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Unit one
Fractions and decimals
Lesson 1 : Revision on fractions
Lesson 2 : Adding a fraction and a whole number.
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Lesson 3 : Decimals.
Lesson 4 : more about decimals.
Lesson 5 : Comparing decimals .
Lesson 6 : Operations on decimals.
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Notice that :
Is a fraction ,3 is called a numerator and 4 is called a denominator.
If the numerator and the denominator is multiplied or dividedby any
number other than zero , we get an equal fraction.
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If the numerator the denominator ,then its called an improper fraction
If the numerator the denominator ,then its is called propr fraction.
Improper fraction quotient
EX: 2
The decimal is a fraction with denominator 10 , 100 0r 1000 ,.
17
16
8
2
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This read as three hundred twenty five and nine hundred twenty seven
thousandths.
Writing zeroes at the end of the decimal fraction does not change its
value.
2.5
Units Hundredthstenths thousandthstens Decimal point
3
Hundreds
2 9 7
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Remember that
2 x 5 10
4 x 25 100
8 x 125 1000
1L.E 100 P.T
1 m 100 cm
1cm 100 mm
1 Km 1000 m
1 Kg 1000 gm
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Sheet 1
Lesson 1, 2
1 Complete each of the following:
a b
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c
d
e6
f Three fifths
2 Convert into an improper fraction:
a
b
c4
d1
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e5 f 1
3 Convert into a mixed numbers:
a
b
cThirteen thirds
d17 quarters
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4 Complete each of the following:
a3 halves
b , then
cIn the improper fraction, the numerator is ..the denominator.
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sheet 2
lesson 3 , 4
1write in a decimal form:
a Six and four tenths . ..
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b Thirty two and five hundredths . ..
c Twelve and twelve hundredths. ..
d Five and fortytwo thousandths. ..
2complete each of the following:
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a 5 as a decimal form
b 3.36 . in words
c 3.7 3 .
d 3.456 3 .. 0.006
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e 0.4 1
f 0.2 0.3 .. 1
g . 3 hundreds 6 units 4 tenths.
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h The place value of the digit 3 in the number 25 . 23 is ..and its
value is
3write in a decimal form:
a b .
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c
d .
e
f
4choose the correct answer:
a The place value of 3 in 2.37 is .. units , tens , tenths , hundredths
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b 0.6 hundredths . 6 , 60 , 600
c 0.25 .. , ,
d Thirty five thousandths 3.5 , 0.35 , 0.035
e 0.3 0.7 . 0.1 , 1 , 10
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f 27 tenths . 2.7 , 0.27 , 270
5write the missing numbers on the number line:
........................
............
2 4 2 5
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Sheet 3
Lesson 5
1write the missing numbers :
a0.6 b. 0.16
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c0.2 . 0.3
d. 0.3 .
e73.02 . 73.022
f 0.19 .. 0.2
g0.14 0.15
h 0.6 ..
2 put the suitable sign , , :
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a6.98 5.98
b5.25 5.23
c3.60 3.6
d1.2 1
e 1.25 1
f 1 1.05
g 3hundreds and 4 tenths 30.04
h 1 0.999
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3aArrange in an ascending order:
0.35 , 0.53 , 5.3 , 3.5 , 0.5
.
bArrange in a descending order:
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2.7 , 1.8 , 2 , 2.43
Sheet 4
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Lesson 6
1find the result:
a 4 . 6 2 b 6 . 3 5
4 . 8 1 2 . 5 9 4
+ +
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C 7 . 9 8 d 6 . 3 8
5 . 1 3 2 2 . 9
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e 3.3
7 1 . 3 2 .
f 8
2 . 2 6
g 7
3 . 8 5 ..
h
0. 1 2 5 .
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2Fill in the missing numbers:
a . 3 . 6 6
b 4 . 2 .. 5. 3
c 3 . 8 1 . 4
d 1 . 3 2.3 .. 7
e 2 .. 3 .7
f 2.2 5
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g 4 . 3 1 . 8
h 4 . 8 . 3 . 1 4
i 4 10
j 3 10
k Two fifths .. whole one.
3 put the suitable sign , , :
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a 2 . 1 3 . 2 5 . 1 1 . 3
b 2 . 3 5 . 4 8 0 . 3
c 7 . 32 1.93 6 . 78 0.42
d 6 . 3 1.4 2 . 1 0 . 4
e 5 5. 125
f 8 5 . 3 1 . 6 0 . 9
4fill in the m issing digits:
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a 3 . 2 b 8 3 . 5 7
5 . 3 . 7 3 4
. 7 9 2 4 .
