2017/2018
2nd Term
1
Unit one
Lesson (1) :Set of natural numbers
* The set of counting numbers is
C = { 1 , 2 , 3 , 4 ,-------}
*The set of natural numbers is
N = { 0 , 1 , 2 , 3 , ……}
*The set of even numbers is
E = { 0 , 2 , 4 , 6 , 8 , -------}
*The set of odd numbers is
O
= { 1 , 3 , 5 , 7 , 9 , ……} *The set of prime
numbers is
P
= { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , …..}
1- Complete:
a) The smallest natural number is ------, while the smallest
counting number is -----b) The set of natural numbers less than 8 = -----c) The set of natural numbers between 0 and 5 = ------d) The set of natural numbers between and
2- Complete by using
,
,
a) {5} ----- N
2
,
:
= ------
b) zero -----N
c) {87} ----- N
d) {2 , 4 , 6} ----- N
e) {2 , 0.5}----- N
f)
------ N
g) {3 , 4 , 5 , ... , 30} ------ N
h) zero ----- C (the set of counting numbers)
Lesson (2)
Some subset of N
Notes:
N
E=E
N
P=P
N
O=O
N
P=N
E
O=N
E
P={2}
E
E
O=
N =N
1-Complete:
a. N - C =------3
b. N - {0} =------c. E
p = -------
d. O - E = ------e. N - E = ------f. N p = ------g. E
O = -------
h. E
O = -------
i. E
O = -------
j. N
O = ------
k. N
p = -------
l. N
E = -------
m. N
O = ------
n. E – N = ------o. N – O = -----p. N – {0}= ------
_______________________________________
2-If N = {0, 1, 2, 3, 4, ……} , O = {1, 3, 5, …} ,
E = {0, 2, 4, …}
P = {2, 3, 5, 7, …} , C = {1, 2, 3, 4, …}, then
Complete.
4
a) {0} ∩ E = ……………
b) E ∩ P = ……………
c) C ∩ {0} = ……………
d) {2} ∩ P = …………
e) E ∩ O = ……………
3-Complete by using
,
a) 22.22------ N
b) {2 , 4 , 6.8 } ------ N
c) {55} ------ N
d)
e)
-----N
------N
f) {0.3} ------N
g) {1 , 3}
{2 , 4} -------N
h) {1 , 2}
{2 , 5} -------N
i)
0} {1 , 2 , 3 ,…} -----N
5
,
,
:
Lesson ( 3 )
Ordering and Comparing Natural numbers
1-Write using the listing method and represent on the
number line :
a) X = {x : x
N , a ≤ 3}
----------------------------------------------------------------------------------------------------------------------------------------b) Y = {y : y
N , 3 ≤ y ≤ 7}
----------------------------------------------------------------------------------------------------------------------------------------c) Z = {z : z
N , z > 6}
----------------------------------------------------------------------------------------------------------------------------------------d) M = {m : m
N , m > 5}
----------------------------------------------------------------------------------------------------------------------------------------e) L = { L : L
N,L
3}
--------------------------------------------------------------------6
--------------------------------------------------------------------f) C = The set of natural numbers between 1 and 5
----------------------------------------------------------------------------------------------------------------------------------------g) D = The set of counting numbers less than 4
---------------------------------------------------------------------- ---------------------------------------------------------------------- h) A
= The set of even numbers
------------------------------------------------------------------------------------------------------------------------------------------------------- i)
B = The set of odd numbers
------------------------------------------------------------------------------------------------------------------------------------------------------- j)
P = The set of prime numbers less than 10
-------------------------------------------------------------------------------------------------------------------------------------------------------
2- Put ( < , = or >):
a) x + 18 ----- x + 17 where x N
b) x - 18 ----- x – 17 where x is a natural number greater
than 20
c) x ----- 75 , where x
{30 , 31 , 32 , 33}
d) y ----- 18 , where y
{20 , 21 , 22 , 23 , 24}
7
e) z ----- 35 , where z {35}
Lesson (4)
Operation on Natural Numbers 1Complete:
a) The additive neutral element in N is ------, while the
multiplicative neutral element in N is -----b) If 6 × 12 = 12 × a ,then a = -----c) 413 + 97 = 97 + ------
( ---------- property)
d) 0 + 3365 = ------
( -----------property)
e) 28 + (72 + 59) = (28 + -----) + 59
( ---------- property)
f) 14 + ----- = ------ + 14 = 14
( ------------ property)
g) 543 + 123 = 123 + -------
(------------ property )
h) 999 added to neutral element of multiplication = -------
2- Find the result by using the properties of addition and
multiplication :
a) 125 + 532 + 875 + 468
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
8
b) 36 + 95 + 64
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------c) 2 × 25 × 5 × 4
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------d) 47 × 98
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------e) 35 × 101
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------f) 8 × 17 × 25
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------g) 38 × 18 + 38 × 82
---------------------------------------------------------------------------------------------------------------------------------------------------------------9
-------------------------------------------------------------------------------h) 17 × 118 – 17 × 18
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3-Complete by using ( odd , even , prime) :
a) An odd numbers + an even numbers = -----------b) An odd numbers + an odd numbers = ------------c) An odd numbers × an even numbers = -----------d) If x is an odd number, then x + 2 is ------------- number.
