1. Page 1 of 3
I. (2 points)
Choose the correct answer and justify your work.
N° Questions Answers
a B C
1 The GCD of 64 and 48 is : 6 2⁴ 2³
2 3
20
represent 3% 1.5% 15%
3 2 𝑛
2³
= 2⁹ then n=
12 6 27
4 In the triangle ABC if :
𝐴̂ = 𝑥 + 15° ; 𝐵̂ = 3𝑥 − 75° and 𝐶̂ = 2𝑥 + 30°. Then
𝑥 =
25 35 42
5 In the following figure : (AB) is parallel at (CD)
Then x=
66° 156° 24°
II. (3 points)
1) Perform the following and simplify the answer if possible.
𝐴 =
13
4
−
7
4
×
12
49
; 𝐵 = (
9
2
−
1
4
) × (6 −
1
3
) ; 𝐶 =
44+20
11−5
+
1
3
𝐸 =
3
5
−
7
9
+
2
3
and F=
24
6
×
81
48
÷
3
18
2) Precise which one from these fraction is decimal and justify.
Name:………………………
Classof G7
Section: A, B, C
Teacher: Hilal Ismail
Zeinab Zeineddine
AbedAl – Karim Al – Khalil Public
School
Final exam
Subject: Mathematics
Date: 17,May, 2016
Duration:2h
2. Page 2 of 3
III. (6 points)
1) Factorise :
a) 15𝑥³𝑦𝑧 − 25𝑥²𝑦𝑧³
b) 8𝑥2 𝑦4 − 12𝑥𝑦²𝑧 + 24𝑥𝑦³𝑧.
c) 24𝑎²𝑏 − 8𝑎 + 16𝑎³.
2) Reduce each of the following expressions , the calculate the numerical value for 𝑥 =
3 𝑎𝑛𝑑 𝑦 = −1
a) 2𝑥 − 4𝑦 + 8 − (𝑥 + 𝑦 − 4)
b) (5𝑥 + 6𝑦 − 10) + ( 𝑥 − 9𝑦 + 7)
3) Develop and reduce :
a) ( 𝑥 − 4)( 𝑥 + 6) + 10𝑥 − 12.
b) −2( 𝑥 − 3) − (4𝑥 − 5).
c) (5𝑚 − 7)(2𝑚 − 𝑚²+ 10).
4) Solve each of the following equations :
a) 3( 𝑥 − 2) − 𝑥 + 4 = 2𝑥 − 1
b)
𝑥−1
3
−
2𝑥−3
2
=
𝑥
6
−
𝑥+1
3
c) 3(2m + 1) – 7 = 2m
d) 5𝑥 − 2 − (7𝑥 − 3) = 2(𝑥 − 1)
IV. (4 points)
1) In an orthogonal system of axes x’Ox, y’Oy, plot the points L( 3 ;3), C(-2 ;3), S(-2 ;-1)
and A(3 ;-1).
2) Determine the nature of the quadrilateral ASCL? Justify.
3) Calculate the perimeter of the quadrilateral.
4) a. Construct the point M image of A by the translation taking C to L.
b. What is the nature of the quadrilateral CAML?
5) a. Construct the translate of the triangle SAC by the translation that taking C to L.
b. Find the nature of the triangle image.
c. Calculate the area of the triangle image.
3. Page 3 of 3
V. (5 points)
In the following figure:
ABC is an isosceles triangle at A such that𝐴𝐵̂ 𝐶 =
𝐴𝐶̂ 𝐵 = 70°.
[AH] is the height issued from A.
The point E is the midpoint of [AH].
The line (d) is perpendicular to (AH) at E.
(d) Cuts [AC] in F and [AB] in I.
1) Prove that (d) is parallel to (BC).
2) Calculate 𝐴𝐹̂ 𝐸 and𝐸𝐴̂ 𝐹.
3) Prove that AEF and EFH are equal. Give their
homologous elements.
4) Deduce that (AB) and (FH) are parallel.
5) Prove that F is the midpoint of [AC].
GOOD WORK.
Best wishes for a
happy summer
and a bright and
a successful
future.
