١ Cairo Governorate Department: Math Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet “Ismailia Road” Branch Sheet ( 1 ) 1) Factorize each of the following:- 1) x 2 + 5x + 6 2) x 2 + 4x – 12 3) x 2 – xy – 20y 2 4) 15m + m 2 - 34 5) 2 x 2 – 24 x 2 y 2 - 26 y 4 6) x y 8 + 10x y 4 + 21 7) x 3 – x 2 – 6x 2) Complete the following:- 1) x 2 + …… + 35 = (x + ……) ( …… + 5) 2) (x + ……) is factor of expression x 2 + 5x -36 3) The expression x 2 + 7x + a can be factorized if a = ………. 4) The number which can be added to the expression x 2 – 13x + 10 to be factorized is ……… 5) If (3x + 5y) = 7 and (x – y) =3 Then 3x 2 + 2xy – 5y 2 = ……… 3) Factorize the following:- 1) 14x 2 – 17x + 5 2) 2x 2 – x – 6 3) 6a – 27 + 5a 2 4) 9x 2 – 6x + 1 5) 6x 3 – 13x 2 y + 6xy 2 4) Complete the following:- 1) If (2x – 7) is factor of the expression 4x 2 – 8x – 21, then the second factor is ……… 2) 2x 2 + 3x – 5 = (2x ………) (x ………) 3) If the expression Cx 2 + x – 15 is factorized then C may be …………
Transcript
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Cairo Governorate Department: Math
Nozha Directorate of Education Form : 2nd
Prep.
Nozha Language Schools Sheet
“Ismailia Road” Branch
Sheet ( 1 ) 1) Factorize each of the following:-
1) x2 + 5x + 6 2) x2 + 4x – 12
3) x2 – xy – 20y2 4) 15m + m2 - 34
5) 2 x2 – 24 x2 y2 - 26 y4 6) x y8 + 10x y4 + 21
7) x3 – x2 – 6x
2) Complete the following:-
1) x2 + …… + 35 = (x + ……) ( …… + 5)
2) (x + ……) is factor of expression x2 + 5x -36
3) The expression x2 + 7x + a can be factorized if a = ……….
4) The number which can be added to the expression x2 – 13x + 10 to be factorized
is ………
5) If (3x + 5y) = 7 and (x – y) =3 Then 3x2 + 2xy – 5y2 = ………
3) Factorize the following:-
1) 14x2 – 17x + 5 2) 2x2 – x – 6
3) 6a – 27 + 5a2 4) 9x2 – 6x + 1
5) 6x3 – 13x2y + 6xy2
4) Complete the following:-
1) If (2x – 7) is factor of the expression 4x2 – 8x – 21, then the second factor is ………
2) 2x2 + 3x – 5 = (2x ………) (x ………)
3) If the expression Cx2 + x – 15 is factorized then C may be …………
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5) factorize the following:-
1) 36x2 + 84x + 49 2) 16m2 + 40mn + 25n2
3) 28x - 49 x2 – 4 4) 25 a4 – 90a2b + 81b2
6) Complete the following:-
1) If x2 + kx + 25 is a perfect square, then k = ………
2) The expression ax2 – 40x + 25 is a perfect square when a = ………
3) 9x2 …… + 36 is perfect square
4) 25m2 + 40mn + ……. Is perfect square
7) Factorize the following:-
1) 100x2 – 49 2) 2x2 – 8
3) 2
1y2 – 2 4) (x + y)2 – 25
5) 2x3 – 72x 6) x4 – y2
8) Complete the following:-
1) (2x + ……) (…… - 7y) = 4x2 - ……
2) If x + y = 5 and x – y = 3 then x2 – y2 = ……….
3) If 3 (a – b) (a + b) = 21 Then a2 – b2 = ………
4) If x + 3y = 4 and x2 – 9y2 = 32 Then x – 3y = ………
9) Use factorization to get the vale of The following easily.
