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**A subject of the brevet blanc de maths 2023 to revise online on Mathovore and to prepare for the brevet des collèges exams in June 2023.**

## Brevet blanc de maths 2023

**Spelling, care, quality and precision of the writing will be taken into account for 4 points out of 40 in the evaluation of the copy. The use of a calculator is allowed.**

**No equipment loans are allowed. Keep the subject for correction.**

### Exercise 1 : ( 4 points )

This exercise is a multiple choice questionnaire (MCQ). No justification is required.

For each question, three answers are proposed; only one is correct.

Each correct answer gives one point, a wrong answer or no answer does not remove any points.

**For each of the four questions, indicate on the copy the number of the question and copy the correct answer.**

### Exercise 2 : ( 4,5 points )

Here is a spreadsheet obtained with the help of a spreadsheet; in this exercise we try to understand how this sheet was filled in.

1. Looking at the values in the table, suggest a formula to enter in cell C1 and then copy down.

2. In this question, all traces of research should be left on the copy: they will be valued. The spreadsheet provides two functions MAX and MIN. From two numbers, MAX returns the larger value and MIN the smaller value. (example: MAX(23 ;12) = 23) Which formula was entered in cell A2 and then copied down?

3. What does the number in cell C5 represent, relative to the numbers 216 and 126?

4. Is the fraction 216/126 irreducible ? If not, make it irreducible by detailing the calculations.

### Exercise 3: ( 4.5 points )

The cycling course is a 10 km loop. The point of departure is therefore also the point of arrival.

At the halfway point, athletes are entitled to a refreshment.

The graph below represents the distance f(t) expressed in kilometers separating Helen from the arrival point as a function of time t expressed in minutes.

We call f the function thus represented.

All answers will be given using the graph.

1) How many kilometers are left to travel after 24 minutes?

2) Determine the image of the number 4 by the function f.

3) Determine f(8).

4) Determine the antecedent(s) of the number 0 by the function f.

5) For what value(s) of t does f(t) = 4?

### Exercise 4 : ( 3 points )

There are different units of temperature measurement: in France we use the degree Celsius (°C), in the United States we use the degree Fahrenheit (°F).

To change from degrees Celsius to degrees Fahrenheit, multiply the starting number by 1.8 and add 32 to the result.

1) What would a thermometer graduated in degrees Fahrenheit indicate if it were immersed in a pan of freezing water? We remind that water freezes at 0°C.

2°) What would a thermometer indicate in degrees Fahrenheit if it were immersed in a pot of water at 23°C?

3°) If we call x the temperature in degrees Celsius and f(x) the temperature in degrees fahrenheit, express f(x) as a function of x.

### Exercise 5 : ( 3 points )

For a good fishing trip by a canal, you need a suitable folding seat ‼

Nicolas is of average height and to be well seated, it is necessary that the height of the seat is between 44 cm and 46 cm.

The angle is right and ABDC is a rectangle.

**Is the height of this seat suitable for him?**

### Exercise 6 : ( 5 points )

A radioactive waste drum (shown here) has the shape of a cylinder with a radius of 0.6 meters and a height of 1.5 meters.

a) Calculate the volume of a single barrel. The exact value and the value rounded to the nearest dm3 will be given.

b) These drums with dangerous contents are to be stored in underground storage tanks with a parallelepiped shape (see photo).

If you have a pool with a length of 360 meters, a width of 150 meters and a height of 9 meters,

show that 225,000 drums can be stored in the warehouse.

c) What is the percentage of space lost in the storage basin?

The result will be rounded to the tenth.

### Exercise 7 : ( 4 points )

**Be careful, the traced figures do not respect the measures of length, nor the measures of angles.**

*Answer “true” or “false” or “can’t tell” to each of the following statements and explain your choice.*

1. Any triangle inscribed in a circle is a rectangle.

2. If a point M belongs to the bisector of a segment [AB], then the triangle AMB is isosceles.

3. In the following triangle ABC: .

4. The quadrilateral ABCD below is a square.

### Exercise 8 : ( 4 points )

Here is a map discovered by Marco that will allow him to unearth the fabulous treasure of Batmath the pirate.

The indications are: R is the skull-shaped rock; C is the coconut tree under which the treasure is buried; P is the lighthouse; C is located on the semicircle of diameter [PR].

We give PR = 3000 fathoms (old unit of measurement of length corresponding to the span of the arms)

a) Show that the triangle PRC is a right triangle.

b) Calculate the RC distance in fathoms.

### Exercise 9: initiative exercise.

Michael has 108 white marbles and 135 black marbles that he wants to sell at the flea market near his home. To do this, he wants to prepare as many identical bags as possible (same number of white marbles and same number of black marbles in each bag) using all his marbles.

**How much does a bag of marbles weigh?**

**How much can Michel earn by selling his bags?**

*Leave a written record of your research, even if incomplete.*

*They will be taken into account in the scoring.*

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