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AMO 2023 Primary 3 (Grade 3)

Question 1

How many triangles are there in the figure below?

Question illustration
  1. 7
  2. 9
  3. 13
  4. 15

Question 2

There were five soccer teams. Each soccer team played one match with every other team. How many matches were played?

Question illustration
  1. 6
  2. 8
  3. 10
  4. 15

Question 3

All the small squares are unit squares. How many squares of any size are there in the $3\times3$ grid?

Question illustration
  1. 10
  2. 12
  3. 14
  4. 16

Question 4

The factor tree of 2023 is shown below. How many whole numbers divide evenly into 2023, including 1 and 2023?

Question illustration
  1. 3
  2. 5
  3. 6
  4. 8

Question 5

Four houses lie along a curved road in the order A, B, C, D. Jason bikes 12 miles from A to D; Katie bikes 6 miles from A to C; Matt bikes 8 miles from D to B. What is the distance from B to C along the road, in miles?

Question illustration
  1. 1 mile
  2. 2 miles
  3. 3 miles
  4. 4 miles

Question 6

Five students raised money for a school event. After a week, they had raised an average of 25 dollars each. A last-minute donation increased the average to 30 dollars per person. How much was that donation, in dollars?

Question illustration

Figure labels: 5 students; initial average 25 dollars each; final average 30 dollars each.
  1. 5 dollars
  2. 25 dollars
  3. 30 dollars
  4. 50 dollars

Question 7

In the tangram below, the marked division points are midpoints of their respective segments. The big square has area 64 square inches. What is the area of the small parallelogram labeled W?

Question illustration
  1. 8 square inches
  2. 12 square inches
  3. 16 square inches
  4. 18 square inches

Question 8

The two-digit number $\overline{AB}$ and the digit B satisfy $\overline{AB}\times B=\overline{3AB}$. A and B are digits from 0 to 9. What is $A\times B$?

Question illustration
  1. 35
  2. 48
  3. 52
  4. 59

Question 9

If the pattern continues, how many balls are there in the 10th step?

Question illustration
  1. 32
  2. 55
  3. 60
  4. 72