المراجعة النهائية فى الماث للشهادة الابتدائية الترم...

1

Math Student's Copy Book Date: -- / -- / 20--

Day: Date: -- / -- / 14--

AL KAMAL AZHARIAN INSTITUTES Primary Six First Term

Revision on

Simplifying the fraction and divisibility

Example (1): Write a number formed from two digits and divisible by two

Example (2): Put a circle around the number that divisible by two and

underline on the number divisible by 3

1324 , 231 , 324 , 380

Drill: Write three whole number divisible by 5

, ,

Example (3): Simplify into simplest form:

a) =

b) = =

c) =

d) =

Remember

1) The numbers that divisible by 2 is the numbers that its unite is (0, 2, 4, 6, 8).

2) The numbers that divisible by 5 is the numbers that unite is (0 , 5)

3) The numbers that divisible by 3 is the numbers that its sum is divisible by 3

(from the multiples of 3)

18

27

..

..

420

490

..

..

13

12

..

..

41

205

..

..

Remember

The prime numbers that

numbers have two

factors

288

120

2

Math Student's Copy Book


Write the prime numbers between 1 , 50

The prime numbers is:

..................................................................................................................................................................................................

..................................................................................................................................................................................................

......................................................................................................................... .........................................................................

..................................................................................................................................................................................................

............................................................................................................................. .....................................................................

Evaluation:

1) Simplify:

a) =

b) =

2) Write 5 numbers divisible by 2 of 5 together:

, , , ,

Drill:

1) Write 3 number divisible by 2 of 3 together:

, ,

2) Write number divisible by 2 of 3 together:

3) Simplify:

a) =

b) =

a) =

Think

72

84

..

..

5

10

..

..

7

21

..

..

16

32

..

..

18

27

..

..

150

450

..

..

3


Day: Date: -- / -- / 14--


Unit (1)

Lesson (1) The meaning of ratio

Ratio: Is comparing between two quantities or numbers as the same type and

same unite.

Example (1): Huda has 20 pound and Yasmin has 40 pounds compare

between them.

Solution:

= = =

and we write it 1 : 2 and we read it 1 to Z

Example (2): Find the ration between two numbers in simplest form 64 , 48

Solution:

1st number : 2

nd number

48 : 64 ( 2)

24 : 32 ( 4)

6 : 8 ( 2)

3 : 4

another solution:

= = = = =

and we write it 1 : 2 and we read it 1 to Z

Example: Complete: The ration between two numbers =

Drill: Find the ratio between two numbers of the following:

a) 16 , 32 b) 150 , 450 c) 34 , 102

: ...... ...... : 2nd number 1st number :2nd number 1st number : ...... ...... : ...... ...... : 32 16 : ...... ...... : ...... ...... : ...... ...... : ...... ...... : ...... ...... : ...... ......

H.W: P.B P.5 no. 1 , 2 , 3

Definitions:

What with Huda

What with Yasmin

205

20

40

2

4

1

2

Simplest

form

1st number

2nd

number What with

Yasmin

205

48

64

24

32

6

8

3

4

1st term

(antecedent)

(consequent)

....

....

4



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Day: Date: -- / -- / 14--


Exercises on

The meaning of ratio Example: Find the ratio between two numbers 16 , 40 then determine

antecedent and the consequent.

Solution: .............................................................................................................................................................................................................

.............................................................................................................................................................................................................

.............................................................................................................................................................................................................

Example (1): In one of the classes of the first grade primary the number of boys is 15 pupils and the number of girls is 20 pupils. Calculate:

1) The ratio between the number of boys and the number of girls. 2) The ratio between the number of girls and the number of all pupils in the

class.

Solution: - Number of girls = 25 girl - Number of boy = 15 boy - The number of pupils = 25 + 15 = 40 pupils 1) Number of boys : number of girls

................................................. : ............................................. ................................................. : .............................................

