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Exercise 1:

- The sum of the probabilities of the outcomes is equal to
`[latex]\frac{1}{5}[/latex]`

1/5. 5/5-2/5=3/5. - No, it will have as many probabilities because the ball is put back in the urn.
- 8 green balls for a probability of 2/5.

1/5 represents 4 balls and 3/5 represents 3×4=12 green balls.

Exercise 2:

- The coordinates of the starting point are D(-200; -100).
- This script draws 5 triangles.
- a. The length of the second triangle drawn is 100-20= 80 pixels.

b.

To obtain this new figure, simply add the instruction in step 7 or 9.

Exercise 3:

- No, there is no proportionality because the curve is not a straight line.
- The voltage is 4.4 V.
- 60×5/100=300/100=3 V

i.e. a time t=0.09 s.

Exercise 4:

- 31 420 x 0,1395 =4 383,09 € .
- The triangle is right-angled, we use trigonometry with the tangent.
- a. The triangle is rectangular, we use the direct part of the Pythagorean theorem.

b. S=5×7,5=37,5 m².

20/37,5

Exercise 5:

50 m for 24.07 s

50/24.07 m for 1 s

or 50/24.07 m/s which corresponds to 50×3.6/24.07 km/h.

2. E= (3x+8)²-64

a. E = 9x²+48x+64-64

E= 9x²+48x

b. E= 3x*3x+3x*16

E = 3x(3x+16)

c. (3x+8)²-64 = 0

is equivalent to 3x(3x+16)=0

It’s a product equation.

*
Property:
* A product of factors is zero if and only if, at least one of the factors, is zero.

3x = 0 or 3x + 16 =0

x = 0 or x = – 16/3

3.

d=kxV²

15=0.14xV²

V²=15/0.14

so either :

V=-rac(15/0.14) or V= +rac(15/0.14)

Now V is positive, hence V=rac(15/0.14)

Exercise 6:

1.a. There are 3 overweight employees.

b. =B2/(B1*B1)

2.a.

c.(2+1+1+2)/41=6/41=0,1463=14,63 %.

Exercise 7:

- 700 g sugar for 1 kg of strawberries

S for 1.8 kg of strawberries.

This is a situation of proportionality,

S=1800×700/1000=1,260 g.

It needs 1260 grams of sugar.

Answer key for the maths brevet France 2017

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