Polynesia 2017 : subject of the mathematics patent

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Subject of the mathematics patent
Session 2017
Polynesia

Exercise 1 : 7 points
This exercise is a multiple choice questionnaire.
For each row in the table, only one statement is correct.
Indicate the question number and copy the correct statement on your copy.
No justification is expected. No points are deducted for incorrect
answer.

Exercise 2 : 8 points
In this exercise, we will be interested in the speed of a TGV passing in a station without
stop.

How fast (in km/h) did the TGV pass me without stopping?
The result will be rounded to the nearest whole number.

Exercise 3 : 9 points
1) a) Draw a triangle CDE rectangular at D such that CD = 6.8 cm and DE = 3.4 cm.
b) Calculate CE to the nearest tenth of a cm.
2) a) Place the point F on [CD] such that CF = 2 cm.
b) Place the point G on [CE] such that FG = 1 cm.
c) Are the lines (FG) and (DE) parallel?

Exercise 4 : 6 points
Baklava is a traditional pastry in several countries such as Bulgaria or
Morocco. It is a long dessert to prepare, based on puff pastry, honey, and
nuts or pistachios or hazelnuts, depending on the region.
In a non-transparent bag, there are seven baklavas indistinguishable to the touch with
the letters of the word BAKLAVA.

We draw a cake at random from this bag and look at the letter written on the
cake.
1) What are the outcomes of this experiment?
2) Determine the following probabilities:
a) The letter drawn is an L
b) The letter drawn is not an A.
3) Enzo buys a bag containing 10 baklavas all indistinguishable to the touch.
This bag contains 2 pistachio baklavas, 4 hazelnut baklavas
and the other baklavas are based on nuts. Enzo picks a cake at random and puts it in the
eats; it is a cake made of nuts. He wants to eat another one.
His friend Laura says that if he now wants to have a new cake, he
will be more likely to pick a nut cake.
Is she right? Justify the answer.

Exercise 5 : 7 points
We consider the following calculation program:

1) Verify that when we choose -2 with this program, we get 13.
2) What number must be chosen at the beginning to obtain -3?
3) Salome runs the following script:

a) What will be the pixie’s answer if she chooses the number 12?
b) What will the pixie’s answer be if she chooses the number -5?
4) The above calculation program can be translated into the literal expression
with representing the chosen number.
Solve the following inequation:
5) Under which condition, concerning the chosen number, is it certain that the answer
of the leprechaun will be “Bravo”?

Exercise 6 : 8 points
Here is a map of two bus lines:

At 6:30 a.m., the two buses of lines 1 and 2 leave from the “Mairie” stop in the
clockwise. Line 1 bus takes 3 minutes between each stop
(including parking time), while the line 2 bus takes 4 minutes. All
both will perform the complete circuit a large number of times . They will just stop
after 8pm.
Will the two buses meet at some point during the day at the stop
What is the name of the “City Hall” at the same time? If so, give all the precise times of these meetings.

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