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**WHITE BREVET ****MATHEMATICS**

**Session: January 2021**

** **Duration of the test: 2 hours – 40 points including 1 point for the care.

The use of a calculator is allowed.

__Exercise n° 1 : 5 points.__

This exercise is a multiple choice questionnaire (MCQ).

For each of the five questions, four answers are proposed, only one of them is correct.

**For each of the five questions, indicate on the copy the question number and the answer chosen.**

**Remember that all answers must be justified.**

A wrong answer or the absence of an answer does not remove a point.

__Exercise n° 2 : 6 points.__

- Give the prime factor decomposition of the integers 108 and 225.
- Using the previous prime factor decompositions, make the fraction irreducible.
- Carole wants to make a mosaic on a wall of her house. The surface to be paved is a rectangle of dimensions 108 cm and 225 cm and must be entirely covered by square tiles of the same size without cutting.

Can Carol use 3 cm squares? 6 cm on a side?

4 . What is the maximum size of tile that Carol can lay? How many tiles will she use?

__Exercise n°3 : 4 points.__

Students stretched two ropes between points A and D, then between points B and C. The two ropes intersect at E.

We know that: EA=7 m, EB = 13 m, EC= 10 m and ED = 9 m.

**Are the lines (AC) and (BD) parallel ?**

__Exercise n° 4 : 7 points.__

A family wants to buy a cylindrical above-ground pool for their children, equipped with an electric pump. She plans to use it this summer from June to September inclusive.

It has a budget of 200 €.

Using the following documents, tell us if this family’s budget is sufficient for the purchase of this pool and the operating costs.

*Leave any trace of research, even if it is not completed.*

__Exercise n° 5 : 4 points.__

Claude, a carpenter, takes the following measurements in the corner of a wall 1 meter above the floor to build an ABC shelf:

AB = 65 cm; AC = 72 cm and BC = 97 cm

He thinks for a few minutes and ensures that the shelf has a right angle.

**Is he right? Justify your answer.**

__Exercise n° 6 : 3 points.__

Here are three figures made with the Scratch software.

**Associate each figure with its corresponding program (justify your answers).**

__Exercise 7: 7 points__

We consider the following calculation program:

- Show that if the number chosen at the beginning is 2, then the result obtained is 5.
- What is the result obtained with this program if the number chosen at the beginning is -10 ?
- A student realizes that by calculating double 2 and adding 1, he gets 5, the same result he got in question 1.

He then thinks that the calculation program amounts to calculating double the starting number and adding 1.

Is he right?

- If is the number chosen at the beginning, show that the result of the calculation program is .

What number(s) must be chosen at the start of the calculation program to obtain 17 as the result?

__Exercise n° 8 : 3 points.__

Here is the course of the cross-country race of the Arthur Rimbaud school schematized by the figure RIMBAUD below:

- Third graders are required to complete four laps of the course. Calculate the total length of their stroke.

- Tery, the winner of the ninth grade boys’ race, completed his race in 10 minutes and 42 seconds.

Calculate its speed in m/s (round the result to the hundredth).

- If Tery maintained his average speed, do you think he could beat champion George Richmond, who won the 15km Foulées du Front de mer race in 55 minutes and 11 seconds?

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