Skip to content / Đến nội dung
ThichHocToan.com

Australian AMC 2013 - Junior

Question 1

$1999+24$ is equal to
  1. 1923
  2. 2003
  3. 2013
  4. 2023
  5. 2113

Question 2

$PQR$ is a straight line. Find the value of $x$.

Question illustration
  1. 40
  2. 90
  3. 100
  4. 110
  5. 120

Question 3

The value of the fraction $\frac12$ is closest to
  1. 0.45
  2. 0.6
  3. $\frac13$
  4. $\frac58$
  5. $\frac25$

Question 4

Which of the following is equal to 20?
  1. $3+2\times4$
  2. $(9+5)\times2-4\times2$
  3. $10^2$
  4. $20+20\div2$
  5. $10\div2$

Question 5

How many minutes are there between 8:37 am and 10:16 am?
  1. 39
  2. 79
  3. 99
  4. 141
  5. 179

Question 6

Three squares each with an area of $25\text{ cm}^2$ are placed side by side to form a rectangle. The perimeter, in centimetres, of the rectangle is
  1. 20
  2. 36
  3. 40
  4. 75
  5. 100

Question 7

If every digit of a whole number is either a 3 or a 5, the number will always be
  1. divisible by 3
  2. divisible by 5
  3. prime
  4. even
  5. odd

Question 8

$P$ is the point at 0.56 and $Q$ is the point at 1.2 on a number line. The point which is halfway between $P$ and $Q$ is at
  1. 0.34
  2. 0.64
  3. 0.83
  4. 0.88
  5. 0.93

Question 9

If triangle $ABC$ is isosceles with $\angle A=40^\circ$, what are all of the possible values for $\angle B$?
  1. $40^\circ$
  2. $40^\circ$ and $70^\circ$
  3. $40^\circ$ and $100^\circ$
  4. $70^\circ$ and $100^\circ$
  5. $40^\circ$, $70^\circ$ and $100^\circ$

Question 10

In Gwen’s classroom, the desks are arranged in a grid. Each row has the same number of desks. Gwen’s desk is third from the front, second from the back and has one desk to the left and four to the right. How many desks are there?
  1. 20
  2. 24
  3. 25
  4. 28
  5. 30

Question 11

William travels to school in two different ways. Either he walks to school and takes the bus home, or he takes the bus to school and walks home. In each case his total travelling time is 40 minutes. If he were to take the bus both ways, his total travelling time would be 20 minutes. How many minutes would it take if he walked both ways?
  1. 30
  2. 40
  3. 50
  4. 60
  5. 80

Question 12

The opposite faces on a standard dice add to give a total of 7. The game of Corners is played by rolling a dice and then choosing a vertex of the dice with your eyes closed. For example, the score for the vertex chosen below would be $4+5+6=15$.

Question illustration

Which of the following scores is NOT possible when playing Corners?
  1. 6
  2. 7
  3. 8
  4. 9
  5. 10

Question 13

A piece of paper in the shape of an equilateral triangle has one corner folded over, as shown.

Question illustration

What is the value of x?
  1. 60
  2. 70
  3. 80
  4. 90
  5. 100

Question 14

Beginning at the point A, Joel draws the spiral pattern of line segments below on a 1 cm grid. If he continues this pattern, how long, in centimetres, is the 97th segment?

Question illustration
  1. 46
  2. 47
  3. 48
  4. 49
  5. 50

Question 15

Sixteen discs are arranged in four rows of four. The discs have a number on one side and are either red or green on the other. The number shows how many discs touching that disc have green on the other side.

Question illustration

Which of the following statements is true?
  1. All of the rows have the same number of green discs.
  2. Row one has more green discs than any other row.
  3. Row two has more green discs than any other row.
  4. Row three has fewer green discs than any other row.
  5. Row four has fewer green discs than any other row.

Question 16

While shopping this week I misread my shopping list and bought 5 loaves of bread and 2 bottles of milk. So I went back to the supermarket, got a full refund, and bought 2 loaves of bread and 5 bottles of milk. This cost me \$4.20 less than my first purchase. How do the prices of bread and milk compare?
  1. A loaf of bread costs \$1.40 more than a bottle of milk.
  2. A loaf of bread costs \$0.60 more than a bottle of milk.
  3. A loaf of bread costs \$0.42 more than a bottle of milk.
  4. A loaf of bread costs \$0.60 less than a bottle of milk.
  5. A loaf of bread costs \$1.40 less than a bottle of milk.

Question 17

Starting with the number 0 on my calculator, I do a calculation in five steps. At each step, I either add 1 or multiply by 2. What is the smallest number that cannot be the final result?
  1. 11
  2. 10
  3. 9
  4. 8
  5. 7

Question 18

The three squares in the figure below are the same size. Find the value, in degrees, of $\angle AMT$.

Question illustration
  1. $45^\circ$
  2. $50^\circ$
  3. $55^\circ$
  4. $60^\circ$
  5. $75^\circ$

Question 19

Eight $1\times1$ square tiles are laid as shown.

Question illustration

Two more $1\times1$ tiles are added, so that at least one side of each new tile is shared with a side of the original shape. Several different perimeter lengths are now possible. What is the sum of the shortest and longest possible perimeter of the modified shape?
  1. 28
  2. 30
  3. 32
  4. 34
  5. 36

Question 20

In the triangle $PQR$, $S$ is a point on $PR$ such that $PQS$ and $SQR$ are both isosceles triangles (as shown). Angle $QPS$ is equal to angle $SQR$.

Question illustration

What is the value of $x$?
  1. 30
  2. 36
  3. 40
  4. 45
  5. 48