1) (99)2 – 1 2) (65)2 – (25)2
10) Factorize each of the following:-
1) 27x3 – y3 2) 2x3 + 16
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3) 16a3b + 686b 4) 3
1x3 – 9
5) 8x3 + 0.001 6) m3 - 64
1
11) Complete the following:-
1) If x + y = 5 and x2 – xy + y2 = 7 Then x3 + y3 = ………
2) If a3 – b3 = 27 and a – b = 3 Then a2 + ab + b2 = ………
3) If y3 – a = (y – 2) (y2 + 2y + 4) Then a = ………
4) x3 – 64 = (x - ……) (……………………)
12) Factorize each of the following perfectly:-
1) xy + 5y + 7x + 35
2) abx2 + bx – ax – 1
3) y4 – 3y3 – 15y + 5y2
4) 4x4 – 9m2 + 6m – 1
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Sheet (2)
1) Factorize the following:-
1) 2
1x3 – 4
2) x3 – x2 – 20x
3) 25x2 + 40xy + 16y2
4) 5x2 – 20
2) Complete the following:-
1) If m3 – n3 = 12 and m2 + mn + n2 = 4 Then m – n = ……………
2) If the expression x2 + bx – 10 can be factorized, then b may be …………
3) The expression ax2 – 40x + 25 is a perfect square when a = …………
4) If a – b = 5 and 3a2 – 3b2 = 12 Then a + b = …………
5) (5x + ……) (…… - 2y) = 15x2 - …… - 8y2
3) a) use the factorization to find
(999)2 – 1
b) Find the missing term of trinomial expression ……… - 18y2 + 81 to be a perfect
square.
4) Factorize.
1) x2 – 2xz – 2xy + 4zy
2) 3 x2 + 10x + 8
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5) If xy = 8, find The numerical value of expression
(x + y)2 – (x – y)2
6) Factorize the following:-
1) x4 + x2y2 + y4 2) x4 – 6 x2y + 9y2
3) 9x4 + 2x2 - 1 4) 18a2b4 – 114b2c2a + 128a2c4
5) x8 – 16y8 6) 12x4 + 3y4
7) 8x3 + 27 8) (x + 2)3 – 4x -8
9) a6 – 625b2 10) 4x2 – 12x + 9
7) Find S.S of the following equations:-
1) x2 – 7x + 10 = 0 2) x3 – 125 = 0
3) -2x2 – 15x = 7 4) 1 – 4x2 = 0
5) 2x2 – 8 = 0 6) 49x4 + 70x2y2 + 25y4 = 0
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Sheet ( 3 )
1- Find S.S in R:-
1) x ² + 5 x = 0
2) x ² - 25 = 0
3) 4 x ² - 49 = 0
4) x² + 5x + 6 = 0
5) x² - x – 20 = 0
6) 2x² - 7x – 3 = 0
7) 3x² = 7x
8) x² - 15 = 2x
9) 2x² - 10x=-12
10) 5(x²+3) = 60
11) (x-3)(x+1)=5
12) (x-2) ²=81
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13) 4(x+5) ² =25
14) 2x³-8x=0
15) x 4 -26x²=-25
16) x+x
2 = 3
17) x - x
5 =
2
1
18) x ( x-2) = 0
19) 9
x =
x
4
20) x- x
2 =
2
7
2- What is the real no. if it is added to its square the result will be 12
3- Find the positive rational no. whose square is more than its twice by 48
3- Find two real no. whose product is 45 and one of them is 4 more than the
other
4- What is the real no. which exceed its multiplicative inverse by 6
5
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Sheet ( 4 )
1-Complete
1) The probability of impossible event = , the probability of certain event = …..
2) For every event A we find that p ( A ) ∈ ………
3) 10 cards are numbered from 1 to 10 a card is drawn randomly then the probability
that the card carries a prime no. = …………
4) If the probability of the occurrence of an event is 8
5 then the probability of the non
occurrence of this event = ………..
