Skip to content / Đến nội dung
ThichHocToan.com

Australian AMC 2009 - Junior

Question 1

The value of $2.6+0.12$ is
  1. 3.8
  2. 2.7
  3. 2.02
  4. 2.9
  5. 2.72

Question 2

The value of $1^2+2^2+3^2+4^2$ is
  1. 10
  2. 30
  3. 32
  4. 36
  5. 100

Question 3

Darcy went for a 35-minute walk after dinner. If he finished his walk at 7:10 pm, he started at
  1. 6:35 pm
  2. 6:30 pm
  3. 6:40 pm
  4. 6:25 pm
  5. 6:45 pm

Question 4

I have \$10 in 10-cent coins, \$10 in 20-cent coins and \$10 in 50-cent coins. How many coins do I have?
  1. 80
  2. 650
  3. 90
  4. 200
  5. 170

Question 5

If $\angle RPQ=20^\circ$ and $\angle RQU=120^\circ$, what is the size, in degrees, of $\angle SRT$?

Question illustration
  1. 60
  2. 140
  3. 80
  4. 100
  5. 120

Question 6

$(2000+9)+(2000-9)$ equals
  1. 4000
  2. 4009
  3. 200
  4. 2000
  5. 5000

Question 7

A painted straight line is 0.5 mm wide and covers an area of 1 square metre. How long, in metres, is the line?
  1. 2
  2. 20
  3. 200
  4. 2000
  5. 5000

Question 8

A teacher can mark 26 tests in 2 hours. At this rate, the number of hours the teacher needs to mark 91 tests is
  1. 6
  2. 7
  3. 8
  4. 9
  5. 10

Question 9

What is the area, in square centimetres, of the shape marked out on the 1-cm grid below?

Question illustration
  1. 18.5
  2. 19
  3. 19.5
  4. 20
  5. 20.5

Question 10

Which of the following has the largest value?
  1. $\frac13$
  2. $\frac13+\frac13$
  3. $\frac13\times\frac13$
  4. $\frac13-\frac13$
  5. $\frac13\div\frac13$

Question 11

Which of the following values can replace the box so that

Question illustration
  1. 500
  2. 50
  3. 5
  4. 0.5
  5. 0.05

Question 12

The figure $PQRS$ is a rectangle divided into 10 squares as shown. The perimeter of this rectangle is 21 centimetres. In centimetres, what is the perimeter of each square?

Question illustration
  1. 2.1
  2. 3
  3. 6
  4. 8.4
  5. 12

Question 13

The odd numbers from 1 to 999 are multiplied together. The last digit of the result is
  1. 1
  2. 3
  3. 5
  4. 7
  5. 9

Question 14

In the diagram, triangles $PQT,QTS$ and $QRS$ are isosceles and $\angle PQR$ is a right angle. Angles $PQT$ and $RQS$ are $2x^\circ$ and angle $QTS$ is $5x^\circ$. The value of $x$ is

Question illustration
  1. 10
  2. 12
  3. 14
  4. 15
  5. 20

Question 15

In Mrs Atkins’ class, every student swims or cycles and half the students do both. The total number of students who swim is the same as the total number of students who cycle. If 24 students in total swim, how many students are in Mrs Atkins’ class?
  1. 24
  2. 28
  3. 32
  4. 36
  5. 48

Question 16

Australia has rectangular currency notes for \$5, \$10, \$20, \$50 and \$100. These notes are all 65 mm wide but each note is 7 mm longer than the note of the next lowest value, so the \$10 note is 7 mm longer than the \$5 note, and so on.

The difference in area, in square millimetres, between the \$10 note and the \$100 note is
  1. 455
  2. 910
  3. 1365
  4. 1820
  5. 2275

Question 17

In this magic square, the sum of each row, column and diagonal is the same. The value of $x+y$ is

Question illustration
  1. 34
  2. 35
  3. 36
  4. 37
  5. 38

Question 18

A train leaves Canberra for Sydney at 12 noon and another train leaves Sydney for Canberra forty minutes later. Both travel at the same constant speed, taking $3\frac12$ hours to complete the journey. At what time will they pass?
  1. 1:45 pm
  2. 2:00 pm
  3. 2:05 pm
  4. 2:15 pm
  5. 2:25 pm

Question 19

Consider the following number pattern.

The 83rd number on the 57th row is

Question illustration
  1. 26
  2. 31
  3. 57
  4. 29
  5. 35

Question 20

$PQRS$ is a rectangle with $PQ=4$ m, $PS=3$ m and $QS=5$ m. $PT$ is the perpendicular from $P$ to $QS$. What is the length, in metres, of $PT$?

Question illustration
  1. 2.1
  2. 2.2
  3. 2.3
  4. 2.4
  5. 2.5