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Diplôme National du Brevet

Session 2019

Topic Asia

Monday, June 23, 2019

Mathematics

General Series

Duration of the test: 2 hours – 100 points

**Exercise 1 : 14 points**

Nina and Claire each have a calculation program.

1. Show that if both girls choose 1 as their starting number, Nina will get a final result 4 times larger

than Claire’s.

2. What starting number must Nina choose to get 0 at the end?

3. Nina says to Claire: “If we choose the same starting number, my result will always be four times greater than yours”.

Is she right?

**Exercise 2 11 points**

The table below presents the greenhouse gas emissions for France and the European Union, in millions of

tons of CO2 equivalent, in 1990 and 2013.

1. Between 1990 and 2013, greenhouse gas emissions in the European Union decreased by 21%.

How much greenhouse gas was emitted in 2013 by the European Union?

Give an answer to the nearest 0.1 million tons of CO2 equivalent.

2. France is committed to reducing its greenhouse gas emissions by by 2030 compared to 1990.

Justify that this corresponds to a reduction of approximately in France’s greenhouse gas emissions compared to 2013.

**Exercise 3: 17 points**

A program allows a robot to move on the squares of a grid. Each square reached

is colored in gray. At the beginning of a program, all the boxes are white, the robot positions itself

on a starting square marked with a “d” and immediately colors it in gray.

Here are examples of programs and their effects:

1. Here is a program:

Program: 1W 2N 2E 4S 2W

We want to draw the pattern obtained with this program.

On your copy, make this pattern using tiles, as in the previous examples. A “d” will be marked on the starting square.

2. Here are two programs:

Program #1: 1S 3(1N 3E 2S)

Program #2: 3(1S 1N 3E 1S)

a. Which of the two programs produces the pattern shown on the right?

b. Explain why the other program does not produce the pattern below.

3. Here is another program:

Program #3: 4(1S 1E 1N)

It gives the following result:

Rewrite this program #3 by changing only one instruction to obtain this:

**Exercise 4 : 16 points**

To make a well in her garden, Mrs. Martin needs to buy 5 concrete cylinders like the one described below.

In its trailer, it has the space to put the 5 cylinders but it can only carry a maximum of 500 kg.

Using the characteristics of the cylinder, determine the minimum number of round trips required for Mrs. Martin to bring back her 5 cylinders with her trailer.

**Reminder:** volume of a cylinder V = ×radius×height

**Exercise 5 : 12 points**

The figure below is coded and made freehand.

It represents a quadrilateral ABCD whose diagonals intersect at a point O.

We give: OA = 3.5 cm and AB = 5 cm.

We are interested in the nature of the quadrilateral ABCD which has been represented.

1. Can we affirm that ABCD is a rectangle ?

2. Can we say that ABCD is a square?

**Exercise 6 : 14 points**

Here is a table (document 1) concerning “diesel or gasoline” passenger cars in circulation in France in 2014.

1. Verify that there were 31,725,000 “diesel or gasoline” cars in circulation in France in 2014.

2. What is the proportion of gasoline cars among “diesel or gasoline” cars in circulation in France in 2014?

Express this proportion as a percentage.

The result will be rounded to the unit.

3. At the end of December 2014, during a TV game show, a car was drawn from among the “diesel or gasoline” cars on the road in France. The owner of the car drawn was then offered to trade it in for a new electric vehicle.

The presenter called Hugo, the lucky owner of the car drawn.

Here is an excerpt from the dialogue (document 2) between the presenter and Hugo:

Using the data in Handout 1 and Handout 2:

3.a Explain why the presenter thinks Hugo has a diesel vehicle.

3.b Explain whether it is possible that Hugo’s car is a gasoline vehicle.

**Exercise 7 : 16 points**

The graphical representations C1 and C2 of two functions are given in the reference frame below.

One of these two functions is the function f defined by f (x) = -2x+8.

1. Which of these two representations is that of the function f ?

2. What is f (3) ?

3. Calculate the number whose image is 6 by the function f .

4. The spreadsheet below is used to calculate images by the function f .

What formula can be entered in cell B2 before stretching it to the right to cell G2?

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