1) The document contains a mathematics exam with multiple choice and free response questions covering topics like GCD, percentages, solving equations, factoring expressions, and geometry. 2) In part III, students are asked to factorize and simplify algebraic expressions, reduce expressions by combining like terms, and solve equations. 3) Part IV involves plotting points in the coordinate plane, determining properties of quadrilaterals formed by the points, calculating perimeters, and performing translations.

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.