Maths

1. Cairo Governorate
Nozha Directorate of Education
Nozha Language Schools
Ismailia Road
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LLLLeeeessssssssoooonnnn 1: Thousands
1- Write each of the following numbers in numerals form:
a- Three thousand, five hundred
b- Four thousand, one hundred, and seventy
c- Nine thousand, and four
d- Fifteen hundred
e- 3 units, 5 hundreds, and 4 thousand
f- 9 thousands and 18 units
2- Write each of the following numbers in letters:
a- 3725 = ---------------------------------------------------------------------
b- 2012 = ---------------------------------------------------------------------
c- 5605 = ---------------------------------------------------------------------
d- 7002 = -------------------------------------
e- 6055 = ---------------------------------------------------------------------
3- Complete in the same pattern:
a- ….…… , 5100 , 5200- , -------------
b- 2000 , 2001 , 2002 , ------------
c- 3400 , 3450 , ------------ , ------------
d- 9500 , 9000 , ------------ , 8000 , 7500 ,
e- 7760 , 7770 , 7780 , ----------------
Date …../……../ 201
- 1 -
he hundred, and eighty-four ( --------------------
, ( --------------------
( --------------------
( --------------------
, thousands ( --------------------
( --------------------
--------------------------------------------------------------------
, ------------ , 5500 , ---------
, ----------- , ----------- , -------------
, ------------ , 3650 , ------------
------------
, --------------
Department :
Form : 3
Sheet
2014
)
)
)
)
)
)
-------------------------------
Math
3rd primary

2. Date …../……../ 2014
4- Write the place value of the underline digits:
a- 4657 ( --------------------- ) b- 2635 ( --------------------- )
c- 6719 ( --------------------- ) d- 3045 ( --------------------- )
5- Write in expanded form as the given examples:
a- 6841 = ------------- + 800 + --------- + 1
b- 3695 = 5 + ----------- + ---------------- + -------------------
c- 2073 = ----------------- + ------------------ + ------------------
- 2 -
6- Complete as in the example:
4823
Example: ------------- = 4000 + 800 + 20 + 3
a- ---------------- = 9000 + 100 + 30 + 2
b- --------------- = 1000 + 800 + 4
c- --------------- = 3000 + 5
d- --------------- = 8 + 4000 + 20
7- Complete using > , < , or =:
a- 2689 ---------- 2896 b- 707 ----------- 4004
c- 5000 + 321 ---------- 5321 d- 8548 --------- 8458
8- Arrange the following numbers :
A- 6987 , 6978 , 6897 , 987
Ascending order = ------------ , ------------ , ------------ , ----------

3. Date …../……../ 2014
B- 8715 , 5781 , 5780 and 8755
Ascending order………………….,……………….. , …………… , …………..
Descending order = ------------ , ----------- , ----------- , -----------
- 3 -
The greatest number ………………..
The smallest number…………………..
9- Write the smallest number, and the greatest number which can be
formed using each of the cards:
5 7 2 8
The smallest number = ------------
The greatest number = -----------
8 0 3 1
The smallest number = ------------
The greatest number = -----------
10- Complete:
a- The greatest number formed from 4-digit number is ----------------
b- The smallest number formed from 4-digit number is ----------------
c- The greatest number formed from 4-different digit is ------------
d- The smallest number formed from 4-different digit is ------------
e- The greatest number formed from 4-similar digit is ------------
f- The smallest number formed from 4-similar digit is ------------

4. Date …../……../ 2014
- 4 -
11- Choose between the brackets:
a- One thousands is the smallest number which is formed from -------------- digits.
( 3 , 4 , 5 )
b- The number just after 999 is ----------------- ( 10 000 , 1000 , 9 999 )
c- The number which if added to the number 999 the result will be 1000 is --------
( 3 , 2 , 1 )
LLLLeeeessssssssoooonnnn 2
TTTTeeeennnn Thousands ( T.TH ):
1- Write each of the following numbers in numerals form:
a- Fifty two thousand ( -------------------- )
b- Ninety one thousand, nine hundred, and fifty seven ( ------------------ )
c- Forty thousand, and eight ( -------------------- )
d- Seventy nine thousand, and two ( -------------------- )
e- Twenty nine thousand, three hundred, and nine ( -------------------- )
f- 84 thousands, 3 hundreds, 9 units, 3 tens ( -------------------- )
g- 9 units, 7 hundred, 43 thousand ( -------------------- )
2- Write each of the following numbers in letters:
a- 35237 = ---------------------------------------------------------------------------------------
b- 30001= ---------------------------------------------------------------------------------------
d- 27019 = ----------------------------------------------------------------------------------
d- 89301= ----------------------------------------------------------------------------------
e- 10070 = ----------------------------------------------------------------------------------

