Brevet Polynesia (September 2019) Catch-up session

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MATHEMATICS
General Series – French Polynesia
Length of test: 2 h 00 100 points

Exercise 1: (15 points)
In this multiple choice questionnaire, for each question, answers are proposed,
only one is correct. On the copy, write the question number and copy the correct answer.
No justification is expected.

Exercise 2: (12 points)
Hugo downloaded music tracks on his phone. He classified them by musical genre
as shown in the table below:

1) How many tracks has he downloaded?
2) He wants to use the “shuffle” function of his phone which consists in choosing
randomly among all the downloaded music titles, a title to broadcast. All titles
are different and each title has an equal chance of being chosen. We are interested in gender
of the first track played.
a) What is the probability of the event: “Get a Pop title”?
b) What is the probability of the event “The title broadcast is not Rap”?

c) An audio music file is about 4 MB (Megabytes) in size. On the phone
of Hugo, there is still 1.5 GB (Gigabyte) available. He wants to download new
music titles. How many can he download at most?
Reminder: 1 GB = 1,000 MB

Exercise 3: (14 points)
A nursery assistant was looking after several children, including Farida who started school in
September 2017. Her parents then broke their contract with this childminder. The
The law requires them to pay a “severance payment”.
The amount of this allowance is equal to 1/120th of the total net salary received by
the childminder for the duration of the contract.
They reported the amount of net wages paid, from March 2015 to August 2017, in a spreadsheet
as below:

1) a) What does the value 1783.04 in cell M4 represent?
b) What formula was written in cell M4 to obtain this value?
c) In which cell should the formula = M4 + M9 + M14 be written?
2) Determine the amount of the “termination fee”. Round to the nearest cent.
3) Determine the average net monthly salary paid to this childminder over the entire
the duration of Farida’s family’s contract. Round to the nearest cent.
4) Calculate the extent of wages paid.

Exercise 4: (14 points)
We are interested in the wings of a windmill
decorative garden. They are represented
by the figure opposite :
We give:
– BCDE, FGHI, JKLM and PQRS are
overlapping rectangles.
– C, B, A, J, K on the one hand and
G, F, A, P, Q on the other hand are aligned.
– AB = AF = AJ = AP

1) Which transformation allows us to go from rectangle FGHI to rectangle PQRS?
2) What is the image of rectangle FGHI by the rotation of center A of angle 90° in the direction
counterclockwise?

3) Let V be a point of [EB] such that BV = 4 cm.
We give:
AB = 10 cm and AC = 30 cm.
Be careful, the figure is not built to actual size.

a) Justify that (DC) and (VB) are parallel.
b) Calculate DC.
c) Determine the measure of the angle . Round to the nearest degree.

Exercise 5: (16 points)
We built a sandbox for children.

This tray has the shape of a right prism of 15 cm height. The base of this right prism is represented
by the polygon ABCDE below :
Be careful, the figure is not built to actual size.

We give:
– PC = PD = 1.30 m
– ED = BC = 40 cm
– E, D, P are aligned
– B, C, P are aligned

1) Calculate CD. Round to the nearest centimeter.
2) Justify that the quadrilateral ABPE is a square.
3) Determine the perimeter of polygon ABCDE. Round to the nearest centimeter.
4) The sandbox was built with wooden planks of length 2.40 m and
of 15 cm height each. How many boards were needed?
5) Calculate, in m², the area of polygon ABCDE.
6) Was more than 300 L of sand needed to completely fill the bin?
Reminder: Volume of a right prism = area of the basex height

Exercise 6: (15 points)
Eco-driving is a more responsible driving behavior that allows :
– reduce expenses: less fuel consumption and lower maintenance costs for the
reduced vehicle ;
– limit greenhouse gas emissions;
– reduce the risk of accidents by an average of 10 to 15%.
1) One of the main principles is to check the tire pressure of your vehicle. We consider
tires with a pressure recommended by the manufacturer of 2.4 bars.
a) Knowing that a tire loses about 0.1 bar per month, in how many months can the pressure of the
will be down to 1.9 bar, if there was no inflation?
b) The graph below gives an approximate percentage of consumption
additional fuel depending on tire pressure (shaded area) :

According to the graph, for tires inflated to 1.9 bar when the pressure
is 2.4 bar, give an approximate value for the percentage of the
additional fuel consumption.
2) Paul noticed that when the tires were properly inflated, his car consumed
on average 6 L per 100 km. He decides to enroll in an eco-driving course in order to reduce
fuel consumption and therefore CO2 emissions. By adopting the principles of eco-driving,
a driver can reduce fuel consumption by about 15%. He
wishes, at the end of the course, to reach this objective.
a) What will be the average fuel consumption of Paul’s car?
b) Knowing that he travels about 20,000 km in a year, how many liters of fuel
can he expect to save?
c) His car runs on unleaded gasoline. The average price is 1,35 €/L. What would be then
the amount of savings over a year?
d) This course cost him 200 €. After one year, can he expect to recoup this expense?

Exercise 7: (14 points)
We give the program below where we consider 2 sprites. For each sprite, we wrote a
script corresponding to a different calculation program.

1) Verify that if you enter 7 as a number, the result of sprite #1 is 17 and the result of sprite #2 is 17.
n°2 poster 41.
2) What result does the leprechaun #2 display if you enter the number – 4?
3) a) If we call the number entered, write in terms of .

b) Show that this expression can be written .

4) Celia states that several instructions in the script
of the sprite n°1 can be deleted and replaced by the one below.

Indicate, on the copy, the numbers of the instructions which are then useless.
5) Paul has entered a number for which sprites #1 and #2 display the same result. What
is this number? the expressions that translate
the calculation program of the sprite n°1, at each step (instructions 3 to 5).

Consult the online answer key

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