Brevet de maths 2022 : subject and answer key in PDF

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Session: 2022 – 2 hours

Exercise 1 (6 points)
For each of the following five statements, indicate on the copy whether it is true or false. Remember that each answer must be justified.

Assertion #1:
“The expression =(-5)(+1) has the expanded and reduced form x^2-4x-5 “.

Assertion #2:
“When the positive integer n is equal to 5, the number 2^n+1 is a prime number.

Assertion #3:
“The sum of two integers that are multiples of 5 is a multiple of 10.

Assertion #4:
“The expression F=3x^2-8x+7 takes the value =35 if =-2.

Assertion #5:
“The diagonals of a rectangle ABCD of length 160 cm and width 95 cm measure exactly 186 cm”.

Exercise 2 (5 points)
1) Justify that the number 102 is divisible by 3.

2) The prime factor decomposition of 85 is given: 85\,=\,5\,\times  \,17.
Decompose 102 into a product of prime factors.

3) Give 3 non-prime divisors of the number 102. A bookseller has a 85 cm × 102 cm hardback sheet.
He wants to cut out square labels from it, using the whole sheet. The sides of these labels all have the same measurement.

4) Can the labels be 34 cm square? Justify your answer.

5) The bookseller cuts out 17 cm square labels. How many labels will he be able to cut out in this case?

Exercise 3 (7.5 points)

Aurélie is cycling in England at the Hardknott Pass.

It started from an altitude of 251 meters and will reach the summit at an altitude of 393 meters.

In the diagram below, which is not full-scale, the starting point is represented by point A and the vertex by point E.

Aurélie is currently at point D.

patent maths 2022 exercise 1

The lines (AB) and (DB) are perpendicular.

The lines (AC) and (CE) are perpendicular.

The points A, D and E are aligned.

The points A, B and C are aligned. AD = 51.25 m and DB = 11.25 m.
1) Justify that the height difference that Aurelie will have covered, i.e. the height EC, is equal to 142 m.

2) a) Prove that the lines (DB) and (EC) are parallel.

b) Show that the distance Aurelie still has to travel, i.e. the length DE, is about 596 m.

3) We will use for the length DE the value 596 m.

Knowing that Aurelie drives at an average speed of 8 km/h, if she leaves at 9:55 a.m. from point D, at what time will she arrive at point E? Round up to the minute.

Exercise 4 (9 points)
On the figure below which is not full size :
The segments [OA] and [UI] intersect in M.
MO = 21 mm, MA = 27 mm, MU = 28 mm, Ml = 36 mm and Al= 45 mm.

patent maths 2022 exercise 2
1) Prove that the lines (OR) and (AI) are parallel.
2) Calculate the OR length.
3) Prove that the triangle AMI is a rectangle.
4) Determine, to the nearest degree, the measure of the angle \widehat{AIM}.

Exercise 5 (6 points)

patent maths 2022 exercise 3

1) Justify that if the starting number N is equal to 18, the final result of this algorithm is
2) What is the final result if we choose 14 as the starting number N?
3) By applying this algorithm, two different starting numbers allow to obtain 32
as the final result. What are these two numbers?
4) We program the previous algorithm:

patent maths 2022 exercise 4

a) Copy line 3 by completing the dotted lines. Line 3: If Answer >………. then.
b) Copy line 6 by completing the dotted lines. Line 6: Say ………. * ( …….. + ………. )
for 2 seconds.

Exercise 6 (6.5 points)
For her comfort, Elise wants to install a triangular shade sail in her garden.
The area of this one must be of 6 m² minimum.
Which of the following three sails would be suitable?

patent maths 2022 exercise 5

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