Team round 1

This round will last for approximately 90 minutes – there is no break!

There are 16 questions of varying difficulty.

Each question has a time limit in which to complete it.

For each question that is answered fully you get 10 marks.

(Note: Some questions have more than one part to the answer so it may be possible to gain some of the marks if you don’t answer the whole question)

Only answers are required – it is not necessary to show any working out.

Once the time limit is up you must hand in the correct piece of white paper with the answer filled in where indicated.

You have 17 answer sheets – one for each question and one for the trial question.

Each answer sheet also gives the question

Each team also has 6 sheets of pink paper - each is an opportunity to gain bonus marks.

If you have answered a question within the first 90 seconds you can write your answer on the pink paper and then hold this paper up to be collected.

If you have answered the question correctly you will gain bonus marks equal to the time limit allowed for that question.

But remember – you only have six of these attempts for bonus marks.

You now have 30 seconds left

A whistle will be blown after 90 seconds to indicate that no more bonus answers will be accepted.

IMPORTANT: You MUST write down the question number on your pink sheet.

You now have 30 seconds left

Are there any questions?

You now have 30 seconds left

Trial question – You have 2 minutes for this question.

DO NOT use a bonus sheet.

Trial question.

a and b are prime numbers If 5a + 9b = 103, find a.

You now have 30 seconds left

We will now start the actual questions.

Remember - bonus marks if you submit a correct answer on the pink sheet within 90 seconds.

You have 4 minutes for question 1.

Question 1

(4 minutes) If the 13-digit number 123432N234321 is divisible by 3, what is the product of all possible values of N?

You now have 30 seconds left

Please hand in your answer.

You have 7 minutes for question 2.

Question 2

(7 minutes) On a circular track there are two zombies, George and Sam, shuffling along at constant speeds.

When they go in opposite directions, they meet every 10 minutes.

When they go in the same direction George catches up with Sam every 50 minutes.

Find the speed of each zombie in

centimetres per second

if the circular track is 120 metres long.

You now have 30 seconds left

Please hand in your answer.

You have 6 minutes for question 3.

Question 3

(6 minutes) What is the next number in each sequence?

(a) 1 (b) 23 (c) 6 8 28 8 11 38 11 69 49 15 88 62 20 96 70 26 101 77 33 What is the square root of the mean of these next numbers?

(Note: For this question you can get marks for each part you get correct even if you are unable to answer the whole question. )

You now have 30 seconds left

Please hand in your answer.

You have 5 minutes for question 4.

Question 4

(5 minutes) A triangle has sides of length 15 cm, 20 cm and 25 cm, with the 20 cm side being horizontal.

A square is inscribed in the triangle such that one side of the square is also horizontal.

What is the area of the square?

You now have 30 seconds left

Please hand in your answer.

You have 7 minutes for question 5.

Question 5

(7 minutes) My DAD was always listening to Iron Maiden in his youth.

He HAD A HI-FI but always used to listen to it at full volume.

Now he needs a hearing AID.

If

DAD + HAD + A = HIFI

and each letter represents a different digit, what is the value of AID?

You now have 30 seconds left

Please hand in your answer.

You have 4 minutes for question 6.

Question 6

(4 minutes) Two concentric circles have diameters of 10 cm and 20 cm.

What is the length of the longest straight line that can be drawn between them?

(Leave your answer as a square root)

You now have 30 seconds left

Please hand in your answer.

You have 6 minutes for question 7.

Question 7

(6 minutes) Sylvia the Slug crawls downhill at 30 metres per hour, on the level at 24 metres per hour, and uphill at 20 metres per hour.

Sylvia takes 3 1 / 2 hours to travel directly between two tree stumps.

The return journey takes 4 hours and 15 minutes.

Find the distance between the two tree stumps.

You now have 30 seconds left

Please hand in your answer.

You have 5 minutes for question 8.

Question 8

(5 minutes) I think of a 2-digit number.

I reverse the digits to get a second number.

The sum of these two numbers is a factor of the product of these two numbers.

What is the smallest number I can be thinking of?

You now have 30 seconds left

Please hand in your answer.

You have 6 minutes for question 9.

Question 9

(6 minutes) Running Rabbit’s great grandmother Scratching Bear only gave birth to daughters.

Each of her daughters gave birth to only sons – each having as many sons as they had sisters.

Then each of her grandsons had as many daughters as he had brothers.

The total number of daughters, grandsons and great-granddaughters was the same as Scratching Bear’s age.

If Scratching Bear is older than 50 but younger than 100, (a) (b) how many sisters does Running Rabbit have, how old is Scratching Bear?

You now have 30 seconds left

Please hand in your answer.

You have 5 minutes for question 10.

Question 10

(5 minutes) 123 is a number in modulo 5.

123 is a further number but in modulo 4.

What is the product of these two numbers in modulo 9?

You now have 30 seconds left

Please hand in your answer.

You have 6 minutes for question 11.

Question 11

(6 minutes) Harvey the Head Collector bought some heads on E-bay.

A woman’s head costs $25, a man’s head costs $20 and a dog’s head costs $4.

If Harvey bought 15 heads for $240, how many men’s heads did he buy?

You now have 30 seconds left

Please hand in your answer.

You have 7 minutes for Question 12.

Question 12

(7 minutes) In the diagram we have a cuboid where AB = AE = 1 / 2 BC.

If the volume of the tetrahedron ACFH is 144 cm 3 find the total surface area of the cuboid.

You now have 30 seconds left

Please hand in your answer.

You have 6 minutes for Question 13.

Question 13

(6 minutes) 40 animals go on holiday to Egypt.

The animals are either giraffes, elephants or zebras and half of the animals are female.

There are twice as many elephants as there are female zebras.

The probability of a giraffe being male is twice the probability of a zebra being male.

If there are 8 male elephants and 10 male giraffes, how many female elephants are there?

You now have 30 seconds left

Please hand in your answer.

You have 7 minutes for question 14.

Question 14

(7 minutes) The ruler of the Wors (an extremely important person in mathematics) is thinking of a positive integer less than 100.

His number is not a multiple of the square of any prime number.

The sum of its digits is not a factor of 12.

One of the digits is a multiple of one more than the other digit.

10 less than the number or 9 more than the number is a prime number.

The number is not 2 more or 2 less than a square number.

The number is not prime.

What is the number?

You now have 30 seconds left

Please hand in your answer.

You have 5 minutes for Question 15.

Question 15

(5 minutes) Charlie, Wing and Petra were discussing how they had each done in a training test for SEAMC 2090.

Petra said, “Wing answered twice as many as I missed, and he missed exactly a third as many as I answered.” “Wow, you both did so good,” said Charlie, “I only answered 20% of the paper – that’s 6 less than Petra missed.

How many questions did each student answer?

You now have 30 seconds left

Please hand in your answer.

You have 4 minutes for question 16.

This is the last question!!!

Question 16

(4 minutes) If x, y and z are integers and x y z = z x y and x x and x < y < z = z what are the values of x, y and z?

You now have 30 seconds left

Please hand in your answer.

…this is...

THE END

Time to breathe a sigh of relief, eat some lunch and pretend that you’re a pink kangaroo.

Try not to destroy the universe On your way out!!!