Download Sheet (1) sheet (1) [1] Complete:

Supervisor of mathematics
Sheet (1)
Mrs.Maha Ahmed
1
sheet (1)
[1] Complete:a) Z = ………….. U ……………. U …………….
b) Z = ………….. U …………….
c) N = ………….. U …………….
d) The smallest positive integer number is ……………….
e) The greatest negative integer number is ………………
f) ……………….. is called neuteral element
g) The complement of
h) N U
with respect to Z is …………
= …………….
==================================================
2- Express each of the following sets using the listing methods :
a) The set of integers which are less than 6
b) The set of integers which are more than 5
c) The sets of integers which are smaller than 4 and bigger than -3
d) The sets ofnon-negative odd integers
e) The set of integers even numbers
2
sheet (2)
1- Arrange in ascending order :
a) 0 , -5 , 9 , 2 , -2
b) 8 , -1 , 6 , 3 , l 4 l , -5
--------------------------------------------------------------------------------2- complete :
a) -4 , -3 , ………… , ………… , ………..
b) -15 , -10 , -5 , ………….. ,…………. ,…………
c)1 , 4 , 9 , 16 , ……….. , ……… , ………..
d)
, …………… , …………… , …………..
----------------------------------------------------------------------------3- Complete :
a) Z
N = ………………….
b) Z – N = …………………
c)
d) Z -
N
= …………….
= ……………
e) –l 4 l = ……………..
f) –l – 5l = …………...
g) 9 =l b l , then b = ……………..
3
4- Put < ,> , = :
a) 9 .............. 8
b) - 5 ........... 0
c) 3 ........l -3 l
d) 6 + l2l .......- l-8 l
------------------------------------------------------------------------------5- write the integers between :
a) -2 and 0
b) 8 and 5
c) -6 and -10
---------------------------------------------------------------------------
4
sheet (3)
1- Find the result of, the represent the operation on number line
a) 7 + (-4 )= ……..
b) -8 + 5 = ………..
c) 10 – 7 = …………….
d) -3 + ( -3 )= …………..
--------------------------------------------------------------------------------2- Complete using
:
a) 6 .........Z –
b) {8 , 3.7 } ...............Z
c ) 0 .............Z
d) { , 9 } ..............Z
e)
..............Z +
5
6
sheet 4
1- Find the result of and represent each on number line :
a) 2 x 3 = .............
b) -2 x -4 = .....................
c) 5 x -2 = ………….
-------------------------------------------------------------------------------2- Find the result of each of the followings in two ways :
a) ( 4 + (-5 ) )x 8 =
b) -5 ( -3 + (-2 ) =
---------------------------------------------------------------------------------------3- If x = 2 , y = -3 , z = 4
Find the value of each :
a) xyz
b) 2xy – z
7
c) ( z÷x ) + y
4-Complete :
a)The product of two negative integers = ………… integer
b) ………….. is the additive identity in Z
c )6 x 7 x 4 = 7 x … x 6
d )If a
{2 , -5 , -3}
{5 , -2 , -3} then a = …………….
e)7 (3 + (-2) ) = 7 ×……….. + 7 × ………….
= ……………. + …………….
= ……………….
---------------------------------------------------------------------------------5- Find the value of X:a) 9X = – 450
b) 7X = – 35
------------------------------------------------------------------------------------
8
Sheet 5
1- Find the result of each :
a) 4 3
b ) (-5) 2
c) (-15)o + (15)o = …………….
d)
= 1 then n = …………..
e )
×
f)
÷
= ……………..
= ……………..
-----------------------------------------------------------------------------2 Simplify :
a)
b)
9
d)(- 5)3× ( -1 )17
e)
f)
---------------------------------------------------------------------------------------3- Complete the table :
The number
The square of The cube of the The
seventh
the number
number
power of the
number
9
-6
4
-------------------------------------------------------------------------------------4- Put (<) , (>) or (=):5
…………….
-5
32
……………
23
24
……………
43
(- 1)17
……………
(-1)2
10
-2
……………
-
5
Sheet 6
1-] Write the integers which represent each of the following
a) X > 1
b) X < 1
c) -3 < X < 3
----------------------------------------------------------------------------------------2- Write the number of dots below each figure of the following:
……
…..
