Answer key for the maths brevet France 2016

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The answer key to the June 2016 math patent topic.

Exercise 1:

  1. \frac{27}{100}
  2. 2. \frac{27}{27+38}=\frac{27}{65}
  3. Plant A: \frac{27}{500}\times  ,100=5,4

Plant B: \frac{38}{500}\times  ,100=7,6

Only plant A has a satisfactory control?

Exercise 2:

  1. Program A : 2*(-2)+13=-4+13=9
  2. Program B:9:3+7=3+7=10
  3. Program A = Program B

-2x+13=3(x+7)

-2x+13=3x+21

5x=-8

x=-\frac{8}{5}=-1,6

Exercise 3:

Figure 1: ABC is a right triangle and AB=\sqrt{12^2-6^2}=10,4\,cm.

Figure 2: ABC is a right triangle and

sin53%C2%B0=\frac{AB}{36} so AB=36\times  ,sin53=28,8\,cm

Figure 3:

P=\pi\times  ,D=154

D=\frac{154}{\pi}=49\,cm

Exercise 4:

  1. 54\times  ,(1-\frac{30}{100})=54*0,7=37,8
  2. a. {\color{DarkRed},=(B_1*30)/100}

b. {\color{DarkRed},=B_1-B_2}

3. x\times  ,0,7=42

x=\frac{42}{0,7}=60

Exercise 5:

  1. A_{APS}=\frac{30\times  ,18}{2}=15*18=270\,m^2

It will take 2 bags or 2*13,90=27,80

Property: (AS) // (RC) because two lines perpendicular to a third are parallel to each other.

2. We know that A\in,(RP);S\in(RC);(AS)//\,(RC%C2%B0)))

according to the direct part of Thales’ theorem, we have :

\frac{PA}{PR}=\frac{AS}{RC}

\frac{30}{40}=\frac{18}{RC}

so RC=\frac{18*40}{30}=24\,m

A_{skatepark}=A_{PRC}-A_{PAS}\\=\frac{40*24}{2}-270\\=480-270\\=210\,m^2

Exercise 6:

Part 1:

  1. Piece 1 = 8 cm and piece 2 = 12 cm.a square of side 8:4=2cm and an equilateral triangle of side 12 : 3 = 4 cm.
  2. 2*2=4\,cm^2
  3. AH=\sqrt{4^2-2^2}=3,5\,cm with AH the height of the equilateral triangle.

We obtain \frac{4*3,5}{2}=7\,cm^2.

Part 2:

  1. Let x : the length of the piece 1.

Aire_carre=(\frac{x}{4})^2=\frac{x^2}{16}

2. a. \simeq,3\,cm

b. \simeq,8,6\,cm

Exercise 7:

V_{vase}=(9-0,2*2)^2*(21,7-1,7)=1479,2\,cm^3

V_{150billes}=150\times  ,\frac{4}{3}\times  ,\pi\times  ,0,9^3\simeq,458\,cm^3

V_{vide}=1479,2-458=1021,2cm^3=1,021L

Yes, he can add a liter of colored water without risking an overflow.


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