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**MATHEMATICS MOCK EXAM**

**Session: MAY 2022**

Duration of the test: 2 hours

Scoring out of 50 points.

Exercise 1 : ( 12 points)

1. In this exercise, consider the rectangle ABCD opposite such that its perimeter is equal to 32 cm. We call the length AB.

a. Represent this rectangle in real size when = 10 cm.

b. Using the fact that the perimeter of the rectangle is 32 cm, express the length BC in terms of .

c. Deduce the area of rectangle ABCD as a function of .

2. Consider the function f defined by ()=(16-).

a. What is the image of 4 by the function f? What is the concrete meaning of this result?

b. Determine the antecedents of 0 by the function f.

3. On the graph below, the area of rectangle ABCD has been plotted as a function of .

Using the graph, answer the following questions by giving approximate values:

a. For what values of is an area of 40 cm² obtained?

b. What is the maximum area of this rectangle? For what value of ?

Does the point A(2; 28 ) belong to the representative curve of the function f? Justify with a calculation.

Exercise 2: (6 points)

To access her mezzanine, Lola must install a staircase. (Photo and diagram below)

1. Give an approximate value to the nearest centimeter of the length AB.

2. Knowing that the height BD of a step is 20 cm, calculate the depth DE of a step at

millimeter.

Exercise 3: (6 points)

Samia lives in an apartment with a floor area of 35 m².

She compares it with a yurt, the traditional Mongolian habitat.

We model this yurt by a cylinder and a cone.

1. Show that Samia’s apartment has a smaller floor area than the yurt.

2. Calculate the volume of the yurt in <. (We will round up to the tenth of <)

3. Samia makes a scale model of this yurt . What is the height of the model?

Exercise 4: (11 points)

On the figure opposite, the point J belongs to the segment [IM] and the point K

belongs to the segment [IL], the lengths are given in meters.

1. Show that IKJ is a right triangle.

2. Show that LM is equal to 3.75 m.

3. Calculate the length KM to the nearest centimeter.

Exercise 5: (4 points)

Students stretched two ropes between points A and D,

then between points B and C.

The two strings intersect at E.

We know that EA = 7 m, EB = 13 m, EC = 10 m and ED = 9 m.

Are the lines (AC) and (BD) parallel ?

Exercise 6: (6 points)

The figure below is not full size.

Are the points E, A and B aligned? Justify your answer.

Exercise 7: (7 points)

Anna has created a program with Scratch software. The sprite is initially located at point A.

1. After running this program, Anne entered the following 4-digit code: 0-0-1-0.

At which door will the leprechaun arrive?

2. Suggest a code that leads to the door 3.

3. a. Determine the six codes that lead to door 2.

b. In each case in question a, add up the numbers in the code. What do we see?

4. What is the sum of the digits of a code obtained after the execution of Anna’s program?

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