Brevet de maths 2023 with the blank subject and its answer key

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A subject of brevet blanc 2023 in maths containing a MCQ, trigonometry and regular polygons, generalities on functions with exploitation of the curve and calculation of an average speed, literal calculation and application of the theorem of Thales.
The use of the calculator is allowed, but any exchange of material is prohibited
The exercises are independent and can be done in any order.

Exercise 1

This exercise is a multiple choice questionnaire (MCQ). No justification is required. For each question, four answers are proposed, only one is correct.
For each question, write on your copy the question number and the letter A, B, or C chosen.


Exercise 2

Here is a regular octagon ABCDEFGH.

Regular octagon

1. Show an enlargement of this octagon by inscribing it in a circle of radius 3 cm. No justification is expected for this construction.
2. Prove that the triangle DAH is right-angled.
Calculate the measure of the angle \widehat{BEH}.

Exercise 3

Cedric is training for a triathlon bike race.
The curve below shows the distance in kilometers versus the elapsed time in minutes.


For the first three questions, the answers will be given through graphic readings.
No justification is expected on the copy.
1. How far did Cedric travel after 20 minutes?
2. How long did it take Cedric to cover the first 30 km?
3. Cedric’s circuit includes a climb, a descent and two flat portions. Re-
constitute in order the route taken by Cedric.
4. Calculate Cedric’s average speed (expressed in km/h) on the first of the four
parts of the route.

Exercise 4

ABCD is a rectangle such that AB = 30 cm and BC = 24 cm.
Four identical squares are colored in gray at the four corners of the rectangle. We delimit
thus a central rectangle that is colored in black.


1. In this question, the four gray squares are all 7 cm on a side. In this case :
a. what is the perimeter of a gray square?
b. what is the perimeter of the black rectangle?
2. In this question, the length of the side of the four gray squares can vary, and we call it x
a. Express the length L and width l of the rectangle as a function of x
b. Calculate the perimeter of the rectangle as a function of x
c. Is it possible that the perimeter of the black rectangle is equal to the sum of the perimeters of the four gray squares?

Exercise 5

In the drawing below, points A, B and E are aligned, and C is the middle of [BD].

figure and patent of maths 2023

1. What is the nature of the triangle ABC?
2. Deduce the nature of the triangle BDE.
3. Calculate ED. Round the result to the tenth.

Exercise 6

Indicate whether the following statements are true or false.
Reminder: all answers must be justified.

Assertion 1:
“The average speed of a runner traveling 18 km in one hour is strictly greater than that of a remote-controlled car traveling 5 m per second.”

Assertion 2:
“For any number x, we have the equality: (3x-5)^2=9x^2-25

Assertion 3:
“The PGCD of 18 and 36 is 9.”

Assertion 4:
“The duplicate of \frac{9}{4} is \frac{9}{2}.

Exercise 7

When choosing a TV screen, computer screen or touch tablet, you can look at:
– its format which is the ratio length of the screen width of the screen
– to its diagonal which is measured in inches. One inch is equal to 2.54 cm.
1. A television screen is 80 cm long and 45 cm wide. Is it a \frac{4}{3} or \frac{16}{9} screen?
2. A screen is sold with the mention ” 15 inches “. We take the following measurements: the length is 30.5 cm and the width is 22.9 cm. Is the “15” label appropriate for this screen?
3. A touch tablet has a screen of diagonal 7 inches and of format \frac{4}{3}, its length being equal to 14,3 cm, calculate its width, rounded to the nearest mm.

Exercise 8

Here is a calculation program:

Calculation program

1. Show that if we choose 8 as the starting number, the program gives 12 as the result.
2. For each of the following statements, indicate whether it is true or false.

Remember that answers must be justified.

Proposition 1:
The program can give a negative result;

Proposition 2:
if we choose \frac{1}{2} as the starting number, the program gives \frac{33}{4} as the result;
Proposition 3:
The program gives 0 as the result for exactly two numbers.

Exercise 9

1. Without doing any calculations, explain why we can simplify the fraction \frac{258}{1204}.
2. Calculate the PGCD of the numbers 258 and 1,204 with the method of your choice by detailing the calculations.
3. Deduct the irreducible fraction equal to \frac{258}{1204}.

Exercise 10

Students participate in a foot race. Before the test, they were given a plan. It is shown below.


We agree that:
The lines (AE) and (BD) intersect at C.
The lines (AB) and (DE) are parallel.
ABC is a right triangle at A.
Calculate the actual length of the path ABCDE.

If the work is not completed, leave a record of the research anyway. It will be taken into account in the scoring.

Answers to the mathematics patent Consult the online answer key

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