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**BREVET of MATHS 2021**

BLANK SUBJECT N° 3

_______________

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:**

This exercise is a Multiple Choice Questionnaire (MCQ).

For each question there can be one or more answers, or even one.

Each correct answer earns 0.5 points, each wrong answer cancels a correct answer.

For each of the following questions, write without justification the question number and the letter(s) of the correct answer(s).

1. Calculate the PGCD of 1755 and 1053.

2. Write the fraction in irreducible form.

3. A shell collector (a conchyliologist) has 1755 cones and 1053 porcelains.

He wishes to sell all his collection by making identical lots, that is to say comprising the same number of shells and the same distribution of cones and porcelains.

(a) What is the maximum number of lots he can make?

(b) How many cones and porcelain will there be per batch in this case?

**Exercise 3: Road safety**

When turning around while reversing, the driver of a pickup truck sees the ground 6 meters away

On the diagram, the grey area corresponds to what the driver does not see when he looks back.

1. Calculate DC.

2. Deduce that ED = 1.60 m.

3. A girl is 1.10 m tall. It passes 1.40 m behind the van.

Can the driver see it? Explain.

**Exercise 4:**

Mr. Archi and Mr. Mede are celebrating the birthday of their neighbor Mrs. Eureka.

All three have a flute of champagne in their hands.

This flute is a pyramid with a square base, the top of which rests on a square base.

We give:

EF = 12 cm and IG = 4 cm.

1. Show that the maximum capacity of each flute is 64 .

2. Mr. Archi filled each flute to three quarters of its capacity.

How much champagne is in each flute?

3. As the champagne is not very fresh anymore, Mr. Mede goes to get some cubic ice cubes

of edges 1, 5 cm.

(a) What is the volume of each ice cube?

(b) An ice cube floats in champagne in such a way that one fifth of its volume remains above the surface of the champagne (a bit like an iceberg in the ocean).

How many ice cubes must Mr. Mede put in Mrs. Eureka’s flute so that the champagne overflows from the flute?

**Exercise 5:**

Within the framework of a pedagogical project, teachers prepare an outing to Mont Saint Michel

with 48 students of 3e.

Two activities are on the program:

– the visit of the Mont and its abbey;

– the crossing of the Mont Saint Michel bay on foot.

The total cost of this outing (bus, accommodation and food, activities, … ) is 120 € per student.

1. To reduce the cost of the trip, the teachers decide to organize a raffle.

Each student has a card containing 20 squares that he must sell at 2 € per square.

In December, the teachers check with the 48 students on the number of boxes sold by each of them.

Here are the results:

(a) What is the total number of boxes already sold in December?

(b) How much money does this represent?

(c) What percentage of students sold 15 or fewer boxes? (round up to the nearest unit).

(d) What is the average number of boxes sold per student? (round up to the nearest unit).

2. The 92 prizes to be won are as follows:

– a bicycle;

– a DVD player;

– 20 DVDS;

– 20 x 4GB USB drives;

– 50 bags of chocolates.

These lots are provided free of charge by three stores that have agreed to sponsor the project.

The lottery is held in March and all 960 boxes have been sold.

One person has purchased a box.

(a) What is the probability that this person will win a prize? (round to the hundredth)

(b) What is the probability that this person will win a flash drive? (round to the hundredth)

**Exercise 6:**

Jean-Michel owns a field, represented by the triangle ABC below. He buys from

its neighbor the adjacent field, represented by the triangle ADC. We thus obtain a new field

formed by the quadrilateral ABCD.

John Michael knows that the perimeter of his field ABC is 154 meters and that BC = 56 m.

His neighbor informs him that the perimeter of the field ADC is 144 meters and that AC = 65 m.

Moreover, he knows that AD = 16 m.

(a) Justify that the lengths AB and DC are equal to 33 m and 63 m respectively.

(b) Calculate the perimeter of field ABCD.

2. Show that the triangle ADC is right-angled at D.

We admit that the triangle ABC is rectangular in B.

3. Calculate the area of the field ABCD.

4. Jean-Michel wants to fence off his field with wire mesh. He goes to his usual retailer

and comes across the following ad:

**Mesh : 0,85 € per meter**

How much will he pay to fence his field?

**Exercise 7:**

**In this exercise, any trace of research, even if incomplete, will be taken into account in the evaluation.**

One drug may read:

- In children (12 months to 17 years of age), dosing should be based on the patient’s body surface area [voir formule de Mosteller].
- A single loading dose of 70 mg per square meter (not to exceed 70 mg per day) should be administered .

To calculate the body surface in m² we use the following formula (called Mosteller formula):

**Question:**

**Were the dosages followed for these two children?**

You will round your results to the nearest hundredth.

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