5) A city has 200000 people the probability that a person gets infected by a disease in
this city is 0.003 the expected no. of infection is ………… people
6) In an experiment of throwing a fair die the probability of getting a no. more than 4
is ………..
7) If the probability that a pupil succeeds is 70% then the probability of this failure is
………..
8) A box contains balls colored with red , green and yellow if a box contains 20 yellow
balls and the probability of selecting a yellow ball randomly is 4
1 what is the no. of balls
in the box
2- A no. card is selected randomly from a set of similar cards no. from 1 to 24 find the
probability of getting a card that carries
a) A multiple of 4
b) No. divisible by 3
c) Prim no.
1- 53 of 100 school students prefer reading the books of the family library on a survey
has been conducted . how many students don't read books out of 400 students
2- A garment factory products 6000 units daily as a sample of 1000 units was examined
20 defective
units were found calculate the number of defective units
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Non – negative integer power in R
Complete :
1) 3 X – 2 = 1 then X = ……………
2) = …………
3) = then X = ………….
4) If ( X – 5 )° = 1 then X ………….
5) If X = , then X– 1 = ………..
6) If 32X – 1 = then X = …………..
7) 43 + 43 + 43 + 43 = ………….
8) If 5X = 4 then 5X – 1 = ………..
9) × =
10) × =
11) X4 × X2 × X = ……….
12) If a = 5X , b = 5 – X then ab = ………..
13) If 4a = 5 , 4b = 6 , 4 a+b
14) If 2X = 10 , 2Y = 2 then 2X-Y
15) If a7 = 3 then a14 = ………..
16) If X = , Y = then X11 Y10 = ………….
17) 35 + - 2 (3)5 = ……….
18) + = ………….
19) of the number 420 = …………..
20) of 212 × 412 = …………
21) 25 + = ………..
22) 220 + 221 = …………
23)
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24)
25) If = 1 then X = ………………
26) If = 1 then X = …………
27) If 5X = 5 then 5X – 1 = …………..
Find the value of X in each of X :
1) = 1 2)
3) ( 3 ) X+2 = 27 4) ( 32 )X – 3 = 82X + 1
5) (5)3X – 1 = ( 7 6) = 9
7) 25 × 3X – 1 = 9 × 5 X – 1 8) =
9) = 10) = 9 2X – 1
11) = 12) = 2n
13) = 14) 6X2 – 6 =
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Sheet ( 5 )
1) Complete:-
1) The image of the point (-2 , 4) by reflection in x-axis is …………
2) The image of the point (3 , 2) by reflection in x axis then by y- axis is ………
3) The reflection. In a plane reserves
a) ……… b) ………
c) ……… d) ………
4) The number of axes of symmetry of the isosceles ∆ is …………
5) The number of axes of symmetry of the rhombus is …………
6) The number of axes of symmetry of the circle is …………
7) If the axis of symmetry of ∆ ABC where A(3 , 0) B(1 , 4) is the x axis then C(... , …)
8) ABC is an equilateral triangle, A is the reflected image of A by reflection in BC then
the type of ∆ ABC is ………. A
2) using the opposite figure complete
1) FB is the image of FA by reflection in …………….. F D
2) The axis of symmetry of ∆ ABC is ……………..
3) The image of ∆ ADF by reflection in DF is ……………..
4) The ∆ BFE is the image of ∆ …… by reflection in BF C E B
L A
3) ∆ ABC is a right angled at A D m( ∠ B) = 320 and L is the axis of symmetry
of ∆ DBC .Find the values of y , x , m & n B C B 4) If C is the image of B
By reflection in S – t line L BC I L = {D} D M ( ∠ BAD) = 300 A AB = 4 X -3 AC = 9 – 2X
Calculate the perimeter of ∆ ABC C
n
y m
x
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Sheet ( 6 )
1) Complete using the figure:-
1) The image of point A by reflection in M is ……… D L A
2) The image of AL by reflection in M is ………
3) The image of ZM by reflection in M is ……… Z X
4) The image of AX by reflection in X is ……… M
5) The image of ∆ ALM is by reflection in M is ………… C B
6) The image of ∆ AMB by reflection in M is …………
7) The image of square AXML by reflection in M is …………..
