62nd Prep – 2nd Term Revision

1) Factorize each of the following expressions: 1) 3𝒳2-14𝒳-5------------------------------------------------------------------------------------------------------------------------------------------------------------------2) 2𝒳2 -5𝒳y+ 2y2------------------------------------------------------------------------------------------------------------------------------------------------------------------3) 6a2+5ab + b2------------------------------------------------------------------------------------------------------------------------------------------------------------------4) 10a2 +11ab-18b2------------------------------------------------------------------------------------------------------------------------------------------------------------------5) 7𝒳4 +23𝒳2y -30y2------------------------------------------------------------------------------------------------------------------------------------------------------------------6) 6𝒳2 -21𝒳+18---------------------------------------------------------------------------------

7) 𝒳2 - 4------------------------------------------------------------------------------------------------------------------------------------------------------------------8) 49y2 - 1------------------------------------------------------------------------------------------------------------------------------------------------------------------9) 49𝒳2 - 64y2

------------------------------------------------------------------------------------------------------------------------------------------------------------------10) 2𝒳2 - 32------------------------------------------------------------------------------------------------------------------------------------------------------------------11) 𝒳4 - 𝒳2------------------------------------------------------------------------------------------------------------------------------------------------------------------12) 3y2 - 27------------------------------------------------------------------------------------------------------------------------------------------------------------------13) 𝒳3 - 25𝒳---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Alsun Modern School

62nd Prep – 2nd Term Revision

===============================================2) Find the missing term in each of the following trinomial expressions to be a perfect square expression:1) 4𝒳2 …………. + 1

2) a2 – 6 a + ………….

3) …………. - 18 y2 + 81

4) 9a2 …………. + 36

5) 4𝒳2 + 28𝒳 + ………….

6) …………. -24 ab + 16b2

Alsun Modern School

62nd Prep – 2nd Term Revision

3)Complete the following:1) Surfaces of two parallelograms with common base and between two

paralled straight lines, one is carrying this base, are …………………….

2) The parallelogram and ………….. with common base and between

two paralled straight lines are equal in area.

3) The area of parallelogram = …………. X …………………

4) The areas of the parallelograms with bases equal in length and

lying on a straight line, while the opposite sides to these bases are on

another straight line, are ………………….

5) The two triangles drawn on a common base and their vertices

located on a straight line parallel to the base are ……………….

6) Triangles with congruent bases and drawn between two parallel

lines are …………..

7) The median in the triangle divides its area into …………………

=====================================================

4) In the opposite figure: ABCD and EBCF are two prallelograms,

E∈ AD and F∈ AD

Prove that: the area of ∆ ABE = the area of ∆ DCF

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Alsun Modern School

62nd Prep – 2nd Term Revision

5) In the opposite figure: ABCD is a rectangle , AE // DF

Prove that: The area of the figure ABCM = the area of the figure DMEF

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------=====================================================

6) In the opposite figure: AB// DE , Xand Y ∈ AB

, XDEY is a rectangle , AD // BE

1) find the area of the figure ABED

2) if AD=30cm, find the length of perpendicular from B to AD

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------=====================================================

7) In the opposite figure: ABCD and XBCY are two prallelograms,X∈ AD

And the area of ∆ XCY = 15 cm2.Find: the area of ABCD

Alsun Modern School

62nd Prep – 2nd Term Revision

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------8) In the opposite figure: ABC is a right-angled triangle at A ,

AD MBC , AB=4cm andAC=3 cm

Find:1) the area of ∆ ABC 2) the length of AD

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------9) In the opposite figure: ABCD is a rectangle, ABEF is a prallelogram

,D∈CF ,X∈BE ,E∈CF , AB=4cm andBC=10 cm

Find by proof:1) the area of ABEF 2) the area of ∆ XAF

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Alsun Modern School

62nd Prep – 2nd Term Revision

10) In the opposite figure: ABCD is a quadrilateral in which

AD // BC and BA ∩CD={E }, Such that BA=AE

Proove that: the area of ∆ ADC = the area of ∆ ADE

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

11) In the opposite figure: D is the midpoint of BC

E is the midpoint of AC

the area of ∆ DEC = 5 cm2.Calculate: the area of ∆ ABC

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Alsun Modern School