This document contains a multi-part math exam with the following questions: 1) Verify whether a given quadrilateral is a rhombus based on given side lengths. 2) Simplify and write expressions in specific forms, such as irreducible fractions or scientific notation. 3) Write fractions in irreducible form. 4) Calculate angles and determine the nature of quadrilaterals based on given properties. 5) Construct a figure with given properties and determine the nature of quadrilaterals, midpoints, and centers of gravity. 6) Determine values based on given angle properties of quadrilaterals and calculate areas.

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CCS Mathematics Dec. 2014
Class ofG8 Exam of 𝟏 𝒕𝒉 semester Duration : 2 hs
Name:…………………………………..
I. (3 points)
Given a quadrilateral ABCD such that:
AB =(
8
5
+ 5) ÷ (1 −
2
5
) ; BC=
55×103×210
104×29
CD= (3 − √5)(2 − √5) + √125 and AD= 2√45 + √81 − 3√20 + 2
Verify that ABCD is a rhombus.
II. (3 points)
Given the following numbers: 𝐴 =
7
18
×
2
7
− (
5
3
− 1)
2
; 𝐵 =
3×10²×5×104
12×(10³)3
𝐶 = 2√5 + 2√125 − √45 ; 𝐷 =
3³×5⁸×15²
45³×5⁶
All the steps of calculation must be shown:
1) Write A in the form of irreducible fraction.
2) Write the scientific notation of B.
3) Write C in the form of 𝑎√5; a is a natural number.
4) Write D in the form of 𝑎 𝑚
× 𝑏 𝑛
where a and b are two prime numbers.
III.(2 points)
Write in the form of irreducible fraction:
𝐴 =
1+
1
2
1+
1
1+
1
1+
1
3−
1
2
; 𝐵 =
34+35
34 et 𝐶 =
3
4
+
1
5
×
7
2
2
3
−
5
6
×
1
10
IV. (3 points)
In the following figure:
 SOIR is a rectangle.
 LION is a parallelogram.
 𝐿𝐼̂ 𝑅 = 𝐿𝐼̂ 𝑂.
 𝑅𝐼 = 𝐿𝐼.
1) Calculate the angles of LION.
2) What is the nature of LNSR? Justify.
3) Calculate the angles of LNSR.

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V. (6 points)
PAIN is a rectangle of center C. O and S are the symmetric respectively for A and N with
respect to I.
1) Construct the figure.
2) What is the nature of SONA? Justify.
3) What is the nature of PISA? Justify.
4) The line (PI) cuts [OS] in E. What is the nature of the quadrilateral CASE? And that of
ONCE? Justify.
5) Verify that E is the midpoint of [OS].
6) Verify that (SN) cuts [PO] at its midpoint.
7) Deduce that I is the center of gravity of the triangle POS.
VI. (3 points)
1) Let IRAM be a quadrilateral such that: 𝐴̂ = 𝐼̂ = 𝑥 , 𝑀̂ = 180° − 𝑥 and 𝑅̂ = 2𝑥 − 90°.
What is the value of𝑥?
2) ABCD is a parallelogram where 𝐴̂ = 𝑥 and 𝐵̂ = 2𝑥 − 90°.
Prove that ABCD is a rectangle.
3) LORD is a parallelogram where𝐿𝑂̂ 𝐷 + 𝐿𝑅̂ 𝐷 = 90°.
Prove that LORD is a rhombus.
4) In the following figure,
PARC is a parallelogram
(PH) is perpendicular at
(AC), and AC=3PH= 9 cm.
Calculate the area of
PARC.
GOOD WORK.