5. Date …../……../ 2014
3- Write the place value of the underline digits:
- 5 -
a- 83100 ( --------------------- )
c- 67480 ( --------------------- )
e- 32479 ( --------------------- )
g- 13800 ( --------------------- )
4-complete
a- In 15983 , the digit 5 is in the …………… place .its value is ……….
b- In 67098, the digit 6 is in the …………… place . its value is ………
5- Write in expanded form as the given examples:
Example: 92536 = 90 000 + 2000 + 500 + 30 + 6
a- 76841 =----------- + 6000 + --------- + --------- + 1
b- 13695 = ------------- + ------------ + --------- + --------- + ---------
c- 70452 = ------------ + --------- + 50+ --------
d- 50005 = ---------------- + 5
6- Complete as in the example:
49823
Example: ------------- = 40 000 + 9000 + 800 + 20 + 3
a- ---------------- = 70 000 + 3000 + 100 + 20 + 0
b- --------------- = 5 + 10 + 20 000
c- --------------- = 30 000 + 9000 + 6
d- --------------- = 80 000 + 500 + 7
e- --------------- = 5 + 700 + 8000 + 40 000

6. Date …../……../ 2014
- 6 -
7- Complete using , , or =:
a- 9999+1 --------- 10000
c- Sixty three thousands . seven hundred and forty ……………….. 968 3
d- 9002 -------- 2 + 900
e- 15000 ………..…. 150 hundreds
8- Arrange the following numbers:
A- 49210 , 6799 , 94280 , 92480
Ascending order = ------------ , ------------ , ------------ , ----------
B- 89345 , 98345 , 95843 , 89543
Descending order = ------------ , ----------- , ----------- , -----------
C- 77 849 , 84 325 , 76 042 , 32 567
Ascending order = ------------ , ----------- , ----------- , -----------
9-Complete
a-790 hundreds = …………… thousands = …………….. tens =………………
b- 16000= ……………...hundreds = ……………….. thousands =………………tens
c- 53000 = ………….hundreds
Model on Unit (1)
[1] Complete :
a) 5896 = ……….. + 800 + 90 + 6
b) In 4058 , the digit 0 is in the ………..place . its value .
c) 6000 + 800 + 70 + 7 = ………….
d) 6406 is read as ……………………
e) 1005 is read as ……………………

7. Date …../……../ 2014
[2] Complete in the same patterns :
a) 9000 , 7000 , …………… , ………….. , 1000
b) 1000 , ……. , 1002 , ………. , ……….. , …
c) 30 000 , 40 000 , 50 000 , …………… , ………….. , 80 000
d) 11 000 , 33 222 , ………….. , 77 666 , ………….
e) 62 378 , 62 366 , 62 354 , …………. , ………..
[3] a) Arrange in an ascending order :
78 203 , 7820 , 78 302 , 7802 and 78 021
The order : ............... , …….…. , …….…. , ….……… and ….……..
b) Arrange in a descending order :
84 935 , 89 345 , 83 945 , 98 345 and 89 543
The order : ............... , …….…. , …….…. , ….……… and ….……..
4] Complete by using , = ,
a) 4000 + 400 + 40 + 4 Four thousands + 44
b) 18000 + 850 81800 + 50 + 18
c) 3000 + 400 + 56 3000 + 456
[5] Complete :
a) 790 hundreds = …………………….
b) 38 thousands = ………………tens
c) 9400 tens = ……………. hundreds
d) 53000 = ……………hundreds .
e) The number just after 5326 is …………….
f) The number just before 23 480 is …………
g) 999 + ………… = 1000
h) …………… + 1 = 10 000
i) The place value of digit 2 in the number 78 529 is ……………
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8. Date …../……../ 2014
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99999999999999999999
LLLLeeeessssssssoooonnnn 2 : FFFFiiiinnnnddddiiiinnnngggg tttthhhheeee ssssuuuummmm ooooffff ttttwwwwoooo nnnnuuuummmmbbbbeeeerrrrssss
(1)))) AAAAddddddddiiiinnnngggg
4 5 6 1 2 4 3 3
+ 3 1 2 2 + 3 1 2 1
__________ __________
--------------- --------------
5 0 2 4 3 2 5 4
+ 3 5 2 + 6 7 2 1
__________ __________
------------- --------------
6 3 6 0 6 3 4 5 6
+ 1 2 7 8 + 2 1 5 2 4
________________ ___________________
----------------- -----------------
Story Problems
a- Omar bought 1246 cows and 3120 camels. How many animals did he buy
- 8 -
all together?
He bought = ----------------------------------------------------

