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DIPLÔME NATIONAL DU BREVET

SESSION 2022

FOREIGN CENTERS

MATHEMATICS

General series

Duration of the test: 2 hours

Exercise 1: 19 points.

The two parts of this exercise are independent.

Part A:

This part is a multiple choice questionnaire (MCQ). For each question, three answers are proposed, only one is correct.

Copy the question number and indicate, without justification in this section only, the answer chosen.

In this part, we consider the function defined by f(x) = 2x + 3.

Part B:

1. Show that: .

2. Consider the triangle CDE such that: CD = 3.6 cm; CE =4.2 cm and DE = 5.5 cm.

Is the triangle CDE rectangular ?

Exercise 2: 20 points.

The Paris-Nice is a cycling race that takes place every year and leads the riders from the Paris region to the Nice region. The 2021 edition took place in 7 stages described below:

1. We study the series of distances traveled per step.

a. Calculate the average distance covered per stage, rounded to the tenth of a km.

b. Calculate the median of the distances traveled per step.

c. Calculate the range of the series formed by the distances traveled per step.

2. A reporter says, “About 57% of the total number of stages in this edition were on a hilly course.” Is he right? Explain your answer.

3. The German Maximilian SCHACHMANN won the race in 28 h 50 min.

The last one in the general classification completed the whole course in 30 h 12 min.

How far behind the winner does the last ranked person fall?

4. The Irishman Sam BENNETT won the first stage in 3 hrs 51 min. Determine his average speed in km/h, rounded to the unit, during this step.

Exercise 3: 21 points.

Consider the following figure, where all lengths are given in centimeters.

Points C, A and E are aligned and points B, A and D are aligned.

The figure is not shown at full size.

1. Prove that the segment [AB] measures 4 cm.

2. Using the previous question, show that the lines (BC) and (DE) are parallel.

3. Deduce that the line (DB) is perpendicular to the line (DE).

4. Calculate the area of triangle ADE rounded to the unit.

Exercise 4: 15 points.

In this exercise, all lengths are expressed in pixels.

Part A:

A teacher gives his students a parallelogram pattern and the script, partially written, that allows them to draw this pattern. We specify that the sprite is at the starting point, as shown in the figure below, and that it is oriented to the right:

Part B:

The teacher then asks the students to integrate this script into a program of their choice that allows them to draw figures composed of several of these patterns.

Here are the programs written by two students.

We remind you that “orienting at 90” means that you are oriented to the right.

1.Which keyboard action launches the program of student B?

2. Among the following figures, indicate, here without justification.

a. which one is obtained with the program of student A?

b. which one is obtained with student B’s program?

Exercise 5: 25 points.

To celebrate the 25th anniversary of his store, a chocolatier wants to offer the first customers of the day a box containing chocolate truffles.

1. He made 300 truffles: 125 coffee-flavored truffles and 175 coconut-coated truffles.

He wants to make these boxes so that

- The number of coffee-flavored truffles is the same in each box;
- The number of coconut-coated truffles is the same in each box,
- All the truffles are used.

a. Decompose 125 and 175 into products of prime factors.

b. Deduce the list of common divisors of 125 and 175.

c. What is the maximum number of boxes that can be made?

d. In this case, how many truffles of each kind will there be in each box?

2. The chocolate maker wants to make boxes containing 12 truffles.

To do this, he has the choice between two types of boxes that can contain the 12 truffles, and whose characteristics are given below:

In this question, each of the 12 truffles is assimilated to a ball of diameter 1.5 cm.

Inside a box, in order for the truffles not to be damaged during transport, the volume occupied by the truffles must be greater than the volume not occupied by the truffles.

What type(s) of box(es) should the chocolatier choose for this condition to be met?

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