Question bank AMC AUSTRALIA 2014

Evaluate $1+2-3-4+5+6-7-8+9+10$.

In the diagram, what is $x$ in degrees?

If $p=9$ and $q=-3$, what is $p^2-q^2$?

What number belongs in the shape so that $2014\div\boxed{\phantom{x}}=100$?

If $5/6$ of a number is 30, what is $3/4$ of that number?

The diagram is an open square of order 4: three equal sides, each with four evenly spaced posts. How many posts are on an open square of order 10?

Which of the objects A–E is not the same as the given object on the right? Objects may be rotated.

The graph gives the goals scored by Ranjit’s soccer team in its first thirteen matches. After match fourteen, the median has increased but the mode is unchanged. Which best describes the number of goals in the last match?



The horizontal axis is number of goals and the vertical axis is frequency.

Forty-eight square pavers, each 1 m by 1 m, form a path 1 m wide around a square garden. What is the area inside the path, in square metres?

Each May a farmer plants barley seed and in October harvests twelve times the weight planted. From each harvest he sells 50 tonnes and keeps the rest as next year’s seed. This year he planted enough to harvest 120 tonnes. How many tonnes did he plant last year?

If $x$ is an integer and $x<-1$, which expression has the greatest value?

The eleven boys in Tom’s cricket team throw a ball. Their distances, to the nearest metre, are 19, 26, 31, 31, 31, 33, 37, 42, 42, 48, 56. Which list puts the statistical measures in ascending order?

Jug X contains 800 mL of water and jug Y 800 mL of milk. Pour 200 mL from X into Y and mix thoroughly. Then pour 200 mL of this mixture from Y into X. How much milk is now in X?

The problem states that the women’s 400-metre world record was set in Canberra in 47.60 seconds. Which option is closest to the runner’s average speed in kilometres per hour?

Ten points Q, R, S, T, U, V, W, X, Y and Z are equally and consecutively spaced on a circle. What is the size in degrees of $\angle QTW$?

A 3 by 5 grid of dots is shown. How many straight segments join two dots and pass through exactly one other dot?

A hotel has rooms for up to two people. Couples may share, but otherwise men share only with men and women only with women. How many rooms guarantee accommodation for any group of 100 people?

Two rectangular prisms measure $4\times6\times x$ cm and $3\times8\times y$ cm, where $x,y$ are integers. If their surface areas are equal, what is the smallest possible $x+y$?

A four-digit number $\overline{abcd}$ is cool if $a$ is divisible by 4, $\overline{ab}$ by 5, $\overline{abc}$ by 6, and $\overline{abcd}$ by 7. How many cool numbers have no digit 8?

The boundary of the shown shape consists of four identical arcs, each one quarter of a circle of radius 5 cm. What is its area in square centimetres?