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**New topic for the new math test for the 2017 session following the college reform.**

This official subject is taken from the site *
Eduscol
*.

**Exercise 1**

For each of the following statements, say whether it is true or false, carefully justifying the answer.

1) A bag contains 6 red chips, 2 yellow chips and green chips.

The probability of drawing a green chip is 0.5.

**Assertion:** the bag contains 4 green chips.

2) In computing, the following multiples of the byte are used as units of measurement:

, , , ,

where KB is the abbreviation for kilobyte, MB for megabyte, GB for gigabyte, and TB for terabyte.

A 1.5 TB hard disk is divided into folders of 60 GB each.

**Affirmation:** This results in 25 files.

3) In the coded figure below, points B, A and E are aligned.

**Assertion :** the angle measures 137°.

4) A cone-shaped glass is completely filled.

The contents are poured so that the height of the liquid is divided by 2.

**Assertion:** the volume of the liquid is divided by 6.

**Exercise 2**

The tidal range is the difference in height between low water and the following high water.

It is considered that from the moment the sea is low, it rises by 1/12 of the tidal range during the first hour, by 2/12 during the second hour, by 3/12 during the third hour, by 3/12 during the fourth hour, by 2/12 during the fifth hour and by 1/12 during the sixth hour. During each of these hours, the sea rise is assumed to be regular.

1) At what point does the sea rise reach a quarter of the tidal range?

2) At what point does the sea rise reach one-third of the tidal range?

**Exercise 3**

For a village festival, a bicycle race is organized. A total bonus of 320 euros will be distributed among the first three runners.

The first will receive 70 euros more than the second and the third will receive 80 euros less than the second.

Determine the bonus for each of the top three runners.

**Exercise 4**

1) To make the above figure, a diamond-shaped pattern was defined and one of the two programs A and B below was used.

Determine which one and indicate with a freehand figure the result that would be obtained with the other program.

2) How much is the space between two successive patterns?

3) We want to make the figure below:

To do this, we consider inserting the instruction into the program used in question 1.

Where should this instruction be inserted?

**Exercise 5**

To adjust the low beam of a car, it is placed in front of a vertical wall. The headlight, identified at point P, emits a light beam directed towards the ground.

The following measures are noted:

PA = 0.7 m, AC = QP = 5 m and CK = 0.61 m.

On the diagram opposite, which is not to scale, the point S represents the place where

the upper beam would hit the ground without the wall.

The low beam is considered to be properly adjusted if the ratio is between 0.015 and 0.02.

1) Check that the car’s low beam lights are set correctly.

2) At what maximum distance from the car is an obstacle on the road illuminated by the low beam?

**Exercise 6**

The dimensions of a wall panel are 240 cm and 360 cm. We want to cover it with square tiles, all of the same size, laid edge to edge with no joints.

1) Can we use tiles of : 10 cm side ? 14 cm on a side ? 18 cm on a side ?

2) What are all possible tile sizes between 10 and 20 cm?

3) We choose tiles of 15 cm side. A row of blue tiles is placed around the edge and white tiles elsewhere.

How many blue tiles will we use?

**Exercise 7**

The braking distance of a vehicle is the distance the vehicle travels from the moment the driver starts braking to the moment the vehicle stops. This depends on the speed of the vehicle. The curve below gives the braking distance d, expressed in meters, as a function of the vehicle speed v, in m/s, on a wet road.

1) Show that 10 m/s = 36 km/h.

2) a. According to this graph, is the braking distance proportional to the vehicle speed?

b. Estimate the braking distance of a car travelling at a speed of 36 km/h.

c. A driver, seeing an obstacle, decides to brake. We see that he has traveled 25 meters from the time he starts braking to the time he stops. Determine, with the precision allowed by the graph, the speed at which he was traveling in m/s.

3) It is assumed that the braking distance d, in meters, and the speed v, in m/s, are related by the relation .

a. Find the result obtained in question 2b by calculation.

b. A driver, seeing an obstacle, brakes; it takes him 35 meters to stop.

How fast was he driving?

Consult the online answer key

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