Brevet des collèges June 14, 2016
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
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.
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
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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