2) Number of boys : number of pupils ................................................. : ............................................. ................................................. : .............................................

Example (2): Find the ration between 2.3 , 5.75

Solution: 1st number : 2nd number 2.3 : 5.75

. : ..

. : ..

. : ..

. : ..

Example (3): If the number of sum pupils in school is 540 pupil, the number of boys is 405 pupil. Find:

1) The ratio between the number of boys 2) The ratio between number of boys and the number of girls in two ways: and the number of pupils: ... ..

... ..

... ..

H.W: P.B P.5 no. 4 , 5 , 6 , 7

6



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Day: Date: -- / -- / 14--


Lesson (2) The properties of ratio

- Ton = 1000 kgm - Pound = 100 piasters

- Kg = 1000 gm - metre = 100 cm

- (feddan kirate sahm) are units of cultivated lands.

feddan = 24 Kirat kirat = 24 sahm

Properties of ratio:

- Property 1: The ratio has the same properties of the fraction as reduction, simplifying and comparison.

- Property 2: in its simplest form, the two terms of the ratio should be two whole numbers.

- Property 3: At comparing two quantities of the same type to form the ratio between them, they must have the same unit.

- Property 4: The ratio between two quantities of the same kind doesn't have any units.

- Property 5: The ratio keeps the order.

Example (1) : Find the ratio between:

a) 1 : 2.2 (convert into decimal number)

1.6 : 2.2 ( 10 the two terms)

16 : 22 ( )

.. :

b) Two areas 0.75 kirats, 16 sahm

convert 0.75 kirats = 0.75 24 = 18 sahm

1st area : 2

nd area

18 : 16 (2)

9 : 8

c) :

3

5

Definitions:

Remember

1

2

3

4

8



4 : 6 (2)

2 : 3

Example (2)

A rectangle its length 30 cm and width is 18 cm. Find the ratio between

perimeter of rectangle and its length.

Solution:

Perimeter of rectangle = (length + width) 2

= (30 + 18) 2

= 48 2 = 96 cm

Perimeter of rectangle : length

96 : 30

... : ..

... : ..

Drill:

Find the ratio between two amounts:

250 P.T : 7 pounds

Solution:

.. : ..

.. : ..

.. : ..

.. : ..

H.W: P.B P.9 no. 1 , 2 , 3

1

2

9


Day: Date: -- / -- / 14--


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Day: Date: -- / -- / 14--


Exercises on

Properties of ratio 1) Circumference of the circle = 2r 2) Perimeter of equilateral triangle = side length.

Complete: a) Perimeter of square = b) The diameter of circle =

Example 1: Find the ratio between the perimeter of square and its length.

Solution: perimeter : side length side length 4 : side length 4 : 1

Drill 1:Find the ratio between the perimeter of equilateral triangle and its side length.

Solution: ............................................................................................................................................................................................ ..............................................................................................................................................................................................................................

..............................................................................................................................................................................................................................

Example 2: Find the ratio between the circumference of the circle and its radius.

Solution: ............................................................................................................................................................................................ ..............................................................................................................................................................................................................................

..............................................................................................................................................................................................................................

Drill 2: Find the ratio between the circumference of the circle and its diameter.

Solution: ............................................................................................................................................................................................ ..............................................................................................................................................................................................................................

..............................................................................................................................................................................................................................

Example 3: A rectangle its area is 32 cm2 and its width is 4cm find: 1) Length of rectangle. 2) The ratio between the length and width of rectangle.

Solution: ............................................................................................................................................................................................ ..............................................................................................................................................................................................................................

..............................................................................................................................................................................................................................

Drill 3: Complete:

1) The ratio between side length of square and its perimeter = .... : ....

2) The ratio between the two side lengths of square = . : .

3) The ratio between the radius of circle and its circumference = .. : ....

