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ÞÏíã 2012-12-28, 09:07 AM   #1
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ãÑÇÌÚÉ ÔÇãáÉ Úáì ÇáåäÏÓÉ ÇáÑíÇÖíÇÊ áÛÇÊ ááÕÝ ÇáËÇáË ÇáÇÚÏÇÏì ÇáÔåÇÏÉ ÇáÇÚÏÇÏíÉ ááÃÓÊÇÐ ãÍãæÏ ãÍãÏ
3) The slope of the straight line which is parallel to
the straight line passing through the two points
( 2 , 3 ) , (  2 , 3 ) equals ...........
………………………………………………………………
9
4) If the straight line AB is parallel to x - axis , where
A ( 8 , 3 ) , B ( 2 , k ) then k ........


………………………………………………………………
5) If the straight line CD is parallel to the y - axis where
C ( m , 4 ) , D ( 5 , 7 ) then m ..........

 
………………………………………………………………
6) ABC is a right angled triangle at B , A ( 1 , 4 ) ,
B ( 1 , 2 ) then the slope of BC ..........

  
………………………………………………………………
7) The slope of the straight line 2 x  3 y  6  0 is ........
………………………………………………………………
8) If the two straight line 3 x 4 y 3 0 and
k y 4 x 8 0 are both perpendicular then k ......
  
   
………………………………………………………………
………………………………………………………………
10
9) If the straight line passing through the two points
( A , 0 ) , ( 0 , 3 ) and the straight line that makes
a triangle its measure is 30 with the positive direction
to the x - axes are

perpendicular then A  ........
………………………………………………………………
………………………………………………………………
10) If the two straight line x y 5 and k x 2 y 0
are both parallel , then k ......
   

………………………………………………………………
11) The area of the triangle in square unit , identified by
straight lines 3 x 4 y 12 , x 0 , y 0
equals ..........
   
………………………………………………………………
………………………………………………………………
12) If A ( 1 , 2 ) , B ( 3 , 4 ) and C is the midpoint
of AB then C ( .......... , .......... )
11
…………………………………………………………
 
13) AB is a straight line passes through the two points
( 2 , 5 ) and ( 5 , 2 ) which of the following
points AB ( 1 , 6 ) , ( 2 , 3 ) , ( 0 , 0 ) , ( 3 , 4 )

………………………………………………………………
………………………………………………………………
14) If A ( 3 , 5 ) , B ( 2 , 1 ) and C ( x , y ) then the
coordinates of the point C. the makes the triangle
ABC a right angle triangle at B is .........
( 6 , 1 ) , ( 4 , 5 ) ,

   ( 3 ,  2 ) , ( 8 ,  2) 
………………………………………………………………
………………………………………………………………
………………………………………………………………
15) If the two straight lines : 2 x b y 3 0 and
3 x y 2 0 are parallel m, then b equals .........
  
  
12
………………………………………………………………
16) The equation of the straight line that passes through
the point ( 3 , 5 ) and is parallel to the X - axis is ......
………………………………………………………………
[2] Complete:
1) If sin x = 1 where x is an acute angle
2
then m( x) = .............................................
.................................................. ................

2) If cos x 1 where x is an acute angle
2 2
then m( x) = .............................................
.................................................. ........................


3) sin 60 cos 30 tan 60 ......................
.................................................. .....................
     
13
4) If tan ( x + 10 ) = 3 where x is an acute angle
then m ( x ) = .............................................
.................................................. .....................

..
5) If tan 3 x = 3 where x is an acute angle
then m ( x ) = .......................................
.................................................. ....................
[3]
ABCD is a quadrilateral where A ( 2 , 4 ) , B ( - 3 , 0 ) ,
C ( - 7 , 5 ) and D ( - 2 , 9 ) Prove that ABCD is a square
………………………………………………………………
[4]
of the circle.
the point M ( 1 , 2 )then find the circumference
C ( 2 , 2 ) , are located in circle whose center is
Pr ove that the points A ( 3 , 1 ) , B ( 4 , 6 ) and

………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
[5]Complete the following:
15
1) The distance between the point ( - 3 , 4 ) and the
point of origin equals ……….
………………………………………………………………
2) The distance between the two points ( - 5 , 0 ) ,
( 0 , 12 ) = ……………….
………………………………………………………………
3) The distance between the two oints ( 15 , 0 ) , ( 6 , 0 )
equals …………
………………………………………………………………
4) The radius length of the circle of centre ( 7 , 4 )
passing through the point ( 3 , 1 ) equals ……..
………………………………………………………………
5) If the distance between two points ( a , 0 ) , ( 0 , 1 ) is
unit length , then a = …….
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
[11] ABC is an isosceles triangle where
AB = AC = 8 cmBC = 12 cm then find:
1) m(B)
2) Area of the triangle to the nearest two decimal
places
………………………………………………………………
………………………………………………………………
8 cm
A
C E B
D
20
…………………………………
…………………………………
…………………………………
…………………………………
………………………………………………………………
………………………………………………………………
[12]
prove that ABCD is a rhombus , then find its area.
A ( 5 , 3 ) , B ( 6 , 2 ) , C ( 1 , 1 ) , D ( 0 , 4 ).
ABCD is a quadrilateral , where points
 