+
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5a Ibrahim bought a ball for L.E 9. 75 and a book for L.E 8 . 5 .How much
money did he pay?
.
b Ahmed has L.E 5. 35 and his sister Heba has L.E 8.7 ,find the difference
between what they have.
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..
c The price of one Kg of meat is L.E 35 , a family eats one and half Kg .of meat
every week ,How much money did this family pay for the meat in a month?.
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Sheet 5
Lesson 6
1complete each of the following:
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a7 3 4 100
b340 1000
c. 10 45 . 2
d393 10 .
e230 P.T L.E ..
f 3267 gm ..Kg
g285 cm .. m
h39 dm. ..m
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2put the suitable sign , , :
a3 7 2 10 3 7 2 100
b4 . 3 2 . 5 480 100
c1325 m 1. 325 Km
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d6140 gm 6 . 1 4 Kg
3choose the correct answer:
a2 5 . 4 , ,
b1 .. 0 . 4 , 1 . 4 , 4 . 1 , 14
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c. 10 4 . 5 4 . 5 , 0. 45 , 54 , 45
d75 .. 0.75 10 , 100 , 1000 , 1
e 4 . 3 2 . 7 10 .. 6 , 7 , 0.7 , 70
f 4 9 50 Kg 5 tons , ,
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Unit 1 test
1complete each of the following:
a 1 . 6 8 . 6
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b 3 . 65 3 . 0 . 05
c 530 . 64 237 . 1 894 . 7 89 . 58 .
d The value of the digit 5 in 2 . 354 is
e 2 hundredths.
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2choose the correct answer:
a2 , ,
b .. , ,
c0 . 8 .. , ,
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d . 0 . 007 , 0 . 07 , 0 . 7
e 0.1 .. 0.2 0.3 , 0.12 , 0.002
3a write the value of the circled digit:
a 3 . 8 5 ..
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b 2 5 5 . 2 5
c 3 8 . 1 0 2
bwrite three decimal numbers between 0.3 and 0.4 .
..
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4 a Find the result:
a4 . 47 3
b 285 100 ..
c 1 5 . 2 9 12
d 3. 8 2 . 5 3 . 9 ..
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b put the suitable sign , , :
a `6 . 37 10 637 1000
b 12 . 5 1 . 7 7 . 82 7 . 75
c 4 . 3 2 . 9 5 . 1 3 .8
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d 385 cm 4 meters
5a Arrange in an ascending order :
5 . 38 , 5 . 83 , 3 . 85 , 3 . 58 , 5 . 3
The order : ..
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b Ibrahim has L.E 60 , he bought a toy for L.E 32 . 75 and a book for L.E 19 . 5
.find the left money with him.
.
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Lesson 1 : Approximating to the nearest 10
Lesson 2 : Approximating to the nearest 100 and 1000
Lesson 3 : Approximating to the nearest 10 000 and 100 000
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Lesson 4 : Approximating to the nearest unit
Lesson 5 : Approximating to the nearest tenth
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Notice that:
The approximation is replacing the exact number by a simpler number closer
to it.
Rules:
When approximating a number to the nearest 10 :
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increase the tens digit by 1 and replace the units digit by 0 if the units
digit is 5 or more.
Keep the tens digit as it is and replace the units digit by o if the units
digit is less than 5
When approximating a number to the nearest 100 :
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increase the hundreds digit by 1 and replace all the digits to its right by
0 if the tens digit is 5 or more.
Keep the hundreds digit as it is and replace all the digits by o if the tens
digit is less than 5
When approximating a number to the nearest unitwhole number:
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Cancel the fraction or the decimal part and increase the units digit by 1
if the fraction is 0.5 or more
Cancel the fraction or the decimal part and keep the whole number as it
is ,if the fraction is less than 0.5.
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Sheet 6
Lesson 1 , 2 , 3
1complete each of the following:
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a 4 6 to the nearest 10
b 3 2 8 to the nearest 100
c 152 8 to the nearest 1000
d 629 .. to the nearest 1000
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e 392 to the nearest hundreds
2choose the correct answer:
a 38 40 to the nearest .. ten , hundred , thousand
b 450 to the nearest 10 455 , 443 , 448
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c .. 5000 to the nearest 1000 5432 , 5623 , 4236
d 279 to the nearest hundred 200 , 700 , 270 , 300
e 47765 to the nearest ten thousands 40000 , 50000 , 30000
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f 6584 . 37 6600 to the nearest .. 10 , 100 , 1000
g 9 to the nearest 10 1 , 0 , 90 , 10
h 8 . 56 to the nearest 10 10 , 9 . 56 , 9
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3Find the result then complete:
a3765 2437 .. . to the nearest 100
b8173 2534 .. to the nearest 1000
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c534 . 3 28 . 37 to the nearest 100
d85372 100 . .. to the nearest 100
e623 . 3 53 . 5 .. to the nearest 10
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4 a write four whole numbers if each approximated to the nearest 100 , the
result is 600.