H.W: P.B P.9 no. 4 , 5 / P.10 no. 6 , 7 , 8

Remember

12



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13


Day: Date: -- / -- / 14--


Lesson (3) Miscellaneous exercises

on ratio and its properties

Example (1): Find the ratio between 1 , 3

Solution:

1 : 3

: = = = =

= 1 : 2

Example (2): If the ratio between the weight of Hani to the weight of Ahmed is 5 : 6 and the weight of Ahmed is 72 kgm.

Find the weight of Hani.

Solution: Hani weight : Ahmed weight

5 : 6 parts

. : 72 real value

The value of one part = 72 6 = 12 kg.

The weight of Hani = 12 5 = 50 kg.

Example (2): A primary school has 540 pupils, if the ration between the number of boys to the number of girls is 4 : 5

Calculate the number of each boys and girls.

Solution: Number of boys : number of girls : sum 4 : 5 : 9 . : : 540

The value of one part = 540 9 = 60 pupils The number of boys = 4 60 = 240 boys. The number of boys = 5 60 = 300 girls Chick the solution: Sum = 240 + 300 = 540 pupils.

Drill (2): If the ratio between the weight of (Samia) to the weight of (Seham) is 7 : 5 and the difference between the weights is 9.6 kg. Find the weight of each of them.

Solution: Samia weight : Seham weight : . .. : ... : ..... .. : ... : ..... .. : ... : .....

H.W: P.B P.14 no. 1 , 2 , 5

To convert the mixed number into improper

fraction 1 = (14)+3= 4+3= 7

7

4

3

4

3 4

1 2

3 4

1 2

7 4

7 2

7 4

7 2

7 4

7 2

14 28

1 2

14



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15


Day: Date: -- / -- / 14--


Exercises on The ratio and its proprrties

Complete: a) One hour = ... minutes. b) One day = . hours. c) Perimeter of rectangle = .. Drill (1): Find the ratio between:

a) 8 hours , 2 days b) 18 : 6.3

Solution Solution ....................................................................................................... ..................................................................................... ............................................... ............................................................................................................................................. ....................................................................................................................................... ..................................................... ........................ ............................................................................... ..................................................................................... ............................................... .............................................................................................................................................

Drill (2): A piece of land is a shape of rectangle the ratio between its dimension 4 : 7 and its perimeter is 44 meter.

Find the area of land.

Solution: ............................................................................................................................................................................................

..............................................................................................................................................................................................................................

..............................................................................................................................................................................................................................

..............................................................................................................................................................................................................................

..............................................................................................................................................................................................................................

Drill (3): The ration between the heights of two buildings in a town is 4 : 7 if the difference between their in 9 meters.

Find the height of each of them.

Solution: ............................................................................................................................................................................................

..............................................................................................................................................................................................................................

..............................................................................................................................................................................................................................

..............................................................................................................................................................................................................................

..............................................................................................................................................................................................................................

H.W: P.B P.14 no. 3 , 4 , 6

16



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17


Day: Date: -- / -- / 14--


Lesson (4)

Ratio among three numbers

Complete: 1) If A is half B then A : B = : .. 2) If A is double B then A : B = : ..

Example (1): Three persons start commerce the first paid 400 pounds, the second paid 600 pounds and the third paid 1000 pounds.

Find the ration between them.

Solution

1st : 2

nd : 3

rd

400 : 600 : 1000 (100)

4 : 6 : 10 (100)

2 : 3 : 5

Example (2): a , b and c are three numbers such that the ration a : b = 4 : 3 and the ratio b : c = 2 : 3

Find the ratio among the three numbers a , b and c.

Solution: A : B : C

4 : 3 : ..

. : 2 : 3

. : .. :

Drill (1): Find the ratio between 0.5 , , 0.125

Solution: 0.5 : : 0.125

0.5 : 0.25 : 0.125

Drill (2): If A : B = 2 : 3 , B : C = 6 : 5 , Find A : B : C

Solution: A : B : C

H.W: P.B P.18 no. 2 , 5

1 4

18



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19


Day: Date: -- / -- / 14--


Exercises on The ratio among three numbers

Complete: a) If A is third B then A : B = : ..

b) If A : B = 5 : 6 , B : C = 8 : 9 then A : B : C = .. : : ..

