YEAR TEN Mathex 2009
Team
Question 1
Robin uses all the digits 1,2,3 to make a three-digit number with no repeating digits. What is
the mean of all the different numbers Robin can make?
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 2
A cheddar cheese is sold in packages shaped as half of a rectangular prism 10 cm by 20 cm by
15 cm. Each cubic centimetre of this cheese has a mass of 2.5g. A company orders 3tonnes
of these cheese packages. How many of these cheese packages has the company ordered?
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 3
What is the last digit of
?
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 4
David Cain’s shoe is 299 mm long. This is 115% of the length of his footprint. How many
millimetres long is David’s footprint?
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 5
The Rams basketball team lost 20% of their games, drew 25% and won 7 more games than
they lost.
How many games did the Rams play?
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 6
David has a toy made up of balls and sticks. The mass of three sticks and two balls is 285g.
The mass of seven sticks and five balls is 685g. What is the mass in grams of one stick and
one ball?
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 7
A safe can be opened by the correct combination of four digits. Each of the four sets of digits
shown here has two and only two correct digits in the correct position.
What number opens the safe?
1475
5975
5485
1971
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 8
On his birthday in the year 2013, Stephen’s age will be one sixtieth of the year he was born.
How old was Stephen on his birthday in the year 2000?
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 9
Three adults and three children wish to cross a river in a canoe that will only hold one adult or
two children. They can all row on their own, but no one can swim. If a one-way trip in the
canoe takes 8 minutes, what is the minimum time in minutes in which all six people can cross
the river?
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 10
If a cake were to be cut into six equal pieces, then the mass of each piece would be 30g more
than the mass of each piece if the cake were to be cut into eight equal pieces. What is the
mass in grams of the whole cake?
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 11
Find the area in square centimetres of the isosceles triangle with sides of length 5 cm, 5 cm
and 6 cm.
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 12
A cube has its side lengths decreased by 10%. By exactly what percentage has its volume
been decreased?
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 13
Find the value of n.
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 14
For how many pairs of (non zero) positive integers is the following equation true?
3x + 2y = 135
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 15
How many minutes after 12 o’clock will there be an exact angle of 132 between the hour
and minutes hands of a clock?
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 16
Two trains are on the same track heading straight for each other. One train is travelling at 60
km per hour while the other train is travelling at 45 km per hour. If the trains are notified two
minutes before they collide, they can avoid the accident. How far apart in kilometres will the
trains be two minutes before the point of impact?
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 17
The sum of the ages in years of Max, Ash and Nicholas is 40. Max is twice as old as
Nicholas and Nicholas is 6 years younger than Ash. How old is Ash?
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 18
A 40 litre tank is full of water when it suddenly develops a leak and loses water at the steady
rate of 10 mL every six seconds. Every hour after it first began to leak, a four litre bucket of
water is added to the tank to try and top it up. How long in hours will it take for the tank to be
empty?
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 19
I am a four-digit positive integer and all my digits are different. When the order of my digits
is reversed, the new number is exactly four times greater than myself. What number am I?
Answer ___________________
YEAR TEN Mathex 2009
Team
Question 20
A cone-shaped plastic container has a height of 8 cm and a radius of 3 cm. Water is poured
into this container until the water’s depth is 4 cm. What fraction of the container is full of
water?
(Volume of a cone =
)
Answer ___________________
YEAR TEN Mathex 2009
Team
Tie Breaker Question 1
Seven students sat a test. Their mean score on the test was 23 and the range of their scores
was 5. Their median score was 23 and the mode of their scores was 25.
What was the sum of the lowest three scores?
Answer ___________________
YEAR TEN Mathex 2009
Team
Tie Breaker Question 2
AA + BB + CC = ABC
Each letter stands for a different digit. What number does ABC represent?
Answer ___________________
YEAR 10 ANSWERS
Year 10 Mathex 2009 Answers
Tiebreaker 2
198
Tiebreaker 1
63
Question 20
Question 19
2178
Question 18
18
Question 17
14.5 or 14
Question 16
3.5 or 3
Question 15
24
Question 14
22
Question 13
or
Question 12
27.1 or
Question 11
12
Question 10
720
Question 9
120
Question 8
20
Question 7
1985
Question 6
115
Question 5
20
Question 4
260
Question 3
1
Question 2
800
Question 1
222
or 2.4