Australian AMC 2020 - Senior

What is the value of $2020\div20$?

In the diagram provided, find the sum of $x$ and $y$.

Evaluate $\sqrt{7+18\div(10-1^5)}$.

Sebastien is thinking of two numbers whose sum is 26 and whose difference is 14.
The product of Sebastien’s two numbers is

If $\frac45$ of $\frac56$ of $\frac{\star}7$ of $\frac78$ is equal to 1, then the value of $\star$ is

A square garden of area 10000 m² is to be enlarged by increasing both its length and width by 10%. The increase in area, in square metres, is

Given that $f(x)=2x^2-3x+c$ and $f(2)=6$, then $c$ is equal to

An equilateral triangle is subdivided into a number of smaller equilateral triangles, as shown. The shaded triangle has side length 2. What is the perimeter of the large triangle?

If a ≠ 0, then $\dfrac{a^{x+y}}{a^x}$ is equivalent to

What is the area of the pentagon shown?

In the diagram, $PQ$ is a diameter of the circle, $OR$ is a radius, and $\angle OPR=33^\circ$.
The value of $x+y$ is

This diagram is composed entirely of semicircles. The diameter of each of the eight smallest semicircles is exactly one-quarter of the diameter of the two biggest semicircles.
What fraction of the large circle is shaded?

In Paradise, all days are either fine or wet.
If today is fine, the probability of tomorrow being fine is $\frac34$.
If today is wet, the probability of tomorrow being fine is $\frac13$.
Today is Friday and it is fine. I am having a BBQ on Sunday. What is the probability that it will be fine on Sunday?

Given that $x$ and $y$ are both integers and $2^{x+1}+2^x=3^{y+2}-3^y$, the value of $x+y$ is

A bag contains exactly 50 coins. The coins are either worth 10 cents,20 cents or 50 cents, and there is at least one of each. The total value of the coins is \$10.
How many different ways can this occur?

A regular hexagon is partially covered by six right-angled triangles, as shown.
What fraction of the hexagon is not covered?

In a paddock of sheep, there are 4 times as many male sheep as female sheep. In another paddock, there are 5 times as many females as males. When the two flocks of sheep are combined, there are equal numbers of males and females. What is the smallest possible total number of sheep?

The rectangle $OABC$ is drawn in the quadrant of a circle $ODE$, so that $AD=2$ and $CE=9$.
What is the radius of the circle?

The minimum value of the function $f(x)=2^{x^2-2x-3}$ is

Two sides of a regular pentagon are extended to create a triangle.
Inside this triangle, a smaller regular pentagon is drawn, as shown.
In area, how many times bigger is the larger pentagon than the smaller pentagon?