Problem 1:

Which of these numbers is the smallest?
(A) 655
(B) 566
(C) 565
(D) 555
(E) 556

Problem 2:

Two pizzas are sliced into quarters. How many slices will there be?
(A) 2
(B) 10
(C) 6
(D) 8
(E) 16

Problem 3:

Join the dots \(P, Q, R\) to form the triangle \(P Q R\).

How many dots lie inside the triangle \(P Q R\) ?
(A) 13
(B) 14
(C) 15
(D) 17
(E) 18

Problem 4:

\(0.3+0.4\) is
(A) 0.07
(B) 0.7
(C) 0.12
(D) 0.1
(E) 7

Problem 5:

Lee's favourite chocolates are 80 c each. He has five dollars to spend. How many of these chocolates can he buy?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Problem 6:

Ten chairs are equally spaced around a round table. They are numbered 1 to 10 in order. Which chair is opposite chair 9 ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Problem 7:

In a piece of music, a note like is worth one beat, is worth half a beat, is worth
2 beats and is worth 4 beats. How many beats are in the following piece of music?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Problem 8:

Phoebe put her hand in her pocket and pulled out 60 cents. How many different ways could this amount be made using \(10 \mathrm{c}, 20 \mathrm{c}\) and 50 c coins?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Problem 9:

Which of these containers is currently holding the most water?

Problem 10:

Which of these shapes has the most axes of symmetry (mirror lines)?

Problem 11:

A sailor coiled a rope on his ship's deck, and some paint was spilled across half of it. What did the rope look like when it was uncoiled?

Problem 12:

If the area of the tangram shown is 64 square centimetres, what is the area in square centimetres of the small square?
(A) 32
(B) 24
(C) 16
(D) 8
(E) 4

Problem 13:

For each batch of 25 biscuits, Jack uses \(2 \frac{1}{2}\) packets of chocolate chips. How many packets does he need if he wants to bake 200 biscuits?
(A) 20
(B) 8
(C) 80
(D) 10
(E) 50

Problem 14:

Which one of the following is correct?
(A) Two even numbers add to an odd number.
(B) An odd number minus an odd number is always odd.
(C) Adding 2 odd numbers and an even number is always odd.
(D) Adding 3 odd numbers is always odd.
(E) An odd number multiplied by an odd number always equals an even number.

Problem 15:

The perimeter of the outer square is 36 cm , and the perimeter of the inner square is 20 cm .
If the four rectangles are all identical, what is the perimeter of the shaded rectangle in centimetres?
(A) 12
(B) 14
(C) 24
(D) 20
(E) 18

Problem 16:

George has a new lock that opens if the four numbers \(1,2,3\) and 4 are pressed once each in the correct order.
If the first number must be larger than the second number, how many combinations are possible?
(A) 10
(B) 12
(C) 15
(D) 18
(E) 20

Problem 17:

A straight cut is made through the hexagon shown to create two new shapes. Which of the following could not be made?
(A) one triangle and one hexagon
(B) two pentagons
(C) two quadrilaterals
(D) one quadrilateral and one pentagon
(E) one triangle and one quadrilateral

Problem 18:

The numbers \(3,9,15,18,24\) and 29 are divided into two groups of 3 numbers and each group is added. The difference between the two sums (totals) of 3 numbers is as small as possible. What is the smallest difference?
(A) 0
(B) 1
(C) 2
(D) 5
(E) 8

Problem 19:

Benny built a magic square using the numbers from 1 to 16 , where the numbers in each row, each column and each diagonal add up to the same total.
What number does he place at the X ?
(A) 16
(B) 15
(C) 17
(D) 11
(E) 14

Problem 20:

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?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

Problem 21:

I have five coloured discs in a pile as shown.
I take the top two discs and put them on the bottom (with the red dise still on top of the blue disc).
Then I again take the top two discs and put them on the bottom.
If I do this until I have made a total of 21 moves, which dise will be on the bottom?

