9-11 State Maths Paper 2021. docx



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9-11 State Maths Paper 2021



1 STATE
DA VINCI DECATHLON 2021 CELEBRATING THE ACADEMIC GIFTS OF STUDENTS IN YEARS 9, 10 & 11







MATHEMATICS


TEAM NUMBER
_____________
1 2
3 4 Total Rank
/9
/16
/16
/9
/50


Task developed by Giacomo Rotolo-Ross, University of Sydney, 2020
2
QUESTION ONE
ROLL UP, ROLL UP
9 MARKS
When one thinks of
numbers and β€˜chance’, a dice is the first thing that comes to mind. Almost everyone, it can be said with certainty, will picture ab six-sided
one. Dice with more or less sides
do exist but are very uncommon, and at the most they might have a few extra sides – perhaps 12 at the maximum.
Dice Lab, however, a small Arizonan company, had other ideas, and set about creating a sided dice back in
2016. The mathematical name for this shape is ab disdyakis triacontahedron
, and this is the focus of the present task
1. How many edges does a disdyakis triacontahedron have ______________
(1 mark)
2. How many vertices does the shape have _______________
(1 mark)
3. What type of triangles are the faces _______________
(1 mark)
4. Which feature of the shape does the equation below represent _________
(1 mark)
180 11 (5 + 4
√5)
5. Which feature of the shape does the equation below represent ________
(1 mark)
180 11
οΏ½179 βˆ’ 24√5 6. Complete the equation, which represents the number of possible combinations of numbers from 1 to 120 that could be placed on the shape, by inserting a number in the brackets
(3 marks).
𝑁𝑁 = 10
( )
7. The above number is greater than the estimated number of atoms in the universe. True or false _________________
(1 mark)


Task developed by Giacomo Rotolo-Ross, University of Sydney, 2020
3

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