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AMO 2024 – Secondary 2 (Grade 8)

Question 1

The polynomial $p(x)=2x^3+12x^2-2x-60$ has roots $a,b,c$. Find $abc$.

Question illustration
  1. 60
  2. 48
  3. 36
  4. 30

Question 2

Points $A,B$ lie on $f(x)=x^2-4x-12$. Their $x$-coordinates are 1 and 5 respectively. Where does line $AB$ meet the $y$-axis? Clarification: the source omits the letter x before “coordinate” for B; the intended x-coordinate is used.

Question illustration
  1. $(0,-17)$
  2. $(-2,0)$
  3. $(6,-0)$
  4. $(0,-12)$

Question 3

For what value of $k$ does $x^2+10x+21=2kx+6k$ have exactly one real solution?

Question illustration
  1. 1
  2. 2
  3. 3
  4. 4

Question 4

A ring of width 1 surrounds a circle of radius $R$, as shown. What type of relation expresses its area $A(R)$ in terms of $R$?

Question illustration
  1. Cubic relation
  2. Quadratic relation
  3. Linear relation
  4. Logarithmic relation

Question 5

Joe’s integer leaves remainder 4 when divided by 11. What remainder does four times his number leave when divided by 11?

Question illustration
  1. 5
  2. 4
  3. 3
  4. 0

Question 6

The hexagon shown joins the midpoints of six edges of a unit cube. What is its area?

Question illustration
  1. $\frac{4\sqrt2}{5}$
  2. $5\sqrt2$
  3. $6\sqrt3$
  4. $\frac{3\sqrt3}{4}$

Question 7

Reflect the line $y=2x-6$ in the line $y=x$. What is the equation of its image?

Question illustration
  1. $y=6x-2$
  2. $y=x-3$
  3. $y=-4x+1$
  4. $y=0.5x+3$

Question 8

Finn defines a function from $\{A,B,C\}$ to $\{1,2,3,4\}$. How many distinct functions are possible?

Question illustration
  1. 64
  2. 27
  3. 12
  4. 6

Question 9

The algebra test scores are $55,60,64,70,75,77,82,86,90,96$. Find the interquartile range (IQR) represented by the boxplot. Use the median of the lower five and upper five values for the quartiles, as intended by the source.

Question illustration
  1. 32
  2. 27
  3. 22
  4. 18