…..
……
The numerical pattern
: ……………………………………….
The rule of the pattern
: ……………………………………….
…….
----------------------------------------------------------------------------------------3- Complete the table :
The numerical pattern
Description of the pattern
11
Sheet 7
[1] Determine whether each of the following represents an equation or
not.
a) X + 7
b) X – 8 = 6
c) 7 – 2 = 5
________________________________________________________
[2]Determine which of the following represents an equation or an
inequality
a) X – 3 > 4
b) 2X – 18
c) 3x <8
----------------------------------------------------------------------------------
3] Determine the degree of each of the following:a) X – 9 = 3
b) X + 4 > 3
c) 4 X 2 –1 = 11
d) 3 X – Y = 6
e) 43 – 8 X 2 = O
--------------------------------------------------------------------------
12
4- Given the substitution set L = {-2 , -1 , 0 , 1 , 2}
Find the solution set of :
a) X + 4 = 6
b) X + 4 < 6
c) 3 (X – 2 ) = – X – 10
d) 2 – X
3
______________________________________________
[5] Complete:a) The
equation
is
a
mathematical
sentence
………………
…………………………
b) The
in
equality
is
a
mathematical
sentence
………………………….
c) The substitution set is ……………………………………………
13
……………
d) The solution set is ………………………………………………….
[6] Solve the following Equations in N and Z
a) X + 5 = 17
b) 6X = - 18
c) 3 X – 2 = 19
d) 8 – X = -5
e) 3X – 1 = 5 X + 9
f) 6 (X – 4 ) = 5 ( X – 3 )
g) X = 2 X + 12
h) 2 m – 17 = 10
i) (4K – 7 ) + 6 = 2 K – 11
j) 2 (3 – n ) – 4 = 6
k)
= –2
14
7- Express each word statement by the suitable math statement :
Word statement
Math statement
10 added to a number gives the
result of 55
A number is multiplied by 9, the
product is divided by 15 , the
result is 3
Six times a number added to 5
gives the result of - 33
780 minus 4 times a number
equals 10
8
subtracted
from
triple
a
number the result <8
15
Sheet 8
1] Two even consecutive numbers their sum is 34. Find the two
numbers:-
[2] A rectangle its width is half its length and its perimeter is 48 cm. Find
its length , width and area.
[3] A metal wire of length 128 cm. is divided into two parts one of them is
of length three times the length of the other, Calculate the length of
each part.
(4)-If 7 is added to twice a number, the result is 39. Find the number.
[5] Three consecutive odd number, their sum is 57. Find them
[6] Two integers one of them is four times the other and their sum is –
40 Find the two integers.
16
[7] If a man's age is five times his son's age and the sum of their ages is 42
years. What is the age of each of them.
[8 If the number of pupils of the sixth form in a school is 639 pupils and
the number of boys is twice the number of girls. Calculate the number
of each of boys and girls.
[9) The sum of the three dimensions of a cuboid is 35 cm. If the length of
its base is four times its width and its height is twice its width.
Calculate the volume of the cuboid
[10] If Ahmed's age exceeds khaled's age by 4 years and next year the
sum of their ages will be 48 years. What is the age of each of the
is the age of each of them now?
[11] Three consecutive numbers their sum is 69. Find these numbers.
[12] A number consists of two digit its unit digit is three times its tens
digit. If the sum of the two digits is 8 . Find this number.
17
[13]Find the solution set of the following inequalities and represent it
on the number line.
a) X – 2 < – 3 , there X
b) 2X – 7
Z
- 1 , where X
N
c) 5 X – 3 > 4 X + 2 , where X
Z
d) 7 X + 2
N
9 X – 4 , where X
e) 3 (X + 2) > X – 7 , where X
f) – 2 < 2 X – 4
g) – 5
Z
6 , where X
1 – X < 2 , where X
N
Z
18
[14] Choose:a) If 2 X + 6 > 4 then the solution set in Z is ……………..
