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MathematicsFifth Form Primary Second Term Unit 1: Numbers and operationsLesson 1 : The set of natural numbers Lesson 2 : Representing natural numbers on the number line Lesson 3 : Addition of natural numbers Lesson 4 : Subtraction of natural numbers Lesson 5 : Multiplication of natural numbers Lesson 6 : Division of natural numbers Unit 2: Equations and number patternsLesson 1 : Equations Lesson 2 : Number patterns Unit 3: GeometryLesson 1 : Graphing points and figures Lesson 2 : Geometric transformations Lesson 3 : Reflection Unit 4: MeasurementLesson 1 : Investigating circumference Lesson 2 : Area of a triangle Lesson 3 : Area of a parallelogram Lesson 4 : Area of a rhombus Lesson 5 : Area of a square Unit 5: StatisticsLesson 1 : Collecting and organizing data Lesson 2 : Displaying data Lesson 3 : Representing data by pie charts Lesson 4 : Reading and Interpreting data

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Lesson 1 : The set of natural numbers Set of Counting numbers C= { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , …………………}Set of natural numbers N = { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , …………………}Set of odd numbers O = { 1 , 3 , 5 , 7 , 9 , 1 1 , ……………………. }Set of even numbers E = { 0 , 2 , 4 , 6 , 8 , 10 , 12 , ………………..}

Set of prime numbers = { 2,3, 5,7,11,13,…………}

1)Complete:a) The least counting number is ------b) The least natural number is -------c) The least even natural number is ------d) The least prime natural number is ------e) The least odd natural number is ------

2Put suitable sign (

1 1.52 ……….. N 9 N - C ……….. { 0 }

2 { 0 } …………N 10 7………………. N

3 3 ……………. N 11 ………….. N

4 3.8 …………. N 12 { 19 } ……… N

5 4.5 …………. N 13 24/4 ……….. N

6 0.15 ……….. N 14 { 4 , 3 , 2 , 0.5 } { 2 , 1 , 0 ) ….. N

7 { 5 , 8 } { 4 , 9 }…. N

8 ( 7 , 9 , 11 , 3 } ……. N

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(3)Which of the following questions has answers of naturalnumbers.( a ) How many oranges are there in this basket?( b ) What is your weight in kilograms?( c ) How many cities are there in Egypt?( d ) How many pages are there in this story?( e ) How many metres is this tower high?(f)The number of students in your class.(g)The number of teachers in your school.(h)The number of your brothers.

(4)Underline the natural numbers from the following numbers:

15 - 6.2 - 0 - 417- 45 -0.7 - 9.1 - 328

- - 3

6 - 4.5 - - - 5¾ - 17 ¼ -

(5)State three things counted always by natural numbers.

(6)state three things may be counted not by natural numbers.

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Lesson 2

Using number line:

0 1 2 3 4 5 6the line is called number line

start from origin ( 0 )

then the number arranged in ascending order

note : there is no decimal or fraction in N

(1)Graph the following:( a ) 2 ( b )The natural number between the origin and 5( c) The natural number less than 5 but greater than 3( d) The number less than 3 ( e ) The natural number half way between 5 and 7( f ) The natural numbers less than 1

(2)Make graphs for each of the following. ( a) The even numbers between 2 and 6 ( b ) The number one - third of the way from 0 to 6(c ) The number one - fourth of the way from 1 to 9(d)Graphs the set of natural numbers greater than 4,(e){2 , 3}( f ) The set of natural numbers not less than 7 ( g ) The set of natural numbers divisible by 1( h ) The set of natural numbers equal to or greater than 5( i){3 , 4 , 5 , 6 , ...} (j){4 , 8 , 12 , 16 , ...}

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4)complete Using listing method :

a) Natural number greater than 5 and less than 9 .

N = {

b) Natural number not less than 7 .

N = {

C) Natural numbers between 7 and 9 .

N = {

d) Set of Natural numbers not less than 2 and not more than 7 .

N = {

e) Things counted by Natural Number =

f) Things not counted by Natural Numbers =

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Lesson 3

Addition of natural numbers

Operations On Natural Numbers

Addition Subtraction Multiplication Division

Properties of operations :

1- Closure : means possibility of operations to give a natural number

2- Commutation : means changing positions

3- Association : means doing operations in steps

4- Neutral element : means the element which does not affect the operation

5- Distribution : means simplifying operations

Remark : 1) natural numbers closed under addition and multiplication Ex: 3 + 5 = 8 N N + N = N 3 x 5 = 15 N

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2) natural numbers not closed under subtraction and division

1)Use the number line to add the following natural numbers.

a) 5 + 3 = ……b) 1 + 6 = ……c) 6 + 2 = .......

