Brevet de maths 2022 : corrected blank subject of the DNB 2022.

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Indications for the whole subject :
All answers must be justified unless otherwise stated.
For each question, if the work is not completed, leave a trace of the research; it will be taken into account in the marking.

Exercise 1: 20 points.
This exercise is a M.C.Q. (Multiple Choice Questionnaire).
Each question has only one correct answer.
For each question, indicate on the copy the question number and the answer chosen.
No justification is required for this exercise.
patent maths 2022 1

Exercise 2: 20 points.
On the island of Madagascar, a scientist is conducting a study on green turtles.
The scientific name of the green turtle is “Chelonia Mydas”.
The carapace measures on average 115 cm and the animal weighs between 80 and 130 kg.
It is classified as a species “In Danger”.

In order to monitor the good health of the turtles, they are regularly weighed.

Here are the data collected by this scientist in May 2021.
patent maths 2022 2

  1. Calculate the range of this statistical series.
  2. Calculate the average mass of these 7 turtles. Round the result to the unit.
  3. Determine the median of this statistical series. Interpret the result.
  4. Is it true that males represent less than 20% of this sample?
  5. The island of Madagascar has geographical coordinates South; 450 East).
    Place a cross on the planisphere provided in the appendix to mark the position of the island of Madagascar.
    The appendix is to be returned with the copy.

Exercise 3: 20 points.

The following calculation program is considered.
patent maths 2022 3

The spreadsheet below was used to apply this calculation program to the number 5; the result is 24. patent maths 2022 4

1. For the following questions, show the calculations on the copy.
a. If you choose 2 as the starting number, check that you get 12 as the result.
b. If we choose -8 as our starting number, what result do we get?
2. Among the three following proposals, copy on your copy the formula that has been entered in
cell B5.

patent maths 2022 5

3. a. If we choose x as the starting number, express the final result of this calculation program as a function of x.
b. Show that (x\,+2)^2-x^2\,=\,4x\,+4.
4. If we choose an integer at the beginning, is it true that the result of the program is always
a multiple of 4? Justify.

Exercise 4: 20 points.
Here are three programs made with the Scratch application. patent maths 2022 6

1. They give the following three figures made of identical triangles and quadrilaterals. patent maths 2022 7

a. What is the nature of the triangle and quadrilateral in each figure? No justification is expected.
b. What is the missing value in line 8 in these 3 programs?
c. Indicate on the copy, for each figure, the number of the program which allows to obtain it.
2. a. Now we will modify the previous programs to build other figures for
where the perimeter of the quadrilateral is equal to the perimeter of the triangle. What value of step should be chosen in line 8 of each program?
b. Represent the figure A obtained with this new value, taking 1 cm for 25 steps.

Exercise 5: 20 points.
A family has purchased a shelf that they want to place along a wall.
1. The shelf was priced at 139,90 €. The family received a discount of 10 What was the amount of the discount?
2. This is the profile picture that can be seen on the shelf assembly guide; this drawing is not to scale. patent maths 2022 8

The shelf was mounted flat on the floor of the room, so it is in position 1.
We want to make sure that it will not touch the ceiling when we raise it to position 2.
No measuring instrument is available.
Using the data from the previous diagram, check that the shelf will not touch the ceiling.
3. In this question, it will be assumed that the cabinet may have been placed against the wall.
We now install four horizontal shelves regularly spaced and represented here by the segments [DE], [FG], [HI] and [ JK ].

patent maths 2022 9

a. Calculate the length C′E.
b. Calculate the length of the shelf [DE].
c. Calculate the length of the shelf [HI].

patent maths 2022 10

APPENDIX to be returned with the copy
Exercise 2 – Question 5

patent maths 2022 11

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