Australian AMC 2022 - Intermediate

Calculate: $2220-2022=$

This shape is built from 29 squares, each 1 cm × 1 cm. What is its perimeter in centimetres?

A digital clock shows the time as 20:22. In how many minutes will it be midnight?

The value of $\dfrac{1^2+2^2}{3^2+4^2}$ is

In the triangle $PQR$ shown, $PQ=PR$ and $\angle QPR=48^\circ$. What is $\angle PQR$?

What fraction of this rectangle is shaded? The diagram gives rectangle width 12, height 7, and the upper parallel side of the shaded trapezium as 8.

$(0.4)^2+(0.1)^2=$

Australia uses 160 million litres of petrol each day. There is enough petrol stored to last 60 days. How much more petrol does Australia need to buy to have enough stored for 90 days?

Calculate: $\dfrac{2022}{2}-\dfrac{2022}{3}=$

Which algebraic term should replace $\triangle$ in the equation below? $\triangle+\triangle+\triangle=27x^3y^6$.

Three vertices of a rectangle are the points (1, 4), (7, 4) and (1, 8). At which point do the diagonals of the rectangle cross?

What value should be placed in the box to satisfy the equation? $$\frac53=1+\frac1{1+\frac1{\boxed{\phantom{2}}}}.$$

The angles of a triangle are in the ratio 2 : 3 : 4. What is the size of the largest angle in degrees?

In this puzzle, each circle should contain an integer. Each of the five lines of four circles should add to 40. When the puzzle is completed, what is the largest number used?

Daniel and Luke arrange to meet at a cafe. Luke leaves work, walking at 6 km/h. Five minutes later, Daniel starts cycling from his flat at 20 km/h. A further 15 minutes later, both arrive at the cafe at the same time. What is the total distance they travelled?

My family of 7 adults and 5 children gather each year to celebrate Chinese Mid-Autumn festival. Each adult gives one gift to everyone else. Each child gives one gift to every other child. How many gifts are given?

This spinner is spun twice to form a two-digit number using the following rules:
- The first value spun forms the tens digit.
- If the second value rolled is larger than the first, it becomes the units digit.
- If the second value spun is not larger than the first, the tens digit is repeated as the units digit.
What is the probability that the resulting two-digit number is divisible by 11?

Eight overlapping unit squares are drawn to produce a flower shape as shown. The parts where two squares overlap are isosceles triangles. What is the total shaded area?

Rick and Nic started learning guitar recently. Two weeks ago, Rick had been learning five times as long as Nic. Two days ago, Rick had been learning twice as long as Nic. Today, what is the number of days that Rick has been learning plus the number of days that Nic has been learning?

Over the last 20 years, the standard ratio of television screens has changed from 4 : 3 to 16 : 9. When the ratio of content does not match the ratio of the screen it is being viewed on, black bars are often used to compensate, as illustrated. The left diagram is a 4 : 3 image on a 16 : 9 screen; the right is a 16 : 9 image on a 4 : 3 screen. If ℓ is the fraction of the screen blacked out in the left diagram, and r is the fraction blacked out in the right diagram, then the ratio ℓ : r equals