Problems And Answers PHIMO MOCK 2020 JUNIOR SECONDARY

6. Given that \(P(x)\) is a polynomial such that \(P(x^2 +1) = x^4 +5x^2 +3\), what is \(P(x^2 -1)\)?

A. \(x^4 + x^2 – 3\)
B. \(x^4 + 5x^2 – 1\)
C. \(x^2(x + 1)(x – 1)\)
D. \(x^4 + x^2 + 1\)
E. \(x^4 – x^2 – 1\)

7. Which number below is the greatest?

A. \(6^{100}\)
B. \(5^{200}\)
C. \(4^{300}\)
D. \(3^{400}\)
E. \(2^{500}\)

8. A cube measuring 100 units on each side is painted only on the outside and cut into unit cubes. The number of cubes with paint only on two sides is

A. 1000
B. 1125
C. 1176
D. 980
E. none of these

9. What is the length of the shortest path that begins at the point (2,5), touches the x-axis and then ends at a point on the circle

\((x + 6)^2 + (y – 10)^2 = 16\)

A. \(12\)
B. \(13\)
C. \(4\sqrt {10}\)
D. \(6\sqrt 5\)
E. \(4 +\sqrt{89}\)

10. Wilson’s Theorem states that if n is a prime number, then n divides \((n-1)!+1\). Which of the following is a divisor of \(12! · 6! + 12! + 6! + 1\)?

A. 21
B. 77
C. 91
D. 115
E. 143