# French Polynesia : subject of the patent of maths 2019

DIPLÔME NATIONAL DU BREVET

FRENCH POLYNESIA
SESSION 2019
The use of any model of calculator, with or without exam mode, is allowed.
General series
Length of test: 2 h 00 100 points

Exercise 1 (12 points)
In this multiple choice questionnaire, for each question, answers are proposed,
only one is correct. On the copy, write the question number and copy the correct answer.
For question 4, a justification is expected.

Exercise 2 (20 points)
1. A spreadsheet was used to obtain images of different values of by a
affine function f.
Here is a copy of the resulting screen:

a) What is the image of – 1 by the function f?
b) What is the antecedent of 5 by the function f?
c) Give the expression of f () .
d) Calculate f(10).
2. We give the following program which translates a calculation program.

a) Write the last two steps of the calculation program on your copy:

b) If we choose the number 8 at the beginning, what will be the result?
c) If we choose x as the starting number, show that the result obtained with this
The calculation program will be 2 + 1.
d) What number must be chosen at the beginning to obtain 6?
3. What number should be chosen so that the function f and the calculation program give the
same result?

Exercise 3 (15 points)
Sam prefers blue candy.
In his pack of 500 candies, 150 are blue, the others are red, yellow or green.
1. What is the probability that he will randomly draw a blue candy from his pack?
2. 20% of the candy in this package is red. How many red candies are there?
3. Knowing that there are 130 green candies in this package, is Sam more likely to pick at the
is it a green or yellow candy?
4. Aïcha had bought the same package two weeks ago, she has only 140 blue candies left,
100 yellow, 60 red and 100 green. She said to Sam, “You should pick from my pack,
rather than your own, you’d have a better chance of getting a bruise.
Is she right?

Exercise 4 (12 points)

The pyramid of the Louvre in Paris is a pyramid with a square base of 35,4 m side and height
21,6 m.
It is a reduction of the pyramid of Cheops in Egypt, which measures approximately 230.5 m on each side.
1. Show that the height of the pyramid of Cheops is approximately 140.6 m.
2. Calculate the volume in of the Louvre pyramid. (Round up to the nearest unit)
3. By what number can we multiply the volume of the Louvre pyramid to obtain the volume of
the pyramid of Cheops ? (Round up to the nearest unit)

Exercise 5 (14 points)
When a sailboat is facing the wind, it cannot move forward.
If the chosen destination requires heading into the wind, the sailboat will have to zigzag.
Compare the trajectories of these two sailboats by calculating the distance, in kilometers and rounded to the tenth, that each has
travelled.

Exercise 6 (12 points)
The table below gathers the results of the final of the 200 m men of the Games
Olympics in Rio de Janeiro in 2016, won by Usain BOLT in 19.78 seconds.

1. Calculate the average speed in m/s of the fastest athlete. Round to the hundredth.
2. Calculate the average performance of the athletes. Round to the hundredth.
3. In 1964 in Tokyo, the average performance of the athletes in the men’s 200 m was
20.68 s and the range was 0.6 s. When comparing these results to those of 2016, what do you observe
?

Exercise 7 (15 points)
The graph below gives the water level in the port of La Rochelle on Wednesday, August 15
2018.

1. What was the highest water level in the harbor?
2. At what approximate times was the water height 5 m?
3. Using the data in the table to the right, calculate :
a) The time that elapsed between high and low tide.
b) The difference in water height between high and low tide.

4. Using the following two documents, how would you describe the tide on August 15, 2018 between 8:16 am and 2:30 pm in La Rochelle?

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