Download Manaret Heliopolis Language School ( Revision sheet Geometry)

Manaret Heliopolis Language School
( Revision sheet Geometry)
Name / ………………………
1st prep
1) Complete:
a) Polygons are plane figures with ……………………………………………………
b) The sum of measures of the interior angles of a polygon with n sides = ………………
c) The sum of measures of the exterior angles of a polygon with n sides = ………………
d) The measure of an angle of a regular polygon with n sides = ………………
e) The sum of measure of the interior angles of a hexagon = …………………
f) The measure of any angle of a regular decagon = ……………………
g) The sum of measure of the exterior angle of a heptagon = …………………
h) All sides in regular polygon are ……………… and all its angles are ………………
i) In the hexagon the diagonals ……………… its angles.
j) The polygon that has 7 sides is called ………………
k) The sum of measure of the interior angles of a decagon = …………………
l) The sum of measure of the interior angles of a pentagon = …………………
m) ABCD is a parallelogram in which m(A) = 50 , then m(C) = …………
n) The image of the point ……………….by rotation about the origin with an
angle with measure 90° is ( -1 , 4 )
o) In the parallelogram ABCD if m(A) =  m(B) then m(B) = ……………
p) The point ( 3 , - 2 ) is the image of the point ( 2 , 3 ) by rotation about the origin
with an angle of measure ………………………..
q The square is a rectangle in which sides are ……………………………………
u) In …………… the diagonal makes an angle of measure 45° with the adjacent side.
v) A parallelogram whose angles are right angles is called ……………………
s) A rhombus whose diagonals are equal in length is called …………………….
t) The image of ( 2 , - 3 ) by reflection in …………………is ( 2 , 3 )
w) The image of ( -1 , -4 ) by reflection in …………………..is ( 1 , 4 )
x) the image of A ( 2 , 1 ) by reflection in x – axis following by reflection in the y-axis is …..
y) The image of the point (2,-3) by reflection in the y- axis followed by reflection in x-axis is…..
z) If A ( -2 , 3 ) is the image of A ( 2, 3 ) by reflection then the image of A by
reflection in y axis is …………………
2- Complete :
(a) The image of point ( -1 , 1 ) by translation ( x + 5 , y + 2 ) is ……………..
(b) The image of point ( 2 , 3 ) by translation ( x + 2 , y + 3 ) is …………………
(c) The image of the point ( 2 , - 3 ) by rotation about the origin with an angle of
measure 90° is ………..and with an angle of measure 180 is ……
(d) The image of the point ( -1 , 0 ) by rotation about the origin with an angle of
measure 90° is …………………………
(e) The image of the point ( 1 , 1 ) by rotation about the origin with an angle of
measure 360° is …………………………
(f) The image of the point ( -2 , 0 ) by translation ( 3 , -1 ) followed by rotation
about the origin with an angle of measure 90° is ……………..
(g) The rotation with an angle of measure 90° about the origin maps the point
( x,-y ) to the point …………………
(h) The image of the point (2,7) by translation (x,y)
(x+2,y+1) is ………………
(i) The image of the point (-2,-5) by translation (x,y)
(x-2,y) is ……………
(j) The image of the point (-1,2) by translation of magnitude of 3 units in the positive
direction of x-axis is ……………………
(k) The point whose image by reflection in y-axis is (2,5) is ……………
(l) The point whose image by reflection in x-axis is (2,5) is ……………
(m) The point whose image by rotation about the origin with an angle 90 is (2,5) is ……………
(n) The point whose image by rotation about the origin with an angle 180 is (3,9) is ……………
(o) The image of the point (2,3) by rotation 90 about the origin is ………………
(p) The image of the point (2,3) by rotation 180 about the origin is ………………
(q) The image of the point (2,3) by reflection in the x-axis is ……………..
(u) The image of the point (3,2) by reflection in the y-axis is ……………..
(r) If A'(2,-3) is the image of A by translation(x,y)
(x+1,-y) then the point A(…,….)
(s) The image of the point (1,3) by translation (x,y)
x-axis is ……………
(t) The point (a,-1) is the image of (2,4) by translation (x,y)
(x+1,y-2) followed by reflection in
(x+1,y-b) then (a,b)=(……,.…)
3- Choose the correct answer
(1) In the parallelogram ABCD if m(A) + m(C) = 160 , then m(B)=….
(a) 110
(b) 100
(c) 80
(d) 20
(2) The sum of measure of the interior angles of a hexagon = …….
