1

Unit (1)

1) Put ( ) or ( X ) :

0 N ( )

5

2 N ( )

2.5 N ( ) 1254 N ( )

Ø N ( ) { 1 , 2 , 3 } N ( )

{ 0 , 1 , 2 , ………. } N ( { 0 } N ( )

The set of counting numbers begins with the number 1 and

continue without ending . { 1 , 2 , 3 , 4 , 5 , 7 , ………. }

If 0 is added to the set of the counting numbers , then we

obtain new set called natural numbers

It is usually denoted by N = {0,1,2,3,4,5,6, ………}

N = the set of counting numbers { 0 }

N – {0}= the set of counting numbers

The set of counting numbers is the set of natural numbers

2

1) Use the number line to find each natural number :

The natural number greater than 3 but less than 5 is --------

---

The natural number between 0 and 2 is ---------

The least natural number between 6 and 10 is -------------

The greatest natural number between 4 and 8 is -----------

The natural number between 3

9 and

3

15 is -------------

2) Put ( ) or ( X ) : The natural number between 23 and 25 is 24.5 ( )

There is only one natural number between 99 and 101 ( )

There is no natural numbers between 1 and 2 ( )

3

3) Make graph for each of the following or ( represent on the number line ) :

The number 5

The natural number between 1 and 3

The natural numbers less than 4

The counting numbers less than 5

The even numbers between 0 and 8

The natural numbers greater than 7

The set of natural numbers greater than or equal to 3

The set of natural numbers greater than 1 and less than 5

The set of prime numbers less than 8

4) Represent ( graph ) each of the following sets on the number line :

{ 2 , 3 , 4 }

{ 2 , 4 , 6 , ……….. }

4

1) Complete :

2 + -------- = 5

3 + -------- = 7

------- + ------ = -------

------- + ------ = -------

2) Use the number line to add the following natural numbers :

1 + 5

3 + 2

4 + 4

Addition is always possible for the natural numbers

5

Properties of addition of natural numbers :

1) Write the name of the property in each of the following :

125 + 50 = 50 + 125 ( ------------------- property)

0 + 45 = 45 ( ------------------- property)

( 12 + 23 ) + 25 = 12 + ( 23 + 25 ) ( -------------------

property)

30 + 40 = 70 ( ------------------- property)

2) Use the properties of addition to find the result of :

32 + 52 + 68

28 + 15 + 72

71 + 82 + 29 + 18

Closure property

Commutative property

Associative property

Additive identity

6

1) Complete : 6 - -------- = 2

------ - 1 = 4

------ - ------ = -------

------ - ------ = -------

Subtraction is not always possible for the natural numbers

Subtraction of natural numbers is : - not commutative

- not associative

Notice that

7

2) Using the number line , Ca2) Using the number line , Calculate the following subtraction : 7 – 2 = -----------

4 – 4 = -----------

5 – 3 = -----------

3) Mention which of the following subtraction are possible in N :

8 – 1

----------------

-

3 – 9

----------------

-

0 – 0

----------------

-

1 – 11

----------------

-

4) Put ( ) or ( X ) :

The set of natural number is closed under subtraction ( )

The addition operation of natural numbers is associative ( )

Zero is the neutral element for addition ( )

8

Properties of multiplication of natural numbers :

1) Use the number line to represent the following :

1 x 3

2 x 4

5 x 1

multiplication is always possible for the natural numbers

Closure property

Commutative property

Associative property

Multiplicative identity

Multiplication by zero

Multiplication distributes over addition

9

2) Find the number that will make the following statements true :

47 x 123 = 123 x ----------

( 10 x 5 ) x -------- = 10 x ( 5 x 7 )

( 12 x 6 ) x 5 = -------- x ( 6 x 5 )

------ x 25 = 25 x 1 = --------

98 x 0 = 0 x -------- = ----------

8 x ( 2 + 3 ) = 8 x ------ + 8 x -------

12 x ( 10 + 9 ) = ------ x ------- + ------ x --------

15 x 3 + 15 x 7 = ------- x ( ------ + ------- )

Use the distributive property to find the result of each of the following :

20 x 13 + 20 x 17 = --------------------------------------------------

---------------------------------------------------------------

11

1) Put ( ) or ( X ) :

The set of natural numbers is closed under division ( )