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
A
B D C
8 cm 8 cm
6 cm 6 cm
21
[13] Find the equation of the straight line in the
following cases:
the y - axis that equals 7 units
1) When its slope is 2 and intersects a positive part from
……………………………………………………………
……………………………………………………………
2) Passes through the two points 2 ,  1 , 1 , 1
……………………………………………………………
……………………………………………………………
……………………………………………………………
and intersects a part from the negative direction 3
3
1
x
3) When slope is the slope of the straight line y 1 

……………………………………………………………
……………………………………………………………
……………………………………………………………
22
, c zero
4) The equation of the straight line where m zero


……………………………………………………………
[14]
     
midpoint of BC
of the straight line passes through the point A and the
A 3 , 5 , B 3 , 7 and C 1 ,  3 , then find the equation
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
[15*] Find the equation of the straight line which
Intercepts from the y-axis a positive part of
length 3 Units and parallel to the straight line
passing Through the points ( 2 , 3 ) and ( 5 , 1 )
……………………………………………………………
23
……………………………………………………………
……………………………………………………………
……………………………………………………………
[16*] Find the equation of the straight line passing
Through the origin and parallel to AB where
A = ( 1 , 3 ) and B = ( 5 , 4 )
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
[17*] Show that the points A ( - 1 , 1 ) , B ( 0 , 5 ) ,
C ( 4 , 2 ) and D ( 5 , 6 ) are the vertices of a
Parallelogram.
……………………………………………………………
……………………………………………………………
24
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
[18*] Prove that : the points A ( 0 , 2 ) , B ( 4 , 8 ) and
C ( 6 , 11 ) are collinear.
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
[19*] Prove that : The point ( 2 , 3 ) lies on the straight
Line passing through the points ( 1 , 1 ) and ( 0 , - 1 )
……………………………………………………………
25
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
[20*] If the straight line passing through the two
points
( 1 , 3 ) and ( - 1 , 5 ) is parallel to the straight line
passing through the two points ( 3 , 5 ) and ( x , y ) ,
Find the relation between x and y.
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
26
[21*] Find the slope of the straight line perpendicular
to The straight line passing through the points
A ( 2 , - 3 ) and B ( 3 , 5 )
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
[22*] If the straight line passing through the two
points
( 2 , 3 ) and ( 5 , 7 ) is perpendicular to the straight
Line a x – 3 y = 7 , then find the value of a
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
[23*]