9. Date …../……../ 2014
b- Mona saved money in a bank. In the ;irst year, she put L.E 6846, in the second
year, she put L.E 9856, and in the third year, she put L.E 9297 . How much money
did she save after the three years in the bank?
Mona saved = -----------------------------------------------------
c- Omar reads 2351 papers of a story in one day, 1230 papers in the next day,
and 3118 papers in the third day. How many papers did he read?
Omar reads = --------------------------------------------------
d- A man bought a house for L.E 75625, and a car for L.E 23515. How much
money did he pay?
He paid = --------------------------------------------------------
e- Eman has saved 2650 pounds and her father gave her2530 pounds. How much
money does she have now?
The total amount = --------------------------------------------------------
Properties of Addition
- 9 -
Complete the following:
a- 4331 + 2154 = 2154 + ----------------
b- 2035 + ----------------- = 571 + 2035
c- ( 6012 + 2563 ) + 300 = 6012 + ( 2563 + ----------------)
d- 4598 + ( --------------- + 3294 ) = ( 4598 + ---------------)
e-

10. Date …../……../ 2014
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Formed from Formed from
2-digits. 4-digits.
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Circle the symmetrical numbers:
7575 , 66 , 8008 , 1122 , 3113 , 4545 , 44 , 5555 .
Model on Units (2)
[1] Complete :
a) The place value of 6 in the number 6584 is ……………
b) 4925 = ……….. + ………… + 20 + ………….
c) 6958 , 6968 , ……… , ……….. , ………….
d) The greatest 4 – digit number is ………..
e) The smallest number that formed from the digits 2 , 5 , 3 and 7 is ………
f) 1 unit , 3 hundreds , 3 thousands , 6 tens = ………..
( 6331 – 3361 – 1336 )
[2] Choose :
a) The value of the digit 8 in 8473 is ………… [ 8 , 1000 , 8000 ]
b) The number just after 5999 is ………… [ 600 , 6000 , 60 000 ]
c) 7815 = 815 + ……….. [ 70 , 700 , 7000 ]
d) The symmetrical number is ………….. [ 6116 , 616 , 161 ]
e) Three thousand and seventy two in digits is …..........
[ 3702 , 3072 , 300721 ]

11. Date …../……../ 2014
[3] Complete :
a) The number ………..lies between 43999 and 44001
b) 852 + 211 = 63 + ………..
c) The smallest number formed from the digits 5 , 7 , 1 and 4 is …………..
d) ( 5642 + ……….. ) + 2139 = 5642 + ( 1347 + 2139 )
e) Eight thousand and one is written in digits as …………..
f) 7 + 2 + 0 + 1 = ……………
g) 65 481 = 481 + ………. + ……….
h) 5 thousand = ………… tens = …………. hundred .
[4] Arrange the following numbers ascending :
8905 , 4687 , 9124 , 7458
The order : ……….. , …………. , ………… and …………….
[5] a) Put , = ,
1) 16 numbers 160 tens
2) Seven thousand and ten 7100
3) Four thousands 40 hundred
b) Write in letters :
1) 5911 : …………………………………………….
2) 12600 : ………………………………………….…
- 11111111 -

