Australian AMC 2011 - Intermediate

Question 1

The value of $2011-1102$ is

1111
1191
1001
989
909

Question 2

In the diagram, the value of $x$ is

Question illustration

Question 3

The value of $14\div 0.4$ is

3.5
35
5.6
350
0.14

Question 4

Which of the following could be the graph of $y=2 x+1$?

Question 5

The expression $8 x-4 y-3 x+2 y$ equals

$4x-y$
$5x-2y$
$5x-6y$
$11x-2y$
$11x-6y$

Question 6

By what number must $\frac 13$ be divided to obtain 4 as a result?

$\frac1{12}$
6
$1\frac13$
$\frac14$
12

Question 7

Which one of the following is not equal to $3^9$?

$(3^3)^3$
$3^3\times3^3\times3^3$
$27^3$
$9^3\times27$
$9^4$

Question 8

The numbers represented by points $R$ and $P$ on the number line below are multiplied. Which point would best represent the product of these two numbers?

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Question 9

$PQRS$ is a trapezium in which $PQ=2$ units and $RS=3$ units. What fraction of the trapezium is shaded?

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$\frac15$
$\frac14$
$\frac13$
$\frac25$
$\frac12$

Question 10

An $8\times 8\times 8$ hollow cube is constructed from $1\times 1\times 1$ cubes so that its six walls are 1 cube thick. The number of $1\times 1\times 1$ cubes needed to make the hollow cube is

Question 11

In my neighbourhood, 90% of the properties are houses and 10% are shops. 10% of the houses are for sale and 30% of the shops are for sale. What percentage of the properties for sale are houses?

9%
80%
$33\frac13\%$
75%
25%

Question 12

$PQRS$ is a square. $TUVW$ is a smaller square placed inside as shown with $PR=2 TV$. The ratio of the shaded area to the area of the square $PQRS$ is

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2 : 3
3 : 4
1 : 3
1 : 2
2 : 5

Question 13

The numbers on the six faces of this cube are consecutive even numbers.

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If the sums of the numbers on each of the three pairs of opposite faces are equal, find the sum of all six numbers on this cube.

Question 14

The positive integers are arranged in a zigzag fashion across five rows as follows:

Question illustration

In which row will 2011 appear?

Two tourists are walking 12 km apart along a flat track at a constant speed of 4 km/h. When each tourist reaches the slope of a mountain, he begins to climb with a constant speed of 3 km/h.

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What is the distance, in kilometres, between the two tourists during the climb?

Question 16

The six faces of a dice are numbered $-3,-2,-1,0,1,2$. If the dice is rolled twice and the two numbers are multiplied together, what is the probability that the result is negative?

$\frac12$
$\frac14$
$\frac{11}{36}$
$\frac{13}{36}$
$\frac13$

Question 17

A 36 cm by 24 cm rectangle is drawn on 1 cm grid paper such that the 36 cm side contains 37 grid points and the 24 cm side contains 25 grid points. A diagonal of the rectangle is drawn. How many grid points lie on that diagonal?

Question 18

Three people play a game with a total of 24 counters where the result is always that one person loses and two people win. The loser must then double the number of counters that each of the other players has at that time.

At the end of three games, each player has lost one game and each person has 8 counters. At the beginning, Holly had more counters than either of the others. How many did she have at the start?

Question 19

Mary has 62 square blue tiles and a number of square red tiles. All tiles are the same size. She makes a rectangle with red tiles inside and blue tiles on the perimeter. What is the largest number of red tiles she could have used?

Question 20

An isosceles triangle has a horizontal base of length 12 centimetres. It is divided into four equal areas by three parallel lines as shown.

Question illustration

What is the value of x?

$3\sqrt2$
4
4.5
3
$3\sqrt3$