e) If x is an odd number, then x – 1 is ------------- number.
4- Complete using ( ,
):
a) ( 3 + 7) ----- N
b) (8 + 10) ----- N
c) (45 – 35) ----- N
d)
----- N
e) (8 – 8) ----- N
f)
----- N
g) (7 × 2 – 7 × 5) ----- N
h)
----- N
10
Lesson (5)
Numerical Pattern
1- Complete in the same pattern:
a) 1 , 4 , 7 , 10 , --------- , ---------b) 5 , 15 , 25 , 35 , --------- , ---------c)
1 , 3 , 6 , 10 , ---------- , ---------
d) 1 , 4 , 8 , 13 , --------- , ---------e)
1 , 3 , 9 , 27 , --------- , ----------
f)
2 , 8 , 32 , ---------- , ----------
g) 2 , 6 , 18 , 54 , --------- , ---------h) 1× 2 , 2 × 4 , 3 × 8 , ---------- , --------i)
2 , 22 , 222 , ---------- , ----------
j)
2 , 5 , 8 , 11 , ---------- , ----------
k) 4 , 12 , 36 , ---------- , ---------
11
Unit (2)
Lesson (1): Mathematical Expression Notes:
• Perimeter of square = Side Length
• Area of a square = Side Length
Side Length
• Perimeter of a rectangle = ( L + W )
• Area of a rectangle = L
4
2
W
• Perimeter of a parallelogram = sum of two adjacent
sides 2
___________________________________________________
(1) Complete each of the following.
a) If Mona has X pounds and she took 8 pounds from her father,
then she has-------------------------------------------------- pounds.
b) A rectangle, its length is more than its width by 3cm. If the
length = L cm, then its width = --------------------------------- cm.
c) A rectangle, its perimeter is 30 cm. its width is X cm, then its
length is --------------------------------------------------------- cm
d) If a side length of a square is x cm, then its perimeter
= -------------------------------------------------------------- cm
e) If Rana has 9 pounds, she spent Y pounds, then the remainder
with her is ----------------------------------------------------- pounds.
f) An equilateral triangle, its side length L cm, then its perimeter =
12
---------------------------------------------------------------------- cm
e) Bassem is X years old now , then his age after 5 years
is -----------------------------------------------------------years
e) Basma is X years old now , then her age 3 years ago
was ---------------------------------------------------- years
_____________________________________________________
(2) Express each by mathematical relations.
a) Subtract half a number from 15.
-----------------------------------------------------------------------------b) Subtract 11 from 5 times of a number.
-----------------------------------------------------------------------------c) Add 2 to two thirds of a number.
-----------------------------------------------------------------------------d) Add 3 to the third of a number.
----------------------------------------------------------------------------e) Subtract 5 from double of a number.
------------------------------------------------------------------------------
Lesson (2)
The Constant and the Variable
Write the mathematical relations that express each of
the following.
a) The number X exceeds the number Y by 5.
13
-----------------------------------------------------------------------------b) The number L is less than double the number M by 7.
-----------------------------------------------------------------------------c) A triangle its side length 6cm, 2cm, 5Y cm. Find its perimeter.
-----------------------------------------------------------------------------d) Two numbers X and Y, one of them exceeds the other by 3. (the
smaller is Y)
-----------------------------------------------------------------------------e) If the side length of a rhombus is X cm and its perimeter is P.
Write the relation between X and P.
