Skip to content / Đến nội dung
ThichHocToan.com

AMO 2023 Secondary 1 (Grade 7)

Question 1

Given $2023=7\times17^2$ and $2024=2^3\times11\times23$, how many distinct positive divisors does $2023\times2024$ have?

Question illustration
  1. 24
  2. 72
  3. 96
  4. 100

Question 2

Positive integers $M,N$ satisfy $M^2+16^2=N^2+2023^2$. Which is a possible value of $M+N$?

Question illustration
  1. 2022
  2. 2024
  3. 2035
  4. 2039

Question 3

Bob agreed to work 40 hours at a bookstore for an electric bike and 900 dollars. He quit after 30 hours and fairly received the same bike and 400 dollars. How much was the bike worth, in dollars?

Question illustration
  1. 1050
  2. 1100
  3. 1200
  4. 1250

Question 4

A circle has radius 5 units and center $(2,3)$. It meets the $x$-axis at $B,C$. Find $BC$, in units.

Question illustration
  1. 5
  2. 8
  3. 9
  4. 10

Question 5

$ABCDEFGH$ is a unit cube with $AB=1$. A square pyramid $ABCDG$ is constructed inside it. What is its surface area? The source options say “units”; for an area these mean square units.

Question illustration
  1. $1+\sqrt5$
  2. $4-\sqrt2$
  3. $2+\sqrt2$
  4. $2+\sqrt6$

Question 6

For nonnegative integers, $f(0)=3$ and $f(n)=f(n-1)+2$ when $n>0$. Express $f(n)$ in terms of $n$.

Question illustration
  1. $2n+3$
  2. $4n+3$
  3. $n^3-4$
  4. $n^4+3$

Question 7

If the dot pattern continues, how many more dots are at step 100 than at step 99?

Question illustration
  1. 223
  2. 224
  3. 301
  4. 311

Question 8

If $(60-x)(40-x)=80$, find $(60-x)^2+(40-x)^2$.

Question illustration
  1. 100
  2. 560
  3. 750
  4. 1000

Question 9

In the figure, $AB=AC$, and $D$ lies on $AC$ with $BD=BC=AD$. Find $x=\angle BAC$ in degrees.

Question illustration
  1. $24^\circ$
  2. $30^\circ$
  3. $36^\circ$
  4. $45^\circ$