12. Date …../……../ 2014
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SSSSuuuubbbbttttrrrraaaaccccttttiiiioooonnnn uuuupppp ttttoooo nnnnoooo mmmmoooorrrreeee tttthhhhaaaannnn 99999999 999999999999
Story Problems
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‘
LLLLeeeessssssssoooonnnn 2 ::::
Subtracting two numbers
Without renaming With renaming
1- Subtract the following numbers:
5 3 5 4 2 5 3 4 5 3 8 1
- 4 2 1 2 - 1 4 1 2 - 2 3 5 0
_______________ __________________ ________________
----------------- ----------------- -------------------
2- Subtract:
a- 5435 – 2317 = ----------------- b- 3542 – 2731 = -----------------
c- 56470 – 21236 = -------------- d- 48964 – 32649 = -------------
1- In a school of 973 pupils, 328 pupils participate in different
activities. How many pupils don't participate in the activities?
Number of pupils = ----------------------------------------
2- Ahmed has 1630 piasters. If he wants to buy a bar of chocolate for 750
piasters. How much money will be left with him?
Money left with him = ----------------------------------------
3- A merchant has 35685 kg of wheat. If he sells 23485 kg of them, then calculate
the remainder of wheat.
The remainder = ---------------------------------------

13. Date …../……../ 2014
- 11113333 -
4- Complete in the same pattern:
b- 9534 , -------------- , 9334 , ------------ , --------------
c- 64580 , -------------- , 64560 , ------------ , --------------
5- From the digits 3 , 0 , 1 , 5 and 9
a- The greatest number = -------------------------
b- The smallest number = -------------------------
c- The difference between them = -------------------------------
Model on Unit (3)
[1] Complete each of the following :
a) 6452 – 2241 = ……………
b) 10 000 – 9 999 = ………….
c) 6954 , 6974 , ……….. , ………… , ………….
d) Fifty thousand and fifty in digits is …………..
[2] Put the suitable relation () , ( = ) or ( ) .
a) 6385 – 6000 385
b) 41500 – 40 000 6525 – 5425
c) 54 237 – 23 544 67 432 + 36 739
d) 1987 – 425 1987 – 452
[3] Arrange the following number in a descending order :
1) 3500 , 6000 , 1500 and 2800
The order : ………….. , …………. , ……………. and ……………
2) 6700 , 7600 , 6500 , 750
The order : ……….. , ………… , …………….. and …………….

14. Date …../……../ 2014
[4] Write the greatest and the smallest number formed from the digits:
2 , 6 , 0 , 7 and 1 , then find their sum and the difference between
them
The greatest number is ……………………...
The smallest number is ……………………..
Their sum = ………………..
The difference between them = ………………….
[5] Omar had L.E. 1500 , he bough a television for L.E. 1145 and
a fan L.E. 250 . How much money was left with him ?
1) The price of television and the fan = …………………………. L.E.
2) The left money = ……………………………… L.E.
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15. Date …../……../ 2014
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GGGGeeeeoooommmmeeeettttrrrryyyy
LLLLeeeessssssssoooonnnn 1 : Solids
- 11115555 -
1- Write the name of each solids:
Faces are all rectangles Faces are all squares
( ------------------------- ) ( ------------------------ )
It has 2 circular bases t has 1 vertex and 1 circular base
( ------------------------- ) ( ------------------------ )
Lateral faces are all rectangles Faces are all triangles
( ------------------------- ) ( ------------------------ )

16. Date …../……../ 2014
- 11116666 -
2- Complete the following table:
Name of
solid
Number of
faces
Number of
edges
Number of
vertices
Cube
-----------------------------------------
-------------------
-----------------
Cuboid
-----------------------------------------
-------------------
-----------------
Pyramid with
a square base
------- faces + ------ base
-------------------
------------
Without counting
the vertices of the
base
Pyramid with
a triangle
base
------- faces + ------- base
-------------------
-----------------
Prism
------- faces + ------- bases
-------------------
-----------------
Cone
----- base as a -------------------
-----------------
Cylinder
------ bases and each base is a -----
-------------
N.B.
1- A sphere doesn't have faces , edges or vertices.
2- Every vertex is one intersection point of 3 edges.
3- Choose the correct answer:
a- The number of a cuboid vertices is ....................... [ 12 , 6 , 8 ]
b- The number of faces of the cube = ....................... [ 4 , 6 , 8 ]
c- The number of cube's edges is ....................... [ 12 , 8 , 6 ]
d- The triangular pyramid has............... [ 1 base , 2 bases , 3 bases ]