( 36 6 ) 3 = 36 ( 6 3 ) ( )

We can divide any natural number by zero ( )

12 6 = 6 12 ( )

40 ( 8 + 2 ) = ( 40 8 ) + ( 40 2 ) ( )

( 28 6 ) N ( )

Division is not always possible for the natural numbers

Subtraction of natural numbers is : - not commutative

- not associative

- No identity element

Notice that

11

2) Which of the following represents the number zero and which represents meaningless :

0 18 = ------------------

85 0 = ------------------

24

1212 = ------------------

66

2335

= ------ = ---------

Zero divided any non – zero natural number = zero

Any natural number divided by zero has no meaning

12

Unit (2)

1) Solve the following :

+ 6 = 13 for the replacement set { 5 , 6 , 7 }

--------------------------------------------------------------------

--------------------------------------------------------------------

a – 1.2 = 0.7 for the replacement set { 1.8 , 1.9 , 2.0 }

--------------------------------------------------------------------

--------------------------------------------------------------------

7 = 49 for the replacement set { 7 , 49 , 343 , 2401 }

-----------------------------------------------------------------------

-----------------------------------------------------------------------

13

2) Tell whether the equation is true or false for the given value of the variables :

+ 9 = 11 ; = 2 -----------------------------------------------

z – 6 = 17 ; z = 11 ------------------------------------------------

6 x k = 42 ; k = 8 ------------------------------------------------

m 6 = 5 ; m = 30 -----------------------------------------------

1.3 + p = 4 ; p = 3.7 -----------------------------------------------

3) Choose :

If + 5 = 11 then : = ------- ( 5 , 8 , 7 , 6 )

If z x 9 = 63 then : z = ------- ( 7 , 9 , 8 , 6 )

If k 8 = 7 then : k = ------- ( 15 , 1 , 56 , 8 )

14

1) Use the inverse operation to write a related equation and solve for the variables : z + 9 = 15

-----------------------------------------------------------------------

n - 10 = 3

--------------------------------------------------------------------

5 = 8

--------------------------------------------------------------------

10 y = 120

--------------------------------------------------------------------

32 n = 32

+ , - are inverse operations

are inverse operations ÷ × ,

15

1) Represent each word by a variable expression :

seven more than a number : ----------------------------------

-

more than two : ---------------------------------------

Two less than a number : -------------------------------------

less than a number 10 : ----------------------------------

Three times a number y : ---------------------------------------

Take away a number k from 15 : ------------------------------

A number m is divided by 12 : ------------------------------

Eight divided by a number n : ------------------------------

One sixth of a number y : ----------------------------------

Add a number z to 23 : -------------------------------------

A number h divided by 3 : ----------------------------------

16

1) Represent each word by a variable expression :

a) Three more than a number y : --------------------------------------

b) less than a number 12 : ----------------------------------

c) Four divided by a number q : ------------------------------

d) Seven less than a number t : --------------------------------

e) Product of a number f and 3.5 : ----------------------------

f) Two times a number w : ---------------------------------------

g) Add a number z to 13 : -------------------------------------

h) One fifth of a number y : ----------------------------------

i) 5 subtracted from twice the number f ----------------------------

j) Seven decreased by three times a number ------------------------

k) The difference between three times a number and nine ----------

l) Six times the difference of a number and eight ------------------

2) Write an equation for each word sentence :

a) Eight times a number k is 48

--------------------------------------------------------------------------

b) 2 less than half a number m is 10

--------------------------------------------------------------------------

17

1 2 3 4 5 6 7

1 2 3 4 5 6 7

Unit(3)

I–Graph each point in the coordinate plane:

1) A = (3 , 5)

2) B = (4 , 4)

3) C = (0 , 7)

4) D = (2 , 0)

II– a) Graph the ABCD where:

A = (2 , 8) , B = (3 , 4) , C = (8 , 4)

And D = (7 , 8)

B) What is the name of the figure ABCD?

18

1 2 3 4 5 6 7

1 2 3 4 5 6 7

3) a) Graph the figure XYZT, where:

X = (1 , 5) , Y = (5 , 1) , Z = (9 , 5) and

T = (5 , 9)

b) What is the name of the figure XYZT?

c) Use of the geometric instruments to find the

coordinates of the intersection of the two

straight lines XZ and YT the coordinate are (…..,….)

