Problem 11 (paper folding): When doing problems about folding something, just draw a perpendicular line across the midpoint and that is the line of reflection.
Problem 15 (symmetry): Always consider symmetry, but also consider the edge cases too.
Problem 17 (area geometry): Not everything is as it seems! Also, don’t be set on just either addition or subtraction when calculating areas.
Problem 18 (area and ratio geometry): Angle bisector theorem: In triangle $ABC$, if a ray from angle $A$ bisects the angle and intersects side $BC$ at point $D$, then $\frac{AB}{BD}=\frac{AC}{CD}$. Also, it’s often unnecessary to calculate smaller things for an area (e.g. side lengths, angles) when using ratios is sufficient.
Problem 19 (summation): Don’t overcomplicate things without trying simpler methods first! (For this problem I put everything on a common denominator for some reason)
Problem 20 (geometry): Make progress with whatever possible first and use it to lead towards more information.
Problem 23 (geometry): If nothing else works, use transformations to create new things.
Problem 24 (combinatorics): Use expected value when possible to simplify everything.
Problem 25 (equations): If a quadratic has more than 2 solutions, then all the coefficients are 0.