2)Complete :

(a) ………….+……….=………

(b) ……….+……….=………

(c) ……….+……..=….

( d) The sum of the two natural numbers 2 and .......... is 9, 9 is also a.......... number, then the sum of two natural numbers is a ..........

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1)Properties of addition of natural numbers

Complete the following mentioning property the:

a) a + b = b + …… ( ………………………………. Property )

b) 5 + …… = 5 ( ………………………………. Property )

c) ( a + b ) + …… = a + ( b + c ) ( ………………………………. Property )

d) (a + b) = ( b + a) ( ………………………………. Property )

e) (a + b) + c = a + ( b + c) = a + b + c ( ………………………………. Property )

f) (a + 0) = a = 0 + a ( ………………………………. Property )

g) 7 + 2 = 2 + 7 ( ………………………………. Property )

h) 7 + 1 = 1 + 7 ( ………………………………. Property )

i) (7 + 1) + 8 = 7 + (1 + 8) ( ………………………………. Property )

j) 7 + 0 = 7 ( ………………………………. Property )

k) 7 + 0 = 0 + 7 ( ………………………………. Property )

l) 17 + ....... = ....... + 17 = 17m)(6 + 8) + 9 = 6 + (....... + 9)n) (22 + .......) + 16 = 22 + (8 + 16)

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

a) 34 + 48 + 66=

b) 59 + 42 + 41 + 36 + 58=

c) 576 + 637 + 424 + 863=

d) 44 + 67 + 56 + 33=

e) 218 + 125 + 782 + 375 =

f) 572 + 324 + 176 + 447 + 428 + 253=

g) 53 + 28 + 47 =

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Lesson 4Subtraction of natural numbers

1)Mention, stating reasons, which of the following subtractions are possible in N.

a) 7 – 1

b) 5 – 9

c) 0 – 0

d) 1 – 11

e) 4 – 4

f) 3 – 8

______________________________________________________________2) Find:

a) (8 – 5) – 2

b) 8 – (5 – 2)

c) (12 – 7) – 3

d) 12 – (7 – 3)

____________________________________________________________

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3 Find if possible: a) 9 – 6 b) 6 – 9c) 8 – 5 d) 5 – 8

_________________________________________________________________4)Is the subtraction in N associative?___________________________________________________________________5)It the subtraction in N commutative?

Lesson 5

Multiplication of natural numbers

1)Complete :

a)

......x……..=…..

b)

......x……..=…..

c)

......x……..=…..

d)

......x……..=…..

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e)

......x……..=…..

2)Find the product using the number line (a ) 2 × .......... = 8

( b ) 3 × .......... = 6

( c )3× .......... = 12

( d ) 5 × .......... = 10

3)Completea) 3 × 5 = .... is the product a natural number?

b) 7 × 6 = .... is the product a natural number?

c) 4 × 5 =5 × 4 = ... (is called ……property)

d) (2 × 3) × 5 = 2 × (3 × 5) = .... ....(is called ……property)

e) 4 × 0 =5 × 0 = .... .... (is called ……property)

f) 7 × 1 = .... .... (is called ……property)

g) 8 × 1 = .... .... (is called ……property)

h) 3 × (6 + 2) = .... ( is called ……… property )

i) 7 × 0 =0 × 7 = ....... .... (is called ……property)

j) 9 × 1 = ....... ... (is called ……property)

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k) 73 × 1 = ....... (is called ……property)

l) (3 × 2) + (3 × 6) = ....... + ....... = ....... ....(is called ……property)

m)25x19 x 4x2 = ( ….. x ….. ) x ( …...x ….) = ……. X ……. = ……..

n) 27x17 + 27x13 = ….. x ( …… x …… ) ( is called ……. Property)

o) 3x …….= …. X 3 = 0 (is called …….. property )

p) 50x (12 + 18 ) = ….. x ….. + ……. X …….

