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CCS Mathematics June 2013
Class of G7 Exam of 𝟑 𝒕𝒉
semester Duration : 2h
Name :…………………………….
I. (2 points)
1) Decompose into product of prime factors the numbers 1458 and 2187.
2) Find the GCD of 1458 and 2187.
3) Deduce the irreducible fraction of
1458
2187
.
II. (2 points)
Calculate, showing the details of calculation, and give the result in the form of irreducible fraction.
𝐴 = 2 −
1
5
+
3
5
÷
9
10
; 𝐵 =
7
3
+ (
1
2
−
7
3
) × 2
III. (4 points)
1) Solve the following equations:
a.
3𝑥−4
5
+
3
20
= 7 −
3−𝑥
10
b. ( 𝑥 + 2)( 𝑥 − 2) + 𝑥 = 2 + 𝑥².
2) Given 𝐴( 𝑥) = (2𝑥 + 3)( 𝑥 − 5) − 4𝑥(𝑥 − 5)
a. Factorize 𝐴( 𝑥).
b. Develop 𝐴( 𝑥).
c. Calculate 𝐴 (
1
2
).
IV. (3 points)
A florist offers its customers to take a free bouquet of 5 roses, 4 irises and 6 tulips at 50 euros if they
figure out the price of every kind.
The price of an iris costs half the price of a rose.
The price of a tulip is triple that of a rose.
1) Complete the following table:
Price of a rose 𝑥
Price of 5 roses
Price of one iris
Price of 4 irises
Price of one tulipe
Price of 6 tulipes
Price of a bouquet
2) Write an equation translates the problem and then solve it.

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V. (2 point)
At the market, Hiba bought 5 kg of sugar at 7250 LL.
1) Calculate the price of 11 kg of sugar.
2) How many kg of sugar Hiba can buy with 11600 LL?
VI. (4 points)
200 people are surveyed about
their favorite football team. The
following table represents the
results of this survey.
1) What is the population under
study?
2) What is the individual?
3) What is the studied
character?
4) Draw a table containing the
cumulative frequencies and
the percentage relative
frequencies and the
corresponding angles.
5) Draw the pie chart of this distribution.
VII. (7 points)
In the following figure the lines (xy) and (uv) are parallel. The secant (zt) cuts (xy) in E and (uv) in F.
From the point O midpoint of [EF]
draw the perpendicular at (xy) which
cuts (uv) in K and (xy) in H.
1) a. Prove that the triangles OHE
and OKF are equal.
b. Deduce the homologous
elements.
2) a. Prove the equality of the
triangles HOF and EOK.
b. Prove the equality of the
triangles HKF and HKE.
c. Deduce that (HF) is parallel at (EK).
3) a. Construct the point D translate of E by translation of vector 𝐻𝐾⃗⃗⃗⃗⃗⃗ .
b. What is the nature of the quadrilateral HEDK? Justify.
4)What is the locus of the points that are at 4 cm from O?
GOOD WORK.
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Italy Brazil Spain Algeria Teams
Frequencies