Asia and Pacific: maths patent 2022 with subject and answer key

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DIPLÔME NATIONAL DU BREVET

ASIA PACIFIC 2022 SESSION

MATHEMATICS

General series

Length of test: 2 h 00 100 points

Exercise 1: 20 points.

This exercise is composed of three unrelated situations.

Situation 1:

The following calculation program is considered:

Show that if the starting number is 10, the result is – 5.

2. We note the starting number to which we apply this calculation program.

Which of the following expressions is the result of the calculation program?

No justification is expected for this question.

Expression A: $x\,-7\,\times \,5\,-\,2x$ Expression B: $5(x\,-\,7)-\,2x$

Expression C: $5(x\,-\,7)\,-\,x^2$ Expression D: $5x-\,7-\,2x$

Situation 2:

In the reference frame, the line (d) represents a linear function f.

The point A belongs to the line (d).

Using the graph, determine the image of – 2 by the function f.

2. Determine an expression for f (x) as a function of x.

Situation Three:

The drawing below represents a pyramid with vertex G and whose base CDEF is a rectangle.

Is the volume of this pyramid greater than 20 L?

ED = 30 cm; DC = 40 cm; GH = 55 cm.

Exercise 2: 20 points.

The figure below is freehand.

The lines (AB) and (CD) are parallel.

The lines (AD) and (BC) are secant at E.

We have: ED = 3.6 cm; CD = 6 cm; EB = 7, 2 cm and AB = 9 cm.

Show that the segment [EC] measures 4.8 cm.
Is the triangle ECD rectangular ?
Among the transformations below, which one allows to obtain the triangle ABE from the triangle ECD ? Copy the answer on the copy. No justification is expected.

4. It is known that the length BE is 1.5 times greater than the length EC.

Is the following statement true? Remember that the answer must be justified.

Assertion: “The area of triangle ABE is 1.5 times larger than the area of triangle ECD.”

Exercise 3: 20 points.

During the Paralympic Games of 2021, the media proposed a classification of the countries according to the distribution of the obtained medals.

Here is the ranking obtained for the top 15 countries:

How many silver medals did Australia get?
Calculate the number of bronze medals obtained by Italy.
Which formula could have been entered in F2 before being stretched down?
For each of the following two statements, indicate whether it is true or false. Remember that answers must be justified.

Assertion 1:

“20% of the medals obtained by the French team are gold.

Assertion 2:

“The median number of silver medals earned by these 15 countries is 29.”

5. At the Rio Paralympics in 2016, the premium for a French gold medal was

50,000 euros. For those of Tokyo in 2021, this bonus was 65 000 euros.

What is the percentage increase in this bonus between 2016 and 2021?

Exercise 4: 25 points.

An online store sells photos and displays the following prices:

1.a.What is the price for 35 photos?

b. Check that the price to pay for 150 photos is 23,50 €.

c. We have a budget of 10 €. How many photos can I order at most?

We have started to build a program that will calculate the price to pay according to the number of photos ordered:

In this question, no justification is expected.

What values can be added to the instructions on lines 3, 4 and 7 so that the program can calculate the price to be paid according to the number of photos ordered?

On the copy, write the number of each line to be completed and the corresponding value.

3. During the sales period, the site offers a 30% discount on the price to be paid, for any order over 20 €.

a. Calculate the price to pay for 150 photos during the sales period.

b. In this question, no justification is expected.

We modify the program so that it gives the price to be paid during the sales period by inserting the block below between lines 8 and 9.

From the following list, indicate an appropriate proposal to fill in the blank:

Exercise 5: 15 points.

The Iss (International Space Station) is an international space station placed in orbit around the Earth.

1. During the day of June 21, 2021, the ISS passed over Canberra (Australia) and then over Miami (USA).

Using the planisphere below, give the geographic coordinates of these two cities with the precision allowed by the graph.

We represent the Earth, the ISS and its orbit (ISS trajectory) using the diagram below.

We consider that:

the Earth is assimilated to a sphere of radius 6 371 km ;

the orbit of the ISS is a circle with the same center as that of the Earth;
The ISS orbits the Earth at an altitude of 380 km.

2. Show that the ISS travels approximately 42,400 km to complete one complete revolution of the Earth.

3. It is estimated that the ISS orbits the Earth at an average speed of 27,600 km/h.

a. Show that it takes about 1 hr 32 min for the ISS to complete a full circle of the Earth.

b. On June 19, 2020, from 2:30 p.m. to 9:45 p.m. (Paris time), French astronaut Thomas Pesquet performed a spacewalk while tethered to the ISS.

During this outing, how many times did Thomas Pesquet circle the Earth?

Consult the online answer key

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