AB is perpendicular to the straight line
5 x – 4 y = 7 where A ( 3 , 4 ) and B ( 5 , y ) , find the
Value of y.
27
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
[24*] Find the equation of the straight line which
Intercepts from the y-axis a positive part of
length 4 Units and is perpendicular to the
straight line :
3 x – 4 y + 1 = 0
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
[25*] Prove that : The shape whose vertices A ( 1 , 1 ) ,
28
B ( 4 , - 2 ) , C ( 6 , 0 ) and D ( 3 , 3 ) is a rectangle.
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
[26*] Prove that : the points A ( 1 , 3 ) , B ( 6 , 4 ) ,
C ( 7 , 9 ) and D ( 2 , 8 ) are the vertices of
A rhombus.
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
29
[27*] Prove that : ABC is a right-angled triangle at B
Where A ( - 1 , - 1 ) , B ( 2 , 3 ) and C ( 6 , 0 )
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
[28*] Find the value of y which makes the triangle
ABC A right-angled triangle at C , where
A ( 2 , 3 ) , B ( 5 , 7 ) and C ( 1 , y ) .
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
30
[29*] Find the value of k which makes the triangle
XYZ is an isosceles and right-angled triangle at
Y , where X ( 1 , 2 ) , Y ( - 2 , 6 ) and Z ( 2 , k )
Find its area.
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
[30*] Prove that the points A ( 7 , 0 ) , B ( 7 , 6 ) and
C ( - 1 , 6 ) form a right-angled triangle then find :
1) The centre of the circle that passes through A ,
B and C.
2) The radius length of obtained circle.
3) The value of k where N ( 0 , k ) the obtained
circle.
……………………………………………………………
……………………………………………………………
……………………………………………………………
31
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
……………………………………………………………
[31*] Complete :
2) If the two slopes of two straight lines in the plane are
equal , then the two straight lines are ……………
……………………………………………………………
5) If the straight line L is perpendicular to the straight
line passing the two points ( 2 , -3 ) and ( 3 , 5 ) ,
then the slope of the straight line L is ….………..
……………………………………………………………
8) The midpoint of the line segment drawn between the
two points ( 3 , 2 ) and ( - 1 , 4 ) is the point …….…
32
……………………………………………………………
[32*] Complete:
1) The slope of any straight line parallel to y-axis = …….....
……………………………………………………………
2) The measure of the angle between the two straight Lines
x – 3 = 0 and y = 2 is ………………………………..……
……………………………………………………………
3) If Z is a mid-point of XY where X ( 3 , 5 ) and
Z ( 1 , 3 ) then the point Y has coordinates ( … , ...)
……………………………………………………………
4) The slope of the straight line y – 5 = 0 is ……………..…..
5) The length of the line segment joining A ( 6 , - 3 ) And B
( 2 , 0 ) equals ………………………………………….
………………………………………………………………
6) Length of the perpendicular line segment from the point
( - 2 , 3 ) to the x-axis = ……………..…. Unit lengths .
33
………………………………………………………………
7) The slope of a straight line is 2
3
, the slope of the
Perpendicular straight line on it is ……………………
………………………………………………………………
8) The equation of the straight line that passes through The
point ( 2 , - 3 ) and is parallel to the x-axis is ……..
………………………………………………………………
9) The slope of the straight line x – 3 y + 1 = 0 is …….........
………………………………………………………………
10) The straight line 3 x + 5 y – 15 = 0 cuts an intercept
Of ………………………... Unit length from the y-axis.
………………………………………………………………
11) If the straight line 2 x + 3 y = 1 is parallel to the straight
line 4 x + k y = 7, then k = ……………………………....
………………………………………………………………
34
12) The perpendicular distance between the point
( 4 , 7 ) and the x-axis = ……………………unit lengths.
………………………………………………………………
13) If A , B and C are three collinear points. Then the
Number of circles passing through them is ……………
………………………………………………………………
14) The two tangents of a circle at the two end points of Its
diameter are ……………………………………………..
………………………………………………………………
15) The equation of the straight line that passes through
The point ( 8 , 3 ) and is parallel to the y-axis is ……….
………………………………………………………………
16) The slope of the straight line which is perpendicular To
the straight line x – 5 y + 5 = 0 is …………………….…
………………………………………………………………
17) If ( 4 , H )  the straight line 2 x + y – 6 = 0 , then
H = ……………………………………………………..
35
………………………………………………………………
18) The distance between the point ( - 6 , 8 ) and the Origin
is …………………………………………………….….
………………………………………………………………
19) Measure of angle between the straight line of slopes
2 , 3 is .................................................. ..........
3 2

………………………………………………………………
[33*] Complete :
1) The distance between the two points ( 2 , 2 ) and
( - 1 , 6 ) equals ……………………….... length unit.
………………………………………………………………
2) If C is the midpoint of AB where A ( 4 , 1 ) and
B ( 2 , - 3 ) , then C = ………………………………
………………………………………………………………
36
3) If m1 and m2 are two slopes of two orthogonal
straight lines and 5
m 2 1  , then m2 = ……………….
………………………………………………………………
4) If the straight line whose slope = 2
1
is parallel to the
Straight line whose equation is y = a x + 3 , then
a = ………………………………………………….…
………………………………………………………………
5) If the slope of the straight line passing through the
Two points A ( 3 , 1 ) and B ( 1 , y ) equals 2
1
Then y = ………………………………………….…
………………………………………………………………
6) If the distance between the points A ( 0 , y ) ,
B ( 4 , 0 ) equals 5 length unit , y  0 then y  .......
………………………………………………………………
37
[34]
AB from its midpoint C where A ( 1 , 3 ) and B ( 3 , 5 )
Find the equation of the straight line perpendicular to
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
[35]
2
2 2 2
Find the value of the following:
a) cos 60 sin 30 sin 60 tan 60 cos 30
b) cos 60 cos 30 tan 45
sin 60 tan 60 sin 30
 
 

    
  
  
………………………………………………………………
………………………………………………………………
38
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
[36]
 
2 3 2
2 2 2
Pr ove that:
a) sin 30 5 cos 60 tan 45
b) tan 60 tan 30 1 tan 60 tan 30 cos 30
 
   
  
    
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
[37] Complete the following:
39
 
1) If sin x = 1 where C is an acute angle
2
then m X  ...............................
 
2) If cos x 1 where X is an acute angle
2 2
then m X ........................