..
b write four whole numbers if each approximated to the nearest 1000 , we
get 3000.
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..
5a Ibrahim bought 8 books for L.E 7 each ,How much did he pay ?to the
nearest 10
.
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b Ibrahim bought a fridge for L.E 1346.4 and a stove for L.E 925.8 ,calculate
what did he pay approximating the result to the nearest 1000.
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Sheet 7
Lesson 4
1complete each of the following:
a 5 . 7 . to the nearest unit
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b 3 .. to the nearest unit
c 6 . 3 8 .. to the nearest unit
d 24 . to the nearest unit
e 0 . 7 2 to the nearest unit
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f 7 . to the nearest unit
g 240 P.T .L.E to the nearest L.E
h 2 . 3 5 Km ..m to the nearest metre
i 235 cm m to the nearest metre
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j 450 cm2 ..m2 to the nearest squared metre
k 5 Kg .Kg to the nearest Kg
l 3165 dm2 m2 to the nearest m2
m17 days week/s. to the nearest week
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n 34 months .year. to the nearest year
2choose the correct answer:
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a3 . 85 to the nearest whole number . 3 , 4 , 3 . 9
bP.T 1935 L.E 20 , 19 , 19 .6
c725 gm ..K.g 1 , 8 , 7. 25
dP.T 325 L.E 4 , 3 , 5 , 6
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3aIbrahim bought a book for L.E 7 and a sharpener for L.E 0.45, How
much money did he pay?Approximated to the nearest L.E .
.
bSarah bought 3 K.g of apples for P.T 475 each .How much money did she
pay ? approximated to the nearest pound.
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cThe length of a rectangle is 13.7 cm and its width is 8.2 cm .find its
perimeter.Approximated to the nearest cm.
..
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.
dThe side length of a square is 24 cm .find its perimeter .Approximated to
the nearest metre.
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Sheet 8
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Lesson 5
1Approximate to the nearest :
a 6. 2 8 b 0 . 57 ...
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c 13 . 2 3 1
d 5 ..
e 12 .
f 7 . 26
2 Complete the following:
538 . 254
To the nearest 10
To the nearest 100
To the nearest unit
To the nearest tenth
.
.
.
.
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3Find the result then approximate to the nearest tenth:
a 23 . 75 16 . 4 0 . 386 ..
b 538 1000 .
c 15 . 4 6 . 916 . 5.3 cm
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d 0 . 5678 1000 ..
4Find the perimeter of the opposite figure:
approximated to the nearest cm.
..
3.7cm
2.1
cm
4.2 cm
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Unit 2 test
1complete each of the following:
a 376 P.T L.E
b 240 cm2 .. m2
c 4 .. to the nearest unit
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d 4 . 2 .to the nearest tenth.
e 782 100 to the nearest 10.
2choose the correct answer:
a . 1 . 5 to the nearest tenth. 1 . 44 , 1 . 56 , 1 . 52
b 29 days .weeks 4 , 5 , 6 , 7
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c 327 300 to the nearest .. unit , ten , hundred
d 443 . 2 0 to the nearest .. unit , ten , thousand
e 20 months .. year/s. 1 , 2 , 3 , 4
3awrite the greatest number and the smallest whole number that if
approximated to the nearest ten , we get 50 .
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The greatest .. the smallest ..
b complete:
To the nearest 100
382 . 85
To the nearest tenth
To the nearest unit
To the nearest 10
.
.
.
.
To the nearest 1000 .
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4find the result ,then approximate to the nearest . :
a 34 . 77 3 . one decimal place
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b 37 . 59 28 . 461 .. whole one .
c 18540 1000 .. . ten .
d 43 . 8 21 . 04 .. .. hundred
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5Mariam bought a dress for L.E 89 . 6 and a blouse for L.E 30 . 75 .if she had
L.E 200 .Find the left money with her .approximated to the nearest pound.
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Lesson 1 :Congruency
Lesson 2 : Symm etric figures ,line of symmetry.
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Lesson 3 : Coordinate system.
Lesson 4 : Visual patterns.
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Sheet 9
Lesson 1
1Put or x :
A circle and a square can be congruent.
