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**Brevet de maths 2017 with a blank subject on the Pythagorean theorem and trigonometry as well as a MCQ and use of the spreadsheet and calculation of the volume of a solid.**

**Exercise N°1: QCM 5 points.**

This exercise is a multiple choice questionnaire.

For each row in the table, only one statement is correct.

On your copy, indicate the question number and copy the correct statement.

No justification is required.

**Exercise N°2: Pattern and Scratch (from subject zero DNB 2017) 4 points.**

1. To make the above figure, a diamond-shaped pattern was defined and one of the two programs A and B below was used.

Determine which one and indicate with a freehand figure the result that would be obtained with the other program.

2. How big is the space between two successive patterns?

3. We want to make the figure below:

To do this, we plan to insert the instruction in the program used in question 1.

Where should this instruction be inserted?

**Exercise N°3: Rectangle or not rectangle… 3 points.**

Is the triangle ABC right-angled at B? Justify the answer.

**Exercise N°4: Height of the Stromboli … 6 points**

Three people measure the height of this impressive volcano, Stromboli, located in Italy, using different methods.

**1. Cécile and Lydia’s method**

Cecile lies down on the ground facing the volcano.

Lydia is standing perpendicular to the ground between her and the volcano, where Cecile’s eye B, Lydia’s head D and the top A of the volcano are aligned.

The distance BC between Cecile’s eye B and the bottom C of the volcano is 1200 m.

The distance BE between Cecile’s eye B and Lydia’s feet E is 2.20 m.

Lydia’s ED height is 1.70 m.

Help Cécile and Lydia to calculate the AC height of the volcano.

You will give the value rounded to the nearest meter.

**2. Adelaide’s method …**

Adelaide lies on the ground facing the Volcano (on the village side)

She places an angle measuring instrument in front of her eye B.

The distance BA between Adelaide eye B and the top A of the volcano is 1385 m.

The angle measures 42°.

Help Adelaide calculate the AC height of the volcano.

You will give the value rounded to the nearest meter.

**Exercise N°5: The Piton de la Fournaise … 5 points**

The Piton de la Fournaise is considered as a cone of 7500 m height and its base is 240 km in diameter.

1. Calculate the volume of this cone in .

We recall the formula for calculating the volume of a cone: .

2. Calculate the length of the slope CD that the lava will descend. Round the result to the thousandth.

3. The age of the volcano (in years) is equal to

with the average volume of lava emitted each year or .

Calculate the age of Piton de la Fournaise. Round the result to the year.

**Exercise N°6: Piton de la Fournaise (continuation)… 6 points**

Here is the satellite image of Piton de la Fournaise during an eruption:

1. The lava took 4 minutes and 10 seconds to travel the distance from marker 1 to marker 2.

Calculate its average speed in m/s.

2. The scientists observe that the lava reaches the marker 2 at 17h 15min 25s.

Assuming that its average speed remains 16 m/s, how long does it take the scientists to evacuate the observation post?

**Exercise N°7: Earthquake in Taiwan 4 points.**

1. Using the document above, determine in which year the deadliest earthquake in Taiwan occurred?

2. Using the document above, determine in which year the largest earthquake occurred?

3. Calculate the average magnitude of the deadliest earthquakes in Taiwan between 1904 and 1999.

4. Calculate the average number of people killed due to earthquakes in Taiwan between 1897 and 1999.

5. We want to calculate the total number of people killed due to the last 10 deadliest earthquakes in Taiwan, using the spreadsheet.

Which formula should be written in cell L2?

**Exercise N°8: Ash cloud 12 points.**

**TIP: Read ALL the documents before starting the resolution to select all the useful information.**

An ash cloud from a volcano eruption forces an aircraft to divert from its usual route.

**Question**

Assist the captain in selecting a new route:

Can he bypass the cloud and land the plane at a nearby airport?

Can he turn back?

**Document 1: distances**

- Perdito – Las Playa : 1920 km
- Las Playa – South Island : 550 km

**Document 2: The flight planned Perdita – Las Playa**

- Passengers : 140
- Departure time: 3:40 pm
- Arrival time 6:04 pm
- Fuel from Perdito : 9000 L
- Consumption : 400L per 100 km

If the work is not completed, leave a record of the process on your copy.

It will be taken into account in the evaluation.

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