AMC 12C 2020 Problems

Problem 1

What is the sum of the solutions of the equation $(x + 4)(x - 5)(x + 6) = 0$ ?

$\textbf{(A)}\ -5 \qquad\textbf{(B)}\ 0 \qquad\textbf{(C)}\ 5 \qquad\textbf{(D)}\ 12 \qquad\textbf{(E)}\ 14$

Problem 2

What is the numerical value of the sum $\sum_{k = 1}^{11}(i^{3} + i^{2})$

$\textbf{(A)}\ 4000 \qquad\textbf{(B)}\ 4608 \qquad\textbf{(C)}\ 4862 \qquad\textbf{(D)}\ 5792 \qquad\textbf{(E)}\ 6100$

Problem 3

A field in the shape of a circle on the real $xy$ plane is centered at $(5, 6)$ and has a radius of $8$ . The entire field is planted except for the part that is under the line $y = 0$ . What fraction of the circular field is planted?

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AMC 12C 2020 Problems

Problem 1

Problem 2

Problem 3