Team round 1

1
(No Transcript)
2
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.
3

• 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 dont answer the whole question)
• Only answers are required it is not necessary
  to show any working out.

4
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 and your team name.
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
5
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
10
9
8
7
6
5
4
3
2
1
6
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
10
9
8
7
6
5
4
3
2
1
7
Are there any questions?
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
8
Trial question You have 2 minutes for this
question. DO NOT use a bonus sheet.
9
Trial question. a and b are prime numbers If
5a 9b 103, find a.
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
10
We will now start the actual questions. Remember
- bonus marks if you submit a correct answer on
the pink sheet within 90 seconds.
11
You have 4 minutes for question 1.
12
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
10
9
8
7
6
5
4
3
2
1
STOP
13
Please hand in your answer. You have 7 minutes
for question 2.
14
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
10
9
8
7
6
5
4
3
2
1
STOP
15
Please hand in your answer. You have 6 minutes
for question 3.
16

• 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
• 6 8 11 15 20 26 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
10
9
8
7
6
5
4
3
2
1
STOP
17
Please hand in your answer. You have 5 minutes
for question 4.
18
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
10
9
8
7
6
5
4
3
2
1
STOP
19
Please hand in your answer. You have 7 minutes
for question 5.
20
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
10
9
8
7
6
5
4
3
2
1
STOP
21
Please hand in your answer. You have 4 minutes
for question 6.
22

• 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
10
9
8
7
6
5
4
3
2
1
STOP
23
Please hand in your answer. You have 6 minutes
for question 7.
24

• 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
10
9
8
7
6
5
4
3
2
1
STOP
25
Please hand in your answer. You have 5 minutes
for question 8.
26
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
10
9
8
7
6
5
4
3
2
1
STOP
27
Please hand in your answer. You have 6 minutes
for question 9.
28
Question 9 (6 minutes) Running Rabbits 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 Bears age. If
Scratching Bear is older than 50 but younger than
100, (a) how many sisters does Running Rabbit
have, (b) how old is Scratching Bear?
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
29
Please hand in your answer. You have 5 minutes
for question 10.
30
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
10
9
8
7
6
5
4
3
2
1
STOP
31
Please hand in your answer. You have 6 minutes
for question 11.
32
Question 11 (6 minutes) Harvey the Head
Collector bought some heads on E-bay. A womans
head costs 25, a mans head costs 20 and a
dogs head costs 4. If Harvey bought 15 heads
for 240, how many mens heads did he buy?
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
33
Please hand in your answer. You have 7 minutes
for Question 12.
34
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
10
9
8
7
6
5
4
3
2
1
STOP
35
Please hand in your answer. You have 6 minutes
for Question 13.
36
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
10
9
8
7
6
5
4
3
2
1
STOP
37
Please hand in your answer. You have 7 minutes
for question 14.
38
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
10
9
8
7
6
5
4
3
2
1
STOP
39
Please hand in your answer. You have 5 minutes
for Question 15.
40
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 thats 6 less than
Petra missed. How many questions did each
student answer?
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
41
Please hand in your answer. You have 4 minutes
for question 16. This is the last question!!!
42
Question 16 (4 minutes) If x, y and z are
integers and xy z zx y and xx
z and x lt y lt z what are the values of
x, y and z?
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
43
Please hand in your answer. this is... THE END
44
Time to breathe a sigh of relief, eat some lunch
and pretend that youre a pink kangaroo. Try not
to destroy the universe On your way out!!!
45
(No Transcript)