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AMO 2025 Secondary 2 (Grade 8)

Question 1

Function $g(x)=5x^4-160x^3+1710x^2-7200x+10125$ has four roots a, b, c and d. Find $abcd$.

Question illustration
  1. 1200
  2. 1895
  3. 2025
  4. 2375

Question 2

A cube has edge length 12 cm and diagonal section ACGE. The perpendiculars $GM\perp CE$ and $AN\perp CE$ meet CE at M and N. Find MN in cm.

Question illustration
  1. $10\sqrt2$
  2. $2\sqrt5$
  3. $4\sqrt3$
  4. $6\sqrt2$

Question 3

A and B are the intersection points of $y=x^2-4$ and $y=3x$. Find AB.

Question illustration
  1. 16
  2. $5\sqrt{10}$
  3. $10\sqrt2$
  4. $12\sqrt3$

Question 4

Which number is between $\sqrt5$ and $\sqrt7$?

Question illustration
  1. $10/3$
  2. $5\pi/2$
  3. $7/3$
  4. $15/7$

Question 5

Triangle ABC is bounded by the graphs $y=|2x-6|$ and $y=10$. Find its area.

Question illustration
  1. 60
  2. 50
  3. 45
  4. 36

Question 6

Given $2025=A\cdot8^3+B\cdot8^2+C\cdot8+D$, where A, B, C, D are digits from 0 to 7, what is the four-digit numeral ABCD?

Question illustration
  1. 3751
  2. 3352
  3. 2520
  4. 4252

Question 7

The sum of the squares of three consecutive integers is 365. Find the product of the smallest and largest integers.

Question illustration
  1. 200
  2. 180
  3. 120
  4. 144

Question 8

Reflect the line $3x-2y=5$ across $x-y=0$. What is the new equation?

Question illustration
  1. $3x-5y=1$
  2. $2x-3y=-5$
  3. $4x+3y=6$
  4. $\frac23x+y=5$

Question 9

Felix assigns each of the four shapes {Triangle, Square, Hexagon, Circle} a different color from {Red, Blue, Green, Yellow}. How many one-to-one functions are possible?

Question illustration
  1. 64
  2. 128
  3. 192
  4. 24