**math certificate**Report an error / Note?

**BREVET of MATHS 2021**

WHITE SUBJECT

_______________

Duration of the test: 2 hours

_______________

The use of a calculator is allowed

(circular n°99-186 of November 16, 1999)

The use of the dictionary is not allowed.

**Exercise 1 (5 points)**

This exercise is a multiple choice questionnaire.

For each row in the table, only one statement is correct.

On your copy, indicate the question number and copy the correct statement.

No justification is required.

A chocolate maker has just made 2,622 Easter eggs and 2,530 chocolate fish.

He wants to sell assorted eggs and fish so that :

– all packages have the same composition;

– after packing, there are no eggs or fish left.

1. Can the chocolate maker make 19 packages? Justify.

2. What is the largest number of packages it can make? In this case, what

will be the composition of each package?

**Exercise 3 (6 points)**

Peio, a young Basque decides to sell ice cream from June 1st to August 31st inclusive in

Hendaye.

To sell his ice cream, Peio hesitates between two locations:

– a straw hut on the beach

– a store in the city center.

Using the information below, help Peio choose the most appropriate location for his

more profitable.

**Information 1:**

the rents of the two proposed locations:

– the straw hut on the beach : 2500 € per month.

-the store in the city center: 60 € per day.

Information 2 : the weather in Hendaye

From June 1st to August 31st included:

– The sun shines 75% of the time

– The rest of the time, the weather is cloudy or rainy.

Information 3: Sales forecast by day according to weather:

**Any research lead, even if not completed, will be taken into account in the ****the evaluation.**

**Exercise 4 (6 points)**

The last bottle of perfume from Chenal has the shape of a SABC pyramid with a triangular base of height [AS] such as :

– ABC is a right-angled triangle and isosceles in A ;

– AB = 7.5 cm and AS = 15 cm.

1. Calculate the volume of the SABC pyramid. (Round to the nearest cm3.)

2. To make its cap SS’MN, the designers cut this pyramid by a plane P parallel to its base and passing through the point S’ such that SS’ = 6 cm.

a) What is the nature of the plane section S’MN obtained?

b) Calculate the length S’N.

3. Calculate the maximum volume of perfume that this bottle can hold by .

**Exercise 5 (4 points)**

A TV game show offers two tests to candidates:

– For the first test, the candidate faces 5 doors: one

door gives access to the treasure room while the other 4 open

on the consolation room.

– For the second test, the candidate finds himself in a room facing

to 8 envelopes.

**
In the treasure room :
** 1 envelope contains €1,000 , 5 envelopes contain €200. The others contain 100 €.

**In the consolation room:**

5 envelopes contain €100 and the rest are empty.

He has to choose only one envelope and then finds out how much he has won.

1) What is the probability that the candidate will reach the treasure room?

2) A candidate finds himself in the treasure room.

a) Draw a diagram of the situation.

b) What is the probability that he will earn at least 200 €?

3) Another candidate is in the consolation room.

What is the probability that he wins nothing?

**Exercise 6 (7 points)**

[AB] is a segment of middle O such that AB = 12 cm.

The point C belongs to the circle of center O passing by A. Moreover AC = 6 cm

The angle measures 30°.

1) Construct the figure in full size.

2) Are the following statements true or false? Justify.

a) Triangle ABC is right-angled.

b) The segment [BC] measures 10 cm.

c) The angle measures 60°.

d) The area of triangle ABC is cm².

e) The angle measures 31°.

**Exercise 7 (4 points)**

Three identical equilateral triangles are cut out of the corners of a triangle

equilateral of side 6 cm. The sum of the perimeters of the three small triangles is equal to

to the perimeter of the remaining gray hexagon.

** What is the measure of the side of the small triangles?**

**Any trace of research, even if not completed, will appear on the copy and will be taken into **

**taken into account in the marking.**

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