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DIPLÔME NATIONAL DU BREVET

SESSION 2017

FIRST TEST

Part 1

MATHEMATICS

General series

Duration of the test: 2 hours – 50 points

**Common theme of the subject of Mathematics, Physics-Chemistry and Life and Earth Sciences**

**The Sport**

**Exercise 1: (9 points)**

On a spreadsheet, the top ten countries were ranked by

number of medals, at the Rio Olympic Games in 2016.

1. Which of the three formulas proposed was entered in cell F2 of

this spreadsheet, before it is stretched down?

2. We observe the series of gold medals of these ten countries.

a. What is the extent of this series?

b. What is the average of this series?

3. What is the percentage of gold medals won by France in relation to

to its total number of medals? Round the result to the tenth of a percent.

4. The ranking at the Olympic Games is established according to the number of gold medals

obtained and not according to the total number of medals. For this reason, France

with 42 medals is behind Japan which has only 41. By observing

Italy and Australia, establish the ranking rule in case of a tie on the number of

of gold medals.

5. A sports journalist proposes a new procedure for ranking countries:

each gold medal earns 3 points, each silver medal earns 2

points and each bronze medal is worth 1 point. Under these conditions, the

Would France overtake Japan?

**Exercise 2: (10 points)**

On July 17, 2016, a spectator watches the “Bourg-enBresse / Culoz” stage of the Tour de France.

She notes, every half hour, the distance covered by the French cyclist Thomas VOECKLER who took 4 h 30 min to cover this 160 km stage; she only forgets to note the

distance covered by this one at the end of 1 hour of race.

She gets the following table:

1. How far did he run after 2 hours and 30 minutes?

2. Show that he has covered 30 km in the third hour of the race.

3. Was he faster in the third or fourth hour of

race?

4. Answer the following questions on the APPENDIX page 7 of 7, which is

to be returned with the copy.

a. Place the 9 points of the table in the marker. We can’t place the

point of abscissa 1 since we do not know its ordinate.

b. Using your ruler, connect the consecutive points together.

5. Considering that the speed of the cyclist is constant between two readings,

determine, by graphical reading, the time it took him to travel 75 km.

6. We consider that the speed of the cyclist is constant between the first reading

after 0.5 hours of running, and after 1.5 hours of running

run; determine by graphical reading the distance covered after 1 hour

of the race.

7. Let be the function, which to the time of course of the cyclist Thomas VOECKLER,

associates the distance traveled. Is the function linear?

**Exercise 3: (6 points)**

The gardener of a soccer club decides to reseed the grass on the field.

game. In order for it to grow properly, he installs a watering system

which is activated in the morning and in the evening, each time, for 15 minutes.

– The watering system consists of 12 independent circuits.

– Each circuit is composed of 4 sprinklers.

– Each sprinkler has a flow rate of 0.4 m3 of water per hour.

How many liters of water will have been consumed if the lawn is watered for the entire

month of July?

Remember that 1 m3 = 1,000 liters and that the month of July has 31 days.

**Exercise 4: (7 points)**

The figure below shows a cross-section of a gymnasium grandstand. For

to see the game in progress, a spectator in the last row sitting in C should look over the

of the spectator placed in front of him and sitting in D. A part of the ground in front of the

tribune is then hidden from him. We will consider that the average height of a spectator

sitting is 80 cm (CT = DS = 80 cm).

On this cutaway of the grandstand :

– the points R, A and B are horizontally aligned and the points B, C and T are

vertically aligned;

– the points R, S and T are aligned parallel to the inclination (AC) of the stand;

– we will consider that the area represented by the segment [RA] is not visible

by the spectator in the last row;

– the width of the stand is 11 m and the angle of inclination of the

grandstand measures 30°.

1. Show that the height BC of the stand is 6.35 m, rounded to the hundredth

of meter.

2. What is the measure of the angle?

3. Calculate the length RA in centimeters. Round the result to the nearest centimeter.

**Exercise 5: (7 points)**

The marathon event consists of covering the distance of

42.195 km in running. This distance refers historically to the feat performed

by the Greek PHILLIPIDES, in 490 BC. J-C, to announce the victory of the Greeks against

the Persians. It is the distance between Marathon and Athens.

1. In 2014, the Kenyan Dennis KIMETTO broke the old world record in

covering this distance in 2 h 2 min 57 s. What is then the order of magnitude

of its average speed: 5 km/h, 10 km/h or 20 km/h?

2. During the same race, the British Scott OVERALL took 2 h 15 min

to complete his marathon. Calculate its average speed in km/h. Round up the

value obtained to the hundredth of km/h.

3. In this question, we will consider that Scott OVERALL runs at a speed

constant. As Dennis KIMETTO crossed the finish line, determine :

a. Scott OVERALL’s time left to run;

b. the distance he has to go. Round the result to the nearest meter.

**Exercise 6: (6 points)**

The figure below is a screenshot of a program made with the software “Scratch”.

1. Show that if we choose 2 as the starting number, then the program returns -5

2. What does the program return if we choose :

a. the number 5 ?

b. the number -4 ?

3. Determine the numbers that must be chosen at the beginning for the program to return 0.

**APPENDIX**

To be detached from the subject and attached with the copy.

**Exercise 2 question 4**

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