AMC 12B 2019 Notes

Problem 8 (centroids): Given points $(a,b)$, $(c,d)$, and $(e,f)$ on the coordinate plane, the coordinates of the centroid are $(\frac{a+c+e}{3},\frac{b+d+f}{3})$.

Problem 11 (divisibility): READING THE QUESTION MULTIPLE TIMES WON’T HURT. More time would be wasted just guessing around the the problem meant.

Problem 13 (centroids): Centroids of a triangle will have $2:1$ ratios, and those could be used towards ratios of areas.

Problem 14 (paper folding): If unsure about a problem statement just re-read it again.

Problem 20 (area): Though it is common to find areas of bounds using subtraction, problems will be easier using addition just as equally often.

Problem 21 (geometry): Tangents will lead to right angles, which will lead to more facts such as perpendiculars / similar triangles / cyclic quadrilaterals / etc.

Problem 23 (3D geometry): Coordinate geometry is commonly used to solve 3-D problems.

Problem 25 (equilateral triangles): Equilateral triangles will lead to many 30, 60, and 90 degrees, and the right angles can lead to similar triangles.

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