Skip to content / Đến nội dung
ThichHocToan.com

Australian AMC 2016 - Junior

Question 1

The value of $2016\times2$ is
  1. 4026
  2. 4212
  3. 4022
  4. 432
  5. 4032

Question 2

In the diagram, the value of $x$ is

Question illustration
  1. 30
  2. 20
  3. 90
  4. 140
  5. 100

Question 3

Today is Thursday. What day of the week will it be 30 days from today?
  1. Sunday
  2. Monday
  3. Tuesday
  4. Friday
  5. Saturday

Question 4

Today in Berracan, the minimum temperature was $-5^\circ\mathrm C$ and the maximum was $8^\circ\mathrm C$ warmer than this. What was the maximum temperature?
  1. $-3^\circ\mathrm C$
  2. $8^\circ\mathrm C$
  3. $-13^\circ\mathrm C$
  4. $13^\circ\mathrm C$
  5. $3^\circ\mathrm C$

Question 5

What is $25\%$ of $\frac12$?
  1. $\frac18$
  2. $\frac14$
  3. $\frac12$
  4. 2
  5. 1

Question 6

A circular piece of paper is folded in half twice and then a cut is made as shown.

Question illustration

When the piece of paper is unfolded, what shape is the hole in the centre?
  1. Question illustration
  2. Question illustration
  3. Question illustration
  4. Question illustration
  5. Question illustration

Question 7

I used a \$100 note to pay for a \$29 book, a \$16 calculator and a packet of pens for \$8.95. What change did I get?
  1. \$56.05
  2. \$45.05
  3. \$46.05
  4. \$37.05
  5. \$57.05

Question 8

Which of the following numbers is between 0.08 and 0.4?
  1. 0.019
  2. 0.009
  3. 0.109
  4. 0.91
  5. 0.409

Question 9

The cycling road race through the Adelaide Hills started at 11:50 am and the winner took 74 minutes. The winner crossed the finishing line at
  1. 1:24 pm
  2. 12:54 pm
  3. 12:04 pm
  4. 1:04 pm
  5. 12:24 pm

Question 10

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 11

The three squares shown have side lengths 3, 4 and 5. What percentage of the area of the largest square is shaded?

Question illustration
  1. 27%
  2. 28%
  3. 25%
  4. 24%
  5. 20%

Question 12

Jan has three times as many marbles as Liana. If Jan gives 3 of her marbles to Liana, they will have the same number. How many marbles do they have between them?
  1. 18
  2. 6
  3. 8
  4. 12
  5. 16

Question 13

One of the pedestrian walkways in Hyde Park is exactly $3\frac12$ sandstone pavers wide. The pavers are arranged as shown.

The information sign says that 1750 pavers were used to make the walkway. How many pavers were cut in half in the construction of this walkway?

Question illustration
  1. 250
  2. 350
  3. 175
  4. 125
  5. 500

Question 14

On Monday, I planted 10 apple trees in a row. On Tuesday, I planted orange trees along the same row and noticed at the end of the day that no apple tree was next to an apple tree. On Wednesday, I planted peach trees along the same row and noticed at the end of the day that no apple tree was next to an orange tree. What is the smallest number of trees that I could have planted?
  1. 28
  2. 43
  3. 37
  4. 40
  5. 36

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

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 17

Llewellyn uses four of these L-shaped tiles plus one other tile to completely cover a 5 by 5 grid without any overlaps.

Question illustration

Which one of the following could be the other tile?
  1. Question illustration
  2. Question illustration
  3. Question illustration
  4. Question illustration
  5. Question illustration

Question 18

Andy has a number of red, green and blue counters. He places eight counters equally spaced around a circle according to the following rules:

- No two red counters will be next to each other.
- No two green counters will be diagonally opposite each other.
- As few blue counters as possible will be used.

How many blue counters will Andy need to use?

Question illustration
  1. 0
  2. 1
  3. 2
  4. 3
  5. 4

Question 19

In a packet of spaghetti, one-third of the strands of spaghetti are intact, but the rest have each been snapped into two pieces. Of all the pieces of spaghetti from the packet (broken and whole), what is the largest fraction guaranteed to be at least as long as half an unbroken strand?
  1. $\frac25$
  2. $\frac35$
  3. $\frac23$
  4. $\frac12$
  5. $\frac13$

Question 20

Mary has four children of different ages, all under 10, and the product of their ages is 2016. What is the sum of their ages?
  1. 30
  2. 34
  3. 28
  4. 29
  5. 32