(A) red
(B) blue
(C) green
(D) yellow
(E) orange

Problem 22:

A zoo keeper weighed some of the animals at Melbourne Zoo. He found that the lion weighs 90 kg more than the leopard, and the tiger weighs 50 kg less than the lion. Altogether the three animals weigh 310 kg . How much does the lion weigh?
(A) 180 kg
(B) 150 kg
(C) 140 kg
(D) 130 kg
(E) 100 kg

Problem 23:

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?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

Problem 24:

Jane and Tom are comparing their pocket money. Jane has as many 5c coins as Tom has 10 c coins and as many 10 c coins as Tom has 20 c coins. However, Jane has as many 50c coins as Tom has 5 c coins.
They have no other coins and they find that they each have the same amount of money.
What is the smallest number of coins they each can have?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Problem 25:

A tuckshop has two jars of cordial mixture.
Jar A is \(30 \%\) cordial, while Jar B is \(60 \%\) cordial.
Some of Jar A is mixed with some of Jar B to make 18 litres of \(50 \%\) cordial.
How many litres from Jar A are used?
(A) 9
(B) 12
(C) 4
(D) 3
(E) 6

Problem 26:

Qiang, Rory and Sophia are each wearing a hat with a number on it. Each adds the two numbers on the other two hats, giving totals of 11,17 and 22 . What is the largest number on a hat?

Problem 27:

The number 840 is the 3 -digit number with the most factors. How many factors does it have?

Problem 28:

A class has 2016 matchsticks. Using blobs of modelling clay to join the matches together, they make a long row of cubes. This is how their row starts.

They keep adding cubes to the end of the row until they don't have enough matches left for another cube. How many cubes will they make?

Problem 29:

You have an unlimited supply of five different coloured pop-sticks, and want to make as many different coloured equilateral triangles as possible, using three sticks.
One example is shown here.
Two triangles are not considered different if they are rotations or reflections of each other.
How many different triangles are possible?

Problem 30:

Today my three cousins multiplied their ages together and it came to 2016. This day last year their ages multiplied to 1377 .
When they multiplied their ages together 2 years ago today, what was their answer?

Problem 1:

What is the value of \(7+6+4+3\) ?
(A) 20
(B) 19
(C) 18
(D) 17
(E) 16

Problem 2:

Which shape can make a pyramid if you fold along the dotted lines?

Problem 3:

A square of paper is folded in half to make a triangle, then in half to make a smaller triangle, then in half again to make an even smaller triangle.

How many layers of paper are in the final triangle?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 12

Problem 4:

The year 5 students at my local school were surveyed to find which one of the four teams in the local football competition they followed.

How many more students followed the most popular team than followed the least popular team?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

Problem 5:

This week at my lemonade stand I sold \(\$ 29\) worth of lemonade, but I had spent \(\$ 34\) on lemons and \(\$ 14\) on sugar. My total loss for the week was
(A) \(\$ 1\)
(B) \(\$ 9\)
(C) \(\$ 19\)
(D) \(\$ 21\)
(E) \(\$ 29\)

Problem 6:

A piece of paper is cut out and labelled as shown. It is folded along the dashed lines to form an open box and placed so that the top is open. Which letter is on the bottom of the box?
(A) A
(B) B
(C) C
(D) D
(E) E

Problem 7:

Which of the following gives an odd number?
(A) \(12^2\)
(B) \(141-57\)
(C) \(36 \times 9\)
(D) \(308 \div 7\)
(E) \(\frac{1}{3}\) of 123

Problem 8:

A new block of flats is being built and Trudy is buying the letterbox numbers. The letterboxes are to be labelled from 190 to 212 . How many zeros will she need to buy?
(A) 22
(B) 13
(C) 12
(D) 10
(E) 4

Problem 9:

This \(4 \times 4\) square grid can be covered by three shapes made from \(1 \times 1\) squares. None of the shapes overlap.

If two of the shapes are

then the third shape is

Problem 10:

Given that \(\frac{1001}{77}=13\), what is the value of \(\frac{100.1}{770} ?\)
(A) 0.13
(B) 1.3
(C) 13
(D) 130
(E) 1300

Problem 11:

These two squares, each with a side length of 10 cm , overlap as shown in the diagram. The shape of the overlap is also a square which has an area of 16 square centimetres. In centimetres, what is the perimeter of the combined shape?
(A) 40
(B) 56
(C) 64
(D) 80
(E) 92

Problem 12:

Six boys looked in the fridge and found this much leftover pizza. They shared the leftover pizza equally. How much of the whole pizza did each boy get?
(A) \(\frac{1}{12}\)
(B) \(\frac{1}{8}\)
(C) \(\frac{1}{6}\)
(D) \(\frac{1}{4}\)
(E) \(\frac{1}{3}\)

Problem 13:

Which of the shaded areas below is the largest?

(A) A
(B) B
(C) C
(D) D
(E) E

Problem 14:

A map, 40 cm wide and 20 cm high, is folded along the dashed lines indicated to form a \(10 \mathrm{~cm} \times 10 \mathrm{~cm}\) square so that it just fits in its envelope. It is then pinned to a notice board.

