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Question bank AMC AUSTRALIA 2016

Exam papers

150 questions

Question 1

What is the value of $20\times16$?
  1. 320
  2. 140
  3. 2016
  4. 32
  5. 800

Question 2

In the figure, the shaded region is what fraction of the circle?

Question illustration
  1. $\frac1{20}$
  2. $\frac1{10}$
  3. $\frac12$
  4. $\frac1{60}$
  5. $\frac1{40}$

Question 3

The cycling road race through the Adelaide Hills started at 11:15 am and the winner finished at 2:09 pm the same day. The winner’s time in minutes was
  1. 135
  2. 174
  3. 164
  4. 294
  5. 186

Question 4

The fraction $\frac{720163}{2016}$ is
  1. between 0 and 1
  2. between 1 and 10
  3. between 10 and 100
  4. between 100 and 1000
  5. greater than 1000

Question 5

What is the value of $(1\div2)\div(3\div4)$?
  1. $\frac23$
  2. $\frac32$
  3. $\frac38$
  4. $\frac16$
  5. $\frac1{24}$

Question 6

0.75% of a number is 6. The number is
  1. 800
  2. 300
  3. 1200
  4. 400
  5. 100

Question 7

In the expression below, the letters $A,B,C,D$ and $E$ represent the numbers 1, 2, 3, 4 and 5 in some order.

$$A\times B+C\times D+E$$

What is the largest possible value of the expression?
  1. 24
  2. 27
  3. 26
  4. 51
  5. 25

Question 8

In each of these squares, the marked length is 1 unit. Which of the squares would have the greatest perimeter?

Question illustration
  1. P
  2. Q
  3. R
  4. S
  5. all are the same

Question 9

On a clock face, a line is drawn between 9 and 3 and another between 12 and 8. What is the acute angle between these lines?

Question illustration
  1. $45^\circ$
  2. $60^\circ$
  3. $50^\circ$
  4. $30^\circ$
  5. $22.5^\circ$

Question 10

There are 3 blue pens, 4 red pens and 5 yellow pens in a box. Without looking, I take pens from the box one by one. How many pens do I need to take from the box to be certain that I have at least one pen of each colour?
  1. 8
  2. 9
  3. 10
  4. 11
  5. 12

Question 11

In the diagram, the value of $x$ is

Question illustration
  1. 120
  2. 108
  3. 105
  4. 135
  5. 112.5

Question 12

How far is it from $A$ to $B$ measured in a straight line?

Question illustration
  1. 20
  2. 28
  3. $10+9\sqrt2$
  4. $8+9\sqrt2$
  5. 16

Question 13

A circle of radius 1 metre is inscribed inside a semicircle of radius 2 metres. What is the area in square metres of the semicircle not covered by the circle?

Question illustration
  1. $2\pi$
  2. $\pi-1$
  3. 2
  4. $2\pi-1$
  5. $\pi$

Question 14

The value of $n$ for which $4^{n+1}=2^{10}$ is
  1. 9
  2. 8
  3. 4
  4. 10
  5. 2

Question 15

Adrienne, Betty and Cathy were the only three competitors participating in a series of athletic events. In each event, the winner gets 3 points, second gets 2 points and third gets 1 point. After the events, Adrienne has 8 points, Betty has 11 points and Cathy has 5 points. In how many events did Adrienne come second?
  1. 0
  2. 1
  3. 2
  4. 3
  5. 4

Question 16

What is the smallest number $N$ for which $\frac{2016}{N}$ is a perfect square?
  1. 14
  2. 2
  3. 56
  4. 12
  5. 7

Question 17

Five people are sitting around a circle. Some always tell the truth, whilst the others always lie. Each person claims to be sitting between two liars. How many of them are telling the truth?
  1. 0
  2. 1
  3. 2
  4. 3
  5. 4

Question 18

A cylindrical glass of (inside) diameter 6 cm and height 11 cm is filled and then tilted to a $45^\circ$ angle so that some water overflows. How much water is left in it?

Question illustration
  1. $48\pi$ mL
  2. $45\pi$ mL
  3. $66\pi$ mL
  4. $72\pi$ mL
  5. $63\pi$ mL

Question 19

Ten students sit a test consisting of 20 questions. Two students get 8 questions correct and one student gets 9 questions correct. The remaining seven students all get at least 10 questions correct and the average number of questions answered correctly by these seven students is an integer. If the average number of questions answered correctly by all ten students is also an integer, then that integer is
  1. 10
  2. 11
  3. 12
  4. 13
  5. 14

Question 20

This pedal-powered water pump is made from bicycle parts.

A 30-tooth gear on the pedals has a chain to a 15-tooth gear. On the same axle as the 15-tooth gear is a 32-tooth gear that drives a chain to a 40-tooth gear on the pump.

For every 100 complete revolutions of the pedals, how many times does the gear on the pump turn?

Question illustration
  1. 160
  2. 250
  3. 107
  4. 93
  5. $37\frac12$