(a) 540
(b) 720
(c) 900
(d) 1080
(3) The measure of any angle of a regular octagon = …………
(a) 120
(b) 135
(c) 108
(d) 72
(4) The image of A ( -2 , 1 ) by reflection in y – axis is….
(a) (2,1)
(b) (2,-1)
(c) (-2,-1)
(d) (1,2)
(5) The image of A ( -3 , 5 ) by reflection in x – axis is….
(a) (5,-3)
(b) (3,-5)
(c) (3,5)
(d) (-3,-5) ]
(6) The point ( 5 , 3 ) is the image of the point ( -3 , 5 ) by rotation about the origin
Point with an angle of measure ………
(a) 180
(b) 90
(c) -90
(d) 360
(7) If Á( 2 , -3 ) is the image of A by translation ( x + 1 , y +1 ) then A is ……
(a) (1 , 0 )
(b) ( 1 , -4 )
(c) ( 2 , -2 )
(d) ( 3 , -2)
(8) The sum of measures of the interior angles of a triangle =…….
(a) 180
(b) 90
(c) 270
(d) 360
(9) A parallelogram whose angles are right angles is called ………
(a)trapezium
(b) rectangle
(c) rhombus
(d) hexagon
(10) ABCD is a square m( ACB) = ………………
(a) 90
(b) 60
(c) 45
(d) 30
(11) In …………… the diagonal makes an angle of measure 45° with the adjacent side.
(a) trapezium
(b) rectangle
(c) rhombus
(d) square
(12) A rhombus whose diagonals are equal in length is called ………….
(a) rhombus
(b) square
(c) trapezium
(d) rectangle
(13) A rhombus with perimeter 40 cm , then its side length = ………………
(a) 10 cm
(b) 5 cm
(c) 4 cm
(d) 8 cm
(14) The diagonals of the rectangle is………………
(a) parallel
(c) equal in the length
(b) perpendicular
(d) equal in the length , perpendicular
(15) The image of the point (0 , 4) by translation (-2 , -3) is ………….
(a) (-2 , 1)
(b) (2 , -7)
(c) (2 , 1)
(d) (2 , -1)
(16) The image of the point (3 , 4) by translation 3 units in the positive direction of the
X axis is …………..
(a) (0 , 4)
(b) (3 , 7)
(c) (6 , 4)
(d) (6 , 7)
(17) The image of the point (3 , 2) by the translation ……….. is (1 , -3)
(a) (-2 , -5)
(b) (2 , -5)
(c) (-2 , 5)
(d) (-4 , -5)
(18) The image of the point (-1 , 3) by translation 4 units in the negative direction of the
Y axis is ……
(a) (-1 , 7)
(b)(-1 , -1)
(c)(3 , 7)
(d) (3 , 3)
(19) The image of the point (2 , 3) by the translation ………. is (-1 , -3)
(a)(-2 , -5)
(b) (2 , -5)
(c) (-2 , 5)
(d) (-4 , -5)
A
3) From the opposite figure:
B
60
120 M ?
75
35
, ,m(EMD) = 35 and m(DMC)=75 m(AMB) = 60,
m(EMA) = 120 Find by proof m(CMB)?
C
E
D
D
4) From the opposite figure:
A
400
AB = DC , AC = DB , m(A) = 40°,
prove that  ABC ≡  DCB Then find the measure of (D)?
C
B
5) From the opposite figure:
E  BC , m(D) = 105 , m(B) = 95 ,m(DCE) = 100
Find m(A)
6) From the opposite figure:
OL ∩ KN = {M} ,m(k) = m(P)=45° , m(L) =70°
m(O) = 125° , Find measure (N)
A
D
105
E 100
95 B
C
O
125
k
75
45
M
70
L
‫؟‬
N
P
W
4a
7) From the opposite figure:
X 3a
XYZW is a quadrilateral in which m(<Z) = 100
Find the value of a?
100
6a
Y
Z
8) From the opposite figure:
/
m ( F ) = 50 , m(C)=40.