Remember: 25 x 4 = 100 2 x 5 = 10

125 x 8 = 1000 10 x 10 = 100

99 = 100- 1 98 = 100 -2

101 = 100 + 1 234 = ( 200+ 30 +4 )

7)Use the distributive property of multiplication over additionand subtraction to simplify:

( a ) 25 × 742 =

( b ) 67 × 99=

( c ) 25 × 73 × 4 =

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( d ) 16 × 217 × 125 =

(e) 125x 234x8=

(f) )20x34x5=

(g) 250x45x40=

(i) 101x 34 =

(j)54x 98

(k) 4x8x25x125

Revision

1) Find the numbers that will make the following statements true:( a ) (12 × 4) × ........ = 12 × (4 × 7)( b ) ( ........ × 10) × 5 = 20 × (10 × 5)( c ) (20 × 50) × 30 = ........ × (50 × 30)( d ) 7 × (4 + ........) = 7 × 4 + 7 × 5( e ) 5 × (1 + 4) = 5 × ........ + 5 × ........( f ) 32 × 9 + 32 × 6 = ........ × ( ........ + ........)( g ) 50 × (11+ 17) = ........ × ........ + ........ × ........

2) Complete to get a correct statement :

a) ( 24 x 6) x…. = 24 x ( 6x 18 )

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b) 18 x ( 10 + …..) = 18 x 10 + 18 x 25

c) 101 x ( 200 + …..) = 101 x ….. + 101 x 23

d) 27 x 17 + 27 x 13 = ….. x ( ……+ ….. )

e) 34 x ( 18 + 12 ) = ….. x ….. + ….. x ……

Lesson 6Division of natural numbers

1) Divide:a) 15 ÷ 3 =b) 45 ÷ 9=c) 4 ÷ 16=d) 9 ÷ 45=e) 15 ÷ 3 = .... f) 17 ÷ 3 = ....g) 12 ÷ 5 = ....h) 4 ÷ 2 = ....i) 2 ÷ 4 = ....j) 5 ÷ 0 = ....

2)Does interchanging the dividend and divisor affect the quotient?

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3)Does the commutative property hold for division.

4)Which of the following statements are true?a) 17 ÷ 3 Nb) 12 ÷ 5 Nc) 4 ÷ 2 ≠ 2 ÷ 4d) 5 ÷ 0 is not defined

e) 49 ÷ 7 = 7 ÷ 49f) (75 ÷ 15) ÷ 5 = 75 ÷ (15 ÷ 5)g) 90 ÷ 15 = 15 ÷ 90h) (28 ÷ 6) N

5)Which of the following represents the number zero and which represents meaningless.

a) 0 ÷ 10 b) 14 – 14c) 90 ÷ 0d) 27 – 15e) 5 – 5

6)Find the value of (16 ÷ 8) ÷ 2, 16 ÷ (8 ÷ 2).7)Is the statement (16 ÷ 8) ÷ 2 = 16 ÷ (8 ÷ 2) true?8)Does the associative property hold for division?

General exercises on unit one

Revision 11)Name the property of addition and multiplication illustrated byeach of the following statements( a ) 2 + 3 = 3 + 2

( d ) 7 × 8 = 8 × 7

( c ) 3 + (2 + 5) = (3 + 2) + 5

( d ) 25 × 1 = 1 ×25 = 25

( e ) (9 × 4) × 3 = 9 × (4 × 3)

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( f ) 11 + 0 = 0 + 11 = 11

2)Complete:a) 36 × 173 + 36 × ......... = 36 × 300

b) 53 × 164 + 47 × ......... = 164 × 100

c) 177 × 13 – 13 × ......... = 150 × 13

d) 987 + 36 + 313 + 564 = 600 + 1000 + .........

3)Complete:a) 6 , 18 , 54 , ......... , .........

b) 2 , 8 , 32 , ......... , .....

c)1, 3, 5, 7, 9, ......... , ......... , ......... ,

d)5, 10, 15, 20, 25, 30, 35, …...... , …......

e)1, 2, 4, 7, 11, 16, ......... , ......... , .........

f)3 ,9 , 27,………….,……….,………….,…………

Revision sheet 21)Complete the following :

a. The additive neutral element in N is ……………….………… b. The multiplicative neutral element in N is ……………….………… c. { prime numbers } { even numbers } = ……………….………… d. x + y = y + x is called the ……………….………… Property in Ne. The set of natural numbers is closed under ………………… , …………

but not closed under ……….………… , …………………… f. 7 – x is possible in N only if x { ………….…………………… }

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g. 7 1 = …… …… is called the commutative property of multiplication in N h. ( …………… + 6 ) 2 = 8 2 + …… ……… (………………property)

2)STATE WHICH IS NOT ( TRUE ) IN THE FOLLOWING :1 Zero is the smallest natural number 9 0.5 N

