Skip to content / Đến nội dung
ThichHocToan.com

Australian AMC 2017 - Junior

Question 1

The value of 2 + 0 + 1 + 7 is
  1. 10
  2. 19
  3. 37
  4. 208
  5. 2017

Question 2

What is the value of x in the diagram?

Question illustration
  1. 20
  2. 70
  3. 80
  4. 110
  5. 160

Question 3

This rectangle is 3.2 m wide and 3 m tall. Its area is

Question illustration
  1. 9.6 m²
  2. 15 m²
  3. 90.6 m²
  4. 9.2 m²
  5. 6.5 m²

Question 4

Starting with 13, and counting by fives, you count 13, 18, 23, and so on. Which one of the following numbers will be one of the numbers you count?
  1. 47
  2. 48
  3. 49
  4. 50
  5. 51

Question 5

What fraction of these circles are shaded?

Question illustration
  1. 1/2
  2. 1/3
  3. 2/3
  4. 3/4
  5. 9/16

Question 6

Of the following, which digit could be put in the box to make the three-digit number 1□7 divisible by 3?

Question illustration
  1. 1
  2. 3
  3. 6
  4. 8
  5. 9

Question 7

A pump runs for 150 minutes, using 8 litres of biodiesel. For how many hours can it run with 32 litres of biodiesel?
  1. 6
  2. 7
  3. 8
  4. 10
  5. 12

Question 8

Jonah returned from the shop with a bag carrying 780 g of fish, 1.35 kg of vegetables, and 680 g of fruit for his mother. The bag itself weighed 150 g. The total weight, in kilograms, that Jonah carried was
  1. 1.745
  2. 2
  3. 2.81
  4. 2.96
  5. 3

Question 10

Which one of the following numbers could be put in the box to make the fraction (□ + 3)/6 between 7 and 8?

Question illustration
  1. 47
  2. 25
  3. 32
  4. 37
  5. 41

Question 11

Alice is playing with words. At each tick of her grandfather’s clock she swaps two letters. What is the smallest number of clock ticks during which she can change WORDS to SWORD?
  1. 3
  2. 4
  3. 6
  4. 7
  5. 8

Question 12

This pinwheel star is formed by rotating a right-angled triangle around one of its corners. What is the angle at each of the nine tips that are marked with dots?

Question illustration
  1. 30°
  2. 40°
  3. 45°
  4. 50°
  5. 60°

Question 13

I have twelve paint tins each capable of holding twelve litres. Half of them are half full. A third of them are a third full. The rest are one-sixth full. How many litres of paint do I have in total?
  1. 48
  2. 50
  3. 52
  4. 54
  5. 56

Question 14

How many ways are there of placing a single 3 × 1 rectangle on this grid so that it completely covers three grid squares?

Question illustration
  1. 34
  2. 28
  3. 56
  4. 40
  5. 10

Question 15

The time 2017 minutes after 10 am on Tuesday is closest to
  1. 7.30 pm Tuesday
  2. 7.30 am Wednesday
  3. 7.30 pm Wednesday
  4. 7.30 am Thursday
  5. 7.30 pm Thursday

Question 16

The bottom and left side of this triangle are divided into 4 equal parts by the diagonal lines. What fraction of the large triangle is shaded?

Question illustration
  1. 5/8
  2. 1/2
  3. 3/4
  4. 2/3
  5. 3/5

Question 17

Each of the fractions 4/n, 5/n, 7/n is in its simplest form. Which of the following could be the value of n?
  1. 24
  2. 25
  3. 26
  4. 27
  5. 28

Question 18

The whole numbers from 1 to 7 are to be placed once each in the seven circles. In each of the three triangles drawn, the sum of the three numbers is the same. Two numbers are given. What is X + Y?

Question illustration
  1. 5
  2. 6
  3. 7
  4. 8
  5. 9

Question 19

Farhad, Greg and Huong were dismantling their marble madness machine and had 2017 marbles to share. They split them so that Farhad had exactly twice as many as Greg, and Greg had twice as many as Huong, with as few left over as possible. How many marbles were in Farhad’s share?
  1. 1008
  2. 504
  3. 288
  4. 1344
  5. 1152

Question 20

Whole numbers greater than 1 are arranged in a table in the pattern shown. In which column will the number 501 be found?

Editable source table:

| A | B | C | D | E |
| --- | --- | --- | --- | --- |
| | | 2 | 3 | 4 |
| 5 | 6 | 7 | | |
| | | 8 | 9 | 10 |
| 11 | 12 | 13 | | |
| | | 14 | 15 | 16 |
| 17 | 18 | 19 | | |
| | ⋮ | | ⋮ | |

Question illustration
  1. A
  2. B
  3. C
  4. D
  5. E