Prove that :

D
9) From the opposite figure:
A
ABCD is a square , E  BC and AC // DE
1) Prove that ACED is a parallelogram
E
2) Find m(ACE)
ABCD is a quadrilateral in which AC\\BD
E AC , m(ECD) = 125° ,m(ABD) = 55°
Prove that ABCD is a parallelogram
C
E
125
A
10) From the opposite figure:
B
C
B 55
D
D
H
12) From the opposite figure:
O
A
ABCD is a rectangle , OBCH is a parallelogram
Prove that AO = DH
B
C
X
13) From the opposite figure:
XYZW is a rhombus , find in degrees the value of angle Z
W
25
Y
Z
14) From the opposite figure:
A
ABC is a triangle in which E , M , D are the midpoints of the sides
AB , BC , CA respectively , BC = 8cm , AC =10cm
D
E
Find the perimeter of the parallelogram DEMC
C
M
B
D
15) From the opposite figure:
G
ABC is a triangle , DF // EG // CB , m(<ADF) = 125°
M(<BEG) = 140°.
Calculate the measures of the angles of the triangle ABC
E
140
F
125
A
C
B
A
16) From the opposite figure:
AB // CD , AB // GH , m(<CDB) = 145° ,m(<AGH) = 135°
Find measure angle DEG
C
B
E
?
145
D
135
G
ABCD is a quadrilateral in which AC  BD = {M}
D
A
30
AB // CD , m(<DAB) = 30 ,m(<DBC) = 40 ,m(<DMC) = 70
70
M
Prove that ABCD is a parallelogram
40
C
8) From the opposite figure:
H
B
B
N
A
ABCD is a rectangle in which ME // DC , EN // CB , M ,N are
the midpoint of AD , AB respectively ,if ME = 4cm , NE = 2.5cm
M
E
Find the perimeter of the rectangle ABCD
D
C
9)From the opposite figure:
A
ABC in which X, Y and Z are midpoints
of AB , BC and AC respectively, XZ = 5cm
Z
X
XY = 4cm and ZY = 6cm
find the perimeter of the triangle ABC
10) In the opposite figure:
m(B) = m(ACD) = 90 , AB = 9 cm ,
BC = 12 cm , CD = 20 cm.
Find the perimeter of the figure : ABCD
11) In the opposite figure:
//
, m (DCB)= 90,

AB = BC = 17 cm, and AD = 9 cm .
(1) Find the length of
(2) Calculate the area of the trapezium ABCD
C
Y
B
17) The points A(-4,5) , B(0,4) , C(2,3) are reflected in the x-axis , state the coordinates
of their images.
18)Draw the image of the square ABCD where
A(2,3) and B(2,1) by reflection in the y-axis
19)On the square lattice draw line segment XY ,where X(1,4) , Y(3,2) then draw the image of
XY by the translation (x,y) (x+2,y-1)
20)Draw on graph paper , the triangle ABC where A (3 , -1) , B (5 , 2) and C (-2 , 4) then draw
its image by rotation about the origin with an angle with measure 180°
21) On a lattice , draw the quadrilateral ABCD where A (0 ,4) , B (4,4) , C (7 ,0) and D (0,0) ,
then draw its image:
a) by rotation about the origin with
an angle of measure 270°
22) Draw the image of  ABC , where
A(1,3) and B(0,5) and C(-2 , 4) by reflection in the x-axis
23) ABCD is a rectangle , where A ( 2, 5) , B ( 6, 5) , C ( 6, 8) and D ( 2, 8 )
Find the image of the rectangle ABCD by the translation ( -1 , 3 )
24) Draw the image of the rectangle ABCD where A(1,1) and B(1,4) and length 4cm by
reflection in the y-axis.
25) Draw on graph paper , the triangle ABC where A (3 , -1) , B (5 , 2) and C (-2 , 4) then draw
its image by rotation about the origin with an angle with measure 180
26)
Manaret Heliopolis Language School
Name / ………………………
( Revision sheet Algebra)
1st prep
1) Choose the correct answer:
a) The ordered pair which satisfies the linear relation = 2x – 5 is … [(1,2) ,(2,1) ,(-1,2) ,(2,-1)]
b) If 5x =25 then 10x = ……………
c) 2 x 6 – 4
d)
( 3 , 5 , 50 , 30)
22 = ……………
( 1 , 11 , 10 , 2 )
( 74 , 70 , 7-4 , 7 )
= ……………
( <, = , > ,)
e) If a < b then – a ……… - b
f) If a coin is tossed once then the probability of appearance a head is …
(
, 1)
g) Half the number
(
)
h)
is ………
= ……………
(
,
, )
i) If ( a , 2 ) lies on y- axis , then a = ……………….
( 0 , 1 , 2 , 3)
j) If the point ( 5 , a -3 ) lies on x-axis , then a = ……
(0 , 3 , -3 , 5)
k) The point ………….lies in the second quadrant.