2 division by zero has no meaning 10 (4-2) N

3 Set of natural numbers is closed under

subtraction

11 { 5 , 7 , 9 } N

4 ( 1 ) is the smallest prime number 12 { 0.5 , 7 , 9 } N

5 Addition is always possible in N 13 0 C

6 Every natural number has a natural number less

than it

14 { 0 } =

7 0 is neutral element of multiplication 15 { 8 } N

8 …………………… N 16 …………………… N

3) Put

a) 0 …. N

b) …..N

c) …. N

d) Set of digit of number 1133 ----N

e) …… N

f)

( Revision sheet 3 )

1) Complete :

a) 17 + ….. = ……+ 17 = 17

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b) ( 6 + 8) + 9 = 6+ (….. + 9 )

c) { 1, 2, 3, 4, 5, 6, ……..} is called set of …… numbers .

d) ……... is the multiplicative identity

e) The least natural number is ………

2) Choose :

a) 45 + 99 = 99 + 45 is …………. Property

( Commutative – associative – additive identity )

b) 3 + ( 2+ 5 ) = (3 + 2 ) +5 is ……… property

( Commutative – additive identity – associatve )

c) a + 0 = 0 + a = a is called ………

(Commutative – additive identity – associative )

d) …….. is the smallest odd number ( 0, 1 , 2 )

e) The additive neutral element in N is ……( 0,1,2 )

3) P UT

a) 1 – 11 ….. N

b) { 5 , 1.5 } …… N

c)

d) 5 } …..N

e) …N20

Unit two1-Tell whether the equation is true or false

1- X – 12 = 18 , x =30

2- Y + 15 = 22 , y = 37

3- 5 x y = 35 , y = 5

4- 44 - y = 11 , y = 55

5- 88 , x = 8

6- Z – 2 = 5 , z = 8

7- 2.13 x m = 4.26 , m = 2

8- 216

______________________________________

2- Solve the equation for the given replacement set .

1- 7 + x = 13 , { 2 , 3 , 6 }

2- 5 x y = 125 , { 10 , 25 , 30 }

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3- M , { 156 , 186 , 196 }

4- 42 x n = 294 , { 5 , 6 , 7 }

5- 15 – d = 7 , { 7 , 8 , 9 }

3- solve the equation. The replacement set is all odd whole numbers.

1- X- 2 = 5

2- X + 4 = 10

3- X – 11 = 25

4- 125

5- Y x 7 = 21

6- H + 5 = 8

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7- N

___________________________________________

4- solve the equation the replacement set is all even whole number

1- X – 8 = 12

2- Y + 14 = 27

3- M

4- 11 x m = 33

5- L

5-Find the missing number 1- ( 12 + 5 ) - ……… = 12

2- ( 14 + 7 ) - ……… = 723

3- ( 20 – 4 ) + …….. = 20

4- ( 40

5- ( 16 x 4 )

6- ( 13 m ) m

7- ( 25 x ) …….. = x

8- ( y + 20 ) - ……..= y

9- x ………. = 5

10- x ……. = 3

6) solve by using inverse operation

a. X - 5 = 15

b. X + 7 = 19

c. 2.5 + x = 8

i. 3 x = 18

d. 2 x =24

e. Y

f.

g. = 0

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7)Write the expression for each of the folowing (1) 2 less than a number

(2) sum of a numbers and three

(3) 4 more than a number

(4) The difference between a number and 7

(5) The product of 8 and a number

(6) Five decreased by twice a number

8)Write an equation for each of the following word sentence:

(1) The sum of a number and 5 is 15

(2) The difference of a number and 9 is 20

(3) The product of a number and 13 is 169

(4) The sum of twice a number and three is 17

(5) The difference of the number t and nine is fifty – four is 10

(6) Nine times a number X is 27

9)Complete:

(1) If the age of Mohamed is X then his age after 4 years will be…..

(2) If the age of Ali is y then his age 5 years ago was ………..

(3) The age of Ramy is X, his father age is twice his age then father age is ……………….

(4)The age of yousef is N, his cousine age is half as old as yousef, then the cousin 25

age is …………….

(5) If the length of rectangle is 20units and width is y units. The area of rectangle is ………….

(6) If a side of square is L units then its perimeter = ………….

(7) You buy 5 pencils at X P.T then the price of the pencils = …………….

(8) You buy 2 pencils at y P.T each and 4 rulers at x P.T each.

Then the total cost is ………….. P.T

10) find the value:

1) 2x +4 when x = 6

1) 5h – 7 when h = 5

3) 3y when y = 10

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General exercises on unit two

1-solve using replacement set

a)15-d=7 20 ,10,5

b)4x =12 2 , 3 , 4

c) 11-2 x = 1 2, 3, 4,5

2-Write an equation for each statements

a)Twice the number y increased by five………………….

b)Hatem is x years old then Hatem s age two years ago was ……………..

c)product of 6 and number y is 30 ……………

3-complete the sequence

a) 1 ,3 ,6 ,……….,……….,………,……….

b)3 , 9 , 27 , …….,……….,………,………

c)128 , 64 , ………..,……….,………….

4-Choose

a) 3,6,10,15 ,………...(21,18,19,20)

b) Y x 12 = 96 then y = ………..(10,9,8,7)

c) 3 subtracted from twice the numberχ =…….(χ-3 , 2χ-3,3χ+2 , 2χ)

d) 4less than half a numbe r is ……….(2χ-4 , 1/2χ-4, 4-1/2χ,4-2χ)

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Revision

1)Complete:

a) The neutral additive element in N is………….

b) If 3 x a =30 x 3 then a = …………….

c) The least natural number is ………….

d) Five decreased by a number k is ……….

e) (100x23)x……..=100x(23x105)

f) The neutral multiplicative element in N is …………

g) 4 less than half a number is …………..

h) 7x101=7(100x…..) (………………property)

i) (24x6)x…….=24x(6x18)

j) 91x(10+…..)=91x19+91x10

k) 27x17+27x13=……x(……+……)

l) Aman is χ years old now, then his age 8 years ago is ……………..m) If 19/χ=1 then χ =………..

n) 1,4,8,13……….,……..,……..(in same pattern)

o) K+0=k is called………………..property

p) 3χ =33 . χ € N Then χ = ……………..

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q) If’ χ = 3 Then 2 χ – 6 =……………

r) The value of 3 χ + 4 when χ = 3 equals ………..

s) If’ χ – 4 =6 then χ = ………..

t) Χ + 9 = 25 then χ = ……………

u) If’ y/18 =0 then y = …………

v) 3+(2+5) = (3+2)+5 (…………….property)

w) 35x185+35x……..=35x300

x) 43x186+57x…......=186x100

2-Complete the following using , , ,

a) zero/3………Nb) (10-10)……..Nc) (4 X 3-4 X 5)……..Nd) 9/7+8………...Ne) 44.4 4 ………...Nf) 357 …………...Ng) 0,1,1.5,2……..Nh) ……………….Ni) 7-17 is …………N

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UNIT 3

1) In the figure below, give the ordered pair for each letter in the graph.

2) In the figure below, represent the following points in the graph:

A= ( 6 , 7 ) , B= ( 6 , 4 )

C= ( 1 , 4 ) , D= ( 1 , 7 )

The figure ABCD is …………

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3) In the figure below,

a) What is the distance between :

(1) A and B ? ……… units

(2) A and E ? ……… units

(3) B and D ? ……… units

(4) D and C ? ……… units

b) Give coordinates of mid-point of line segment AB ( … , … )

c) Give coordinates of mid-point of line segment DC ( … , …

3b) Find : If A (3,6) and B(7,6)then the coordinate of mid point AB are (.....,....)

a)If A (6,4) and B(10,4)then the coordinate of mid point AB are (.....,....)

b)If A (0,5) and B(4,5)then the coordinate of mid point AB are (.....,....)

c) If A (1,3) and B(3,3)then the coordinate of mid point AB are (.....,....)

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4) Which of the following pairs of figures formed by connecting the points below are congruent? Graph each figure first.

a) Figure A :

( 2 , 2 ) , ( 2 , 8 ) , ( 5 , 2 ) , ( 2 , 2 )

Figure B :

( 5 , 4 ) , ( 5 , 10 ) , ( 8 , 4 ) , ( 5 , 4 )

b) Figure X

( 2 , 2 ) , ( 2 , 4 ) , ( 4 , 2 ) , ( 2 , 2 )

Figure y :

( 3 , 4 ) , ( 3 , 10 ) , ( 9 , 4 ) , ( 3 , 4 )

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5) Write whether each transformation is the result of a( flip , a slide , or a turn.)

a) b) c)

d) E) f)

____________________________________________________________________

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

a) ( 3 , 2 ) , ( 5 , 9 ) , ( 7 , 2 ) , ( 3 , 2 ) b) (2,3) ,(6,3), (7,7), (1,7) ,(2,3)

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__________________________________________________________

7) give the coordinates of the reflection image of the points X , Y , Z

8) In the figure below:

Draw a triangle which is the reflection image of the triangle ABC

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Unit (4)

