Foreign centers: math patent 2018 with subject and answer key

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Exercise 1: (14 points)
For each of the following statements, say whether it is true or false and justify
carefully the answer.
1. The harvest of lavender begins when at least three quarters of the flowers have faded. The
producer has picked a sample of lavender represented by the drawing below.

Assertion 1: The harvest can begin.
2. In computing, multiples of the byte are used as units of measurement:
1 kb =10^3 bytes, 1 MB =10^6 bytes, 1 GB =10^9 bytes.

Contents of the external hard drive:

• 1,000 photos of 900 kb each
• 65 videos of 700 Mb each.

Assertion 2: The transfer of the entire contents of the external hard disk to the computer is not possible.

3. Consider the calculation program below:

Assertion 3 : this program gives the sum of 1 and double the number
chosen.

Exercise 2: (16 points)
The answers to the questions in this exercise will be read from the graph in Appendix 1, located
on page 8 of this topic.
This one represents the profile of a running race that takes place on the island of La Réunion (this
graph expresses the altitude as a function of the distance covered by the runners).
No justification is expected for questions 1 through 4.
1. How far does a runner travel, in kilometers, when he reaches the top of
the plain of the blackbirds?
2. What is the altitude reached, in meters, at the Piton des Neiges deposit?
3. What is the name of the summit located at 900 meters of altitude?
4. At what distance(s) from the start will a runner reach:t 900 m altitude?
5. The positive difference in altitude is calculated only in the climbs; for each climb, it is equal to
to the difference between the highest and lowest altitude.
a. Calculate the positive difference in altitude between Cilaos and the Piton des Neiges lodge.
b. Show that the total positive elevation gain for this race is 4,000 m.
6. Maëlle ran at an average speed of 7 km/h and Line took 13 h 20 min to
cross the finish line. Which of these two sportswomen came first?

Exercise 3: (16 points)
Thomas has a watch that he composes by assembling dials and bracelets of
several colors.

For this, it has :
– two dials: one red and one yellow;
– four bracelets: one red, one yellow, one green and one black.
1. How many possible assemblies are there?
He chooses at random a dial and a bracelet to compose his watch.
2. Determine the probability of obtaining an all-red watch.
-3. Determine the probability of obtaining a watch of a single color.
4. Determine the probability of having a watch of two colors.

Exercise 4: (18 points)
Every summer, Jean operates his salt marsh on the island of Ré, located in the Atlantic Ocean, near La Rochelle.
Its marshes are made up of squares (4 m square) in which salt is harvested.

Part A. Coarse salt
Every day, he collects coarse salt from 25 tiles. The first day, in order to plan its production,
he records the mass in kilograms of each pile of coarse salt produced per tile.
Here is the statistical series obtained:
34-39-31-45-40-32-36-45-42-34-30-48-43
32 – 39 – 40 – 42 – 38 – 46 – 31 – 38 – 43 – 37 – 47 – 33
1. Calculate the range of this statistical series.
2. Determine the median of this statistical series and interpret the result.
3. Calculate the average mass in kg of the coarse salt piles for this first day.

Part B. The flower of salt
Fleur de sel is the thin layer of white crystals that forms and flushes the surface of
salt marshes. Every evening, Jean picks the salt flower on the surface of the tiles. For
To transport his harvest, he uses a wheelbarrow as shown in the diagram below.

1. Show that this wheelbarrow has a volume of 77 liters.
2. Knowing that 1 liter of fleur de sel weighs 900 grams, calculate the mass in kg of the content
of a wheelbarrow filled with fleur de sel.

Exercise 5: (18 points)
On a gas bill, the amount to be paid takes into account the annual subscription and the price
corresponding to the number of kilowatt hours (kWh) consumed.
Two gas suppliers offer the following rates:

In 2016, Romane’s family consumed 17,500 kWh. The annual invoice amount of
The corresponding gas price was €1,268.18.

1. What is the rate this family pays?
Since 2017, this family has been reducing its gas consumption through simple actions (lowering the
heating a few degrees, put a lid on the water pot to bring it up to
boiling, reducing time under water in the shower, etc.).

2. In 2017, this family kept the same gas supplier, but their consumption in kWh
decreased by 20 percent compared to 2016.
a. Determine the number of kWh consumed in 2017.
b. How much did Romane’s family save between 2016 and
2017 ?

3. We wish to determine the maximum consumption ensuring that rate A is the most
advantageous. For this purpose:
– we note x the number of kWh consumed during the year.
– we model the rates A and B respectively by the functions f and 9 :
f(x) = O.0609x + 202.43 and g(x) = O.0574x + 258.39
a. What is the nature and graphical representation of these functions?
b. Solve the inequation: f(x) < g(x).
c. Deduce an approximate value to the nearest kWh of the maximum consumption for
for which Rate A is the most advantageous.

Exercise 6: (18 points)
Market gardening is the professional activity of growing vegetables, some fruits, flowers or aromatic plants.
In order to reduce the drudgery of market gardening work, a farmer has acquired an electric robot to weed his crops.

Part A. Robot path
The robot has to run 49 parallel lanes at a distance of 1 m, as shown in the diagram below.
The first 48 lanes, located in a rectangular plot, are 80 m long:
– the 1st aisle is [PQ];
– the 2nd aisle is [RS];
– the 3rd aisle is [TU];
– Aisles 4 to 47 are not represented;
– the 48th lane is [CS].
The 49th (last aisle) [DE] is located in a triangular plot.

1. Show that the length of the last aisle is: DE =64 m .

Part B. Robot movement program
We wish to program the movement of the robot from point P to point E. The script below,
made with Scratch, is incomplete. All aisles are walked only once. The image
“Robot” is the expected result when the green flag is clicked.
It is recalled that the instruction means that the robot is moving upwards.

To answer questions 1 and 2, use the blocks as much as necessary:

Lengths must be indicated in meters.
1. The new “Upward motif” block must reproduce a displacement of the type P-Q-R (see
diagram 2) and position the robot ready to make the next pattern. Write a succession of 4
blocks allowing to define: “rising reason”.
2. The new “Descending Pattern” block must reproduce an R-S-T type move (see
diagram 2) and position the robot ready to make the next pattern.

Which modification(s) do you need to make to the “Up Pattern” block to obtain the “Down Pattern” block?
3. What values must be given to x and y in the main script so that the
the robot’s movement gives the expected result.

See the answer key

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