Using the opposite grid , complete : The distance between B and C = ------ units

The coordinates of the

midpoint of AC ( -----,------)

The ordered pair for D ( ----- , ------ )

, B ( ------ , ------ )

19

A transformation of a figure is produced by turning,

sliding, or flipping the figure.

1–Describe the type of transformation in each of

the following figures (reflection, translation,

rotation).

a) b) c)

……………. ……………….

……………….

2– Tell whether each transformation is:

a) b)

c)

D C

A B D\

A\

C\

B\ A B

C

C\ B\

A\

D

C

A B

A\

D\

C\

B\

21

1–Give the coordinates of the reflection images of

points X, Y and Z:

2– On a square lattice: Draw the figures formed by connecting these points and

they are symmetric figure.

Graph each figure and draw its line (or lines) of symmetry:

a) (1 , 2) , (3 , 9) , (5 , 2) (1 , 2)

b) (4 , 8) , (10 , 8) , (9 , 4) , (5 , 4) , (4 , 8)

1

2

3

4

5

6

7

1 2 3 4 5 6 0

Z

Y

X

21

22

23

Is the length of the circle curve drawn by the compass .

Each figure has its own perimeter and the circle has its

own circumference .

Circumference of a circle = C.F = 2 r

or C.F = d

= 7

22 or 3.14

2 r

or D

C.F

X

÷

D =

r =

C.F

π

C.F

2π

24

I– Find the circumference of a circle with a

diameter of 17.5cm. “=722 ”.

………………………………………………………………………………

………………………………………………………………………………

II– Find the circumference of a circle with a radius

of 42cm “=722 ”

………………………………………………………………………………

………………………………………………………………………………

III–Find the difference between the

circumferences of two circles whose two radii

lengths are 14cm, and 9.8cm.

………………………………………………………………………………

………………………………………………………………………………

IV–Complete:

1) The diameter = 2X ……………….

2) If the radius of a circle = 5cm. long, then the length

of the longest chord = ………………..cm.

3) If the length of the greatest chord in a circle =

7cm, then its circumference = …………….cm. where

(=722 ).

4)If the radius length of a circle = X cm, then its

circumference equals………………cm.

25

I– Complete:

1) The area of a triangle = 21…….. ……..

2) b = h

...........

3) If the length of the base = 6cm, and the height = 4cm, then

the area of this triangle = ………………..cm2.

4) If the area of a triangle is 30cm2, and its base length is

6cm, then its height = ……………….cm.

5) The number of the attitudes of the equilateral = ……………

6) The number of the attitudes of the right– angled = …………

II–If the area of a triangle is 60cm2, and its base

length is 7.5cm, calculate its height.

…………………………………………………………………………………………

…………………………………………………………………………………………

III–If the area of is equal to the area of a

square of side length 7cm. Calculate the height of

the if its base length is 14cm.

…………………………………………………………………………………………

…………………………………………………………………………………………

26

1) A parallelogram has a base of 8cm, and a

corresponding height of 5cm. find its area.

……………………………………………………………………...

……………………………………………………………………...

……………………………………………………………………...

2) If the area of a parallelogram is 36cm2, and

its height is 9cm, then find the length of the

corresponding base of this height.

……………………………………………………………………...

……………………………………………………………………...

……………………………………………………………………...

3) If the area of a parallelogram is 90mm2, and

the length of the base is 9mm, find the height.

……………………………………………………………………...

……………………………………………………………………...

……………………………………………………………………...

3) Which is larger in area, a parallelogram of side

length 3.6cm, and its corresponding height is

5cm, or a triangle with base length 10cm, and

height 6.2cm?

27

I–Complete:

1) The area of the rhombus = the side length

………………..

2) The area of the rhombus = 21 the product

of………………...

3) If the lengths of the diagonals of a rhombus are

21cm, and 11cm, then its area = ………………..cm2.

II–A rhombus of side length = 6cm, and its height

is 5cm. find its area.

……………………………………………………………………...

III–The lengths of the diagonals of a rhombus are

3.4cm, and 5.5cm. find its area.

……………………………………………………………………...

IV–If the height of a rhombus is 10cm, and its

area = 54cm2. Find its side length.

……………………………………………………………………...

V–The area of a rhombus is 20cm2, and the

length of one of its diagonals is 5cm, then

find the length of the other diagonal.

