College students worked out their math test for a patent this Thursday, June 30th. Discover the subject.

After passing their French exam this morning, third-graders will take their college patent math exam today, Thursday afternoon, June 30th.

**Read more – Discover the results of the 2022 patent **

More than 770,000 candidates in the general series have passed this test, which lasts two hours and is counted for 100 points. About the professional series, 85,309 students are working on math. Discover the issues.

**Mathematics subject in general course on Thursday 30th June**

**• e****Exercise 1 (20 points)**

A family walks along the river. The children want to know the width of the river. They take landmarks, calculate their steps and draw the figure below on which points C, E and D, as well as A, E and B are aligned. (Image is not resized.)

1. Prove that lines (AC) and (BD) are parallel.

2. In the number of steps, determine the width of the river AC.

For the following questions, we consider the length of a step to be 65 cm.

3. Show that the length CE is 13.3 m, rounded to the nearest decimeter.

4. A child throws a stick into the river at point E. With the current, the stick moves to the point C in a straight line in 5 seconds.

Calculate the speed of the stick in m / s.

B. Is it true that “the stick moves at a speed of less than 10 km / h”?

**Exercise 2 (20 points)**

This exercise is a Multiple Choice Question Paper (MCQ). No justification required. For each question, three answers (A, B and C) are suggested. Only one answer is correct. Copy the question and answer numbers on the copy.

**Exercise 3 (20 points)**

A collector counts to resell his Pokemon cards.

It has 252 “Fire” type cards and 156 “Earth” type cards.

1.a. Among the following three propositions, which corresponds to the decay of one of the basic factors of number 252:

B. Give decomposition as the product of 156 prime factors.

2. He wants to create a uniform deck using all his cards, meaning each has the same number of “Earth” cards and the same number of “Fire” cards.

Can he pack 36?

B. What is the maximum number of packets he can make?

Vs. How many cards of each type in each call?

3. He chooses a random card from all his cards. Cards are assumed to be inseparable by touch.

Calculate the probability that this is an “Earth” type card.

**Exercise 4 (20 points)**

In this exercise, x is a number strictly greater than 3.

We are interested in the following two geometric figures:

A rectangle whose side lengths are x – 3 and x + 7;

Arm is a square of x.

3. We wrote the following script in scratch.

We want this program to return the area of the rectangle when the user enters the value of x (strictly greater than 3).

Copy the contents of the three empty boxes on lines 5, 6 and 7, specifying the line numbers that correspond to your answers.

4. We press the space key then enter the number 8. What does the program return?

5. Which number x should be selected so that the area of the rectangle is equal to the area of the square?

Any traces of research, even unsuccessful ones, will be taken into account.

**Exercise 5 (20 points)**

In a home, water use can be unusually high when water leaks.

We consider the following situations:

A bathroom is equipped with a cylindrical shaped basin, as shown in the picture below.

কল Call leaks at the rate of one drop per second.

On average, 20 drops of water are mixed with one milliliter (1 ml).

1. Due to leaks, show that 86,400 drops fall into the basin throughout the day.

2. In liqueur, calculate the amount of water that falls into the basin in a week due to leakage.

3. Show that the volume of the basin is 18.85 liters, rounded to the nearest centimeter.

4. The basin drain is closed and the place to stay for a week is empty. Will the water overflow in the basin? Justify the answer.

5. In the late 19th century, per capita domestic water consumption in France was about 17 liters per day. It has grown rapidly with the generalization of tap water distribution in the home: it increased to 165 liters per day in 2004 and per resident.

In 2018, French consumption decreased slightly to 148 liters of water per day and per resident.

Calculate the percentage reduction in daily water consumption per capita between 2004 and 2018 This percentage will be filled up to 7 units

## Answer Key (General Sector)

## Mathematics subject to vocational patent on Thursday, June 30th

**Exercise 1 (20 points)**

The full MCQ exercise must be completed in Appendix 1 for a refund with a copy.

**Exercise 2 (20 points) **

A 2020 document provides the following information:

In 2021, Thomas Pesquet completed a second 199-day mission. The purpose of the next two questions is to update the data in the document.

1. Determine the total duration of the two missions of Thomas Pesquet within how many days.

2. Complete the figure in Appendix 2

A journalist has confirmed that Thomas Pesquet spent more than 40% of the total duration of the French astronauts’ mission in space.

3. Check the reporter’s claim.

**Exercise 3 (20 points)**

The cost of launching a satellite provided by a space company is determined as follows: an additional cost of 15,000 euros per kilogram up to 4,500,000 euros.

1. Check that the launch cost of a 350 kg satellite is € 5,250,000.

We model the launch price according to the number of extra kilograms x by a function. The following graph shows the representation of this function.

2. From the following three expressions, select the one that is compatible with this function and copy:

f (x) = 15,000 x + 4,500,000 g (x) = 15,000 xh (x) = 50,000 x + 1,500,000

3. Indicate whether the launch value of a satellite weighing more than 300 kg is proportional to the x number of extra kilograms. Justify the answer.

4. A telecommunications company has a budget of 8,000,000 euros to finance the launch of a satellite.

Determine the maximum number of extra kilograms that can be introduced without exceeding this budget.

B. Determine the maximum total mass per kilogram of satellite for a budget of 8,000,000 euros.

**Exercise 4 (20 points)**