Brevet Asie Pacifique 2016: subject and answer key in PDF.

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Brevet des collèges Asia June 27, 2016
Duration: 2 hours

Exercise 1 : 4 points
This exercise is a multiple choice questionnaire (MCQ). For each line in the table, three answers are proposed, but only one is correct.
Any correct answer is worth 1 point.
Any inaccurate answer or lack of answer does not take away any points.
Indicate on your copy the number of the question and, without justifying, copy the exact answer (A or B or C).


Exercise 2 : 6 points
The Millau viaduct is a bridge crossing the Tarn valley, in the department
of Aveyron, France. It consists of 7 vertical towers each equipped with 22
cables called shrouds.
The diagram below, which is not to scale, represents a tower and two of its


The following information is available:
AB = 89 m; AC = 76 m; AD = 154 m; FD = 12 m and EC = 5 m.

1. Calculate the length of the shroud [CD]. Round to the nearest meter.
2. Calculate the measure of the angle \widehat{CDA} formed by the shroud [CD] and the roadway.
Round to the nearest degree.
3. Are the shrouds [CD] and [EF] parallel?

Exercise 3 : 6 points
A candy company wants to verify the quality of its new
packaging machine. This machine is configured to pack approximately
60 candies per package. To verify its correct configuration, 500 packets were studied at the output of this machine.

Document 1: Results of the study


Document 2: Quality Criteria
To be validated by the company, the machine must meet three quality criteria:
– The average number of candies in a package must be between 59.9
and 60.1.
– The range of the series must be less than or equal to 10.
– The interquartile range (i.e. the difference between the third quartile and the
first quartile) must be less than or equal to 3.
Does the new machine meet the quality criteria?
It is reminded that, for the whole subject, the answers must be justified.

Exercise 4: 5 points
Adèle and Mathéo wish to participate in the Paris Marathon. After training
for months, they want to assess their fitness level before committing. For
To do this, they carried out a test called “Cooper’s test”: the objective is to run, on a track
of athletics, the longest distance possible in 12 minutes. The distance travelled
determines the physical form of the person.

Document 1: Form index according to Cooper’s test
The fitness index of an athlete depends on gender, age and distance covered
during the 12 minutes.



1. Check that the length of the runway is approximately 400 meters.
2. Adèle and Mathéo have decided to participate in the marathon only if their fitness index is at least at the “average” level.
Determine if Adele and Mathéo will participate in the race.

Exercise 5 : 6 points
Consider the functions f and g defined by :
f,(x),=,2x,+1 and g,(x),=,x^2,+4x,-5.

Lea wants to study the functions f and g using a spreadsheet. She has therefore fulfilled the
formulas which she then stretched to obtain the calculation of all the values.
Here is a screenshot of his work:


1. What is the image of 3 by the function f ?
2. Calculate the number that should appear in cell C3.
3. What formula did Lea enter in cell B2?
4. Using the screenshot and without justification, give a solution to the inequation 2x,+1,<,x^2,+4x,-5.
5. Determine an antecedent of 1 by the function f .

Exercise 6: 3 points
In each case, say whether the statement is true or false. Justify your answer.
1. Assertion 1:
Two odd numbers are always prime to each other.
2. Assertion 2:
For any positive integer a and b, \sqrt{a}+\sqrt{b}=\sqrt{a+b}.
3. Assertion 3:
If we increase the price of an item by 20% and then by 30%, then in total the price
increased by 56%.

Exercise 7 : 6 points
Romane wants to prepare a cocktail for her birthday.


– Volume of a sphere : V,=\frac{4}{3}\pi\times  ,r^3
Is the container chosen by Romane big enough to prepare the cocktail for 20
It is reminded that, for the whole subject, the answers must be justified.
It is reminded that all traces of research will be taken into account in the correction.

Consult the
answer key in

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