28

I–Complete:

1) The area of the square = the side length

………………….

2) The area of the square = 21 ……….. ………..

3) The side length of the square = 4cm, then its

area = …….cm2.

4) If the length of the diagonal of the square =

6cm, then its area=…………….cm2.

II–A square is of side length 7cm. Find the area of

the square.

……………………………………………………………………...

……………………………………………………………………...

III–.The diagonal length of a square is 10cm. Find

the area of the square.

……………………………………………………………………...

……………………………………………………………………...

29

IV–The area of a square is 72cm2. Find the length

of its diagonal.

……………………………………………………………………...

……………………………………………………………………...

V–The area of a square equals the area of the

rectangle whose dimensions are 2cm, and 9cm.

Find the length of the diagonal of the square.

……………………………………………………………………...

……………………………………………………………………...

VI–Which is greater in area:

a square , whose diagonals is 10cm or a right–

angled whose right angle sides are 8cm, and

15cm.

……………………………………………………………………...

……………………………………………………………………...

31

1) Find the following :

The area of the shaded part in the following rectangle

---------------------------------------------------

---------------------------------------------------

---------------------------------------------------

The area of the colored triangle shown

---------------------------------------------------

---------------------------------------------------

The area of the shaded part in the following rectangle

---------------------------------------------------

---------------------------------------------------

---------------------------------------------------

The area of the shaded part in the following rectangle

-------------------------------------------------

-------------------------------------------------

-------------------------------------------------

Unit (5)

31

STATISTICS

1) Given the marks of 25 students in a Maths exam :

Make a frequency table

Marks 5 6 7 8 9 10

Tally

Frequency

2) The following data represents the number of days of absence of pupils :

Complete the frequency

table

No. of

days Tally Frequency

1

2

3

4

5

6

7

8

10 6 8 6 5 7 6 9

8 10 6 6 7 6 7 6

6 5 6 8 6 9 9 6

8 1 3 5 4 4 4 6

5 6 4 4 3 5 3 5

4 4 5 2 6 5 3 4

2 8 4 4 5 6 4 7

32

3) The following data shows the age of 20 pupils in a primary school :

Put these data in a frequency table

4) The following data shows the favorite colour of some children in a class :

Put these data in a frequency table

5) The following data shows the weights of 30 pupils in Kgs :

Make a frequency table using sets : 20 - , 30 - , 40 - ,----------

Intervals Tallies Frequency

20 -

30 -

40 -

50 -

60 -70

8 12 9 13 8 7 8 9 8 6

12 9 8 7 8 13 12 12 9 6

Blue Yellow Red Blue Yellow Green Red White Blue Green

Green Red Blue Red Black Yellow Green Black Red Blue

23 25 36 40 25 48 33 49 50 43

27 33 40 56 28 33 60 28 63 45

38 45 33 63 27 53 54 66 24 38

33

6) The following table shows the frequency distribution of marks of 40 pupils in the Mathematics examination :

Sets 10 - 20 - 30 - 40 - 50 -

Frequency 5 7 12 9 7

a) draw the frequency histogram b) draw the frequency

polygon

7) 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

Frequency 8 9 15 13 5 50

a) Draw the frequency histogram b) draw the frequency

polygon

8) The following table shows the frequency distribution of marks of pupils in the Religion examination :

Sets 0 - 4 - 8 - 12 - 16 -

Frequency 12 20 24 14 8

a) Draw the frequency polygon

9) The following data shows the marks of 40 students in Math test :

a) Make a frequency table using suitable sets

53 48 24 36 49 51 32 28 17 44

29 41 25 35 58 24 18 28 15 52

41 34 32 43 25 58 33 31 44 59

46 58 39 37 35 46 57 50 37 49

34

b) Draw a histogram

c) Draw a frequency polygon

10) The following table shows the favorite sports for 120 pupils

football Volley swimming Basket

40 ……. 40 30 d)

Represent these data by a pie chart

11) The following table shows the favorite TV programs for 60 pupils

sports News series movies

15 5 10 30 e)

Represent these data by a pie chart

12) The following table shows the number of tourists come to Egypt from some countries

f)

Represent these data by a pie chart

Which country has the greatest number of tourists ?

Which country has the lowest number of tourists ?

Germany Japan USA France

120000 40000 20000 60000