------------------------------------------------------------------------------
Lesson (3)
Equation
Solve the following equation:
a) X + 3 = 12
----------------------------------------------------------------------------------------------------------------------------------------------------------------b) X - 7 = 25
---------------------------------------------------------------------------------------------------------------------------------------------------------------Y–5=7
14
c)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------
d)
5A = 15
----------------------------------------------------------------------------------------------------------------------------------------------------------------e) X = 12
------------------------------------------------------------------------------------------------------------------------------------------------------------f) 3 Y = 39
---------------------------------------------------------------------------------------------------------------------------------------------------------------g) 6B = 18
---------------------------------------------------------------------------------------------------------------------------------------------------------------h) Y = 3
-------------------------------------------------------------------------------------------------------------------------------------------------------------i) 2 X + 5 = 13
------------------------------------------------------------------------------15
-----------------------------------------------------------------------------J) 5 Y – 3 = 7
--------------------------------------------------------------------------------
-----------
---------------------------------------------------------------------Unit (3)
Lesson (1): Area and its units
Remember that:
Area of square = S × S
Area
Area of rectangle = ( L × W ).
Area
L= W
Length Width
Area
W=
L
_______________________________________________ Units
for measuring Area:
(1) Km2
1000000 m2
100 dm2
100 Cm2
______________________________________________________
16
Area of triangle
Rule:
Area of triangle =
× base × height
2 area height
height
Base =
base
2 area
Height =
base
1)Find the area of each of the following triangle: a)
A
-------------------------------------------------
C2cm
3cmB
------------------------------------------------______________________________________________________
b)
A
8cm
---------------------------------------------B 6cm
C
--------------------------------------------17
______________________________________________________
A
c)
------------------------------------------------------6cm
B
C
----------------------------------------------------------------------------------------
7cm
______________________________________________________
2)In the opposite figure :
If AC = 15 cm , AD = 10 cm and BC = 18 cm
A
(a) Calculate the area of
ABC
E
(b) Find the length of BE
D
C
B
Solution
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
18
3) In the opposite figure:
6cm
DA
(a) Calculate the area of
ABE
3cm
(b) Calculate the area of shaded part
C
2cmE
B
Solution
--------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------
4)
Find the area of the triangle whose base length = 4.2m and
its corresponding height = 5.5 cm.
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------5)
If the area of the triangle is 60 cm2, and the base length is
7.5 cm calculate its corresponding height.
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
19
6)
If the area of the triangle is 80 cm2, and the height is 45 cm
calculate its corresponding the base length.
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Lesson (2) Area of parallelogram
Rule: Area of
= Base × height
Area of
D
height
A
height
Base =
Area of C
base
base B
Height =
_____________________________________________________
1) Calculate the area of each of the following: a)
D
A
20
C 9cm
4cm
B
Solution
-------------------------------------------------------------------------------------------------------------------------- b)
D
A
303030cmcmcm
C
B
60cm
Solution
----------------------------------------------------------------------------------------
2) If the area of a parallelogram is 28 cm2 and height its 7cm,
then find the length of its base.
-------------------------------------------------------------------------------------
3)Find the area of parallelogram whose base length is 5c m and
its corresponding height = 3 m.
----------------------------------------------------------------------------------
21
4)Which is greater in area: The area of a parallelogram whose
base length 60 cm and its height is 40 cm or the area of a
triangle whose base length is 70 cm and its height is 40 cm.
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Lesson (3) Area of square
Rule:
* Area of square " by knowing its side length "
Area = S × S
, S = Area
* Area of square " by knowing its diagonal length "
Area =
× diagonal length × diagonallength,d = 2Area
Area = × d × d , d = 2Area
1) Calculate the area of the square whose side length = 6 cm.
22
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------2) Calculate the area of the square whose length of its diagonal =
6 cm.
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------3) Which is greater in area? A square whose diagonal is 10 cm
long or the right angled in which the lengths of the sides of the
right angle are 8 cm and 15 cm.
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
4) Find the area of the shaded part:
4cm
Solution
-------------------------------------------------------------------------------------------------------------
2cm
--------------------------------------------------------
5) If the area of a square is 64 𝒄𝒎𝟐 , Find its side length and its
perimeter .
23
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Lesson (4)
Area of Rhombus
Rule: Area of rhombus = Side length × height
Area
Side length(S.l)=
height
Area
Height (H) =
Side length
Area of rhombus =
× d1 × d2
1)Find the area of rhombus whose side length = 4 cm and its
height is 3 cm
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------2)The length of diagonals of a rhombus are 5.5 cm and 3.4 cm.
24
Find its area.
--------------------------------------------------------------------------------------3) If the height of a rhombus is 10 cm and its area = 54 cm2 . Find
its side length.