[Z- , N , N – {O} , Z+ ]
b) If X + 5 = 9 , X
Z- then the solution set = ……………
[ {- 4 } , {-5} , {4} ,
]
c) The number that if added to its double the result will be 108 is
………………..
[ 54
, 36
, 216
, 27 ]
d) N is the solution set the inequality ………………….
[ X< O] ,
X>O ,X
O,X
O]
---------------------------------------------------------------------------------
19
Sheet 9
1In the opposite coordinate plane:a) Determine the position of the following points:
A ( - 2 , 4) , B (2 , 4)
C (2 , – 1 ) , D ( – 1 , 2 )
b) Find the perimeter and the area of the shape
4
3
2
1
-5
-4
-3
-2
-1
0
1
-1
-2
-3
-4
20
2
3
4
5
2In the opposite coordinate plane:
Determine the following: the image of
A (0 , 2) , B (2 , 4) , C (2 , 0)
6
By translation (X + 3 , Y +2 )
5
ABC , where
4
B
3
A2
1
-5
-4
-3
-2
-1
0
1
C
2
3
4
5
-1
-2
-3
-4
---------------------------------------------------------------------------------------3-Complete the table :
The point
(0 , 4 )
(....... , ....... )
( -2 , -2 )
The translation
(X +3 , y -2)
( x - ..... , y + ......)
( ............., ..............)
The image
(............ , ..........)
(5,3)
(0,5)
-----------------------------------------------------------------------------------21
Sheet 10
[1 A circle of diameter 14 cm. Calculate its surface area
=
[2] A circle of area 628 cm2 calculate its circumference
[3] A circle of circumference 52.6 cm. Calculate its surface area (
=
or
3.14)
[4] In the opposite figure the circle O is divided into four equal circular
sectors if the surface are of one sector is 92.6 cm2.
Calculate 1) Surface area of the circle
2) The circumference of the circle
=
92.6
0
5-Atable its surface in the form of circle , its diameter is 1.7 m , we want
to cover it by a sheet of glass equals to its surface
Calculate the cost price of sheet if the square meter of the glass costs 50
L.E
22
Sheet 11
1-Complete:= ……….. × …….. × 4
= ………………… × 4
= …………… ×…………
a) The lateral area of the cube
b) The total area of the cube = …………… × 6
c) The sum of edge length of a cube is 36 cm. then its L.S .A =
………………. Cm2 , TSA = …………….. cm2
d) The total area of a cube is 72 cm2 , then the LSA = ………………… cm2
-------------------------------------------------------------------------------------------------------------------------------
[2) Which is bigger in total area?
A cube of edge length 7 cm or a cuboid with dimensions 3 cm , 2 cm , 1
cm
[3] A box without lid its length 10 cm , width 5 cm height 12 cm.
Calculate its lateral area and total are
23
4-The perimeter of one base of a cube = 48cm
Find its LSA, TSA
---------------------------------------------------------------------------------------5- The inner dimensions of a swimming pool are 45 m , 15 m and 1.8 m , it
is wanted to be cover it with a tile squared shape of side length 15 cm
Find the number of the tiles
6-A box truck in the shape of cuboid of dimensions 5 m , 6 m , 3.5 m
It is wanted to be covered with iron sheet with cost price 23 L.E each
squared meter
Find the cost price of the iron sheet
24
Sheet 12
1- Complete the table :
The solid
cube
Length Width
Height LSA
........... .............. ............. ............
TSA
216
cuboid
7
.......
10
240
..............
cuboid
9
8
11
.............. ..............
---------------------------------------------------------------------------------------2- Aroom of a squared ground its length 6 m , its height 2.5 m , it has a
door with width 70 cm and height 180 cm and two rectangular equal
windows of length 55 cm and width 1 m
Calculate the cost of painting of the walls and the ceiling if one square
meter cost 12 L.E
3- A cuboid with square base of side length 6 cm and height 15 cm
Calculate LSA and TSA
25
Sheet 13
[1]The opposite figure shows the favourite sports for children in a club
study the figure then answer
a) What is the ratio between football and the remainder sports
b) What is the measure of central angle of swimming
c) What is the least sport that children prefer?