Which one of the following could be the pattern of pinholes on the map?

Problem 15:

Sally thinks of a number, multiplies it by 2 , adds 2 , divides by 2 and then subtracts 2 . Her answer is 2 . What was her original number?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Problem 16:

The paint colour 'Roebourne Red' is made by mixing 2 parts yellow, 5 parts red and 1 part black.
If a batch of paint was made using 3 litres of yellow, how many litres of paint would be in the whole batch?
(A) 6
(B) 8
(C) 9
(D) 10 ,
(E) 12

Problem 17:

A square of paper has its corners folded in as shown to make a smaller square with an internal square, as shown on the right. What is the area of this internal square?

(A) \(4 \mathrm{~cm}^2\)
(B) \(9 \mathrm{~cm}^2\)
(C) \(16 \mathrm{~cm}^2\)
(D) \(49 \mathrm{~cm}^2\)
(E) \(58 \mathrm{~cm}^2\)

Problem 18:

Ancient Egyptian mathematicians used fractions but only with a numerator of 1 , such as \(\frac{1}{2}\) or \(\frac{1}{7}\) or \(\frac{1}{14}\). They made other fractions by adding these fractions together. For example, \(\frac{3}{4}\) was written as \(\frac{1}{2}+\frac{1}{4}\). Which of the following is an Ancient Egyptian way of writing \(\frac{11}{16}\) ?
(A) \(\frac{1}{2}+\frac{1}{4}+\frac{1}{10}\)
(B) \(\frac{1}{2}+\frac{1}{8}+\frac{1}{16}\)
(C) \(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
(D) \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
(E) \(\frac{1}{3}+\frac{1}{6}+\frac{1}{2}\)

Problem 19:

This symmetrical star is made up of two overlapping equilateral triangles of the same size. The area of the star is 60 square centimetres. What is the area of the shaded region in square centimetres?
(A) 30
(B) 36
(C) 42
(D) 45
(E) 48

Problem 20:

In this correctly worked addition, \(P, Q, R\) and \(S\) represent different digits, and all seven digits are different. What is the sum of \(P, Q, R\) and \(S\) ?
(A) 23
(B) 22
(C) 18
(D) 16
(E) 14

Problem 21:

In a competition between four people, Sally scored twice as many points as Brian and 30 points more than Corrie. Donna scored 50 points more than Brian. Which of the following statements is definitely true?
(A) Sally won the competition.
(B) Brian came last in the competition.
(C) Donna won the competition.
(D) Corrie beat Brian.
(E) Sally and Donna together scored more than Brian and Corrie.

Problem 22:

A plane was travelling at an altitude of 4500 metres for 20 minutes. It then climbed at a rate of 500 metres per minute for 5 minutes before descending at 350 metres per minute for 8 minutes. Which of the following graphs best describes the altitude of the plane over this time?

Problem 23:

Mrs Graham wants to fill her swimming pool for the summer. She knows that if she uses the backyard hose it will take 12 hours, or if she uses the frontyard hose it will take 4 hours. How long will it take if she uses both hoses together?
(A) 3 hours
(B) 2.5 hours
(C) 2 hours
(D) 1.5 hours
(E) 1 hour

Problem 24:

Four soccer teams played each other four times in a season of competition. Each winning team was awarded 3 points. Teams that had a draw were awarded 1 point each, and losing teams were awarded no points. The season ended with Kangaroos on 21 points, Kookaburras on 17 points, Koalas on 16 points and Crocodiles on 12 points. How many games ended in a draw?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3

Problem 25:

Five different whole numbers, chosen from the numbers from 1 to 30 , add up to 30 . What is the greatest possible value of the largest of these numbers?
(A) 6
(B) 10
(C) 15
(D) 20
(E) 26

Problem 26:

A 3 by 5 grid of dots is set out as shown. How many straight line segments can be drawn that join two of these dots and pass through exactly one other dot?

Problem 27:

A cube is made up of \(1 \mathrm{~cm} \times 1 \mathrm{~cm} \times 1 \mathrm{~cm}\) blocks and measures \(12 \mathrm{~cm} \times 12 \mathrm{~cm} \times 12 \mathrm{~cm}\). Sharyn is using the same set of blocks to make a set of stairs.
The picture shows how she started, making a set of stairs 4 blocks high, 4 blocks from front to back and 5 blocks wide.
Her finished set of stairs will use all the blocks and be 8 blocks high and 8 blocks from front to back. How many blocks wide will they be?

