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**Exercise 1: (3 points)**

The graph below represents the water height in meters in the port of Brest on October 26, 2015.

The questions 1) and 2) are independent. 1) Using this graph, answer the following questions. No justification is expected.

(a) On October 26, 2015, approximately what was the water level at 6:00 a.m. in Brest Harbor?

(b) On October 26, 2015 between the hours of 10:00 a.m. and 10:00 p.m., for approximately how long was the

Was the water level higher than 3 meters?

2) In France, the magnitude of the tide is indicated by a whole number called the “coefficient of

tide”.

In the port of Brest, it is calculated using the formula: giving a

result rounded to the nearest integer with :

● C : tidal coefficient

● H: maximum water height in meters during the tide

● N0 = 4.2 m (average level in Brest)

● U = 3.1 m (unit of height in Brest)

On the afternoon of October 26, 2015, the maximum water height was 7.4 meters.

Calculate the coefficient of this tide (result rounded to the unit).

**Exercise 2: (6 points)**

In the figure opposite, point J belongs to the segment [IM] and point K belongs to the segment [IL].

In the figure, the lengths are given in meters.

1) Show that IKJ is a right triangle.

2) Show that LM is equal to 3.75 m.

3) Calculate the length KM to the nearest centimeter.

**Exercise 3: (5.5 points)**

The spreadsheet below gives the world production of vanilla in 2013.

1) Which spreadsheet formula was entered in cell **B15**?

2) Between them, Indonesia and Madagascar produce more than three quarters of the world’s vanilla?

3) We look at the five countries that produced the least vanilla in 2013.

What percentage of the world’s production does the vanilla production of these five countries represent? Round the result to the unit.

**Exercise 4: (4.5 points)**

This exercise is a multiple choice questionnaire. No justification is expected.

For each question, only one answer is correct.

Copy the question number and the correct answer on the copy.

Any correct answer is worth 1.5 points. Any inaccurate answer or lack of answer does not take away from the

point.

**Question 1**

The number 2 is the solution of the inequation :

a) b) c) d)

**Question 2**

The function which associates the number to any number is represented by :

**Question 3**

A runner who covers 100 meters in 10 seconds has a speed equal to :

a) 6 km/min b) 36 km/h c) 3600 m/h d) 10 km/h

**Exercise 5: (5 points)**

On a sewing blog, Archibald found a data sheet for drawing a pentagram (five-pointed star).

This data sheet is given below to be returned with the copy.

**Data sheet found on the blog**

1) Complete and finish below the construction of the five-pointed star started by

Archibald.

**Construction started by Archibald**

The points B, D, J, M, E, F, G, H and I will be shown.

2) Rewrite the third instruction on the copy using the appropriate mathematical vocabulary.

3) Using this data sheet, Anaïs obtained the construction below.

She measures the angles and and finds that they are equal.

Is this the case for all the pentagrams built with this method?

**Exercise 6: (7 points)**

Melanie builds a veranda against one of the walls of her house.

To cover the veranda roof, she goes to a material wholesaler who provides her with

information about two tile models.

**Document 1: Information on the veranda**

**Document 2: information on the tiles**

1. A stain hides the price per m² of “Regency tiles”. Calculate this price.

2. Does the slope of the veranda roof, i.e. the angle , allow for the installation of each model?

3. Melanie finally decides to cover the roof of her veranda with Roman tiles. These tiles are

sold individually.

To determine how many tiles to order, the salesperson explains:

” *First, you need to calculate the area to be covered. This area must then be increased by 5%.* ”

With this advice in mind, how many tiles should she plan to purchase?

**Exercise 7: (5 points)**

A pizzeria makes round pizzas with a diameter of 34 cm and square pizzas with a side of 34 cm.

All pizzas :

– have the same thickness;

– are delivered in identical boxes.

Square pizzas cost 1 € more than round pizzas.

1) Peter buys two pizzas: one round and one square. He pays 14,20 €.

What is the price of each pizza?

2) The pizzas are cut as shown in the diagram: eight equal-sized slices in a round pizza and

nine equal-sized slices in a square pizza.

Which pizza has the largest slices?

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