Solution

.

.

.

.

Drill (1): Amount of money distributes between (Ahmed) , (Ali) and (Tarek)

as the ratio 2 : 5 : 3 if the money with Ali more than the money with

(Ahmed) by 45 pounds. Find the money with each of them and the

total money.

Solution .

.

.

.

.

.

.

.

20



Remember The sum of

interior angles of triangle is

180

Drill (2): If the ratio between the measures of the angles of triangle is 5 : 6 : 7

and the measure. Find the measure of each of angle and find the

type of triangle according to its angles.

Solution

.

.

...

...

Drill (3): If A, B , C are three numbers if A = B , and A = C

Find the ratio between A : B : C.

Solution: A : B : C

.

.

.

.

.

Drill (4): The ratio between the side lengths of triangle is 2 : 3 : 4 if the

perimeter is 54 cm.

Find the lengths of each of side.

Solution

.

.

.

.

.

5 3

10 7

21


Day: Date: -- / -- / 14--


H.W: P.B P.18 no. 1 , 3 , 4 , 6

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23


Day: Date: -- / -- / 14--


Lesson (5) Ratio Applications (Rates)

The rate is: The ratio between two quantities of different kinds and the unit of rate is the

unit of the first quantity per each unit of the second quantity.

Example (1): A factory produces 3000 lamps in 4 hours. Find the rate of production.

Solution

Rate = = 750 lamp / hour

(we read it 750 lamps per hour)

Drill (1): A car consumes 20 liters of petrol to cover a distance 350 km. Calculate: the rate of consumption of the car to benzene.

Solution .

.

Drill (2): Two machines the first produces 3000 meters of cloth in 4 hours and the second produces 2520 meter in three hours and half.

What is more efficient?

Solution .

.

Drill (3): A factory produces 5000 cans in 8 hours. Find the rate.

Solution .

.

Drill (4): A car covers a distance 250 km in 5 hours. Find the velocity (speed)

Solution .

.

3000 lamp 4 hours

3

24



H.W: P.B P.20

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25


Day: Date: -- / -- / 14--


General Revision on Unit (1) Drill (1): Find the ration between:

a) 1 : 2.2 b) 0.75 kirat , 16 sahm, ...................................................................................................................................................................................................................................................................................................... .......................................................................................................................................................................................................................... ............................

...................................................................................................................................................................................................................................................................................................... .......................................................................................................................................................................................................................... ............................ ...................................................................................................................................................................................................................................................................................................... .......................................................................................................................................................................................................................... ............................

c) 250 p.t : 7 pounds d) 5 : 14.5 ...................................................................................................................................................................................................................................................................................................... .......................................................................................................................................................................................................................... ............................ ...................................................................................................................................................................................................................................................................................................... .......................................................................................................................................................................................................................... ............................ ...................................................................................................................................................................................................................................................................................................... .......................................................................................................................................................................................................................... ............................

Drill (2): Find the ration between: Divide 150 pounds between two persons such that the share of the first =

the share of the second. Find the share of each of them. ................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................ .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................ ................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... ............................

................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... ............................ Drill (3): Find the ration between: If the weight of (Aya) = (Mona) weight, and (Mona) weight = (Arwa)

weight. Find the weight of each of them If Arwa weight more than (Aya)

weight by 24.1 kgm. ................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................

.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................ ................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................

.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................ ................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... ............................

.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................

Drill (4): A piece of land in a shape of rectangle the ration between its length to width is 5 : 3, If the perimeter is 64 meter. Find the area of land.

................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................ .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................

................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... ............................

................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... ............................

