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Australian AMC 2018 - Intermediate

Question 1

The value of $\frac{2018-18}{1000}$ is
  1. 0.02
  2. 0.1
  3. 1
  4. 2
  5. 2000

Question 2

What value is indicated on this charisma-meter?

Question illustration
  1. 36.65
  2. 37.65
  3. 38.65
  4. 37.15
  5. 37.3

Question 3

What is the difference between the sum and the product of 4 and 5?
  1. 1
  2. 8
  3. 9
  4. 11
  5. 20

Question 4

In the diagram, $PQRS$ is a square. What is the size of $\angle XPY$?

Question illustration
  1. $25^\circ$
  2. $30^\circ$
  3. $35^\circ$
  4. $40^\circ$
  5. $45^\circ$

Question 5

Which of the following is not a whole number?
  1. $350\div2$
  2. $350\div7$
  3. $350\div5$
  4. $350\div25$
  5. $350\div20$

Question 6

Nora, Anne, Warren and Andrew bought plastic capital letters to spell each of their names on their birthday cakes. Their birthdays are on different dates, so they planned to reuse letters on different cakes.

What is the smallest number of letters they needed?

Question illustration
  1. 8
  2. 9
  3. 10
  4. 11
  5. 12

Question 7

In years, 2018 days is closest to
  1. 4.5 years
  2. 5 years
  3. 5.5 years
  4. 6 years
  5. 6.5 years

Question 8

Two paths from $A$ to $C$ are pictured.

The stepped path consists of horizontal and vertical segments, whereas the dashed path is straight.

What is the difference in length between the two paths?

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

Question 9

The value of $9\times1.2345-9\times0.1234$ is
  1. 9.9999
  2. 9
  3. 9.0909
  4. 10.909
  5. 11.1111

Question 10

What fraction of this regular hexagon is shaded?

Question illustration
  1. $\frac12$
  2. $\frac23$
  3. $\frac34$
  4. $\frac35$
  5. $\frac45$

Question 11

The cost of feeding four dogs for three days is \$60. Using the same food costs per dog per day, what would be the cost of feeding seven dogs for seven days?
  1. \$140
  2. \$200
  3. \$245
  4. \$350
  5. \$420

Question 12

In a certain year there were exactly four Tuesdays and exactly four Fridays in the month of December. What day of the week was 31 December?
  1. Monday
  2. Wednesday
  3. Thursday
  4. Friday
  5. Saturday

Question 13

Fill in this diagram so that each of the rows, columns and diagonals adds to 18.

What is the sum of all the corner numbers?

Question illustration
  1. 20
  2. 22
  3. 23
  4. 24
  5. 25

Question 14

The sum of 4 consecutive integers is $t$.

In terms of $t$, the smallest of the four integers is
  1. $\frac{t-10}{4}$
  2. $\frac{t-2}{4}$
  3. $\frac{t-3}{4}$
  4. $\frac{t-4}{4}$
  5. $\frac{t-6}{4}$

Question 15

A 3-dimensional object is formed by gluing six identical cubes together. Four of the diagrams below show this object viewed from different angles, but one diagram shows a different object. Which diagram shows the different object?

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

Question 16

In the circle shown, $C$ is the centre and $A,B,D,E$ all lie on the circumference.

Reflex $\angle BCD=200^\circ$, $\angle DCA=x^\circ$ and $\angle BCA=3x^\circ$ as shown.

The ratio of $\angle DAC:\angle BAC$ is

Question illustration
  1. 3 : 1
  2. 5 : 2
  3. 8 : 3
  4. 7 : 4
  5. 7 : 3

Question 17

Allan and Zarwa are playing a game tossing a coin. Allan wins as soon as a head is tossed and Zarwa wins if two tails are tossed. The probability that Allan wins is
  1. $\frac12$
  2. $\frac35$
  3. $\frac58$
  4. $\frac23$
  5. $\frac34$

Question 18

In this expression
$$\square\frac13\quad\square\frac14\quad\square\frac15\quad\square\frac16\quad\square\frac17$$
we place either a plus sign or a minus sign in each box so that the result is the smallest positive number possible. The result is
  1. between $0$ and $\frac1{100}$
  2. between $\frac1{100}$ and $\frac1{50}$
  3. between $\frac1{50}$ and $\frac1{20}$
  4. between $\frac1{20}$ and $\frac1{10}$
  5. between $\frac1{10}$ and $1$

Question 19

A town is laid out in a square of side 1 kilometre, with six straight roads as shown.

Each day the postman must walk the full length of every road at least once, starting wherever he likes and ending wherever he likes.

How long is the shortest route he can take, in kilometres?

Question illustration
  1. $4+\frac{\sqrt2}{2}$
  2. $4+\sqrt2$
  3. $4+2\sqrt2$
  4. $4+3\sqrt2$
  5. $5+2\sqrt2$

Question 20

A rectangle with integer sides has a diagonal stripe which starts 1 unit from the diagonal corners, as in the diagram.

The area of the stripe is exactly half of the area of the rectangle.

What is the perimeter of this rectangle?

Question illustration
  1. 14
  2. 16
  3. 18
  4. 20
  5. 22