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**This math homework assignment for students in 1ère S is 3 hours long and covers many chapters.it is intended for première S students and high school teachers.**

This exercise is a multiple choice questionnaire (MCQ). For each question, only one of the four answers

proposed is correct.

A correct answer earns one point; a wrong answer or no answer earns no points.

Write the question number and the letter corresponding to the answer on your copy.

No justification is required.

Note f the function defined on R whose representative curve (C) is the parabola given in the appendix (last page)

of the subject). The point A(4; 0) belongs to the curve (C) and the line (d) is the tangent to the curve (C) at point A.

Consider the function f defined on [0; 15] by .

1. a. Calculate f′(x).

b. Study the sign of f′(x) at [0;15].

c. Derive the table of variations of f on [0; 15].

d. We admit that the equation f(x) = 0 has 2 distinct solutions in the interval [0;15].

Give approximate values, to the nearest 10-1, of these solutions denoted α and β.

2. A manufacturer is considering the production of boxes in the shape of a straight block to pack nails by cutting two

strips of the same width in a square sheet of cardboard.

The side of the sheet measures 30 cm and we denote by x the measurement in cm of the width of the cut strips. We

admits that .

a. Calculate the volume of the box if x = 2.

b. Justify that the volume V (x), in cm3, of the box is V (x) = (15 – x)(30 – 2x)x.

c. Verify that the volume V (x) is equal to f(x) + 500, where f is the function defined above.

d. Deduce the value of x for which the volume of the box is maximum. Specify the value of the maximum volume.

3. The manufacturer wants 500 cc boxes. How many possibilities does he have? Justify the answer.

An urn contains n balls indistinguishable to the touch: 5 red balls and n – 5 black balls (n is a higher integer

or equal to 6).

A player randomly draws two balls from the urn without a delivery.

1. Construct a weighted tree describing this random experiment.

The player wins 2 euros if the two balls drawn are of different colors and loses 1 euro otherwise. We note A

the event: “the two balls drawn are of different colors” and X the random variable giving the algebraic gain

of the player.

ABC is any triangle.

We wish to show that the lines (AJ), (BK) and (CI) are concurrent.

Let E be the point of intersection of lines (AJ) and (BK).

Give, without justification, the coordinates of points B, C, A, I and J.

Calculate the coordinates of the point K.

Determine a Cartesian equation of the line (AJ) and show that it can be put in the form

3x + y – 1 = 0 .

Determine a Cartesian equation of the line (BK).

Deduce the coordinates of point E.

Let U be the sequence of general term Un defined for any natural number n.

Show that U1 = 2 and that U2 = 6. Calculate U3.

We consider the following algorithm:

Start of the algorithm

Input: Enter N a non-zero natural number

Initialization: Assign the value 0 to P

Treatment: ForK ranging from 0 to N :

Assign to P the value P + K

View P

End For

End of the algorithm

a. Run the algorithm with N = 3. The display shows the values of the first four terms of

the sequence U ?

b. Copy the Processing part of this algorithm and modify it, so as to obtain the following values on the display

of the first N + 1 terms of the sequence U.

Subject of the joint maths assignment in Première S

Answer key for the maths homework in Première S

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