[2]The following data represent the percentage of expenditure of a
family in the month.
Expenditure
Rent
Food
Cloths
Education
Saving
Percentage
30%
40%
5%
20%
-
Represent these data by circular sectors
26
[3]The following table shows the number of pupils in classes in primary
six
Class
6A
6B
6C
6D
No. of Pupil
35
30
32
33
a) Represent these data by circular sectors
b) What is the percentage of number of pupils in 6B
-----------------------------------------------------------------------------------------4- The following table shows the percentage of production of a factory
for three kinds of electric water heaters
The kind
First
Second
third
The percentage of
55 %
30%
................
the production
1- complete the table
2- represent these data by circular sectors
27
3- if the total production in the factory is 2000 heater find the number of
heater of the second
Sheet 14
1-In the experiment of forming a 2-digit number from the set of digits
{4 , 5} What is the probability:
a) The event A : the unit digit A is in odd number
b) The event B : sum of the two digit 9
c) The event C : the two digits are
-------------------------------------------------------------------------------
[2]A box contains 6 red balls , 5 yellow balls and 2 green balls . A ball is
selected randomly Calculate:
a) Probability the ball is yellow
b) Probability the ball is black
c) Probability the ball is neither yellow nor green
28
[3] A class of 35 students has got a maths exam its maximum mark is 50 ,
if 15 students got less than 40 marks, 10 students got 40 up to 50 .
Calculate the probability of :
a) The event A , where A is a student has got less than 40
b) Event B : where B is a student has got mark satisfies the
inequality B 40
-------------------------------------------------------------------------------4- in the ideal student competition of one school's 63 students applied
for the competition , if the probability that one of the girls is an ideal
student is
Find the number of girls who participated in the competition
-----------------------------------------------------------------------------------------5-Abox contains 9 symmetric cards each carries a number from 10 to 90
they are mixed well if one card is selected randomly find the probability
of the following events :
a) the event A is a number divisible by 5
29
b) the event B is a number divisible by 3
Revision 1
1- COMPLETE:
a) The image of the point ( 0 , -1 ) with translation x +2 , y -1 = …..
b) The point whose image ( -2 , 3 ) with translation x -3 , y +2 = ….
c) The translation of the point ( 3 , -2 ) with image ( 2 , 1 ) =…….
d) The area of the circle of radius 6 cm = ……
e) The area of the circle of diameter 10 cm = …….
f) The circumference of the circle with area 210 cm 2 = …….
g) The radius of the circle with area 154 cm 2 = ……
h) The complement of N with respect with N = ……
i) The complement of Z with respect of Z - = …….
30
j) The complement of Z + with respect of Z = ……
k) 9 ( 4 + (-2 ) ) = 9 x 4 + …….x…….. = ……….
l) -2 ( -5 – ( 3 ) ) = -2 x -5 - ……x…… = ……
m)
Z - Z + = …….
n) Z + - Z = …….
o) The integer between -3 and -5 is …….
p) The integers between -3 and 0 are ……
q) If X { 3 , 0 , -1 } { 0 , 2 , 4 } then X = ….
r) If L { -2 , 1 , 4 } { 5 , -2 , 7 } then L = …..
2- Find the solution set in Z and N in :
a) 4 X +7 = 21
31
b) 3 X -5 = - 20
3- If a = -2 , b = 3 , c = -1
Find a) 3abc
b) 2ac –ab
4-A circle was divided into 4 equal circular sectors if the area of
Sector = 10.4 cm 2
Find the length of the radius
------------------------------------------------------------------------------------------5 -A circle with radius 7 cm was divided into 6 equal circular sectors
Find the area of each sector
6- Find the area of the shaded part :
9 cm
5cm
32
6 cm
7- Draw the triangle ABC A ( 3 , 2 ) , B ( -1 , 4 ) C ( 0 , 1 )
Then determine its image graphically by translation x -2 , y +3
8- Draw the square ABCD where A ( 4 , 0 ) , B ( 4 , 4 ) ,C ( 0, 4 )
D (0 , 0 ) then determine its image by translation x +3 , y + 2
33
Revision 2
1- Complete :
a) Addition of two negative integers is ………….
b) The lateral area of cuboid = ………x ……….
c) 5 + …….. = 0
d) If x + 9 = 11 then the value of 7 x = ……
e) The inverse of 0 = ………
f) The inverse of -9 = …….
g)
7 2 x 7 5= ………………..
h) ……………. Is the neutral additive element
i) The sum of different integers = ………or …….. integer
34
j) 2 , 6 , 10 , 14 , ……… its formula is ……….