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------4) If the area of a rhombus is 36 cm2 and the length of one of its
diagonals is 8 cm. Then find the length of the other diagonal.
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
25
Lesson (5)
Circumference of the circle
Rule: C = π × d
22
π= 7
Or
C = 2× π × r
or
3.14
d = C π÷
C
r = C ÷ ( π ×2)
C
d
2 r
1) Find the circumference of the circle whose radius = 7 cm.
Solution:
(π =
)
---------------------------------------------------------------------------------------2) Find the radius of the circle whose circumference= 314 cm.
Solution:
(π =3.14)
---------------------------------------------------------------------------------------3) Find the diameter length of the circle If the circumference
equal 36.11 cm
(π=3.14)
Solution:
---------------------------------------------------------------------------------------- 3) Find
the circumference of a circle whose diameter equal
26
21 cm
(π =
)
----------------------------------------------------------------------------------
4) Calculate the perimeter of each of the following :
a)
-------------------------------------------------------------------------------------14 cm
(π =
b)
)
7 cm
(π =
-----------------------------------------------------------------------------------------
)
c)
---------------------------------------------------3.5 cm
(π
-----------------------------------------------------
=)
Unit Four Geometric Transformation
Lesson (1) Symmetric figures and axis of symmetry
27
Figure
Number of Symmetry axes
4
2
2
1
3
Zero
Zero
1
Zero
Very large number
Square
Rectangle
Rhombus
Isosceles triangle
Equilateral triangle
Scalene triangle
Trapezium
Isosceles trapezium
Parallelgram
Circle
Geometric Transformations
F`
D
E`
Rotation
x`
x
Reflection
F
A`
E
A
z` z
y`y
Translation
C`
B`
C
Complete each of the following:
a) The isosceles triangle has ---------------- lines of symmetry.
b) The equilateral triangle has ---------------lines of symmetry.
28
B
c) The scalene triangle has ------------------- lines of symmetry.
d) The rhombus has -------------------------- lines of symmetry.
e) The rectangle has ------------------------- lines of symmetry.
f) The square has ----------------------------- lines of symmetry.
g) The parallelogram has ------------------------ lines of symmetry.
h) The regular pentagon has -------------------- lines of symmetry.
i) The trapezium has ------------------------- lines of symmetry.
j) The isosceles trapezium has --------------- lines of symmetry.
k) The circle has ------------------------ lines of symmetry.
Draw the image of triangle XYZ by reflection on L
L
29
Lesson (2)
Locating points on a ray
Location points on a coordinate plane
1) A (4 , 0) , B (8 , 0) , C (8 , 4) , D (4 , 4)then complete:
30
1) The name of the shape ABCD is -----------------------2) The area of this figure = ----------------------3) Number of axis symmetry = -----------------4) Draw the image of the figure ABCD by reflection across AD
2) On the coordinate plane, complete:
X = ( ------ , ------ )
Y = ( ------ , ------ )
Z = ( ------ , ------ )
M = ( ------ , ------ )
Y
10
9
8
7
6
5
4
X
3
2N
1
Y
12345678 0
31
Z
M
X
N = ( ------ , ------ )
3) On the coordinate plane draw the following :
a) The triangle ABC, where A (1 , 2) , B (1 , 5) , C (5 , 5) then
draw the image of the triangle ABC by reflection across AB
Unit Five Statistics
1) The following table shows the number of hours that a set of
50 students study in a day.
Sets
2-
4-
6-
8-
10-
Total
Frequncy
8
13
15
13
1
50
(A) The number of student whose number of hours less
than 6 hours = --------(B) Draw the histogram and the frequency for this data.
32
2) In an exam:
Sets
5-
10-
15-
20-
25-
30-
35-
Total
No. of
students
4
7
9
13
11
7
9
60
(A) The number of student who got 25 mark and more = -------(B) Draw the histogram and the frequency polygon for this
data.
3) The following table shows the recorded temperatures in 40
cities on a day.
Temperature
20-
22-
24-
26-
28-
Total
No. of cities
7
9
11
8
5
40
(A) The number of cities with temperatures less than 24
degrees
= --------(B) Draw the histogram and the frequency polygon for this
data.
33
Pie graphs
The following table shows the favourite TV programs for 40
pupils :
Sports
5
News Series Movies
10
Represent this data by a pie graph.
34
5
20
35
36
37
38
39
40
41
42
43
44
45
46
47