1. Page 1 of 2
CCS Mathematics Dec. 2014
Class ofG7 Exam of 𝟏 𝒕𝒉 semester Duration : 2 h
Name :…………………………………..
I. ( 2 points)
Determine, with justification, the signs of a, b, c and e in each of the following cases:
1) (−4) × (−2)× 𝑎 × (−7) is positive.
2) (−5)2
× 2,8 × 12 × 𝑏 is positive.
3)
𝑐×(−4)
−10
is negative.
4) (+7 + 3) × 𝑒 × (−5 − 6 − 3) is negative.
II. (3 points)
In an orthonormal system , given the four points M, E, K and L such that the ordinate of each
one of them is equal to twice of the abscissa.
1) Complete this table:
Point M K E L
Abscissa -2 1
Ordinate 0 4
2) Locate these points in the system and the line through two of these points. What do you
notice?
3) Given the point A on this line with an abscissa equal to 3. What is the ordinate this point ?
What relation exists between coordinate of A.
III.(4 points)
1) Write in the form of one power:
a) 96
× 34
c) (23)2
× (35)3
× 211
× 32
b) (
34
8
)× (
9
22
)
3
d)
28
32
2) Write in the form of scientific notation the following numbers:
103,45; 14× 105
; 50 ; 6000
IV. (2 points)
Given the two numbers a= 396 and b=324.
1) Decompose a and b in product of prime factors.
2) Find the GCD and the LCM of a and b.
3) Prove that b is the square of a natural number to be determined.
V. (1 points)
Fadi wants to distribute 120 red balls and 1100 yellow balls in identical package.
What is the largest number of packets that he can do?
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VI. (6 points)
1) Draw a triangle ABC such that BC= 8 cm, 𝐴𝐵̂ 𝐶 = 50°, 𝐴𝐶̂ 𝐵 = 30°,then draw the
bisector of the angle 𝐵𝐴̂ 𝐶 which cuts [BC] in I.
2) Calculate the measure of the angle 𝐵𝐴̂ 𝐶 and prove that the triangle ABI is isosceles.
3) From the point I, trace the perpendicular at [AC] which cuts this segment at H, and let E
be the symmetric of A with respect to H.
4) What does the line (IH) represent for the segment [AE]? Justify.
5) What is the nature of IAE?
6) Prove that the triangle BIE is isosceles at I.
7) What is the nature of triangle AIH? What do you call the segment [IA]?
VII. (2 points)
x𝑂̂y and y𝑂̂z are two adjacent supplementary angles such that : x𝑂̂y= 40°.
1) Construct x𝑂̂y and y𝑂̂z.
2) Calculate y𝑂̂z.
3) [Ou) and [Ov) are two bisectors of x𝑂̂y and y𝑂̂z. Calculate u𝑂̂v.
GOOD WORK
Our best wishes for a Merry Christmas and a happy
new year
![Page 2 of 2
VI. (6 points)
1) Draw a triangle ABC such that BC= 8 cm, 𝐴𝐵̂ 𝐶 = 50°, 𝐴𝐶̂ 𝐵 = 30°,then draw the
bisector of the angle 𝐵𝐴̂ 𝐶 which cuts [BC] in I.
2) Calculate the measure of the angle 𝐵𝐴̂ 𝐶 and prove that the triangle ABI is isosceles.
3) From the point I, trace the perpendicular at [AC] which cuts this segment at H, and let E
be the symmetric of A with respect to H.
4) What does the line (IH) represent for the segment [AE]? Justify.
5) What is the nature of IAE?
6) Prove that the triangle BIE is isosceles at I.
7) What is the nature of triangle AIH? What do you call the segment [IA]?
VII. (2 points)
x𝑂̂y and y𝑂̂z are two adjacent supplementary angles such that : x𝑂̂y= 40°.
1) Construct x𝑂̂y and y𝑂̂z.
2) Calculate y𝑂̂z.
3) [Ou) and [Ov) are two bisectors of x𝑂̂y and y𝑂̂z. Calculate u𝑂̂v.
GOOD WORK
Our best wishes for a Merry Christmas and a happy
new year](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)