DIPLÔME NATIONAL DU BREVET
Length of test: 2 h 00 100 points
Exercise 1 : ( 10 points )
The captain of a ship has a treasure consisting of 69 diamonds, 1,150 pearls and 4,140 gold coins.
1. Decompose 69; 1150 and 4140 into products of prime factors.
2. The captain shares the treasure equally among the sailors.
How many sailors are there knowing that all the coins, pearls and diamonds have been distributed?
Exercise 2 : ( 19 points )
In this exercise, if necessary, the results will be approximated to the nearest hundredth.
To build the set for a play (Figure 1), Joanna has a rectangular plate ABCD measuring 4 m by 2 m from which she must cut out the three triangles of the set before placing them on top of each other.
It proposes a cutting of the plate (Figure 2).
The ADM triangle satisfies the following conditions:
- The triangle ADM is rectangular in A
- AD=2 m
1. Show that [AM] is approximately 3.46 m tall.
2. The unused portion of the plate is shown in a grid pattern in Figure 2. Calculate a value approximating to the hundredth of the proportion of the plate that is not used.
3. To make the triangles overlap smoothly, Joanna wants the three triangles AMD, PNM and PDN to be similar.
Demonstrate that this is the case.
4. Joanna would like the magnification factor to go from the PDN triangle to the AMD triangle to be smaller than 1.5.
Is this the case? Justify.
Exercise 3 : ( 17 points )
Questions 1 and 2 are independent.
An hourglass is composed of :
– Two cylinders C₁ and C₂ of height 4.2 cm and diameter 1.5 cm
– A C3 cylinder
– Two half-spheres S₁ and S₂ of diameter 1,5 cm
We recall the volume of a cylinder of base area and height ℎ :
a. Initially, the sand fills the cylinder C₂ two-thirds of the way. Show that the volume of sand is
approximately 4.95 .
b. We turn over the hourglass. Assuming that the sand flow rate is constant and equal to
1.98 , calculate the time in minutes and seconds that the sand will take to flow into
the lower cylinder.
2. In reality, the flow rate of the same hourglass is not constant.
In a factory where hourglasses like this one are made, you take an hourglass at random and
test the flow time in this hourglass several times . Here are the different times summarized
in the following table:
a. How many tests were performed in total?
b. An hourglass is offered for sale if it meets the three conditions below, otherwise it is eliminated.
– The time range is less than 20 s
– The median time is between 2 min 29 s and 2 min 31 s
– The average time is between 2 min 28 s and 2 min 32 s
Will the tested hourglass be eliminated?
Exercise 4 : ( 19 points )
We want to make a drawing made of two types of elements (dashes and squares) put together.
Each script on the right draws an element, and moves the pen.
Recall that “orienting at 90” means orienting the pen to the right.
1. Taking 1 cm for 2 pixels, represent the figure obtained if you run the Square script.
Specify the starting and ending positions of the pen on your figure.
To draw the complete design, we have made 2 scripts that use the “Square” and “Dash” blocks
We run the two scripts and we obtain the two drawings below.
2. Assign to each script the figure drawn. Justify your choice.
3. We run the script 2.
a. What is the probability that the first element drawn is a square?
b. What is the probability that the first two elements are squares?
4. In script 2, we would like the color of the different elements, dashes or squares, to be random,
with each time a 50% chance to have a black element and a 50% chance to have a
Write the sequence of instructions to be created and specify where to insert it in the script 2.
Exercise 5 : ( 18 points )
Olivia bought a painting to decorate her living room wall.
This table, represented below, is made up of four identical rectangles named 1, 2, 3 and 4 drawn inside a large rectangle ABCD of area equal to 1.215 m².
The length : width ratio is 3 : 2 for each of the five rectangles.
1. Copy and complete the following sentences. No justification is required.
a. Rectangle … is the image of rectangle … by the translation that transforms C into E.
b. Rectangle 3 is the image of rectangle … by the rotation of center F and angle 90° in the
c. Rectangle ABCD is the image of rectangle … by the homothety of center … and ratio 3.
(There are several possible answers, only one is required).
2. What is the area of a small rectangle?
3. What are the length and width of rectangle ABCD?
Exercise 6 : ( 17 points )
Here are two calculation programs.
1. Check that if we choose 5 as the starting number,
– The result of program 1 is 16.
– The result of program 2 is 28
We call the result of program 1 according to the number chosen at the beginning.
The function gives the result of program 2 according to the number chosen at the beginning.
a. Express as a function of .
b. Determine the number that must be chosen at the beginning to obtain 0 as the result of the program 1.
3. Expand and reduce the expression :
a. Show that .
b. What numbers must be chosen at the start for program 1 and program 2 to give the same result? Explain the process.
Cette publication est également disponible en : Français (French) Español (Spanish) العربية (Arabic)
Download and print this document in PDF for free
You have the possibility to download then print this document for free «brevet de maths en France 2019 : subject and answer key to download in PDF» in PDF format.
Other documents in the category math certificate
- Brevet Maths 2022 in France: subject and answers
- French Polynesia : maths patent 2022 with subject and answers
- Asia and Pacific: maths patent 2022 with subject and answer key
- Brevet Maths 2021 : subject and answer key of the brevet blanc de maths
- Brevet Maths 2021 : white subject for the revision of the DNB
- Brevet Maths 2021 : mock subject to revise the brevet
- Brevet de maths 2022 at foreign centers: subject and answer key
- Brevet de maths 2017 : mock subject
- Brevet de maths 2017 subject 0
- Subject of the patent of maths France 2016
Other forms similar to brevet de maths en France 2019 : subject and answer key to download in PDF.
- 96The topic of the 2016 North American math patent test. This subject of the brevet des collèges covers the following concepts: statements to be justified; probabilities statistics and use of the spreadsheet; chairlift in a ski resort; functions and two rates in a ski resort; windsock and Thales' theorem; ski…
- 96Brevet de maths 2017 with a topic for 3rd graders that covers trigonometry in the right triangle, Thales' theorem, functions and Scratch. WHITE PATENT Mathematics 2 hours The use of calculators and geometry equipment is permitted. Five points are awarded for presentation, writing, and adherence to units and scoring. Exercise…
Les dernières fiches mises à jour.
Voici les dernières ressources similaires à brevet de maths en France 2019 : subject and answer key to download in PDF mis à jour sur Mathovore (des cours, exercices, des contrôles et autres), rédigées par notre équipe d'enseignants.
On Mathovore, there is 13 703 943 math lessons and exercises downloaded in PDF.