Transcript Document

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
number
andhave
your
team name.
You now
30 seconds
left
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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
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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.
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Are there any questions?
You now have 30 seconds left
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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
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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?
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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
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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
8
11
69
88
96
101
(b) 23
28
38
49
62
70
77
(c)
8
11
15
20
26
33
6
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
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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
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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
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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)
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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.
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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
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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
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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
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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
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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 cm3 find the
total surface area of the cuboid.
You now have 30 seconds left
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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
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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?
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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
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You have 4 minutes for
question 16.
This is the last question!!!
Question 16
(4 minutes)
If x, y and z are integers and
z
y
x
=
y
x
z
and
and
xx = z
x<y<z
what are the values of x, y and z?
You now have 30 seconds left
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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!!!