The circumference of the circle

Notes:

a) The ratio between the circumference of a circle and its diameter =

cicumferencediameter

= 3.14 or

b) Circumference of the circle = x diameter C= x d = x 2r

1) a- Find the circumference of a circle its diameter = 10 cm ( =3.14)

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b- Find the circumference of a circle its radius = 6 cm ( =3.14)

2) Find the circumference to the nearest whole number “ =3.14”

d=4.2 cm r = 2cm r = 3 cm d = 40 mm

3) Find each circumference to the nearest whole numbe ( = )

a) d = 21 cm b) d = 42 cmc) r = 28 cmd) r = 42 cm

___________________________________________________________

4) Find each circumference to the nearest tenths ( =3.14)

a) d = 6.5 cm

b) r = 4.3 cm

c) d = 7.4 m

d) r = 32.5 mm

___________________________________________________________36

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Note: The circumference of half circle “semi circle” = r

____________________________________________________________

2) The figure represents a fence of a garden. The diameter is 20 m.

If one metre of the fence costs LE 10. Find the cost price of

the fence ( =3.14)

3) a- Calculate the perimeter of the figure if AB=AC=8 cm

and the diameter of the circle M= 7 cm

( = )

_______________________________________________________

b-Calculate the perimeter of the figure if AB=CD= 4cm,

BC = AD =3.5 cm ( = )

A

D C

__________________________________________________________

c- Calculate the perimeter of the opposite figure if ABC is an equilateral

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22

7A

C

B

M

22

7B

triangle with side length 7 cm ( = 227 )

c- A circle of circumference =44 cm. Find the length of its radius.

( = 227 )_______________________________________________________

4) If the half of the circumference of a circle = 314 cm, find its diameter

in meters. ( = 3.14)

Exercises

1) Complete:

a- The ratio between the circumference of a circle and its

diameter =…

b- The circumference of a circle whose diameter = 28 cm

= ……. ( = 227 )

c- If the circumference of a circle = 66 cm then the length

of its diameter= …..cm ( = 227 )

2) In the opposite figure:

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Calculate the perimeter of the quarter of the circle M where MA=MB= 7 cm, = 22

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3) In the opposite figure:

ABCD is a square its side length 3.5 cm. Calculate the perimeter of the figure.

Note :

The distance covered when the tyre makes a complete rotation = the

circumference of the tyre

______________________________________________________________

1) The radius of the tyre of a bicycle is 35 cm. Find the distance covered

when the tyre of the bicycle makes:

a- 10 complete rotations

b- 8 complete rotations

c- 15 complete rotations ( = )

_____________________________________________________________

2) Which is longer, the circumference of a circle of radius =3.5 cm or the 39

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AM

B

perimeter of rectangle 6.4 cm long and 4.5 cm wide

_____________________________________________________________

3)Find the difference between the circumferences of two circles

with radii 8.6 cm and 6.3 cm approximated to the nearest tenth. ( =3.14)

_____________________________________________________________

4) a- A circle of circumference 66 cm.

Find the length of its diameter. ( = )

b- A circle of circumference = 88 cm. Find the length of its radius. ( = 227 )

_____________________________________________________________

The area of triangle

Area of a triangle = 12 x base x height

Base = , h =

a- b- c-

8.6 cm

a- area of the triangle = 12 x b x h = 1

2 x 8.6 x 4.8 = … …cm2

40

4.8 cm

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7

4 cm

3 cm

8 cm

4 cm

b- Area of the triangle = 12 x b x h = …x.... x …. = .......cm2

c- Area of the triangle = …… x ….. x …..= … x... x...= ……cm2

______________________________________________________________________________________________

1) Find the area of each of the following triangles:

a- base = 8.6 cm and height = 4.2 cm

b- Base = 8 cm and height = 6 cm

c- Base = 4.7 cm and height = 4.2 cm

_________________________________________________________

2) Calculate the area of an equilateral triangle whose perimeter is 30 cm and its height is 6.8 cm .

___________________________________________________

3) Which is larger in area a garden in the shape of a triangle with base 10m and

height 8 m or a land in the shape of a rectangle with length 8 m and width =5m.

_____________________________________________________________ 5) Calculate the length of the base of the triangle whose area = 12 cm2

and its height = 4cm.

__________________________________________________________

6) Calculate the length of the height of a triangle whose area = 20cm2

and its base = 10 cm

__________________________________________________________41

7) Calculate the perimeter of the following triangle if its area= 24 cm2

10cm

_______________________________________________________

9) Calculate the area of equilateral triangle whose perimeter = 36cm and its height = 5.4 cm

10) In the figure opposite.XYZL is a rectangle of area 128cm2 and ZM = 10 cm. calculate

the area of LXMZ.

Area of parallelogram

Area of the parallelogram= base x height = b x h

Height = area ÷ base

Base = area ÷ height

1) 42

6 cm

b

h

b

h

3 m

6 m

Area = b x h area = b x h

= ….. x …..=….. = …. x ….=……

2) A parallelogram its area = 60 cm2 and its height = 6 cm. find the length

of its base.

3)A parallelogram its area = 90 cm2 and its base length = 10cm.

find the length of its height

___________________________________________________

4) ABCD is a parallelogram of area =375 cm2whose base is

25 cm. E is a point on CD. Find the area of the triangle AEB.

___________________________________________________

5) ABCD is a rectangle its width= 6 cm and its length = 10 cm. Find the area of the triangle DEC.

____________________________________________________

43

40 cm

60 cm

E

D C

BA

7) Find the area of triangle, then write down the area of the parallelogram

Area of rhombus

L=10 D1=12

H = 8 D2= 8

1

Area of the rhombus Area of the rhombus

= Side length x height = 12 x D1 xD2

= ………….. x ……= ……. = 12 x … x ….= …….cm2

Note: The side length of rhombus = area ÷ height

44

D1

D2

D2 =

1) The lengths of the diagonals of a rhombus are 12cm and 16cm. Find its area.

__________________________________________________

2) The lengths of the diagonals of a rhombus are 24cm and 10cm. Find its area.

___________________________________________________

3) The length of side of a rhombus = 10cm and its height = 4.5cm. Find its area.

_____________________________________________________

5) The length of side of a rhombus = 8cm and its height = 5cm. Find its area.

____________________________________________________

6) If the side length of a rhombus = 9cm and its area= 36cm2. Find the length of its height.

____________________________________________________

7) If the area of rhombus = 48cm2 and its height = 6cm. find its perimeter.

____________________________________________________

8) The lengths of the diagonals of a rhombus are 12cm and 16cm and its height is 9.8cm find its side length.____________________________________________________

45

9) The side length of a rhombus is 5cm, its height is 4.8cm and the length of one of its diagonals is 6cm. calculate the length of the other diagonal.

______________________________________________________

10) If the area of a rhombus =24cm2 and the length of one diagonal = 8 cm. Find the length of the other diagonal.

Area of the square

Area of square= Area of the square=

Side x Side=….. x …=…. cm2 12 x d x d= 1

2 x … x …=cm2

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

Note:

46

5 cm

3.5 cm

A) Area of square = 12 x d x d = 1

2 d2

d2= 2 x area

d = 2area

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

B) Area of square = side length x side length

Side length= area

( Exercise on area of square )

1) A square has area = 50 cm2. Find the length of its diagonals.

2) The diagonal of a square is 10 cm. find its area.

________________________________________________

3) A square its area= 72 cm2. Find the length of its diagonals.

_________________________________________________

4)The area of a square = 100 cm2. Find its perimeter.

5)Which is larger in area a piece of land in the shape of a triangle with base 10m and height 4m or a garden in the shape of a square of side length = 6m

47

6) The perimeter of square is 36 cm .find its area.

.

.

( Revision Test )

( Unit 4 )

1)Complete the following :

a) Area of the rhombus whose diagonals are 8cm , 6cm is….

b) Area of the triangle whose base is 10 cm , height 6cm is…

c) Circumference of the circle of radius 7cm is… .

d) Area of the square whose perimeter is 20cm is….

2)(a) find perimeter of the shown figure :

Where AC is the diameter of the semi- circle , =

(b) Area of triangle is 40 its base is 10 cm , then find its height .

48

C

9cm

A 9cm B

3)Which is greater in area : a rhombus with diagonals 11 cm ,8 cm or area of the triangle whose base is 12 cm and height 7 cm ?

4)A square and a parallelogram are equal in area. If the base of the parallelogram is 10 cm, its height is 4.9 cm, then find perimeter of the square .

Unit ( 5 ) Lesson 1

Collecting and organizing data

A frequency table: shows the number of times each piece of data occurs. Problems:

1-   The number of letters in each of the first twenty-five words of a

story is shown opposite. Make a frequency table.

6   3  4  2  3  5  3  3  7  3  43  3  4  3  3  3  6  6  6  3  5

3  2  3  7  549

14 cm

2-  50 students were surveyed about the number of books they had

read in a year. This table was produced.

6  3  4  5  6  8  4  3  5  2   5  4  6  3  9  3  4  2  3  2  5  6  8  4  5 

 Draw a frequency table.

