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AMO 2024 Secondary 1 (Grade 7)

Question 1

A data set has 12 numbers with mean 18. One number is changed to 5 and the mean becomes 15. What was that number originally?

Question illustration
  1. 18
  2. 24
  3. 36
  4. 41

Question 2

The chance of rain on any day in a region is 20%. You visit for three days. What is the probability of at least one rainy day? Clarification: assume rain on different days is independent, as the source solution does; the daily chance alone does not determine the answer.

Question illustration
  1. 0.875
  2. 0.625
  3. 0.488
  4. 0.168

Question 3

When $3/7$ is written as a decimal, what is its repeating block?

Question illustration
  1. 342857
  2. 324571
  3. 428571
  4. 857123

Question 4

Two dice each have 12 sides numbered 1 to 12. Roll both. What is the probability that the product of the top numbers is 12? Assume fair dice and independent rolls.

Question illustration
  1. 1/4
  2. 1/8
  3. 1/18
  4. 1/24

Question 5

In how many distinct ways can the letters of SEVEN be rearranged into a five-letter word? It need not have a meaning.

Question illustration
  1. 90
  2. 80
  3. 60
  4. 36

Question 6

Calculate $5000-2024^2+2023^2$.

Question illustration
  1. 625
  2. 872
  3. 953
  4. 2753

Question 7

During a tax-free promotion, a T-shirt is discounted by 50%. What percentage increase of the sale price restores its original price?

Question illustration
  1. 50%
  2. 75%
  3. 100%
  4. 120%

Question 8

A unit square is repeatedly divided into four equal squares using side midpoints, as shown. What is the total area of the shaded squares? Count the four shaded squares actually shown; the last two have equal size.

Question illustration
  1. 1/3
  2. 7/16
  3. 9/32
  4. 11/32

Question 9

Jason can paint a warehouse alone in 18 hours; Carla can do it alone in 12 hours. How many hours do they need working together at their usual constant rates?

Question illustration
  1. 6.5
  2. 7.2
  3. 8.4
  4. 9.5