2) Draw ∆ ABC where A(2 , -2) , B(3 , 4) , C(-3 , 2) then map ∆ ABC as the image of
the image of ∆ ABC by reflection y – axis then map ∆ ABC as the image of ∆ ABC
by reflection in x axis what is the image of ∆ ABC by reflection in the origin point.
O
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3) ABCD is a rectangle where A(2 , 5) , B(6 , 5) , C(6 , 8) , D(2 , 8) then find the image of
rectangle ABCD by reflection in the origin point.
4) ABCD is a square M is the point of intersection D A
of its diagonals and X ∈AB find y as the image
of X by reflection in M then prove that
1) ∆ DAX ≡ ∆ BCY M
2) the figure DBXY is parallelogram
C B
5) If CD is the image of AB by reflection in the point M
BA = (2 x + 5) cm , CD = (x + 9)
M( ∠ A) = 2y , m( ∠ D) = 600
Find 1) the length of CD
2) the value of y
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Sheet ( 7 )
Complete:-
1) If two polygons are similar then the corresponding …………… are equal in measure.
2) If the two polygons are similar then the corresponding ………… are proportional.
3) If the measures of the corresponding angles in the two triangles are equal then
the two ∆ 's are …………
4) If the ration between the lengths of two corresponding sides in two similar ∆ is equal
to 1 then the two ∆ 's are ………
5) If two polygons are similar and the ratio between the lengths of two corresponding sides
is 3 : 4
then the ratio between their perimeters is ……………
In the opposite figure :
1) AC // ED , AD ∩ CE = {B} , AC = 5 cm.
, BE = 8 cm. , AB = 3 cm. and BD = 6 cm.
1) Prove that : ∆ ABC ~ ∆ DBE
2) Find the length of each of : BC and ED
3) Find the ratio of enlargement .
2) m ( ∠ AED ) = m ( ∠ B ) , Ad = 3 cm.
AE = 4.5 cm. and BD = 6 cm.
1) Prove that : ∆ ADE ~ ∆ ACB
2) Find the length of EC
3) ∆ ADE ~ ∆ ABC , AD : DB = 1 : 3
1) Find the ratio AC
AE
2) If DE = 4 cm. , find the length of BC
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Sheet ( 8 )
1) Complete:-
1) Surfaces of two parallelograms with common base and between two parallel St. lines
, one is carrying base are ………………
2) The parallelogram and ……………… with common base and between two parallel St.
lines are. equal in area.
3) The area of parallelogram = ……………… × ………………
4) If the base length of parallelogram is 7cm and the corresponding height is 4cm,
then its area = ……………… cm2
5) If ABCD is parallelogram in which AB = 5cm, BC = 10cm and its smaller height is
4cm, then its greater height = ……………… cm
In the opposite figure :
1) ABCD and ABMN are two parallelograms and M ∈ CD
Prove that :
The area of ∆ EBC = 2
1 the area of ABMN
2) ABCD is a rectangle , ABEF is a parallelogram
, D ∈ CF , X ∈ BE , E ∈CF
, AB = 4 cm. and BC = 10 cm .
Find by proof :
1) The area of ABEF
2) The area of ∆ XAF
3) ABCD and EBCF are two parallelograms , BE ∩ CD = {L}
, D ∈ AF and E ∈ AF
Prove that :
1) The area of ∆ ABL = the area of ∆ FCL
2) The area of the figure ABCL = the area of the figure FCBL
١٦
4) ABCD and AEFD are two parallelograms
and AE ∩ DC = {X }
Prove that :
The area of ∆ ABX = the area of ∆ DFX
5) ABCD and AEFD are two parallelogram and AE ∩ CD = {M}
Where E∈ BF and C∈ BF
Prove that :
The area of ∆ ABM = the area of ∆ DMF
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Sheet ( 9 )
1) Complete:-
1- The area of the triangle is …………… the area of the parallelogram
Which has a common base with it and its vertex lies on the st. line
Parallel to this base
2- The area of triangle = ……… × the base length × the corresponding height.
