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AMO 2022 – Secondary 1 (Grade 7)

Question 1

Sam has six different fruits. He picks five different fruits for each cup of juice. How many different flavors can he make?

Question illustration
  1. Five
  2. Six
  3. Twelve
  4. Fifteen
  5. Thirty

Question 2

The average of ten numbers is 12. Replacing one number with 10 makes the average 9. What was the replaced number?

Question illustration
  1. Not enough information
  2. 10
  3. 20
  4. 30
  5. 40

Question 3

After a 20% price cut, a sport shirt sells for 36 dollars before taxes. What percentage increase restores the original price?

Question illustration
  1. 20%
  2. 25%
  3. 40%
  4. 15%
  5. 36%

Question 4

ABCDEFGH is a cube with edge AB equal to 1 inch. Triangle ABG is drawn inside it. What is the perimeter of triangle ABG, in inches?

Question illustration
  1. $3.5$
  2. $\sqrt5$
  3. $\sqrt6$
  4. $\sqrt3+\sqrt2+1$
  5. $\sqrt7$

Question 5

Two circles have the same center A. AB is 2 inches and AC is 4 inches. What is the ratio of the shaded ring area to the small circle area?

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

Question 6

Points A=(1,2), B=(4,4) and C=(4,1) form triangle ABC in the coordinate plane. What is its area in square units?

Question illustration
  1. 3.5
  2. 4
  3. 4.5
  4. 5.6
  5. 6

Question 7

Students measured diameters and circumferences of circular objects and fitted the linear model $y=2.6x-0.5$, where x is diameter and y is circumference, in centimeters. According to this model, what is the circumference for a diameter of 50 cm?

Question illustration
  1. 129.5
  2. 157.5
  3. 314.5
  4. 78.5
  5. 628.5

Question 8

Box A contains 4 green and 6 red balls; box B contains 8 green and 2 red balls. Amy randomly chooses one box and then one ball. Given that her ball is green, what is the probability it came from A? Assume the boxes are equally likely and balls within a box are equally likely.

Question illustration
  1. $\frac12$
  2. $\frac13$
  3. $\frac14$
  4. $\frac15$
  5. $\frac16$

Question 9

A circular coffee filter has radius 3 inches. Linda cuts out the one-third sector shown and rolls that sector into a cone without overlap. What is the radius of the base, in inches?

Question illustration
  1. $\frac12$
  2. $\frac{3\pi}2$
  3. $\pi$
  4. 1
  5. $\frac\pi2$