Australian AMC 2023 - Senior

What is the value of $2023-3202$?

A parallelogram $PQRS$ has an area of $60\text{ cm}^2$ and side $PQ$ of length $10\text{ cm}$. Which length is $6\text{ cm}$?

Which one of these is equal to $57\times953$?

What is the difference between $2^5$ and $5^2$?

What is the value of the angle $\theta^\circ$ in the diagram?

The shaded square is inscribed in the larger square as shown. What is the ratio of shaded to unshaded area in the diagram?

Jemmy multiplies together all the integers from 1 to 18. What are the last three digits of the result?

A fuel tank is 40% empty. Then 40 litres of fuel is removed. The tank is now 40% full. How many litres are in a full tank?

The volume $V$ of a sphere of radius $r$ is given by $V=\frac43\pi r^3$. For a sphere of volume $V=100\text{ cm}^3$, which of the following is closest to the radius?

If I add 3 consecutive odd integers, I get a total of $9m+3$. The largest of these 3 integers is

The value of $(\sqrt{24}+\sqrt{54})^2$ is

In a group of 6 people there are 3 pairs of twins. How many 3-member committees can be chosen that do not contain any pair of twins?

Assuming $a>b>0$, the expression $\frac{a^{-1}-b^{-1}}{a^{-2}-b^{-2}}$ can be written as

A bag contains red and yellow balls such that the ratio red : yellow is $5:7$. Then 10 balls of each colour are removed and the ratio changes to $5:8$. How many balls were originally in the bag?

In the solution to this number puzzle, whenever there are three numbers in a straight line, the middle number is the sum of the other two. What is the value of $x$?

If $f(x)=5+x$ and $g(x)=7-x$, then $f(g(x))-g(f(x))$ equals

The hypotenuse of a right-angled triangle has length $6\text{ cm}$. The perimeter of the triangle is $14\text{ cm}$. What is the area of the triangle in square centimetres?

I have two identical dice, each with faces $1,\frac12,\sqrt3,\frac1{\sqrt3},\frac1{\sqrt2}$ and $\frac{\sqrt3}{2}$. I roll both dice and multiply the two numbers rolled, then simplify my answer. What is the probability that this product is rational?

How many distinct pairs $(x,y)$ satisfy $x^2+y^2<50$ if $x$ and $y$ are both positive integers with $x>y$?

A $15\text{ cm}\times20\text{ cm}$ rectangle is cut into two triangles. One triangle is rotated and placed on top of the other triangle as shown to form a concave pentagon. What is the perimeter of the pentagon?