Any two squares are congruent.
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The diagonal of the rectangle divides it into two congruent triangles.
Two triangles are congruent if their corresponding sides are equal in
length.
Two squares are congruent if the side length of the first equals the side length
of the second.
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The diagonal of the parallelogram divides it into two congruent triangles.
2draw a line to get two congruent figures if possible :
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3complete:
a Two polygons are congruent ,if their corresponding sides are .and
their corresponding angles are
b If the polygon ABCD is congruent to the polygon XYZL ,then
m z m
c The rectangle ABCD the rectangle XYZL, then BC .
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4IN the opposite figure ,polygon ABCDEF the polygon ABXYZK,complete:
a CD ..
b X
c KA ..
d m Y m ..
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5In the opposite figure , if AMN YEJ, complete:
YN
A
M
J E
4555
3 cm
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a AM .
b E ..
c EJ .. .cm
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d m Y m .. ..
e m J ..
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6From the opposite figure ,if FC is a line that divides it into two congruent
figures , complete:
a AB
b BC ..
c M B m . ..
F
C
EA
100 DB
60
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d E .
e The sum of the measures of the interior angles of the polygon CBAF is
.
f m E m . .
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7Draw a rectangle ABCD where AB 3 cm , BC 5 cm ,then draw a line to
divide it into :
1two congruent triangles 2two congruent rectangles
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Sheet 10
Lesson 2
1Complete each of the following:
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a The square has ..line
s of symmetry.
b The rectangle has
..line s of symmetry.
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c The parallelogram has
..line s of symmetry.
d The rhombus has
..line s of symmetry.
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e The trapezium has
..line s of symmetry.
f The isosceles trapezium
has ..line s of symmetry.
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g The equilateral triangle
has ..line s of symmetry.
h The isosceles triangle has
..line s of symmetry.
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i The scalene triangle has
..line s of symmetry.
j The circle has
.line s of symmetry.
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k Number of common lines
of symmetry for two circles and a square is .
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l The diagonal of the
rectangle divides it into two triangles ,but it is not a
.of the rectangle.
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Sheet 11
Lesson 3
1From the coordinates plane ,complete:
aA . , .
bB . , .
8
7
6
5
4
2
10986543
10
3
1
9
721O
.
.
.A
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cC . , .
dD . , .
eABCD is a ..
f AB
.
B
C
D
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2on the coordinates plane show n,plot the points A 2, 1 , B 5 , 1 ,
C 5 , 5 and D 2 , 5 .
aThe figure ABCD is
bIt has line s of symmetry.
8
7
6
5
4
2
10986543
10
3
1
9
721O
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cIts perimeter
dIts area
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3Complete:
aIf 2 , 5 2 , x , then x .
bIf x , 4 3 , y , then x and y
cIf x2 , 5 6 , 5 , then x ..
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Unit 3 test
1 Complete:
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a Two polygons are congruent if their sides are ...and their
angles are
b If point A 3 , 5 , then 1stcoordinate of A is .
c The rhombus has . Lines of symmetry.
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d If 4 , 5 2x , 5 ,then x .
2Choose the correct answer:
a The trapezium has lines of symmetry . 1 , 2 , 4 , 0
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b A square of side length 4 cm can be congruent with another square whose
perimeter is 1 , 4 , 8 , 16
c If ABC RST , then B .. R , S , T
d The parallelogram has .lines of symmetry . 1 , 2 , 0 , 3
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e The diagonal of the rectangle divides it into two triangles
congruent , symmetrical , different
3 in the opposite figure:
If ABC XYZ, then
5cm
A
B C Z
X
Y
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a XY ..
b AC
c B .
d BC ..cm
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4in the 2 dimensional coordinate plane ,draw the figure ABCD where A 2,3 ,B 7 , 3
, C 7 , 8 and D2 , 8 , then answer the following:
What is the name of the figure ?
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How many lines of symmetry does the figure ABCD has?
8
7
6
5
4
2
10986543
10
3
1
9
721O
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Lesson 1 ; Capacity.
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Lesson 2: Weight.
Lesson 3: Time.
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Lesson 4 : Temperature.
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The units of capacity:
1 liter dm3 1000 ml cm3
The units of weights:
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1 ton 1000 Kg
ton 250 Kg
ton 500 Kg
ton 750 Kg
1 Kg 1000 gm
Kg 250 gm
Kg 500 gm
Kg 750 gm
The units of time:
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Century 100 years
Year 12 months
Month 30 days
1 hour 60 min
hour 30 min
hour 20 min
hour 15 min
hour 40 min
hour 45 min
1 minute 60 seconds
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minute 30 seconds
minute 20 seconds
minute 15 seconds
minute 40 seconds
minute 45 seconds.
