رياضيات 3

Examination
1) Show which of the following statements is correct and which is wrong :
a. + 2 = ( )3
b. the multiplicative inverse of ـــــــ is
c.
d. ] 2 , 6 [ - } 6 { = ] 2 , 5 [
e. the function if ( x ) = 3 –2 x is increasing on R
f. the two numbers ( ) , ( ) are conjugate

2)
a. If = 3x then find x
b. Represent the function f ( x ) = 3x – 6 and from the graph find the intersection points with y- axis and x- axis
c. If the points ( -5 , 11 ) , ( 0 , y ) , ( 5 , 5 ) are collinear find the value of y

3) Choose the correct answer from those between brackets :
a. …….. ( , , 5 )
b. If x2 - y2 = 16 , x – y = then x + y = ……… ( )
c. The irrational number witch between 3 , 4 ……… ( )
d. One of solutions of the equation 2x – y = ……… ( ) 2 , 1 ) , ( 1 , 2 ) , ( 0 , 2 ) )
e. ] 2 , 5 [  ] -1 , 3 ] = ……… ( ] 2 , 1 [ , ] 2 , 3 [ , ] -1 , 5 [ )
f. ( )10 = ……… ( 37 , 35 , 81 , 3 )



4)
a. If x = } x : x  N , 0 > x 5} and r is a relation on x s.t. a R b means that a + b = 6 for all , a ,  X write R as an ordered pairs and represent it by an arrow is R a function ? find its range ?
b. ماكينة تروي الفدان الواحد في 3 ساعات وماكينة أخري تروي نفس الفدان في ساعتان إذا عملت الماكينتان معاً فما الزمن اللازم لترويان نفس الأرض؟

5)
a. find the length of diameter of a sphere witch volume is 36  cm3 .
b. a single die is roiled once find the probability of the number will appear is :
1. greater than 4
2. even











Examination
1) Complete the following :
a. = ………
b. … = -3
c. The slope of the straight line 3y – x = 2 is and cuts the y- axis on the point ………
d. [ 2 , 6 ]  { 2 , 5 } = ………
e. If 9 × 3x + 3 = then x = ………
f. The solution set of the strait equation x2 ( x2 – 6 ) ( 2x + 3 ) = 0 is ………

2)
a. simplify to the simplest form :
b. If a = 3 + find A-1 to the simplest form
c. If 6.3x + 3.7x = then find x

3) Choose the correct answer :
a. The suitable value to the function = ………
b. = ………
c. the function f ( x ) = -7 is ………



4)
a. a cylinder witch of volume is 616 cm3 and its height 4 cm find the radius of it If (  = )
b. simplify :
c. If x = { 1 , 2 , 3 , 4 } and R = { ( 1 , 3 ) ,( 2 , 3 ) , ( 3 , 4 ) , ( 4 , 4 ) } represent this relation with an arrow diagram and write if R is a function or not ?
d. Find the equation of the straight line If its slope is = and cuts the Y – axis at the point ( 0 , 3 ) is this line represent an increasing function ?

5)
a. a care movies from A to C passes to B
i. find its uniform velocity which movies from A to B
ii. find its uniform velocity which movies from C to A
b. from15 cards numbered from 1 to 15 a card is choosing randomly find the probability of the number is devisable by 3 ?

1) In the opposite figure :
m ( A ) = 400 , m ( B ) = 700 , M D _|_ A B
, M H _|_ A C prove that M D = M H







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2) In the opposite figure :
A B is a tangent to a circle mat A
,m ( A M B ) = 580 , find m ( A B M ) and find A B

3) In the opposite figure :
A B , A C are tow cords of a circle M , A B =A C ,X , Y are the mid points of A B and A C respectively M X , M Y cut the circle at the points D , H respectively prove that X D = Y H
If A = ( 3 , 5 ) is a point .


Choose the statement from group ( b ) which is suitable for group ( a ) :

Image of the points A The transformation
1) A =(-3 , 5)
2) A =( -3 , -5 )
3) A = ( -5 , 3 )
4) A = (8 , 8 )
5) A = ( 3 , -5 ) 1) by reflection on X ـaxis
2) by rotation about O with angle 900
3) by rotation about O with angle ( 1800 )
4) by reflection on Y ـaxis
5) by translation ( 5 , 3 )



Put ( ) for the correct answer ( ) for the wrong one :
i ) The image of a circle which its center lies on a line L with relocation in L is the circle itself ( )
ii ) The point ( 0 , 0 ) is the image of the point ( 2 , 3 ) by the transition ( -3 , 2 ) ( )
iii ) The transition ( -2 , 5 ) after the translation ( 0 , 0 ) ( )
iv ) The point ( 0 , 2y ) is the image of the point ( x , y ) by translation ( -x , y ) ( )
v ) The image of the point ( 2 , 7 ) by translation A B where A ( 3 , 5 ) B ( 5 , 9 ) is the point ( 4 , 11 ) ( )
vi ) If polygon P1 ~ polygon p2 and polygon P2 ~ polygon p3 then If polygon P1 ~ polygon p3 ¬ ( )
vii ) If an angle in a rhombus equals another one in another rhombus then the two rhombus are similar ( )
viii ) The two isosceles trapezoid are similar ( )
ix ) All squares are similar
: all equilateral triangles are similar ( )

In opposite figure if A B D ~ C A D
and m ( A B D ) = 3X + 30
m ( D A C ) = 2X + 100
then m ( A B D ) = ………
And C D = ………

The cylinder is body which construct from rotation of a rectangle about one of its sides ( )
If A b  L = { c } and A B is the image of A B in L with relocation then C  A B ( )

The shape witch consists of two circle touch each other exothermally has one sym – axes only ( )

Choose the correct answer :
1) In the image of the point ( 5 , -2 ) with the reflection in x – axis is ……… ] ( -2 , 5 ) , ( 5 , 2 ) , ( -5 , 2 ) [
2) The square has ……… axis of symmetry ] 3 , 2 , 4 , 1 [
3) The point ( 1 , 3 ) is the image of the point ( -1 , 3 ) by reflection ……… ] x - axis , y – axis [
For each of the following find the shaded part :







Dies amid point of 8 cm B C , D C = 3 cm , A B = 8 cm
M ( B )= m ( H ) = 900 find the length of D H , H C
By using the similarity



In the opposite figure :
Polygon A B C D ~ Polygon X Y L M
Find the length of A D , L M and m ( B )







In the opposite figure :
Prove that A B C ~ E D F
and then find the length of A B


Plot by using the square paper the triangle A B C in which A = ( 3 , 2 ) , B = ( 3 , 4 ) ,
C = (1 , -1 ) and hens find its image by translation M L where m = ( 3 , 4 ) , L = ( -5 , 4 )





Plot by using the square paper the triangle A B C in which A = ( 3 , 2 ) , B = ( 3 , 4 ) ,
C = (5 ,4 ) and hens find its image by rotation around origin O with measure 900