AMO 2022 – Primary 6 (Grade 6)

Question 1

Which interval is the solution set of $|x-2|\le15$?

1. $(-13,17)$
2. $(13,-17)$
3. $[-13,17]$
4. $[-13,-17]$
5. $(-13,-17]$

Question 2

If the dot pattern continues, how many dots are there at step 25?

1. 925
2. 1001
3. 1080
4. 1162
5. 2022

Question 3

Lines $AB$ and $CD$ intersect at $O$. Given $\angle DOA=(x+y)^\circ$, $\angle BOD=(2x-5y)^\circ$ and $\angle COB=(3x-7y)^\circ$, find $y$.

1. 20
2. 22.5
3. 34
4. 36.5
5. 40

Question 4

April makes seven bracelets. The first takes 5 minutes; each later bracelet takes 20% less time than the previous one. Find the total time, rounded to the nearest minute. Clarification: the source omits the percent sign after 20; its solution confirms 20%.

1. 11 minutes
2. 12 minutes
3. 15 minutes
4. 20 minutes
5. 25 minutes

Question 5

Paul and Matt meet at a restaurant today. Paul visits every 11 days and Matt every 17 days. In how many days will they next meet there if they keep these schedules?

1. 117
2. 125
3. 28
4. 187
5. 171

Question 6

The circle has center $C$, with $F,G,H$ on the circle. If $\angle GFH=60^\circ$, find $\angle GCH$ in radians.

1. $\frac{2\pi}{3}$
2. $\frac{4\pi}{3}$
3. $\frac{5\pi}{3}$
4. $\frac{3\pi}{4}$
5. $\frac{2\pi}{5}$

Question 7

Let $A,B$ be the two solutions of $|-5x+12|-8=10$. Find $AB$.

1. 7.2
2. -7.2
3. 8.4
4. -8.4
5. 12

Question 8

The source gives the relationship $5F=9C+160$ between Fahrenheit and Celsius readings. When $F=86$, what is $C$? Clarification: the reading is missing in the source stem and restored from its solution.

1. $25^\circ\mathrm C$
2. $26^\circ\mathrm C$
3. $27^\circ\mathrm C$
4. $30^\circ\mathrm C$
5. $32.5^\circ\mathrm C$

Question 9

Whole numbers $x,y$ satisfy $3x+5y=31$ and $6x-2y=2$. Find $xy$.

1. 8
2. 10
3. 12
4. 15
5. 18

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20