Australian AMC 2018 - Senior

In the diagram, $PQRS$ is a square. What is the size of $\angle XPY$?

The Great North Walk is a 250 km long trail from Sydney to Newcastle. If you want to complete it in 8 days, approximately how far do you need to walk each day?

Half of a number is 32. What is twice the number?

What fraction of this regular hexagon is shaded?

The value of $9\times1.2345-9\times0.1234$ is

What is $2^0-1^8$?

1000% of a number is 100. What is the number?

The cost of feeding four dogs for three days is \$60. Using the same food costs per dog per day, what would be the cost of feeding seven dogs for seven days?

In the triangle $ABC$, $M$ is the midpoint of $AB$.

Which one of the following statements must be true?

The sum of the numbers from 1 to 100 is 5050. What is the sum of the numbers from 101 to 200?

Leila has a number of identical equilateral triangle shaped tiles. How many of these must she put together in a row (edge to edge) to create a shape which has a perimeter ten times that of a single tile?

In the circle shown, $C$ is the centre and $A,B,D,E$ all lie on the circumference.

Reflex $\angle BCD=200^\circ$, $\angle DCA=x^\circ$ and $\angle BCA=3x^\circ$ as shown.

The ratio of $\angle DAC:\angle BAC$ is

Instead of multiplying a number by 4 and then subtracting 330, I accidentally divided that number by 4 and then added 330. Luckily, my final answer was correct. What was the original number?

The diagram shows a regular octagon of side length 1 metre. In square metres, what is the area of the shaded region?

A netball coach is planning a train trip for players from her two netball clubs, Panthers and Warriors.

The two clubs are in different towns, so the train fares per player are different. For the same cost she can either take 6 Panthers and 7 Warriors or she can take 8 Panthers and 4 Warriors.

If she takes only members of the Warriors on the train journey, the number she could take for the same cost is

The triangle $PQR$ shown has a right angle at $P$. Points $T$ and $S$ are the midpoints of the sides $PR$ and $PQ$, respectively. Also $\angle QTP=\alpha$ and $\angle SRP=\beta$.

The ratio $\tan\alpha:\tan\beta$ equals

Three fair 6-sided dice are thrown. What is the probability that the three numbers rolled are three consecutive numbers, in some order?

How many digits does the number $20^{18}$ have?

In this subtraction, the first number has 100 digits and the second number has 50 digits.





What is the sum of the digits in the result?

I have two regular polygons where the larger polygon has 5 sides more than the smaller polygon. The interior angles of the two polygons differ by $1^\circ$. How many sides does the larger polygon have?