[( 3 , 2) , ( -2 , 3 ) , ( -3 , -2 ) , ( 2 , -3 )]
l) If the point ( a , b ) lies on the fourth quadrant , then a x b ……..0
m) If ( x , y ) = ( y , 9 ) then x = ………….
n) If ( x, 3 ) = ( 4 , y ) then x = ……..y = ………..
o) The third of the number 318 =…..
(=, > , < , ≥)
( 3 , -3 , 9 , -9 )
( 3 , 4 or 4 , 4 or 4 , 7 or 4 , 3 )
( 36 , 39 , 317 , 318 )
p) ( -  )-1 = …..
(-  , 3 , -3 ,  )
q)  ( )2 =…..
(  , -  ,   , - )
u) The side length of a square whose area 9x2 cm2 . is …….
( 3x , 3x2 , 9x , 9x2 )
2- Complete :a) On a die, the probability of appearance a number greater than 3 is ……
b) On a die, the probability of appearance a number less than 2 is ……
c) The probability of appearance an even number on the die is ……
d) The multiplicative inverse of
is ……..
e) The probability of appearance a number divisible by 5 = ……
f) The probability of the impossible event is ……
g) The probability of the certain event is ……
h) If a coin filled once, then the probability of appearance a head is ……
i) (- )7 ÷ (  )5 = ……( In the simplest form )
j) If the probability of occurring an event is , then the probability that the event
doesn’t occur is ……
k) The number 387 x 106 can be written in the standard form as ………………
l) If -2a > 0 then a ……… 0
m) The standard form of the number 0.0023 x 104 is ………………
n) The standard form of ( 2.5x104 + 4.23x105) is …………
o) The additive inverse of (-)2 is ……..
p) 50 – 2x32 + (2x4) = …………
q) If the order pair (3,a) satisfy the equation 3x – 2 = y then a = ………
u) If the point (2,-1) lies on the line 2x – a =y then a = ………
v) If the middle number of three consecutive natural numbers is x then the sum of these
numbers in the simplest form is ………………
t) Two integers , one of them exceed the other by 4 and the small one is x-1 then the
great one is ………………
s) If x > y and c > 0 then x c ……… y c
w) If -2a > 0 then a ……… 0
x)
= ………..
y) ( ) 8 X ( ) 8
=…………………
)16 ÷ (
z) (
aa)
)16 =………………

bb) 
= ……………..
=………………
cc) If ( 1 , 5 ) satisfy the relation: y = kx, then k = ……
ee) If 5x = 25 , then 3x = ……
ff) The S.S. of the inequality -3x < 0 in Q is ……
gg) If a x = 2 , a – y = 3 , then a x – y = ……
2) Find the solution set for each of the following in Q:
1) 2x + 4 = 7
2) 4a – 3 = -2 +3a
3) 2(a+3) = 8
4) 3(a-3) < 4
5) 2(b-4) = 6
6) 2 ( 5 – a) > 5a
7) 2( x – 3 ) – ( 2 + 3x ) = 5
8)5x + 2 = -8
9) 3a – ( 4 – a) > 2
10) 1 – ( 2c + 2 ) < 3c +1
11) 3x – 2 = 4
13) 9x2 + 5 = 21
15) 12 – 4 x = 3
17) 2 < x – 4 < 1
19) 5x + 1 ≤ 3x + 7
21) 4x + 3 < 6 x + 8
23) 2x + 2 > - 11
12) 4x2 – 3 = 13
14) 4x2 + 2 = 27
16) -7x < 14
18) -2 < x – 4 < 1
20) 5x + 1 ≥ 2 (x + 2 )
22) x- 8 ≥ 3x -7
3) Find two points satisfy the following equations then represent them graphically:
a) x = y
b) y = 2x + 1
c) x = 2y
4) Simplify then find the numerical value of the following:
a) 2(a-3) - a+5
if a = 1
b) 2x(x-4) + 4
if x = 3
c) ( 8 -4b) - 2b
if b = -1
5) Two natural numbers, one of them is twice the other and their sum 48, Find the two
numbers.
6) What is the number, which we add 6 to its twice, then the result is 14?
7) An integer which if we add to it 10, the result is the additive inverse of the number ,
Find the number.
8) Find three consecutive even numbers if their sum is 966
(9) If A = - and B =
, find the value of A2 + B3
10) If x = - , y = and z = -
Manaret Heliopolis Language School
Name / ………………………
Find the numerical value of :
( Revision sheet Geometry)
1st prep