Skip to content / Đến nội dung
ThichHocToan.com

Australian AMC 2024 - Senior

Question 1

What is the value of $(57\times346)+(43\times346)$?
  1. 14 878
  2. 19 722
  3. 31 500
  4. 34 600
  5. 46 300

Question 2

The area of the triangle shown is $36\text{ m}^2$. What is the length $h$?

Question illustration
  1. 2 m
  2. 4 m
  3. 4.5 m
  4. 8 m
  5. 16 m

Question 3

What is the value of $\dfrac{1+\frac12+\frac13}{1-\frac12-\frac13}$?
  1. $-3$
  2. $-1$
  3. 3
  4. 6
  5. 11

Question 4

What is the value of $\theta$ in the diagram?

Question illustration
  1. $9^\circ$
  2. $10^\circ$
  3. $12^\circ$
  4. $15^\circ$
  5. $18^\circ$

Question 5

The largest integer $n$ for which $0.6n$ is less than 17 is
  1. 9
  2. 10
  3. 11
  4. 26
  5. 28

Question 6

If $2^n$ is a factor of 2024, then the largest possible value of $n$ is
  1. 0
  2. 1
  3. 2
  4. 3
  5. 8

Question 7

A girl rides a scooter at a constant speed of 6 km/h. The number of metres she travels in one minute is
  1. 20
  2. 100
  3. 200
  4. 400
  5. 600

Question 8

This rectangle has area 96 square centimetres. What is its perimeter, in centimetres?

Question illustration
  1. 24
  2. 28
  3. 32
  4. 36
  5. 40

Question 9

Ell has many \$50 notes and no other currency, while Em has many \$20 notes and no other currency. What is the minimum number of notes that would need to be exchanged between the two if Ell would like to pay Em \$270?
  1. 7
  2. 8
  3. 9
  4. 10
  5. 11

Question 10

This teardrop shape is the logo for my new chat app. Its perimeter is composed of semicircular arcs. What is its perimeter?

Question illustration
  1. $\pi$
  2. $2\pi$
  3. $3\pi$
  4. $4\pi$
  5. $5\pi$

Question 11

This design is for part of a quilt. It is based on five overlapping squares of side 10 cm. The darker areas are two identical squares and two identical isosceles triangles. What is the total area of the design?

Question illustration
  1. $350\text{ cm}^2$
  2. $400\text{ cm}^2$
  3. $425\text{ cm}^2$
  4. $450\text{ cm}^2$
  5. $500\text{ cm}^2$

Question 12

Michael has a pie to heat in the microwave oven. The instructions say to heat it for a number of minutes and seconds, longer than 4 minutes. He inputs the minutes and seconds as 3 digits. However the oven has been programmed to interpret the input as a 3-digit number of seconds. The pie heats for 60% longer than required. In seconds, how long should the pie have been heated?
  1. 250
  2. 300
  3. 400
  4. 500
  5. 600

Question 13

Merle and Simon both collect toy cars. Before Merle’s birthday, Simon had 50% more cars than Merle, but Merle got 20 cars for her birthday, so now she has 50% more cars than Simon. How many cars does Simon have?
  1. 12
  2. 15
  3. 20
  4. 24
  5. 30

Question 14

Which of the following is equal to $(2^7+3^8)^2$?
  1. $4^7+6^8+9^8$
  2. $2^{14}+2^7\times3^8+3^{16}$
  3. $2^{14}+3^{16}$
  4. $2^8+2\times6^8+3^9$
  5. $2^{14}+6^{15}+3^{16}$

Question 15

A cubed cube is a 6-sided dice with the numbers $1^3,2^3,3^3,4^3,5^3,6^3$ on it. A red cubed cube and a blue cubed cube are rolled. What is the probability that the value on the red cube divided by the value on the blue cube is a whole number?

Question illustration
  1. $13/36$
  2. $5/12$
  3. $7/18$
  4. $4/9$
  5. $1/3$

Question 16

Depending on the value $k$, the equation $x^2+kx+2024=0$ can have 0, 1 or 2 integer solutions for $x$. For how many positive integer values of $k$ does the equation have 2 integer solutions?
  1. 3
  2. 6
  3. 8
  4. 14
  5. 16

Question 17

What is the shaded area in this diagram?

Question illustration
  1. $3/2$
  2. $8/5$
  3. $5/3$
  4. $7/4$
  5. 2

Question 18

A researcher surveys 10 households and creates this scatterplot showing how many people and how many internet-connected devices are in each house. To help categorise her data, she adds a vertical line representing the median number of people and a horizontal line representing the median number of devices. One extra household is surveyed and the results are added to the scatterplot. What will happen to the median lines?

Question illustration
  1. Both lines move.
  2. Neither line moves.
  3. Only the vertical line moves.
  4. Only the horizontal line moves.
  5. It depends on the location of the new point.

Question 19

February 2024 had 5 Thursdays. When will February next have 5 Thursdays?
  1. 2028
  2. 2044
  3. 2048
  4. 2052
  5. 2080

Question 20

Abi is walking beside a lake. In the distance she can see a tree and its reflection on the surface of the lake. There is a depth indicator 5 metres away from her with its 0-metre mark at the lake surface level. From Abi’s point of view, the top of the tree is in line with the 1.8-metre mark on the depth indicator, while the reflection of the top of the tree is in line with the 1.1-metre mark. Abi’s eyes are level with the 1.5-metre mark. How tall is the tree in metres?

Question illustration
  1. 9
  2. 9.5
  3. 10
  4. 10.5
  5. 11