17. Date …../……../ 2014
e- The prism with triangular base has ...........side faces [ 1 , 3 , 5 ]
f- The base of a cylinder is .......................... [ square , triangle , circle ]
g- The base of a cone is ................................. [square , triangle , circle ]
h- The cone has ....................... [ one vertex , eight sides , four edges ]
i- Each face of the faces of the cube is a .......[rectangle, square , triangle ]
j- The three dimensions shape which does not have a base or
vertex is called ............................. [ pyramid , sphere , cylinder ]
k- The ................ does not have edges or vertices,but it has 2 circular
bases. [ sphere , cone , cylinder ]
l- The ................... does not have edges , but it has one vertex and one
circular base. [ cylinder , cone , sphere ]
LLLLeeeessssssssoooonnnn 2
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Use your ruler to measure the lengths of the following line segments:
A B E F
AB = --------- cm. EF = ---------- cm.
P K L O
PK = ------ cm. LO = --------- cm.
- 11117777 -

18. Date …../……../ 2014
Lesson 3:
Geometric constructions
1- Draw:
a) A line segment with length 5 cm. long
b) A line segment with length 3 cm. long, which point N is one of its end points.
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.
.
2- In the opposite figure, if we take the length of the side of small squares of
the lattice as 1 unit of length:
Find:
a- The lengths of the two dimensions of the rectangle ABCD
is ----- and ------- of these units.
b- Length = ----- units.
Width = ------ units.
3- In the opposite lattice, draw:
XYZL where XY = 3 units, and
YZ = 4 units.
Complete:
ZL = -------- units, LX = -------- units
XYZL is called -------------------------

19. Date …../……../ 2014
Congruent figure have the same shape and size.
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4- In the opposite lattice, draw:
ABCD where AB = 3 units, and
BC = 3 units.
Complete:
CD = -------- units.
DA = -------- units.
ABCD is called -------------------------
Note that:
1- In the opposite figure identify the two congruent figures:
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Complete in the same pattern:
a- , -----------------------------------------------------
b- , -----------------------------------------------------
c- …………………………………………………

20. Date …../……../ 2014
LLLLeeeessssssssoooonnnn 6: TTTThhhheeee AAAAnnnngggglllleeeessss
Kinds of Angles
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1- Complete the table:
The figure Name of the angle Vertex Sides of the angle
Z
X Y
------------------
------------------
------------------
-----------
------------------
------------------
L
M N
------------------
------------------
------------------
-----------
------------------
------------------
C
A B
------------------
------------------
------------------
-----------
------------------
------------------
H K L
------------------
------------------
------------------
-----------
------------------
------------------
Right angle Acute angle Obtuse angle Straight angle
= 90° greater than 0° and greater than 90° and = 180°
less than 90° less than 180 °

21. Date …../……../ 2014
- 22221111 -
Complete the table:
The figure Kinds of the angle
------------------
------------------
------------------
------------------
1- Measure each of the following angles, then write the type of each angle:
Measure= ………… Measure= ………… Measure = …………..
Type = …………… Type = ……………… Type = ………………..
Name=……or……or………. Name=……or….…or…….. Name=……or….…or…..
.
Its vertex : ……….. Its vertex =………………. Its veterx = ……………
Its sides……and…… Its sides …… and …….. Its sides ……. And ……

22. Date …../……../ 2014
3- Draw angles with the following measures, and state its kind:
35 °
90 °
60 ̊
130 ̊
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4- Choose the correct answer:
1- The angle between the hands of the clock is a right angle,
when it's -------------- ( 7 o'clock , 9 o'clock , 2 o'clock ).
2- The angle between the hands of the clock is an acute angle,
when it's -------------- ( 4 o'clock , 3 o'clock , 11 o'clock ).
3- The angle between the hands of the clock is a straight angle,
when it's -------------- ( 12 o'clock , 5 o'clock , 6 o'clock ).
4- The unit used for measuring angle is ----------------
( protractor , angle , degree )
5- The geometric tool used for measuring angle is --------------------
( vertex , protractor , degree )
6- We use protractor to measure ------------- ( angles , lengths , weights)

23. Date …../……../ 2014
7-The mesure of the acute angle is ……….. ( 90 , less than 90 , more than90)
8-the measure of the straight angle is …………… ( 90 , 180 , 45)
9- the measure of the Right angle is ……… ( 90 , less than 90 , more than 90 )
10- the angle oe measure 108 is ……. Angle (straight , an acute , an obtuse )
Put the suitable sign , or =
A) The measure of the right angle ………….. 90
B)the measure of the straight angle …………. The measure of the obtuse angle
c)the measure of the acute angle …………………. The measure of the obtuse angle
Model on unit (4)
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[1] Complete :
a) The number of faces of the cuboid is ………….
b) The face of cube in the form of ……………….
c) The square has four …………..angle ( right – acute – obtuse )
[2] In the opposite figure , complete :
1) The name of the angle is ……………………
2) The sides of the angle are …………and …………..
3) The type of the angle is ……………….
4) The measure of this angle is ………..°
5) Its vertex is ……………….
[3] Complete :
a) The number of edges of the cuboid is ……………….
b) AB , ABB , ………….. , …………..
X Z
X

24. Date …../……../ 2014
c) ………
d) The cube has …………… faces .
e) The figure is congruent to the figure … [ , , ]
Exam (1)
[1] Choose the correct answer :
a) The value of the digit 8 in the number 28473 is …………….
[ 8 or 1000 or 8000 or thousand ]
b) The number just after 5999 is ………….. [ 600 or 6000 or 60 000 ]
c) 7815 = 815 + ……….. [ 70 or 700 or 7000 ]
d) The base of the cylinder is …………[ circle or square or rectangle ]
e) 9800 = …………..hundreds . [ 98 or 980 or 9800 ]
[2] Complete :
a) 3712 + ………. = 6483 + ………….
b) 325 + ( ………. + 344 ) = ( ………… + 279 ) + 344
c) …………
d) The number of faces of the cuboid is …………….
e) The greatest number formed from 7 , 5 , 9 and 2 is ………….
[3] a) Mona bought a flat for 21 236 pounds and her brother bought a flat
for 69 985 pounds . What is the total amount they both paid ?
The total = …………………………. = …………..pounds
- 22224444 -

25. Date …../……../ 2014
b) Arrange the following in a descending order :
48 928 , 32 567 , 94 328 , 56 394
The order is : ……….. , ………….. , ……………. and …………….
[4] a) Write in letters :
1) 5911 = ………………………………………………………………
2) 12 600 = ……………………………………………………………
b) Put , = ,
1) 7325 – 2965 5269
2) Seven thousand and ten 7100
3) 58 200 + 10 000 48 200 + 20 000
4) The measure of the right angle the measure of the obtuse
5 2 3 4 0
- 1 2 3 3 5
- 22225555 -
angle .
5) Four thousands forty hundreds .
6) 85000 85 hundreds
[5] Find the result :
1) 2)
6 8 5 5
+ 2 1 4 5
b) Draw angle ABC of measure 120° , then state its type .

26. Date …../……../ 2014
Exam (2)
[1] Choose the correct answer :
a) We use ……….to measure the angle . [ protractor or triangle or
ruler ]
b) Number of edges of a cube is ………. [ 8 or 12 or 6 ]
c) The place value of the digit 7 in the numbers 7823 is ………….
[ tens or hundred or thousands ]
d) 2341 + 4517 = ………… [ 6838 or 6858 or 6248 ]
[2] Complete :
a) 52 thousands = …………………
b) 7000 + 253 = ………….
c) 8732 + 1257 = ………… + 8732
d) The smallest number formed from 4 digit is ……………
e) The value of the digit number 48573 is ……………
[3] Complete using the suitable relation , = ,
a) Seventeen thousand , four hundred and fourteen 17412
b) 9658 9000 + 600 + 80 + 5
c) 8756 – 3245 5500 + 11
d) 10 000 The greatest 4 – digit number
[4] a) Find the result :
1) 2)
3) 2000 + 500 + 4 = …………….
- 22226666 -
6 5 2 4 1
+ 3 2 5 5 4
8 7 6 8
- 5 3 2 5

27. Date …../……../ 2014
b) Hany bought a flat for 21236 pounds and his brother Raef bought a flat
for 69985 pounds . What is the total amount they both paid ?
The total amount paid by Hany and Raef = ……………………..
- 22227777 -
= ……….pounds
[5] a) Arrange the following numbers :
17491 , 14971 , 19741 , 19471
1) Ascending order is : ………… , …………. , ………….. and ………….
2) Descending order is : …………. , ……….. , ………… and ………….
b) Draw a line segment , with length 4 cm inside the opposite rectangle