3- If the base length of a triangle is 4 cm. and the corresponding height =3 cm
then its area = ……….. cm2
4- If the triangle whose base length is 12cm and its area is 48cm2, the corresponding
height = ………
5- If ABCD is parallelogram with area 100cm2 and E ∈ AD then
the area of Δ EBC = …………… cm2
In the opposite figure :
1)ABCD is a quadrilateral . E ∈ BC such that AE // DC ,
AC ∩ DE = {M}
Prove that :
The area of ∆ ABC = the area of figure ABED
2) ABCD is a quadrilateral in which AD // BC
and BA ∩ CD = {E} such that BA = AE
Prove that : The area of ∆ ADC = the area of ∆ ADE
3) AC // XY and F is the midpoint of XY
Prove that : The area of ∆ ABF = the area of ∆ CBF
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4) AD // BC , AC ∩ BD = {M} ,
E is the midpoint of BC
Prove that : The area of the figure ABEM = the area of the
Figure DMEC
5) AD // BC and B is the midpoint of YM ,
C is the midpoint of MX
Prove that : The area of ∆ AYB = the area of ∆ DCX
6) AD // BC and AC ∩ BD = {M} ,
D is the midpoint of EC
Prove that :
The area of ∆ MDE = the area of ∆ AMB
١٩
Sheet ( 10 )
1) A square whose area equals the area of the rectangle whose dimensions 2cm and 9cm
find the length of its diagonal.
2) Two land pieces are equal in area, the 1st is in the shape of a square and the 2nd is in the
shape of a rhombus whose diagonals lengths are 8m, 16m find the perimeter of the
square.
3) Find the area of the rhombus whose perimeter is 52cm and the length of one of its
diagonals is 10cm.
4) A rhombus whose diagonals are of length 12cm and 16cm find its height.
5) The perimeter of a rhombus is 64cm. and the measure of one of its angle is 600 find its
area.
6) If the ratio between the two lengths of the diagonals of a rhombus is 3 : 4 and the length
of the smallest diagonal is 9cm find the area of the rhombus.
7) The area of trapezium is 180 cm2 and its height is 12cm find the lengths of its parallel
base if the ratio between their lengths is 3 : 2
8) ABCD is a trapezium in which BCAD // , AD = 27cm and BC = 45cm
if the area of Δ ABC = 225cm2 find the area of the trapezium.
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Sheet ( 11 )
1- complete
1) The projection of a line segment on a st. line not perpendicular to it is ……
2) The projection of a line segment on a st. line perpendicular to it is ……..
3) The length of the projection of a line segment on a given st. line …….. the length of the line segment itself
4) The length of projection of a line segment on a st. line perpendicular to it is …
5) The length of the projection of a line segment on a st. line parallel to it ……the length of the main line segment
2- from the opposite figure :- 1) The projection of AB on BC is ……..
2) The projection of BC on AB is ….….
3) The projection of AC on BC is ….….
4) The projection of BC on AC is ……..
5) The projection of AC on AB is ….….
6) The projection of AB on Ac is ….….
