Question bank AMC AUSTRALIA 2020

$2-(0-(2-0))=$

$1000\%$ of 2 is equal to

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

$\dfrac{1+2+3+4+5}{1+2+3+4}-\dfrac{1+2}{1+2+3}=$

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

Which of the shapes in the diagram have equal area?

$123456-12345+1234-123+12-1=$

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

A piece of paper is folded twice as shown and cut along the dotted lines.
Once unfolded, which letter does the piece of paper most resemble?

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?

Triangle $XYS$ is enclosed by rectangle $PQRS$ as shown in the diagram.
In square centimetres, what is the area of triangle $XYS$?

Let $X=1-\frac13+\frac15-\frac17+\frac19-\frac1{11}$ and $Y=1-\frac13+\frac15-\frac17$. Then $X-Y$ is equal to

The number 25 can be written as the sum of three different primes less than 20. For instance, $25=5+7+13$.
How many multiples of 10 can be written as the sum of three different primes less than 20?

In this circle with centre $O$, four triangles are drawn, with angles as shown.
What is the value of $x$?

There are 10 children in a classroom. The ratio of boys to girls increases when another girl and another boy enter the room. What is the greatest number of boys that could have been in the room at the beginning?

Two triangles, $A$ and $B$, have the same area. Triangle $A$ is isosceles and triangle $B$ is right-angled.



The difference between the perimeters of triangle $A$ and triangle $B$ is

A list of numbers has first term 2 and second term 5. The third term, and each term after this, is found by multiplying the two preceding terms together:
$$2,\ 5,\ 10,\ 50,\ 500,\ldots$$
The value of the eighth term is

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

The number $\dfrac{1\times2\times3\times4\times5\times6\times7\times8\times9\times10}{n}$ is a perfect square.
What is the smallest possible value of $n$?

In the triangle $ABC$ shown, $D$ is the midpoint of $AC$, $E$ is the midpoint of $BD$ and $F$ is the midpoint of $AE$.
If the area of triangle $BEF$ is 5, what is the area of triangle $ABC$?