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**Diplôme national du Brevet**

Duration: 2 hours

**Exercise 1 : 16 points**

For each of the following statements, indicate whether it is TRUE or FALSE and justify the answer.

Data: f is the function defined by f (x) = 2(x -3).

**Assertion 1:** The image of 5 by the function f is 4.

Data: The Prony wind farm consists of 84 wind turbines.

Each wind turbine produces an average of 256,000 watts.

**Statement 2:** The wind farm produces a total of approximately 21.5 megawatts on average.

Data: In the figure below, the lines (AD) and (CB) intersect at E.

**Assertion 3:** Lines (AB) and (CD) are parallel.

Data: The pentagon below is composed of 5 triangles.

**Assertion 4:** The angle of the rotation with center A that transforms C into D in a clockwise direction is 60°.

**Exercise 2 : 12 points**

Laura created three variables and then made the script below.

1. Check that if the value of x is 5 then the result is 63.

2. What result do we get if the value of x is -3?

3. Among the following expressions, copy the one that corresponds to the calculation program given by the script.

4. For which value(s) of x do we obtain a result equal to 0?

**Exercise 3 : 16 points**

An aquaculturist studies the evolution of the average mass of shrimp in a tank.

It has theoretical values.

The graphical representation of the theoretical average mass of shrimp (in grams) as a function of the time spent in the tank (in days) is given in the Appendix.

1. Answer the following questions using the graph in the Appendix.

a. Is the theoretical average mass of shrimp proportional to the number of days spent in the tank? Justify the answer.

b. After 80 days, what is the theoretical average mass of the shrimp?

c. Fishing in a tank can be done when the average mass of shrimp reaches 20 grams.

After how many days can we consider fishing in this pond?

2. The aquaculturist conducts regular surveys of the pond to monitor its progress.

Here are the results of his latest readings:

a. Place points A(120; 23), B(145; 31), and C(175; 38) on the graph in the Appendix.

b. Compare the average masses measured with the theoretical average masses.

**Exercise 4 : 12 points**

Shrimp eat pellets that are stored in tanks called silos.

A silo is composed of a cone of revolution surmounted by a cylinder of the same base with a diameter DC = 2.8m.

The height of the cylinder is equal to 2.4 m.

1. Calculate the volume of the cylinder. Round off to the nearest whole number.

2. Show that the height AB of the cone is about 2.5m.

3. Calculate the volume of the silo. Round off to the nearest whole number.

4. The farmer orders 16 m3 of shrimp pellets.

Here is the information he has:

Calculate the total amount (in F CFP) of the order. Justify the answer.

**Exercise 5 : 12 points**

The satellite image, given in the appendix, represents 6 rectangular basins.

1. From this image, estimate the length and width (in m) of a pond.

2. We consider a basin whose surface measures 4 500 m².

Each tank receives 2 shrimp larvae per square meter.

Calculate the amount of shrimp larvae needed for 6 tanks.

3. Not all shrimp larvae survive during tank transfer. It is necessary to plan to order

10% more shrimp larvae for 6 tanks.

What is the total quantity of shrimp larvae to order?

**Exercise 6 : 12 points**

**Part A:**

In a tank, the aquaculturist records the mass of 100 shrimp.

He has grouped the results obtained in the following table:

1. In cell I2 we enter the formula **=SUM(B2:H2)**. What number is displayed in this cell?

2. A shrimp is chosen at random. All shrimp have the same probability of being selected.

a. What is the probability that the mass of the shrimp is 21 grams?

b. What is the probability that the mass of the shrimp is greater than or equal to 25 grams?

**Part B:**

When fishing, the mass (in grams) of some shrimp is recorded.

Here is the series of values obtained:

20 – 18 – 17 – 28 – 28 – 22 – 24 – 24 – 22 – 24

1. Calculate the mean of this series.

2. Calculate the median of this series. Interpret this result.

**Exercise 7: 10 points**

*In this exercise, any trace of research, even if incomplete or unsuccessful, will be taken into account in the evaluation.*

A side view of an aquaculture pond is shown below.

The bottom of the basin represented by the segment [EB] must be sloped.

The pelvis is well built when the angle is between 0.1° and 0.2°.

Here are the measurements taken on the basin: CE = 2.8 m, BD = CA = 3.2 met AB = 150 m.

Is this pool well constructed? Justify the answer.

**Exercise 8: 10 points**

One wishes to represent 6 rectangular basins with the help of a programming software as on the figure n°1 below:

1. Complete, in the appendix, the script of the “basin” block so that it allows to draw a rectangular basin of width 30 pixels and length 150 pixels.

2. The script below should produce figure #1. It uses the “basin” block of the appendix.

Knowing that the total length of Figure #1 is 220 pixels, what value should be placed on the last line in the “advance from” instruction? Justify the answer.

*In this question, any evidence of research, even if incomplete or unsuccessful, will be considered in the evaluation.*

**Appendix (to be returned with the copy)**

Exercise 3:

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