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**Exercise 1: (15 points)**

This exercise is a multiple choice questionnaire (MCQ).

For each question, only one of the three proposed answers is correct.

On the copy, indicate the number of the question and copy, without justification, the chosen answer.

A correct answer earns 3 points; no points will be deducted for a wrong answer.

**Exercise 2: (14 points)**

We consider the following calculation program:

- Show that if we choose 1 as the starting number, the program gives 6 as the result.
- What result do we get if we choose – 5 as the starting number?
- We call x the starting number, express the result of the program as a function of x.
- Show that this result can also be written as (x+2)(x+1) for all values of x.
- The following spreadsheet contains the results of the previous calculation program:

a. Which formula was written in cell B2 before extending it to cell J2?

b. Find the values of x for which the program gives 0 as the result.

**Exercise 3: (16 points)**

**Part I:**

*In this section, all lengths are expressed in centimeters.*

Consider the two figures below, an equilateral triangle and a rectangle, where x is any positive number.

1.construct the equilateral triangle for x=2.

2.

a. Show that the perimeter of the rectangle as a function of x can be written 12x+3.

b.For what value of x is the perimeter of the rectangle equal to 18 cm?

Is it true that the two figures have the same perimeter for all values of x?

**Part II:**

We created the scripts below on scratch that, after asking the user for the value of x, construct the two figures in Part I.

In these two scripts, the letters A, B, C and D replace numbers.

Give the values to A, B, C and D so that these two scripts can build the

figures in Part I and then specify the figure associated with each of the scripts.

**Exercise 4 : ( 13 points)**

In the window of a store A are presented a total of 45 models of shoes.

Some are designed for the city, others for sports and come in three different colors: black, white or brown.

1.Complete the following table:

2. We choose a shoe model at random in this window.

a. What is the probability of choosing a black model?

b. What is the probability of choosing a model for sports?

c. What is the probability of choosing a brown city model?

3. In the window of a store B, there are 54 models of shoes, 30 of which are coloured.

A shoe model is chosen at random from the window of store A and then from the window of store B.

In which of the two windows is there a greater chance of obtaining a colored model?

**Exercise 5: (14 points)**

In the following exercise, the figures are not to scale.

A decorator has drawn a side view of a storage unit consisting of a metal frame and 2 cm thick wooden shelves, shown in Figure 1.

The floors of the metal structure of this storage unit are all identical and Figure 2 shows one of them.

We give:

- OC = 48 cm; OD = 64 cm; OB = 27 cm; OA = 36 cm and CD = 80 cm;
- the lines (AC) and (CD) are perpendicular.

1. show that the lines (AB) and (CD) are parallel.

Show by calculation that AB = 45 cm.

Calculate the total height of the storage unit.

**Exercise 6: (14 points)**

Does this graph represent a situation of proportionality? Justify the answer.

2.the graph will be used to answer the following questions. No justification is required.

a.What is the total duration of this hike?

b. What is the total distance this family traveled?

c.What is the distance covered after 6 hours of walking?

d. After how long did they cover the first few kilometres?

e. What happened between the 4th and 5th hour of the hike?

An experienced hiker walks at an average speed of 4 km/hr for the entire hike.

Is this family experienced? Justify the answer.

**Exercise 7: (14 points)**

A family wants to buy a cylindrical above-ground pool for their children, equipped with an electric pump. She plans to use it this summer from June to September inclusive.

It has a budget of 200 €.

Using the following documents, tell us if this family’s budget is sufficient for the purchase of this pool and the operating costs.

*Leave any trace of research, even if it is not completed.*

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