3

5

9

4

2

3

4

3

4

4

2

3

4

26



H.W: P.B P.24

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27


Day: Date: -- / -- / 14--


Unit (2)

Lesson (1) The meaning of proportion

The proportion is: The equality of two ratios or more.

Complete:

1) = =

2) = =

Example (1): Complete the table:

a) = = 6

b) 8 = 8 = = 12

From the table we deduce

= =

We consider the number 3 , 2 , 9 , 16 , 12 , 8 proportional numbers

Drill (1):

a) = = =

b) = =

27

..

3

2

.

6

16

..

4

3

.

21

2

3

1

9

1

1

18

3

2

3

1

3

2 24

2

..

8

9

.. 3

2

18

4

3 12

9

..

3

12 .

4

20

3 9 ... 15 ... 2 ... 8 ... 12

2

3 2

3

28



H.W: P.B P.28 ----------------------------------------------------------------------------------------------------------------------------- ---------------------

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Day: Date: -- / -- / 14--


Lesson (2)

The properties of proportion Properties of proportion: Property (1): If we multiply (or divide) each of the two terms of ratio by the

same non-zero number, then resultant ratio is equal to the first ratio and they

together form a proportion.

Property (2): The product of extremes = the product of means.

Example (1): Complete:

1) = 2) =

Solution

1) = 2) =

Example (2): Complete:

=

Notice that: 3 , 5 , 12 , 20

3 20 = 60 (the product of extremes) 5 12 = 60 (the product of means) Example (3): Find the value of X in the following proportion:

a) = b) X , 7 , 24 , 56

= X =

X = = 3 X = 120

Example (4): Find the 3rd proportion of the following 1.8 , 1.5 , 3

1.8 , 1.5 , X , 3

= X = = = 3.6

means

Extremes

12

..

3

5

3

21 1

..

4 3

5 12

20

11

4

3 3

21 1

7

11

3

12

20

3

5

3

24 15

X

X

7 24

56 7 24

56

24 15

3

1.8

1.5

X

3 1.8 3

1.5

5.4

1.5

30



Drill (1): Find the fourth proportion for the following 6 , 4 , 8 , 15

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H.W: P.B P.33 no.1 , 2 ------------------------------------------------------------------------------------------------------------------------------------------------ --

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Day: Date: -- / -- / 14--


(Follow) Lesson (2)

The properties of proportion Example (1): Find the value of X in the following proportion:

1) = 0.8

Solution =

X + 3 =

X + 3 = 4 X = 4 3 X = 1

Example (2): To make fig jam we need 4.8 kgm from sugar to 6 kgm from fig. Find:

1) How many kilograms of sugar added to 15 kgm of fig? 2) How many kilograms of fig added to 14.4 kgm of sugar?

1) Solution 2)

The weight of sugar X = = 12 kgm The weight of fig = X = = 18 kgm

Drill (1): A car needs 14 liter of benzene to cover a distance 175 km.

How many kilometers a care covered if it uses 20 liters?

Solution

Drill (2): Find the value of X in the following proportion =

Solution: -------------------------------------------------------------------------------------------------------------------------

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

Weight of fig 6 15

Weight of sugar 4.8 X

Weight of fig 6 X

Weight of sugar 4.8 14.4

distance 175 ..

liters . .

8

10

X + 3

5

4.8 15

6

X + 3

5 5 8

10

14.4 6

4.8

2 X

12

5

2

The distance =

32



Drill (3): A primary school, its building height is 14 meter and the shade of

this building at a certain moment is 5 m length. What is the height of a tree in

the same moment if its shade length is 3 meters?

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H.W: P.B P.33 no.3 , 4 ----------------------------------------------------------------------------------------------------------------------------- ---------------------

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Day: Date: -- / -- / 14--


Lesson (3)

Drawing Scale

Drawing Scale =

Kilometer = 1000 meter

Meter = 100 cm

Kilometer = 100000 cm

Example (1):

The height of Cairo tower in image 12 cm and the real height 180

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