 
3) sin 60  cos 30  tan60  ..............................
 
 
4) If tan X 10 3 where X is an acute angle then
m X .................................................. .....................
 
 
5) If tan 3 X = 3 where X is an acute angle then m X
.................................................. ......................................


[38] Find the value of the following:
sin45 cos 45  sin 30 cos 60  cos2 30
………………………………………………………………
………………………………………………………………
[39] Prove that:
a) sin 60  2 sin230 1
40
………………………………………………………………
………………………………………………………………
b) tan260  tan2 45  cos2 60  sin2 60  2cos 30
………………………………………………………………
………………………………………………………………
[40] Find the value of x if:
4 x = cos2 30 tan2 30 tan2 45
………………………………………………………………
………………………………………………………………
[41] Find the value of E where E is an acute angle:
sin E = sin 60 cos 30  cos 60 sin30
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
41
[42] In the opposite figure:
 
 
ABCD is a rectangle in which
AB = 15 cm and AC = 25 cm
Find : a) m ACB
b) S.A ABCD


………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
[43]
 
     
2 2
ABC is a triangle in which AB = AC = 10 cm ,
BC = 12 cm , drawn AD BC , AD BC D
a) Find the value of sin CAD ,cos CAD ,tan CAD
b) Prove that : sin C cos C 1
c) Prove that : sin B + cos C > 1
 
  
  
 
15 cm
25 cm
A
B C
D
42
…………………………………
…………………………………
…………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
……………………………………………………………
[44] In the opposite figure:
 
 
A trapezoid shaped piece
of land ABCD in which
AD / / BC , m B 90
, AD = 18 metres , BC = 33 metres and DC = 25 metres
a) Find the length of AB
b) Find m C
c) If the land owner made a circular shaped foun
 


 
tation
inside it ,what is the largest possible area for the
fountation ? find the area of the remaining part
of the land.   3.14
A
B C
18 cm D
33 cm
25 cm
43
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
[45]
ABC is a right angled triangle at C , AB = 13 cm , BC = 12 cm
a) Find the length of AC
b) Find each of the following:
sin A , cos A , tan A , sin B , cos B , tan B
c) Prove that : sin A cos B + cos A
2
sin B = 1
d) Find : 1 + tan A
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
A
C B
13 cm
12 cm
44
………………………………………………………………
………………………………………………………………
[46] In the opposite figure: Complete
a) sin X = …………………..
b) cos X = ………………….
c) tan X = ………………….
d) sin Y = …………………..
e) cos Y = ………………….
f) tan Y = ………………….
[47] If the ratio between two measures of
complementary angles as a ratio 3 : 5 , find the
value of each one .
………………………………………………………………
………………………………………………………………
………………………………………………………………
Y
X Z
3 cm
4 cm
45
………………………………………………………………
………………………………………………………………
[48] If the ratio between two measures of
supplementary angles as a ratio 3 : 5 , find the value
of each one .
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
[49] If the ratio between two measures of the angles of
the triangle as a ratio 3 : 4 : 7 find the measure for
each angle.
………………………………………………………………
………………………………………………………………
………………………………………………………………
46
………………………………………………………………
[50] ABC is a right angle triangle in B , AB = 8 cm ,
BC = 15 cm. write what each trigonometric
ratios equal to the following : sin A , cos A , tan
A , sin C , cos C , tan C

XYZ is a right angled triangle at Y
, where XY = 5 cm , XZ = 13 cm Find the value of :
a) tan X + tan Z b) cos C cos Z sinC cos Z
c) sin C cos Z + cos C sin Z

[54] XYZ is a right angled triangle at Z where
CZ = 7 cm , XY = 25 cm. find the value of each of
the following :
a) tan C  tan Y b) sin2X sin2 Y
…………………………………
49
…………………………………
…………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
[55]
2 2
ABCD is an isosceles trapezoid , AD / /BC , AD = 4 cm
, AB = 5 cm where BC = 12 cm
Prove that: 5 tan B cos C 3
sin C cos B



………………………………………………………………
………………………………………………………………
………………………………………………………………
………………………………………………………………
[58] Without using the calculator find the value of X
(where X is an acute angle) satisfies each of:
a) tan X = 4 cos 60 sin 30
b) 2 sin X = sin 30 cos 60 cos 30 sin 60

ABC is an isosceles triangle in which AB = AC
= 12.6 cm and m C 84 24 find the length of BC
to the nearest decimal number.

[61]
A ladder AB of length 6 metres , its upper edge A lies
on a vertical wall and its other edge B on horizontal
floor. if C is the projection of point A on the surface of
the floor and its angle of slope on the surface of the floor
was 60 ,then  find the length of AC

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