**math certificate**Report an error / Note?

Length of test: 2 hours 100 points

This subject includes 6 exercises.

As soon as you receive the subject, make sure it is complete.

The use of any model of calculator, with or without exam mode, is allowed.

The use of the dictionary is prohibited.

**Exercise 1 (20 points)**

For each of the following statements, say whether it is true or false, carefully justifying the answer.

1) Scratch wants to join a friend, but he forgot the end of the journey. He decides to finish his journey by taking, at the intersections, a random right or left.

**Assertion 1:** The probability that it arrives at A, B or C is the same.

2) It is assumed that a wind turbine produces 5 GWh of electricity per year and that a person needs 7,000 kWh of electricity per year. (Wh: Watt-hour)

**Assertion 2:** A wind turbine does not cover the electricity needs of 1000 people for one year.

3) Here are four numbers: 45%; ; 0.5; .

**Statement 3:** These four numbers are arranged in ascending order.

4) The histogram below represents the distribution of wages in a company:

**Statement 4:** More than 40% of employees have a salary of at least €1,700.

**Exercise 2 (16 points)**

Whales emit sounds, with frequencies between 10 Hz and 10 kHz, that travel through the water at a speed of about 1500 mph.

The study of whale songs aims to elucidate their possible significance; sexual partner selection and social communication are hypotheses considered.

1. Convert the speed of propagation of these sounds in km/h.

2. Two groups of whales located off Alaska communicate with each other.

2.1. Calculate the distance between the two groups of whales.

You will give the result rounded to the nearest 50 km.

2.2. How long does it take a sound wave emitted by a whale in Group 1 to reach the whales in Group 2? You will give the result rounded to the minute.

3. The drawing below gives an idea of the size of a blue whale compared to a human.

Considering that the diver in the image is 1.75 m tall, calculate the approximate size of the whale shown below. You will give the result rounded to the nearest meter.

*The research process and traces of research will be valued and taken into account in the marking.*

**Exercise 3 (16 points)**

Fifteen students in class A and ten students in class B are asked to count the number of text messages they send over a weekend. On Monday, we get the results in a spreadsheet.

1. Calculate the mean and median number of text messages sent over the weekend by these students in class A.

2. What formulas could have been written in cells Q3 and R3 of the spreadsheet ?

3. Calculate the average number of text messages sent over the weekend by these 25 students in classes A and B.

4. Calculate the median number of text messages sent over the weekend by these 25 students in classes A and B.

**Exercise 4 (18 points)**

1. The manager of the largest multi-sport club in the region noted that between January 1, 2010 and December 31, 2012, the club’s total membership increased by 10% and then increased again by 5% between January 1, 2013 and December 31, 2015.

The total number of members in 2010 was 1000.

1.1. Calculate and justify the total number of members as of December 31, 2012.

1.2. Calculate, with justification, the total number of members as of December 31, 2015.

1.3. Martine believes that by December 31, 2015, there should be 1150 members because she says, “a 10% increase and then another 5%, that’s a 15% increase.” What do you think about it? Explain your answer.

2. As of January 1, 2017, membership stood at 1260.

Here is the breakdown of the 2017 membership based on their sport of choice.

2.1. Complete the column entitled “Corresponding angle in degrees” on the appendix, page 8. (To explain your approach, you must include the corresponding calculations on your copy).

2.2. To represent the situation, construct a pie chart of radius 4 cm.

2.3. Complete the column “Frequency in %” on the appendix. (In order to explain your approach, you must include the corresponding calculations on your copy. You will give the result rounded to the nearest hundredth).

**Exercise 5 (16 points)**

**The two parts of this exercise are independent.**

Mario, who runs a fast-growing scuba diving center, decides to build a building to accommodate his clients during lunch break. It will consist of an air-conditioned first floor used as a dining room and a non-air-conditioned floor that can be used for the storage of diving equipment.

To finish establishing his budget, he only has to choose a suitable model of air conditioning and calculate the necessary quantity of tiles to cover the roof of his building that he has schematized below.

**Document 1: Sketch made by Mario.**

The sketch is not to scale.

The two slopes (or sides) of the roof form an angle measuring 76° which is divided into two equal parts of 38°.

**Document 2: Flat tiles chosen by Mario to cover his roof.**

Allow 26 tiles per m².

Price: 0,65 euro each.

1. **PART 1: Calculating the budget for the tiles.**

1.1. Calculate AD. You will give the result rounded to the nearest centimeter.

1.2. Calculate AE. You will give the result rounded to the nearest centimeter.

1.3. Deduct the price of the tiles needed to cover the two slopes of the roof.

2. **PART 2: Choosing a suitable air conditioner.**

With the help of the documents, make a reasoned, suitable and least expensive choice of air conditioner to air condition the first floor of the building, i.e. the dining hall.

**Document 3: How to choose an air conditioner?**

Step 1: Know the required cooling capacity.

This depends on the volume of the parts to be cooled.

The cooling capacity is expressed in BTU which is a unit of refrigeration measurement.

The table below shows the correspondence between the volume of the building to be cooled and the required BTU power.

Step 2: Choose the most suitable air conditioner.

**Exercise 6 (14 points)**

Here is a script entered by Alice in an algorithmic software.

1. Alice has chosen 3 as her number, calculate the values of Result 1 and Result 2? Justify by showing the calculations made.

2. Generalization

2.1. Calling the number chosen in the algorithm, give a literal expression translating the first part of the algorithm corresponding to Result 1.

2.2. Calling the number chosen in the algorithm, give a literal expression translating the second part of the algorithm corresponding to Result 2.

3. Find the number or numbers chosen by Alice that match the result shown below.

**APPENDIX**

Exercise 4 question 2:

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