Question bank AMC AUSTRALIA 2008

The value of $802-208$ is

Given that $1.08\times1.8=1.944$, the value of $108\times18$ is

In the diagram, the sides of the triangles are extended and three angles are as shown. The value of $x$ is

The value of $\dfrac{200\times8}{200\div8}$ is

The digits 5, 6, 7, 8 and 9 can be arranged to form even five-digit numbers. The tens digit in the largest of these numbers is

Four consecutive odd numbers add up to 48. What is the largest of these numbers?

A rectangle has an area of 72 square centimetres and the length is twice the width. The perimeter, in centimetres, of the rectangle is

What percentage of $y$ is $x$?

In the diagram, triangles $PQR$ and $LMN$ are both equilateral and $\angle QSM=20^\circ$. What is the value of $x$?

When $1000^{2008}$ is written as a numeral, the number of digits written is

Anne designs the dart board shown, where she scores $P$ points in the centre circle, $Q$ points in the next ring and $R$ points in the outer ring. She throws three darts in each turn. In her first turn, she gets two darts in ring $Q$ and one in ring $R$ and scores 10 points. In her second turn, she gets two in circle $P$ and one in ring $R$ and scores 22 points.

In her next turn, she gets one dart in each of the regions. How many points does she score?

How many different positive numbers are equal to the product of two odd one-digit numbers?

Points $A,B,C,D$ and $E$ are nodes of a square grid as shown. Which of these five points forms an isosceles triangle with the other two vertices at $X$ and $Y$?

A Fibonacci die has the numbers 1, 1, 2, 3, 5 and 8 on it. Two such dice are thrown. What is the probability that the number on one die is larger than the number on the other?

A fishtank with base 100 cm by 200 cm and depth 100 cm contains water to a depth of 50 cm. A solid metal rectangular prism with dimensions 80 cm by 100 cm by 60 cm is then submerged in the tank with an 80 cm by 100 cm face on the bottom.

The depth of water, in centimetres, above the prism is then

What is the smallest whole number which gives a square number when multiplied by 2008?

AI editorial clarification: The original wording includes zero if whole numbers are taken to include zero; zero is not listed. For this imported multiple-choice item, interpret the requested multiplier as positive.

The interior of a drinking glass is a cylinder of diameter 8 cm and height 12 cm. The glass is held at an angle of $45^\circ$ from the vertical and filled until the base is just covered. How much water, in millilitres, is in the glass?

A number is less than 2008. It is odd, it leaves a remainder of 2 when divided by 3 and a remainder of 4 when divided by 5. What is the sum of the digits of the largest such number?

$PR$ and $QS$ are perpendicular diameters drawn on a circle centre $O$. The points $T,U,V$ and $W$ are the midpoints of $PO,QO,RO$ and $SO$ respectively.

The fraction of the circle covered by the shaded area is

Three numbers $p,q$ and $r$ are all prime numbers less than 50 with the property that $p+q=r$. How many values of $r$ are possible?