7) The projection of AM on AB is ….…
8) The projection of BM on BC is .……
9) The projection of BM on AC is ……
3- From the opposite figure , find:- 1) The length of the projection of BC on DC
2) The length of the projection of AB on DC
3) The area of the trapezium ABCD
4- Find using the figure:- 1) The projection of AD on AC
2) The projection of BE on AC
3) The projection of AE on AC
4) The projection of AB on AD
5) If AC = 26 cm , AB = 30 cm , BC = 28 cm and the area of ∆ABC = 336 cm² find the length of
the projection of AB on BC
G
A
D
٢١
Sheet ( 12)
1- From the opposite figure find :- a) The length of AC b) Prove that m ( ∠ ACD ) = 90 ˚
2- From the opposite figure Prove that m ( ∠ BDC ) = 90 ˚
3- From the opposite figure a) Prove that m ( ∠ DAC ) = 90 ˚ b) Find the area of the figure ABCD
4- Find a) The length of each of CE , AB b) The length of DB c) The length of the projection of DC on AB d) The area of ABCD e) Prove that m ( ∠ DBC ) = 90˚
5- ABCD is a parallelogram in which AB = 8 cm , AC = 20 cm and BD = 12 cm , prove that m ( ∠
ABD ) = 90˚ then find the area of ABCD
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Sheet ( 13 )
1-Complete
1- in ∆ ABC if ( AB )² < ( AC )² + ( BC )² then ∠ C is ………. 2- In ∆ ABC if ( AC )² > ( AB )² + ( BC )² then ∠ B is ………. 3- In ∆ XYZ if ( XY )² > ( YZ )² + ( ZX )² then ∠ Z is ……… 4- in ∆ ABC if ( AB )² + ( BC )² = 48 cm² , AC = 7 cm then ∠ B is …….. 5- if ∠ A complements ∠ B in ∆ ABC then ( AB )² …… ( AC )² + ( BC )² 6- ABC is ∆ in which ( BC )² = ( AC )² + ( AB )² , m ( ∠ B ) = 40 ˚ Then m ( ∠ C ) = ………
2- From the opposite figure Prove that ∠ ABC is an obtuse angle
3- From the opposite figure
Prove that ∠ D is an acute angle
4-From the opposite figure :
A \ is the image of A by rotation around M , identity of type of the angle of rotation
٢٣
Alg. [1] Complete :
1) ( X + Y )2 = X2 + ……..+………..
2) If a + b = 5 , a2 – b2 = 20 Then a – b = …………
3) The expression X 2 + 6X + K is a perfect square when K = …………..
4) If ( X-1 ) is one of the factors of the expression 3X 2 – 4X + 1 then the other factors =
……
5) The S.S of the equation X ( X-3) = 0 in R is ………….
[2] Factorize each of the following :
1) 4X 2 – 9 2) X3 – 8
3) X 2 + X – 6 4) ax – bx + ay – by
[3] a) Find the S.S in R :
i) X 2 + 7X – 18 = 0
ii) 2
1X 2 = 3X
b) Which real umber exceeds its multiplicative inverse by 6
5 ?
[4] a) Evaluate using the factorization :
i) 25 × 66 + 25 × 35 – 25
ii) (64) 2 – ( 36 ) 2
b) Factorize : X4 + 4Y4
Good Luck
Cairo Governorate
Nozha Directorate of Education
Nozha Language Schools
Ismailia Road
Department : Maths
Form :2nd
prep.
Mid-Term Exam
March 2013
٢٤
Geom.
[1] Complete :
1) The median of a triangle divides its surface into …………….
2) The two polygons are similar to a third are ………………
3) ∆ ABC is aright angled triangle at B in which AB = 5 cm , BC = 12 cm .
Then AC = ………cm .
4) The diagonal of a square whose area 50 cm2 equals …………cm2.
5) If the ratio of enlargement between two triangles equals one then two triangle are
……… .
[2] a) In the opposite figure :
1) Prove that ∆ ABC ~ ∆ DBE
2) Find the length of DE , CB
b) A rhombus whose diagonals lengths are 12 cm , 16 cm find the length of its side ?
[3] In the opposite figure :
AD // BC // EF
Prove that :
The area of ∆ ABE = the area of ∆ DCF
[4] a) Find the height of a trapezium with area of 190 cm2 and the two base lengths are
18 cm and 20 cm .
b) ABCD is a parallelogram in which DE ⊥ BC , DO ⊥ AB if AB = 4 cm. , BC = 6 cm.
