AIMO 2021 Secondary 1 — Preliminary (Open Trial 1)

Question 1

A jacket is on sale for 70% of the original price. If the discount saves 140 dollars, what was the original price of the jacket?

Original printed choices: A: 466 dollars; B: 200 dollars; C: 400 dollars; D: 240 dollars.

Editorial response format: give the exact answer; the original choices are retained for reference.

Question 2

In a coordinate plane, $P(2,-1)$ is the midpoint of $A(3,a)$ and $B(b,-3)$. Find $ab$.

Question 3

The foot of a ladder is placed 6 feet from a wall. Its top rests 8 feet up the wall. How long is the ladder?

Original printed choices: A: 14 m; B: 8 m; C: 12 m; D: 10 m.

Editorial response format: give the exact answer; the original choices are retained for reference.

Convention: Give the length in feet, using the units in the statement.

Question 4

Carnival tickets cost 5 dollars for adults and 3 dollars for children. There were 215 attendees and ticket receipts of 925 dollars. How many children's tickets were bought?

Question 5

Anna receives red packets containing 10 dollars, 20 dollars or 50 dollars each. The numbers of 10 dollars and 50 dollars packets are equal, and the total value is 820 dollars. What is the minimum number of packets?

Original printed choices: A: 15; B: 20; C: 25; D: 30.

Editorial response format: give the exact answer; the original choices are retained for reference.

Question 6

Solve $\frac{19}{20}\left[\frac1{10}+\frac45(1+x)\right]-\frac3{20}=x$.

$\frac34$
$\frac58$
$\frac{47}{16}$
$\frac{15}{32}$

Question 7

Points $A,B,C,D$ lie in that order on a line, and $AB:BC:CD=2:3:4$. The midpoints of $AB,BC,CD$ are $S,K,Y$, respectively. If $SY=9$ cm, find $AD$.

$\frac32$
$\frac{15}{4}$
$\frac{25}{8}$
$\frac{27}{2}$

Question 8

Among natural numbers less than 1000, how many have exactly 5 positive factors?

Original printed choices: A: 20; B: 24; C: 50; D: 48.

Editorial response format: give the exact answer; the original choices are retained for reference.

Question 9

A team of 5 students is selected from 5 boys and 6 girls. What is the probability that it contains 2 boys and 3 girls?

Original printed choices: A: $\frac15$; B: $\frac{25}{77}$; C: $\frac6{25}$; D: $\frac{20}{77}$.

Editorial response format: give the exact answer; the original choices are retained for reference.

Convention: Assume every five-student team is equally likely. Give the exact probability.

Question 10

Given $a+b+c+d=2019$, $a+b+c+e=2018$ and $d+e=3$, find $a+b+c+2d$.

2018
2019
2020
2021

Question 11

Find $A=\frac1{1+2}+\frac1{1+2+3}+\frac1{1+2+3+4}+\cdots+\frac1{1+2+\cdots+50}$.

$\frac{40}{51}$
$\frac{49}{51}$
$\frac{49}{102}$
$\frac{49}{50}$

Question 12

A red racing car and a blue racing car move at constant speeds around an 800 m circuit. In the same direction the red car overtakes the blue every 40 seconds; in opposite directions they meet every 8 seconds. Find the red car's speed in m/s.

Question 13

Find the largest integer not greater than $\frac{2019}{2000}+\frac{2019}{2001}+\cdots+\frac{2019}{2009}$.

Question 14

Mrs. Hanna divides 12 candies among 3 children so that each child receives at least one. How many distributions are possible?

Original printed choices: A: 12; B: 20; C: 28; D: 24.

Editorial response format: give the exact answer; the original choices are retained for reference.

Convention: Treat the candies as identical and the three children as distinct. Give the number of distributions.

Question 15

Calculate the area of the shape shown, correct to 1 decimal place.

Question illustration

28
20
36
28.1

Question 16

Jane has 9 identical pieces of bite-size chocolate. She takes at least 1 piece each day. In how many ways can she finish the chocolate?

Original printed choices: A: $2^{10}$; B: $2^9$; C: 18; D: 20.

Editorial response format: give the exact answer; the original choices are retained for reference.

Convention: Count ordered sequences of positive daily amounts, ending on the day the last piece is taken.