3- complete the table for this set of number :

4  2  1  5  2  4  1  5  2 4  1  1

 

number      1      2      4       5Tally      ⁄⁄⁄⁄    ⁄⁄⁄    frequency     4     3    

 

1) The following table shows the maximum temperature degrees registered in some Arabic capitals:

Temperature 18 19 20 21 22 23No. of capitals 3 2 4 6 2 1

Represent this table by histogram.

__________________________________________50

51

52

Lesson 3

(Representing data by pie chart)

(1) Ali had LE. 1200, he divided them among his brother and three sisters.

The following table shows the amount of money each of them received

Represent these data by a pie chart.

DinaAmalMonaBrother14

13

16

14

_______________________________________________________________

(2) The following table shows how Ahmed spent his money on the market

ApplesOrangesRice300300200

(a) Represent these data by a pie chart.

(b)What did he spend least of his money on?

53

(3) The following table shows the distribution of pupils in a primary school according to the four classes' grades

FourthThirdSecondFirst150200300150

(a) Represent these data by a pie chart.

(b) What is the fraction of grade 3?

_______________________________________________________________

(4) As asking a pupil in the class about his favorite TV programs,we obtained

the following results

NewsMusicSportsCulture44168

(a) Represent these data by a pie chart.

54

The following graph shows the marks of 30 pupils in an examination.

02468

10121416

1 2 3 4 5 6

The mark

Number ofpupils

(1)What was the mark which the greatest number of pupils has got?

(2) What was the mark which the least number of pupils has got?

(3)What was the difference between number of pupils that have got the mark 7 and those that have got the mark 10?

55

Lesson (4)

The opposite graph represents the sales in a company in six months

1) When were the least sales?

2) When were the greatest sales?

3) How much money did the company collect in March?

4) In which two months the sales were the same?

56

3) The following pie chart represents the profit of a company

in thousand pounds with in 2003 to 2006

(1) What was the year with the most profit?

(2) What was the year with the least profit?

(3) What was the difference between the profit in 2005 and the profit in 2006?

57

( Final revision )

1) Complete :

a) The area of parallelogram = ……

b) If 9 x 23 = 23 x h , then h = …….

c) 1 , 4 , 8 ,13 ,….., …….., ……..

d) If c( 7, 2 ) , D ( 7, 8 ) , then coordinate of mid point of CD are

( …… , …….)

e) Area of rhombus = ……

f) ( 12 x ….) x k =12x ( h x …..)

g) The multiplicative identity element in N is …..

h) The area of square is 72 the length of its diagonal is……

i) X + 24 = 50 then X =…

58

j) The circumference of circle with diameter = 28 cm is …..

k) 12 x 25 x4 x 7 = (…. X ….) x (…..x ……)

l) 6 x ( 14 + 20 ) = ….. x ….. + ….. x …… ( …………….. property )

m) The perimeter in equilateral triangle = 27 cm , height = 10 cm then the area of the triangle = …

2) Choose :

1) Ahmed age is y years old then his age after 5 years will be

( y + 5 , y – 5 , 5y )

2) 3 x ( 2 + …..) = 24 ( 2 or 3 or 6 or 8 )

3) = …… ( 6 , , 0 , meaningless )

4) 5 f = 25 , then f = ….. ( 10 , 5 , 15 , 1 )

5) Fifteen is three less than a number = ……

59

( 15 = 3- n , 15 = n- 3 , 15 – 3 = n , 3 – 15 = n )

6) The area of rhombus with diagonals are 10 cm , 16 cm is …

( 96 cm , 160 cm ,60 cm , 80

7) ( 4 x 28 ) x 25 = 28 x ( ….x 25 )

( Commutative - Distributive property )

8) The additive identity element in N is ( 1 , 0 , 2 )

9) 987 + 36 + 564 = 600 + 1000 +…..

( 15 – 13 - 20 - 23 )

10) The area of parallel gram is 100 , base = 5cm then the

Height = ( 15 cm – 1o cm – 2ocm ) .

4) Use the properties :

60

a) 132 x 125 x 8

= ….

= ….

= ….

b) 53 x 99

= …..

= …..

= …..

c) 76 + 15 + 85 + 24

= …...

= …..

= …..

5) Diameter of a tyre is 88 cm .find distance after 20 rotations .

= …..

6) If circumference = 66 cm .find the radius .

= ….

7) Calculate the area in equilateral triangle , if perimeter = 30 cm , h = 4 cm .

= ……

61

8) Find area of square with perimeter = 25 cm .

= …..

62