using brute force, Fermat’s Little Theorem and Chinese Remainder Theorem.
How to solve a system of linear equations, when a coefficient of a variable is itself a variable.
How to find the angles and the side lengths of a general triangle — using the law of sines.
How to calculate the probability of randomly filling N balls into k boxes, by looking at the case of 2 boxes, 3 boxes, and the general case of k boxes.
A review on logarithm functions with base less than 1, and some key property which can be used to solve logarithmic inequalities based on it.