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Brevet des collèges June 14, 2016

Foreign centers

The use of a calculator is allowed.

**EXERCISE 1 : 3 points**

This exercise is a multiple choice questionnaire. For each line of the

In the table, only one statement is correct. On your copy, indicate the number of the

question and copy the correct statement.

No justification is required.

**EXERCISE 2 : 4 points**

Answer true or false to the following statements and justify your answers.

Assertion 1: A box of macaroons costs 25 (. If we increase its price by 5

per year for two years, the new price will be $27.50 (

Assertion 2: If a store uses an average of 4 kg of sugar per day, it will use approximately 1.46×106

grams of sugar in one year.

Statement 3: During a delivery of buttons in the city, a truck travelled

12.5 km in 12 minutes. In built-up areas the maximum speed limit is 50

km/h. The delivery man was within the speed limit.

**EXERCISE 3: 5 points**

A new store has opened in Paris. It sells exclusively macaroons (small pastries).

The spreadsheet extract below shows the number of macaroons sold one week

1. What formula should be entered in box I2 to calculate the total number of

of macaroons sold in a week ?

2. Calculate the average number of buttons sold per day. Round the result

per unit.

3. Calculate the median number of buttons.

4. Calculate the difference between the number of buttons sold on Sunday and

those sold on Thursday. What statistical term does this value correspond to?

**EXERCISE 4: 5 points**

To present its macaroons, a store wishes to use displays

whose shape is a regular pyramid with a square base of side 30 cm and whose

the side edges measure 55 cm.

The display is shown in the following figure:

Can this display be placed in a parallelepipedic refrigerated display case whose

height is 50 cm?

**EXERCISE 5 : 3 points**

Pascale, Alexis and Carole share two boxes of 12 macaroons each.

We know that Alexis ate 4 more macaroons than Pascale and that Pascale ate

twice as much as Carole.

How many macaroons did each person eat?

**EXERCISE 6 : 3 points**

To celebrate her birthday, Pascale bought two boxes of macaroons at the store.

The box number 1 is composed of : 4 chocolate macaroons, 3 coffee macaroons, 2 vanilla macaroons and 3 caramel macaroons.

The box number 2 is composed of : 2 chocolate macaroons, 1 strawberry macaroon, 1 raspberry macaroon and 2 vanilla macaroons.

It is assumed in the following that the buttons are indistinguishable to the touch.

1. If we randomly choose a macaroon from box number 1, what is the probability that it is a coffee macaroon ?

2. After one hour there are 3 chocolate macaroons and 2 coffee macaroons left in box number 1 and 2 chocolate macaroons and 1 strawberry macaroon in box number 2.

number 2.

Carole does not like chocolate but enjoys all other flavors. If she chooses a button at random from box number 1, then a second one from box number 2, what is the probability that she will get two buttons

that he likes?

**EXERCISE 7: 3 points**

A macaroon is composed of two cookies and a layer of cream. This layer

of cream can be assimilated to a cylinder of radius 20 mm and height 5 mm.

1. Check that the volume of cream contained in a macaroon is .

2. Alexis has 30 cL of cream in her salad bowl.

How many macaroons can he make?

We remind you that

.

**EXERCISE 8: 5 points**

To bake macaroons, the oven temperature must be 150 °C.

For some time now, the store manager has not been satisfied with the baking of his pastries. So he decided to check the reliability of his oven by setting

on 150 °C and regularly taking the temperature with a probe.

Here is the curve representing the evolution of the temperature of his oven as a function of time.

1. Is the temperature of the oven proportional to time?

2. What is the temperature reached after 3 minutes? No justification

is requested.

3. By how many degrees Celsius did the temperature increase between the second

and the seventh minute?

4. How long does it take to reach the temperature of 150°C needed to bake the macaroons?

5. After this time, what can we say about the temperature of the oven? Explain why the manager is not satisfied with the baking of his macaroons.

**EXERCISE 9: 5 points**

For his wedding on Saturday, August 20, 2016, Norbert wants to have macaroons delivered.

The company asks him to pay 402 ( including delivery costs.

Using the documents below, determine in which zone the delivery address is located.

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