Problems And Answers PHIMO MOCK 2020 SENIOR SECONDARY

The Philippine International Mathematical Olympiad (PhIMO) is the newest and most sophisticated international mathematics competition among Kindergarten to Grade 12 students.

​The PhIMO is designed to honor the best learners in the world in mathematical problem-solving through friendly competition and foster cultural exchange among countries that participate therein.

1. Which of the following is the largest?

A. \(2\log_5 6\)
B. \(2\log_6 5\)
C. \(3\log_6 5\)
D. \(3\log_5 6\)
E. \(3\)

2. Let \(A\) be the set of points in the \(xy-\)plane satisfying the equation \(|x| + |y| = 7\). The area of \(A\) is equal to

A. 7
B. 28
C. 42
D. 63
E. 98

3. What is the smallest altitude in the triangle with sides \(20, 21\), and \(29\).

A. \(21\)
B. \(\frac{21·20}{29}\)
C. \(\frac{20·29}{23}\)
D. \(\frac{20·29}{21}\)
E. 20

4. If \(a + b + c = a^2 + b^2 + c^2 = a^3 + b^3 + c^3 = \frac{3}{2}\) , then \(abc\) equals

A. -2
B. \(-\frac{1}{16}\)
C. 10
D. \(-\frac{1}{2}\)
E. 20

5. Find the exact value of

\(\sqrt{14^3 + 15^3 + 16^3 + … + 24^3 + 25^3}\).

A. 224
B. 104
C. 312
D. 336
E. 676