Problem 28:

Three whole numbers add up to 149 and multiply to give 987 . What is the largest of the three numbers?

Problem 29:

Which three-digit number is 11 times the sum of its digits?

Problem 30:

How many three-digit numbers are there in which one of the digits is the sum of the other two?

Problem 1:

What fraction of this rectangle is shaded?

(A) one-fifth
(B) two-fifths
(C) two-thirds
(D) one-third
(E) three-fifths

Problem 2:

Which of the following numbers is closest to zero?
(A) 0.03
(B) 0.048
(C) 0.009
(D) 0.005
(E) 0.02

Problem 3:

A 737 passenger aircraft has 3 seats on each side of a centre aisle in each row. It is designed to carry 150 passengers. How many rows of seats does it have?
(A) 50
(B) 37
(C) 33
(D) 32
(E) 25

Problem 4:

Alice has two 50c coins, three 20c coins and eight 5c coins. David has four 20c coins and six 10c coins. How much more money does Alice have than David?
(A) 40 c
(B) 60 c
(C) 80 c
(D) \(\$ 1.40\)
(E) \(\$ 2.00\)

Problem 5:

What is the difference between the largest and smallest 5-digit numbers which can be made from rearranging the 5 digit cards below?

(A) 41967
(B) 41976
(C) 44444
(D) 42024
(E) 41076

Problem 6:

At the supermarket, a regular packet of chips is 75 g . A packet of chips on special is advertised at one-third extra. How many grams does the special packet have?
(A) 50
(B) 78
(C) 100
(D) 125
(E) 150

Problem 7:

How many triangles are in the following picture?

(A) 9
(B) 10
(C) 13
(D) 14
(E) 17

Problem 8:

Jan doubles a number then adds two. Then she halves that number and subtracts two. Her final answer is six. What was her original number?
(A) 1
(B) 6
(C) 7
(D) 14
(E) 16

Problem 9:

On the number line, where should the fraction \(\frac{1}{3}\) be placed?

(A) between 0 and 0.3
(B) between 0.3 and 0.4
(C) between 0.4 and 0.7
(D) between 0.7 and 0.8
(E) between 0.8 and 1

Problem 10:

Each triangle in the diagram is equilateral. What fraction of the largest triangle is shaded?

(A) \(\frac{1}{4}\)
(B) \(\frac{15}{64}\)
(C) \(\frac{1}{3}\)
(D) \(\frac{3}{16}\)
(E) \(\frac{7}{32}\)

Problem 11:

In the number sentence below, three of the digits are missing, as shown by the boxes. If the number sentence is correct, what is the sum of the three missing digits?

(A) 7
(B) 8
(C) 10
(D) 11
(E) 17

Problem 12:

In the square shown, the length of the diagonal is 8 cm . What is the area of the square?

(A) \(28 \mathrm{~cm}^2\)
(B) \(32 \mathrm{~cm}^2\)
(C) \(49 \mathrm{~cm}^2\)
(D) \(64 \mathrm{~cm}^2\)
(E) \(81 \mathrm{~cm}^2\)

Problem 13:

A bus leaves a bus stop at \(10: 35 \mathrm{am}\) and then stops at 4 other bus stops. If neighbouring stops are 10 minutes apart and the bus remains at each stop for 3 minutes, at what time does the bus arrive at the last stop?

(A) 11:11 am
(B) 11:14 am
(C) 11:21 am
(D)11:24 am
(E) 11:27 am

Problem 14:

A muffin recipe which makes 12 muffins requires \(\frac{2}{3}\) of a cup of milk. How many muffins can be made using 18 cups of milk?
(A) 90
(B) 108
(C) 144
(D) 216
(E) 324

Problem 15:

Two identical equilateral triangles, each with an area equal to \(36 \mathrm{~cm}^2\), are placed one on top of the other so that the overlap forms a regular hexagon.

What is the area of the hexagon?
(A) \(18 \mathrm{~cm}^2\)
(B) \(20 \mathrm{~cm}^2\)
(C) \(24 \mathrm{~cm}^2\)
(D) \(30 \mathrm{~cm}^2\)
(E) \(36 \mathrm{~cm}^2\)

Problem 16:

A ten-sided dice (numbers \(0-9) \) and a six-sided dice (numbers \(1-6) \) are thrown at the same time. What is the chance of displaying a total of 6 ?
(A) one in ten
(B) one in eight
(C) one in six
(D) one in five
(E) one in two

Problem 17:

Each of the faces of 2 discs has a different whole number on it. The numbers on two of the faces are shown.