1 day 24 hours
day 12 hours
day 8 hours
day 6 hours
day 16 hours
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day 18 hours
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Sheet 12
Lesson 1 , 2
1complete each of the following:
a 5000 ml ..litres b 24 dm3 ml
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c 3 Kg gm
d 2 tons ..Kg.
e 7 liters , 60 ml .ml
f .. tons 7250 Kg
g Liter cm3
h gm 4 Kg , 500 gm
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2put the suitable sign , , :
a 1 liter 1 dm
b 3000 gm 3 Kg
c Liter 0.75 dm3 1000 ml
d 7250 gm Kg 7 tons
e 1750 ml 2 liters
f 2 liters 225 ml
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g 5 Kg , 250 gm 5 Kg h 1 liter , 600 ml 2 liters
3 Choose the correct answer:
a The unit of measuring capacity is ..pound , Kilogram , Litre
b Weight of golden ring may be 3 Kg . 3 gm , 300 gm
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Sheet 13
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Lesson 3 , 4
1complete each of the following:
a 3 hours .min .
b 30 days weeks , .days
c 2 hours , 20 min . ..min.
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d Normal body temperature is
C
e hour .min
f hour ..seconds
g Water boils at ..c
h 180 seconds .min.
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2put the suitable sign , , :
a Hours 40 min
bNormal body temperature 30 c
c1 min 75 seconds
d50 days 2 months
e1800 seconds hour
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f Freezing point of water boiling point of water
3Arrange in an ascending order :
a 1 hours , 120 minutes , 3600 seconds.
..
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b day , 3600 seconds , 44 minutes , 1 week .
..
Unit 4 test
1complete each of the following:
a3 . 5 liters ...ml b2 . 37 tons ..Kg
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c1 hour .seconds
dWater freezes at ..c
e3000 gm .Kg.
2Choose the correct answer:
a 4000 gm Kg 4 , 40 , 400 , 40000
b Liter ml 25 , 250 , 2500
c Minute ..seconds 50 , 12 , 30 , 45
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d 18 hours day , , ,
e 1 . 5 tons ..Kg 15 , 150 , 1500
3aArrange in an ascending order :
Liter , 500 ml , 0.6 liters
bput the suitable sign , , :
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a1 liter , 50 ml 1.5 liters
b4 Kg 4000 gm
c1.3 tons 1.3 Kg
d2 hours , 20 min 100 min
e3 weeks , 4 days 25 days
4a worker earns L.E 5 . 5 for each working hour .if he spends 10 hours working
each day .calculate his earnings for
aOne day
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b15 days
cA month
dA year
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Lesson 1 : Collecting and representing data.
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Lesson 2 : Probability.
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Sheet 14
Lesson 1 , 2
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1There are 40 pupils in a class, 25 of them are girls .if a pupil is chosen
randomly then , find the probability that the pupil is
aA girl
bA boy
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2complete:
aThe probability of the impossible event is
bProbability of getting a tail when tossing a coin is .
cProbability of getting an odd number when rolling a die once is
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dThe probability of any possible event is between and
3 the following table shows the production of a car factory within 6 months in
hundreds.
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Month July Aug. Sep. Oct. Nov. Dec.
Number
of cars
4 5 3 6 2 5
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Represent these data by a histogram.
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Sheet 15
Lesson 1 , 2
1A die is rolled once , find the probability of getting :
aAn odd number
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bThe number 5
cA number less than 7
dA number more than 2
eA number more than 8
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2 A box contains 3 red balls , 5 blue balls and 4 green balls ,if a ball is chosen
at random , the find the probability that the ball is :
aRed
bYellow
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cGreen or red
dNot green
3 The table below represents money which Mona and sandy saved in three
months :
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Name month Jan. Feb. March
Mona 10 25 25
Sandy 20 15 25
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Represent these data by a double bar graph.
Unit 5 test
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130 cards are num bered from 1 to 30 .if a card is chosen at random then find
the probability that the number on this card is :
aEven
bDivisible by 5
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cBetween 10 and 15
dLess than 13
2Choose the correct answer:
aProbability of .event is 1 . possible , sure , impossible
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bWhen rolling a die once , then the probability of getting a number more
than 7 is . , 0 ,
cProbability of getting an even number when rolling a die once is .
. , , .
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3 The following table shows the marks obtained by Mohamed and salma in the
final exams:
Name Arabic Math science S.studies English
Subject