# yr 8 Team 2011 ```MATHEMATICS TEAM CHALLENGE
2011
TEAM EVENT: Year 8
(Calculators are allowed)
Time: 45 mins
Total: 150 points_
T1. (10 points)
1
The fraction when written as a decimal repeats forever.
7
1
7
= 0.142857142857142857142857 … ….
̅̅̅̅̅̅̅̅̅̅
= 0. 142857
What is the millionth digit after the decimal place?
T2. (20 points)
When Matthew arranged his matchbox cars in groups of three he had one left over. After arranging them in
groups of four he had one left over. Finally he arranged them in groups of five and had one left over. What
is the smallest possible number of matchbox cars in his collection?
T3. (20 points)
The world population is approximately 6.7 billion. If the annual growth rate is approximately 2% per year;
approximately how many years will it take for the population to reach 10 billion?
T4. (10 points)
How many factors does 1800 have? [Include 1 and 1800 in your answer]
T5. (15 points)
The intensity of x-rays vary inversely with the distance squared. This can be written as:
1
I  𝑑2
For example if the intensity at 1 metre from the x-ray machine is 100%, then the intensity at 2 metres will be
down to 25%.
100%
(
22
= 25%). At what distance will the intensity be down to 50%?
T6. (20 points)
What is the unit digit when 22011 is expanded?
T7. (10 points)
A ball is dropped from a height of 18 metres and it bounces back two-thirds of the way. How many times
does it bounce over 1 metre in height?
T8. (15 points)
What number has all of the following properties?
 The number has five digits.
 The number is a square number.
 All individual digits of the number are square numbers (Note: 0, 1, 4 and 9 are all square numbers)
 The sum of the number’s individual digits is a square number.
 The first three digits of the number (from the left) form a square number.
 The number uses only 3 different digits.
 Four is the middle digit.
T9. (15 points)
Binary (base 2) uses only ones and zeros. For example 1011101 represents a binary number.
Each digit in binary represents a power of 2, whereas each digit in base 10 represents a power of 10.
For example 2567 = 2 &times; 103 + 5 &times; 102 + 6 &times; 101 + 7 &times; 100 (in base 10)
To convert the binary number 101111 to base 10, first write in expanded form in powers of 2.
1 &times; 25 + 0 &times; 24 + 1 &times; 23 + 1 &times; 22 + 1 &times; 21 + 1 &times; 20
=
47
What does the binary product below equal in base 10?
11001 &times; 11010 =
?
T10. (15 points)
Between 12 noon and 12 midnight, a watch is stopped for 1 minute at the end of the first full hour, for 2
minutes at the end of the second full hour, for 3 minutes at the end of the third full hour, and so forth for the
remaining full hours. What is the true time when the watch shows 12 midnight?
School Name:_____________________________ Team 1:
Team 2:
2011 MATHS TEAM CHALLENGE
YEAR EIGHT
TEAM EVENT
Question
T1. (10 points)
Points
T2. (20 points)
T3. (20 points)
T4. (10 points)
T5. (15 points)
T6. (20 points)
T7. (10 points)
T8. (15 points)
T9. (15 points)
T10. (15 points)
Total
/150
2011 MATHS TEAM CHALLENGE
YEAR EIGHT
TEAM EVENT
Question
T1. (10 points)
8
T2. (20 points)
61
T3. (20 points)
T4. (10 points)
20 years
(accept between 20 and 21)
36 factors
T5. (15 points)
√2 or 1.414 metres
T6. (20 points)
4
T7. (10 points)
7 bounces
T8. (15 points)
14400
T9. (15 points)
650
T10. (15 points)
1: 06 am
Points
```