If the discs are tossed, the possible sums of the numbers showing are \(10,11,12\) and 13 . What is the product of the two numbers that are on the other side of these two discs?
(A) 24
(B) 25
(C) 30
(D) 32
(E) 35

Problem 18:

A school builds a raised vegetable patch in its garden by joining four panels to form an open-ended prism and filling it with soil. Each of the thin plastic panels has sides of length 40 cm and 80 cm . Jessie wants to stand the panels on their long side and Tom wants to stand them on their short side as shown.

Which statement is true?
(A) It is impossible to calculate the volume of soil needed to fill the vegetable patch.
(B) It is impossible to compare the volumes of soil needed to fill the vegetable patch.
(C) Both vegetable patches need the same volume of soil.
(D) Jessie's vegetable patch needs more soil than Tom's.
(E) Tom's vegetable patch needs more soil than Jessie's.

Problem 19:

Aditya's dad is one year older than his mum and next year the product of his parents' ages will be over 1000 for the first time. What is the product of their ages now?
(A) 930
(B) 961
(C) 992
(D) 995
(E) 999

Problem 20:

Jake and Joe wanted to buy the same magazine. Jake needed \(\$ 2.80\) more to buy it, while Joe needed \(\$ 2.60\) more. So they put their money together and bought the magazine. They had \(\$ 2.60\) left. How much was the magazine?
(A) \(\$ 10\)
(B) \(\$ 9\)
(C) \(\$ 8\)
(D) \(\$ 7\)
(E) \(\$ 6\)

Problem 21:

There is a shaded square inside a rectangle as shown. From \(A\) to \(B\) is 6 cm and from \(C\) to \(D\) is 8 cm . What is the perimeter of the large rectangle?

(A) 28 cm
(B) 27 cm
(C) 26 cm
(D) 25 cm
(E) 24 cm

Problem 22:

Karen's class and Jacqui's class are sharing some apples donated by a local farmer and everyone in each classroom will have 6 apples. If Karen's class shared all the apples, each student would have 10 apples. If Jacqui's class shared all the apples, how many apples would each student in the class have?
(A) 5
(B) 8
(C) 10
(D) 12
(E) 15

Problem 23:

Eight \(1 \times 1\) square tiles are laid to form a shape as shown.

Two more \(1 \times 1\) tiles are added, so that at least one side of each new tile is shared with a side of the original shape. Several different perimeter lengths are now possible. What is the sum of the shortest and longest possible perimeters of the modified shape?
(A) 28
(B) 30
(C) 32
(D) 34
(E) 36

Problem 24:

On a special cubic dice the numbers \(1,2,3,4,5\) and 6 are on the faces: 1 is on the face opposite 2,3 is on the face opposite 4 , and 5 is on the face opposite 6 .

Each vertex is given a vertex number, which is the sum of the numbers on the three faces that form the vertex. If I subtract the smallest vertex number from the largest vertex number, what number will I get?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 7

Problem 25:

A number is formed by writing the numbers 1 to 30 in order as shown.

\[
12345678910111213 \ldots \ldots . . . .2930
\]

Simeon removed 45 of these 51 digits leaving 6 in their original order to make the largest 6-digit number possible. What is the sum of the digits of this number?
(A) 33
(B) 38
(C) 41
(D) 43
(E) 51

Problem 26:

Dried dog food is available in three sizes: 1 kg bags, which cost \(\$ 6\); 3 kg bags, which cost \(\$ 15\); and 8 kg bags, which cost \(\$ 25\). What is the smallest number of bags you can buy such that the average price per kilogram is exactly \(\$ 4\) ?

Problem 27:

In how many ways can three different numbers be selected from the numbers 1 to 12 , so that their sum can be exactly divided by 3 ?

Problem 28:

Adam, Barney and Joe carry 999 books out of the library. Adam works for 3 hours, Barney works for 4 hours and Joe works for 5 hours. They work at different speeds, with Adam carrying 5 books for every 3 books Barney carries and every 2 books Joe carries. How many books did Adam carry?

Problem 29:

Find the largest 3-digit number, with no two digits the same and with its digits in ascending order, which when multiplied by 5 has its digits in descending order?

Problem 30:

A hockey game between two teams is 'relatively close' if the number of goals scored by the two teams never differ by more than two. In how many ways can the first 12 goals of a game be scored if the game is 'relatively close'?