2011 MATHEMATICS TEAMS CHALLENGE
Year 8 Relay
Time: 60 mins
Calculators Allowed
100 points
----------------------------------------------------------------------------------------------------------------------------------R1. (4 points)
What number should be in the last triangle?
[96 points remaining]
R2. (4 points)
What number is missing from the sequence?
[92 points remaining]
2, 3, 6, ___, 108
R3. (6 points)
What is the largest prime number that can be made from the digits 4, 5, 6, 3 and 1?
[Note: A prime number only has factors of 1 and itself]
[86 points remaining]
R4. (2 points)
[84 points remaining]
Add up all of the digits in the number below. Do the same to the digits in the total. Keep repeating until you
obtain a one digit number. What is the number?
27975432189
R 5. (4 points)
What two digit square number also has digits which are both square numbers?
[80 points remaining]
R 6. ( 8 points)
What is the next line in the “say aloud” sequence below?
[72 points remaining]
R 7. (4 points)
What number in the grid satisfies both of the two simple rules?
[68 points remaining]
(a) It is not in any row that contains a square number.
(b) It is not in any column that contains an even number.
31
17
8
16
24
11
10
18
52
25
7
9
49
3
13
5
R 8. (8 points)
[60 points remaining]
The angles of a quadrilateral are consecutive odd numbers which add up to 360⁰. What is the size of the
smallest angle?
R 9. (6 points)
What number comes next?
27, 54, 81, 108, ____
[54 points remaining]
R 10. (4 points)
If you have four-fifths of $200 and spend $72. How much will you be left with?
[50 points remaining]
R 11. (6 points)
The number below is divisible by 11. What is the missing digit?
[44 points remaining]
872618__34
R12. (6 points)
[38 points remaining]
If you can type 4 digits to 1 centimetre. How long in kilometres, would the first one million digits of pi(π) be
when written in a straight line?
R 13. (6 points)
[32 points remaining]
In 1920 Professor G.H.Hardy visited his sick dying friend, Srinivasa Ramanujan (who was an Indian
mathematician) On arrival Hardy mentioned that he travelled in taxi-cab No 1729, which was a rather dull
number. Ramanujan replied,’it is a very interesting number; it is the smallest number expressible as the sum of
two cubes in two different ways.’ One way is 13 + 123 = 1729
What is the other way?
R 14. (8 points)
[24 points remaining]
Galileo has been credited with the following pattern involving odd numbers. What does the sum reduce to as a
fraction in simplest form?
1+3+5+7+9+11+⋯+1001
1003 +1005+1007 +1009 +1011 +1013+⋯..+2003
[Hint: Look at the following pattern.
1+3
5+7
=,
1+3+5
7+9+11
=,
=


1+3+5+7
9+11+13+ 15
=, etc]
R 15. (2 points)
Four people all say hello to one another. How many ‘ hellos’ are uttered?
[22 points remaining]
R 16. (4 points)
What is the missing number?
[18 points remaining]
525781331__7525
R 17. (4 points)
[14 points remaining]
Toby built a giant cube from his cubic building bricks. If he had 5,500 bricks to use initially, how many bricks
were left over after he built the cube?
R 18. (4 points)
[10 points remaining]
Emily’s age is equal to twice the sum of its two digits. How old is Emily if she is still a teenager?
R 19. (6 points)
[4 points remaining]
Mary ate one-third of the lollies, Peter ate one-quarter, Luke ate one-sixth and Sarah ate one-tenth. If there were
9 lollies left, how many lollies were there altogether?
R 20. (4 points)
[0 points remaining]
It takes light from the Sun approximately 8 minutes to reach the Earth which is approximately 150,000,000
kilometres away. How long would it take light from the Sun to reach Saturn?
Saturn is approximately1,413,000,000 kilometres from the Sun.
Problem
R 1 (4 points)
R 2 (4 points)
R 3 (6 points)
R 4 (2 points)
Change
R 5 (4 points)
R 6 (8 points)
R 7 (4 points)
R 8 (8 points)
Change
R 9 (6 points)
R 10 (4 points)
R 11 (6 points)
R 12 (6 points)
Change
R 13 (6 points)
R 14 (8 points)
R 15 (2 points)
R 16 (4 points)
Change
R 17 (4 points)
R 18 (4 points)
R 19 (6 points)
R 20 (4 points)
MATHS TEAM CHALLENGE (2011)
Relay Answer Sheet
YEAR 8
Answer
Attempts √ or ×
Score Progressiv
8 7 6 5 4 3 2 1
e Score
64
18
65413
3
Change
Change
49
13112221
13
87⁰
Change
Change
135
$88
9
2.5 kilometres
Change
Change
3
3
9 + 10 = 1729
1
3
6
8
Change
Change
587
18
60
75.36 minutes
(accept from 7576 minutes)
Total
School:___________________________________
Team 1:
Team 2: