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**BREVET of MATHS 2021**

BLANK SUBJECT N° 2

_______________

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:**

One pastry chef prepared 840 financiers and 1,176 macaroons. He wants to make lots, all identical,

by mixing financiers and macaroons. He wants to use all the financiers and all the macaroons.

1. Without doing any calculations, explain why the numbers 840 and 1176 are not prime to each other

them.

2. Can the baker make 21 batches? If yes, calculate the number of financiers and the number of

buttons in each batch.

3. What is the maximum number of batches it can make? What will be the composition of

each of the lots?

**Exercise 2:**

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.

Reconstitute the route taken by Cedric in order.

4. Calculate Cedric’s average speed (expressed in km/h) on the first of the four parts

of the journey.

**Exercise 3:**

In this exercise, the coded figures are not full size.

Is each of the following statements true or false?

All answers must be justified.

**Assertion 1:**

The volume of this solid is .

**Assertion 2:**

The lines (ML) and (NO) are parallel.

**Assertion 3:**

The diagonal of a square of area 36 cm² has length cm.

**Assertion 4:**

0 has only one antecedent by the function which associates 3x +5 to any number x.

**Exercise 4:**

We are interested in the area on the ground that is illuminated at night by two light sources: the street lamp

from the street and the spotlight fixed in F on the front of the building.

The following data are available:

PC = 5.5 m; CF = 5 m; HP = 4 m;

;

1. Justify that the rounding to the decimeter of the length PL is equal to 3.4 m.

2. Calculate the length LM corresponding to the area illuminated by the two light sources.

We will round the answer to the decimeter.

3. We make adjustments to the spot located in F so that M and L are merged.

Determine the measure of the angle . The answer will be rounded to the nearest degree.

**Exercise 5:**

In this exercise, we consider the rectangle ABCD opposite such that its perimeter is equal to 31 cm.

1. a. If such a rectangle is 10 cm long, what is its width?

b. We call x the length AB. Using the fact that the perimeter of ABCD is 31 cm,

express the length BC as a function of x.

c. Deduce the area of rectangle ABCD as a function of x.

2. Consider the function f defined by f (x) = x(15.5-x).

a. Calculate f (4).

b. Check that an antecedent of 52.5 is 5.

3. On the graph below, we have plotted the area of rectangle ABCD as a function of the

value of x.

Using this graph, answer the following questions by giving approximate values:

a. What is the area of rectangle ABCD when x is 3 cm?

b. For what values of x does one obtain an area equal to 40 cm² ?

c. What is the maximum area of this rectangle? For what value of x is it obtained?

4. What can we say about the rectangle ABCD when AB is 7.75 cm?

**Exercise 6:**

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

behind his truck.

On the diagram, the grey triangle corresponds to what the driver does not see when looking at the

back.

Data: AB = 1.50 m and BC = 6 m

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

**Can the driver see it? Explain.**

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