2-Complete to find the result of the following and state the property
used :
116 + 190 + ( -116 ) = 116 + ( …. + (-116 )) ( ……… prop )
= 116 + ( …… + 190 ) ( ……prop )
= ( 116 + ….. ) + 190 ( …..prop )
= ……. + 190 ( …….prop )
= 190
( ……prop)
--------------------------------------------------------------------------3- Find the result of each in two ways :
(-6) x ( (-3 ) + 2
--------------------------------------------------------------------4-Sherif saves 51 L.E every month
How many months does he need to save about L.E 160
---------------------------------------------------------------------------------5 Find the absolute value of -8
----------------------------------------------------------------6- Find the solution set of each :
2x + 5 > 2 if the substitution set is { -3 , -2 , -1 . 0 , 1 }
35
7–The inner dimensions of swimming pool are 30 m , 10 m , 1.5 m
It is wanted to be cover with a tile of squared shape its side 20 cm
If the cost of one square meter is 32 L.E
Calculate the number of tiles
The cost of covering its walls and ground
----------------------------------------------------------------------------------------------9-Calculate the area of the shaded part :
M is a circle of radius 5cm , a rectangle is drawn inside it , its length 8
cm , width 4 cm
---------------------------------------------------------------------------------------------------------------------------------------
36
10 –One of the families spent its salary as the following 40 % food , 20%
house rent , 30 % expenses and save the remainder
Represent these data by circular sectors .Then if the family income is 900
L.E so how much money did they save in the year ? another family saves
70 L.E monthly so what is the monthly salary of that family
Revision 3
1-Choose :
a ) The number which satisfies the inequality x >-2 is …….
(-1 , -4 , -3 , -2 )
b) The total area of the cube is 150 cm 2 then its edge = ……
(25 , 5 , 100 , 20 )
c )All the following numbers satisfy the inequality x > -3 except
( 0 , -1 , -2 , -4 )
d ) The measure of the circular sector whose area from the area of
the circle
( 30 , 45 , 60 , 90 )
(
)
e ) {0 , 10 } ……Z
f )
………. Z
(
)
g ) A circle its circumference is 2 cm then its area = ……
(4
, 2
,
, 2
------------------------------------------------------------------------37
2
)
2-Complete :
a ) The lateral area of cuboid with square base of side 5 cm and
height 3 cm = ……..
b ) The lateral area of a cuboid = 200 cm 2 and its base is in the form
of a square its side 10 cm then its height = …cm
c ) The area of a cube =
its T.S.A
d ) The sum of edges of a cube = 48 cm , then the area of one of one
of its faces = …..
f ) The equation x 2 + 4 6+ y 5 = 100 is of ….. degree
-----------------------------------------------------------------------------------------------3-If x= -8 , y = 2 then find x-2y +4
------------------------------------------------------------------------------------------4-The following table represents the hair coloured of the students
Hair colour
Percentage
Black
70
Brown
15
Yellow
10
red
………
Represent these data by pie chart
If the number of students of these school is 600 determine the number of
black haired students
----------------------------------------------------------------------------------------
38
5-Find S.S of :
a ) 3x +7 = x + 17 where x
Z
b ) 2 (x -1 ) +5 = 15 in Z and N
c )2x -5 = -9 in Z +
d ) 2 ( x – 3 ) + 3 ( x -2 ) = 8 in Z
----------------------------------------------------------------------------------------6-Draw the triangle OBC where O is the origin point , B ( 3 , 0 ) , C (0 , 2 )
Then draw the image by translation (-4 , 1 )
39
7-Find The area of the opposite figure :
10 cm
7cm
40
Revision 4
1-
Complete :
a) The ratio between the area of one face of a cube and its lateral
area = ………..