, DE = 3 cm . Find the length of DO .
Cairo Governorate
Nozha Directorate of Education
Nozha Language Schools
Ismailia Road
Department : Maths
Form :2nd
prep.
Mid-Term Exam
March 2013
A C
E D
B
D A
C B
F E
٢٥
[5] a) In the opposite figure :
If area ∆ AEB = area of ∆ ADC
Prove that : BC // ED
b) In the opposite figure :
∆ AED ~ ∆ ACB , AE = 3 cm , AD = 5 cm
BE = 7 cm , ED = 6 cm
Find 1) The length of DC
2) The perimeter of ∆ ACB
Good Luck
D E
B C
A
A
D
E
C B
5 cm 3 cm
7 cm 6 cm
٢٦
Alg.
[1] Complete:-
a) If X = ( 3 + 2 )6 , Y = ( 3 + 2 )-6 then XY = …………
b) If X – Y = 5 , X2 – Y2 = 30 then X + Y = …………..
c) If ( X + 2 ) is a factor of the expression X2 + 5 X + 6 then the other factor is …………
d) If X2 + 14X + K is a perfect square then K = ……………
e) The probability of a certain event = …………….
[2] Choose the correct answer :
1) The S.S of the equation X2 + 4 = 0 is …………….. [ 2 or -2 or ± 2 or Ø ]
2) If X3 – Y3 = 12 , X2 + XY + Y2 = 4 then X-Y = ….... [ 8 or 16 or 3 or 48 ]
3) If a2 + b2 = 5 , ab = 4 then ( a – b )2 = ………… [ -3 or 9 or 20 or 1 ]
4) If 3x + 3x + 3x = 1 then x = …………. [ zero or 1 or -1 or 3 ]
5) If 5x = 3 then ( 125 )x equals ………… [ 9 or 27 or 15 or 25 ]
[3] Factorize completely each of the following :
1) X3 – 8 2) 4 X4 + Y4
3) X2 – 7X + 10 4) X3 – 4X + X2 – 4
[4] a) If = 16 find X then find the value of (4)-x
b) If X = 2 , Y = 3 find in the simplest form the value of ( X-Y)5 (X+Y)5
[5] a) If the length of a rectangle exceeds its width by 4 its surface area = 60 cm2 .
find its perimeter .
b) A card is selected randomly from a set of similar cards numbered from 1 to 15
find the
probability of getting a card that carries
1) a number divisible by 5 2) an prim number divisible by 5
8x × 9x
(18)x
Cairo Governorate
Nozha Directorate of Education
Nozha Language Schools
Ismailia Road
Department : Maths
Form :2nd
prep.
Final Exam
May 2013
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Geom.
[1] Complete:-
1) ∆ ABC if ( AC )2 = (AB)2 + (BC)2 then m ( ∠ ……) = 90° .
2) The median of a triangle divides its surface into two triangular surfaces ………..
3) The area of a square is 50 cm2 the length of its diagonal = …………..cm .
4) The ratio between the length of two corresponding side in two similar triangles
equals one then the two triangles are ………… .
5) The projection of the point ( 3 , 5 ) on the X – axis is ………….
[2] Choose the correct answer :
1) The ∆ whose sides 5 , 13 and 12 cm is ………….. angled ∆
[ right or acute or obtuse or equilateral ]
2) The trapezium whose middle base is 9 cm and its height 8 cm its area = ………….cm2 .
[ 27 or 72 or 36 or 144 ]
3) A rhombus of diagonals 6 cm and 8 cm then its area is ……….cm2 .
[ 48 or 84 or 24 or 42 ]
4) The number of axes of symmetry of a rectangle is ………….
[ 1 or 4 or 2 or infinite ]
5) A parallelogram whose sides length are 6 cm and 8 cm and its small height is 5 cm
then its area = …………cm2. [ 30 or 40 or 48 or 240 ]
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