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Diplôme national du Brevet de mathématiques

New Caledonia in March 2019

Duration: 2 hours

**Exercise 1: Multiple choice questions (12 points)**

This exercise is a multiple choice questionnaire (MCQ). For each question, only one of the three proposed answers is correct. On the copy, write the number of the question and the chosen answer.

No justification is required.

No points will be deducted for incorrect answers.

**Exercise 2 : 9 points**

During a trip to Osaka, Jade ate TAKOYAKI (Japanese cakes) that she wants to make again at home.

For this purpose, it has a baking tray with several cake pans. All molds are identical.

Each mold is shaped like a half-sphere with a radius of 3 cm.

**Reminders:**

1 L = 1

Volume of a ball of radius r :

1. Calculate the volume of a mold (in ), round the result to the tenth.

2. In this question, the volume of a mold is considered to be 57 .

Jade made 1 L of dough. It must fill each mold to of its volume.

How many TAKOYAKI can she do? Justify the answer.

**Exercise 3 : 12 points**

1. Consider the function g represented in the frame below.

a. Give the antecedent of 4 by the function g .

b. Complete the table of values for the function g below.

2. The function f is given by f (x) = 2x.

a. What is the image of -2 by the function f?

b. Calculate f (3).

c. Draw the graphical representation of the function f .

3. Determine graphically the abscissa of the intersection point S of the two graphs.

Show the reading on the graph in dotted lines.

4. The expression of the function g is g (x) = -2x +8.

a. Solve the equation 2x = -2x +8

b. What does the previous result represent graphically?

**Exercise 4: Caledorail (11 points)**

Calédorail is a bus project that would connect different strategic points of the city of Noumea.

1. **Length of the line**

The average distance between two stations is about 450 meters. Estimate the distance between the

station 1 and station 4.

2. **Average speed**

The Caledorail bus would take 24 minutes to complete a 9.9 km trip.

What would be its average speed in km/h?

3. **Tariff**

Currently, a bus ticket costs 190 F. The Caledorail bus ticket would cost 40% more.

What would be the price of the Caledorail bus ticket?

**Exercise 5 : 17 points**

Here are the rankings of the 21 countries that won gold medals at the 2018 Pyeongchang Winter Olympics in Korea.

We consider the series constituted by the number of gold medals obtained by each country.

The ranking is summarized in the spreadsheet below:

1. a. Calculate the average number of gold medals per country (round the result to the tenth).

b. Determine the median number of gold medals per country.

c. Interpret the result of question 1. b.

2. What formula was entered in cell L2 to obtain the total number of countries that have had at least one of the following

At least a gold medal?

3. We take a country at random among the countries that have at least one gold medal.

a. What is the probability that he will have one gold medal?

Give the answer in fractional form.

b. What is the probability that he has at least 5 gold medals?

Give the answer in fractional form.

**Exercise 6: 10 points**

Here is a program made with Scratch to build a parallelogram.

Depending on the given length and angle, this parallelogram can be particular (rectangle, rhombus,

square).

1. Draw below the parallelogram obtained with the given length and angle.

2. What value should be given to length and what value to angle to obtain the figure below?

3. A student chose the length 50 and the angle 75° and then copied the resulting figure after running the script.

Which of the three parallelograms below did he draw?

Write the corresponding letter on the copy.

**Exercise 8 : 12 points**

For her comfort, Lisa wants to install a triangular shade sail in her garden.

The area of this one must be of 8 m² minimum.

For each of the following three models, indicate on the copy if it is appropriate by justifying each answer.

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