b) 3 , 9 , 27 , 81 , ……..
c) 1 , 4 , 9 , 16 , 25 , ….., ……. Formula ……..
d) Z+
= …………….
e) –I54I = …….
f) The point of the image ( 4 , -2 ) by translation ( x , y +2 ) = …….
g) The area of a circle = 113.04 cm 2 then its circumference = …. Cm
h) If LA of a cuboid = 60 cm2 , and its base area = 8 cm2 then TA =
………
i) The image of the point (-1, 2 ) by translation of magnitude of 3
units in the positive of the x – axis is …….
41
j) The substitution set is ………….
k) The equation = …………
l) The solution set = ………….
m) The inequality = ……………
n) Z = …………. ………..
----------------------------------------------------------------------------------2-
Find LSA and TSA of a cuboid of dimensions 30 cm , 20 cm , 10
cm
-------------------------------------------------------------------------3-
Find LSA and TSA of a cube of area of one face = 29 cm 2
-------------------------------------------------------------------------------------------------------------
4-
Find solution set of 2x-5 = 21 in Z and N
----------------------------------------------------------------------
42
5-
Find solution set in Z
=2
6-
Express the set of integers between -3 and 13
---------------------------------------------------------------7-
Find the result of :-12 +7
------------------------------------------------------------------8-
Khaled decided to loose his weight at the rate of 3 Kg monthly ,if
he is 90 Kg .How many months he needs to reach 69 Kg. write the
expressing pattern and describe it
---------------------------------------------------------------------9-
A container water tank in form of cube with length 1.5m , it is
wanted to be painted with rust Find the cost price if one squared
meter costs 15 L.E
-------------------------------------------------------------------11-Find the value of :
112 x 117 + 112 x (-17)
25 + (-8) + ( -25 ) +7
43
----------------------------------------------------------------------------
12-If :a = 3 , b = -2 , c = 1
Find :2ab – 3 c
--------------------------------------------------------------------------13-Find the area and the circumference of a circle with diameter 14 cm
---------------------------------------------------------------------------------------14-A circle was divided into 8 equal sectors if the radius = 6cm
Find the area of each sector
---------------------------------------------------------------------------------------15-Draw the triangle ABC in which A( -3 , 4 ) B (1,4 ) C ( 1, 2 )
Find its image by translation (0,3)
-------------------------------------------------------------------------------------16- The following table show the number of study hours that ALY done
Represent these data by circular sectors
Subject
Number
Arabic
9
Math
10
Science
6
44
English
7
Social
4
RULES
Notes :
A= area , h = height , b = base length , d = diagonal
S = side length , L = Length , W = width , P= perimeter
1-Triangle :
A=
xbxh , b=
, H=
2-Parallelogram:
A= b x h , b =
,H=
3-Rhombus :
A = b x h or x d 1 x d 2
--------------------------------------------------------------------------------------------------------------------------
4-Square :
P=Sx4 ,S=P÷4
A=SxS ,S=
Or
A=
45
xd xd
,
d=
1P=(L+W)X2 ,
A=L xW
,
Rectangle :
L=P÷2–W ,
W=P÷2=L
L=A÷W ,
W=A÷L
6- – Circle:
Circumference = Diameter x
or
2 x Raduis x
Diameter = Circumference ÷ , Raduis = circumference ÷ ÷ 2
Area =
2Raduis
=
Diameter = 2 x
7 – Cube :
Lateral surface area = Area of one face x 4
Or = Side x side x 4
Area of one face = LSA ÷ 4
Total surface area = Area of one face x 6
Or Side x side x 6
Area of one face = TSA ÷ 6
Volume = side x side x side
8- Cuboid :
Lateral surface area =Perimeter of the base x height
=( L+W)x2xh
46
Total surface area = Lateral surface area + sum of the two areas of the
base
= LSA + 2X base areas
(L +W ) X 2 X h + (2 x L x W )
Volume = L x W x H
47