Australian AMC 2019 - Senior

Question 1

What is the value of $201\times9$?

189
1809
1818
2001
2019

Question 2

What is the area of the shaded triangle?

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$8\text{ m}^2$
$12\text{ m}^2$
$14\text{ m}^2$
$20\text{ m}^2$
$24\text{ m}^2$

Question 3

What is $19\%$ of \$20?

\$20.19
\$1.90
\$0.19
\$3.80
\$0.38

Question 4

What is the value of $z$?

Question illustration

Question 6

Let $f(x)=3x^2-2x$. Then $f(-2)=$

-32
-8
16
32
40

Question 7

This kite has angles $\theta,\theta,\theta$ and $\frac\theta3$.
What is the size of the angle $\theta$?

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$120^\circ$
$105^\circ$
$90^\circ$
$112^\circ$
$108^\circ$

Consider the undulating number sequence

$1,4,7,4,1,4,7,4,1,4,\ldots,$

which repeats every four terms. The running total of the first 3 terms is 12. The running total of the first 7 terms is 28.
Which one of the following is also a running total of this sequence?

Question 9

Mia walks at 1.5 metres per second. Her friend Crystal walks at 2 metres per second. They walk in opposite directions around their favourite bush track, starting together from the same point. They first meet again after 20 minutes.
How long, in kilometres, is the track?

Question 10

$\dfrac{1^1+2^2+3^3+4^4}{1^1+2^2+3^3}=$

$2^3$
$3^2$
11
$4^3$
259

Question 11

The 5-digit number $P679Q$ is divisible by 72. The digit $P$ is equal to

Question 12

The altitude of a right-angled triangle divides the hypotenuse into lengths of 4 and 6. What is the area of the triangle?

Question illustration

$10\sqrt6$
24
25
12
$6\sqrt{10}$

Question 13

In a box of apples, $\frac37$ of the apples are red and the rest are green. Five more green apples are added to the box. Now $\frac58$ of the apples are green.
How many apples are there now in the box?

Question 14

Which number exceeds its square by the greatest possible amount?

$\frac12$
$\frac23$
$\frac14$
$\frac34$
$\frac{\sqrt2}2$

Question 15

A regular nonagram is a nine-pointed star drawn as shown. What is the angle at each of the nine points?

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$100^\circ$
$110^\circ$
$120^\circ$
$130^\circ$
$140^\circ$

Question 16

Two sequences are constructed, each with 900 terms:

$5,8,11,14,\ldots$ (increasing by 3)

$3,7,11,15,\ldots$ (increasing by 4)

How many terms do these two sequences have in common?

Question 17

A circular steel gateway surrounding a rectangular gate is designed as shown. The total height of the gateway is divided into 10 equal intervals by equally-spaced horizontal bars.
The rectangular gate is what fraction of the area of the entire circular gateway?

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