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Cairo Governorate Department : Maths Nozha Directorate of Education Form : 1st.Prep. Nozha Language Schools Revision Sheet “Ismailia Road” Branch

Exercise (1)

1-Complete each of the following : 1) Each integer is …………………….

2) Zero is neither …………………. rational number nor ……………. rational number.

3) If ba is rational , then b ≠ …………….

4) If a5 is rational number , then a ≠ ………………

5) The number 3

4−X

is rational number if X ≠ ………………..

6) The number 55

−+

XX is rational number if X ≠ …………………

7) The number X52 is rational number if X ≠ ………………..

8) The rational number 4

5−−XX = O if X = ………………..

9) The rational number XX 4− = O if X = ………………

10) - 54 =

X20 , then X = …………………

2-Choose the correct answer from the given ones :

1) The number 76

−−aa is not a rational number if a

a) 7 b) – 7 c) 4 d) zero

2) The rational number ba is an integer if …………….

a) a < b b) a > b c) b is a Divisible of a d) a is Divisor of b

3) Express of 0.57 as a rational number in simplest form

a) 10057 b)

9975 c)

1000575 d)

3319

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4) The rational number | 25

8− | = ………………

a) 25

8− b) – 0.32 c) 0.32 d) 32 %

5) The number 12 % ………………….

a) 0.3 b) 1.2 c) 253 d) 0.012

6) The rational number 4−X is negative if X …………………..

a) > zero b)< zero c) ≥ zero d) = zero

7) If - 254 =

X20 , then X = …………….

a) 25 b) -25 c) 5 d) 100

8) If ba is rational number and a b = zero then ………………….

a) a = O , b ≠ O b) O ≠ , b ≠ O c) a = O , b = O d) a ≠ O , b = O

9) The number 5

6−|| XX ……………

a) ± 5 b) 5 c) – 1 d) – 2

3- If X ∈ N find the value of X which make each of the following an integer .

a) X75 b)

215+X

c) X3

37

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Sheet ( 2)

1- Represent each of the following on he number line :

a) 47− b) 1

51 c)

21−

2- Write the correct sign ( < , = or > ) :

1) 21− ……………… zero 2) – 4

21 ……….. – 5

3) |2

15 | ……………. 7 21 4) |

−|

213 ……….. 6

21

5) 39− ………… - 3 6)

54− …..…….

56−

7) 1.6 ………… |−|

58 8) 0.5 ………0.5

3- Write two rational number lying between

1) 31 and

54 2)

21− and 1 3) 0.3 and

54

4- Choose the correct answer :-

1) Between each two successive integers there is ………..

a) unique rational number b) an infinite number of rational numbers

c) one integer only d) an infinite number of intergers

2) The opposite rational number to the rational 31 on the number line is .

a) 31− b)

32 c) 1 d)

33

3) The rational number which between 43 and

54 is

a) 4030 b)

205.15 c)

401 d)

2016

4) The number of integers lying between 75 and

118

a) two only b) only one c) no one d) an infinite

5) Which of the following fraction is the closest to 0.035 numerically ?

a) three fifths b) one half c) one third d) one fourth

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Sheet (3)

1- Complete :-

1) The additive identity element in Q is ……………

2) The additive inverse of no. 53 is ……………….

3) The additive inverse of no . 74− is …………..

4) The additive inverse of no . zero)32( is …………..

5) The additive inverse of no. |−|

54 is …………..

6) The additive inverse of number zero is …………..

7) The additive inverse of the number – 0.5 is ………

2- Calculate the value of each of following in its simplest form :

a) 73 − (

52− ) b)

54 −

43

c) 10019 + (

10049− ) d)

52− −

152

e) 41 + 2

83 f) 2

83 -

41

g) 6 32 - 3

61 h) -2 + 13

73

i) 32 - 0.3 n) 0.18 – 30 %

m) 25 % + 41 O)

73− +

21 + ( -

141 )

3) If X = 65 , Y =

31− and Z =

21 find

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Simplest form :

a) X + Z b) X – Y

c) ( Y + Z ) d) ( X + Y) – Z

4) If a = 21 , b =

23− find the vaule of ( a – b )4 , ( a – b )5

5) Complete :

1) The remainder of subtracting 51 from

56 equals ……………

2) The remainder of subtracting 31 from

34− is ………..

3) The remainder of subtracting 81 from zero equals ……….

4) The remainder of subtracting 23− from zero equals …………

5) A + 87 = Zero then A = …………..

6) If ( A + 41 ) is additive inverse of the number

43 then A = …………

7) If X = 2 , Y = 3 and Z = 4 then YX -

XZ = …………..

6- Use the number line to find the result of the following :-

a) 51 +

52 b)

75 –

73

c) 31− +

37 d)

53− + ( -

51 )

7- Using the addition properties in

a) 85 + (

43− ) +

83 +

43 b) 7

41 + ( - 11

41 )

c) 72 +

43 +

75 d)

32 +

54 +

43

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Sheet ( 4 )

1- Complete :

1) The multiplicative Identity of the rational no . is ……………

2) The multiplicative inverse of no . 73 is ……………….

3) The multiplicative inverse of no . 94− is …………

4) The multiplicative inverse of ( 53− ) zero is ………….

5) The multiplicative inverse 0.7 is ……………..

6) The rational number 5

1−a has a multiplicative inverse if a ≠…………

7) The rational number which has no multiplicative inverse is ………….

8) 32 × (

54− ) =

54− × …………

9) 54− × ……….. =

54

10) 2 53 ………….. = 1

11) If ba = 80 , then

bX2

= ………….

12) If YX =

32 then

YX

23 = ………….

8

7- Using properties to simplify following :

1) 21 × |- 12 | 2)

32 ×

43 ×

54 × ……….×

5150

3) Zero ÷ 53 = 4)

125 × 3 +

125 × 9

5) 376 × 7 +

376 × 5 +

376 × ( - 11 )

6) 1127 ×

49 -

1127 ×

41 +

1127 × 9

7) 73− × 8 + 5 × (

73− ) +

73 × 9

8) - 85 ÷ (

43 +

21 -

31 )

4- Find the value of (n) in each of following :-

a) 37− × (

73− ) = n

b) 35− × n = 0

c) 73 × n =

73 × (

54− )

d) n × 3

19 = 1

e) 95 × n =

95

9

g) n × [ 21 + (

53− ) ] = n ×

21 + 5 × (

53− )

5- If X = 23 , Y =

41− and Z = -2 find following :

a) XYZ

1 b) YX -

YZ

c) X – ( 2 ÷ Y ) d) ( X + Z ) ÷ ( Y – Z )

6) Find the national no . lying between middle between :-

a) 83 ,

85 b)

21− ,

43−

c) 0.1 , - 52− d) zero ,

52

7- Find the rational number lying at :

a) One fourth of way between 75 ,

73−

b) One tenth of way between 21− ,

53−

c) One eighth f the way zero , - 1 21

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Unit Two

1- Complete :

1) The degree of term 3 X2 Y is ………………….. its coefficient is ………….

2) The coefficient of the algebraic term 32 X4YZ3 is ……………. and its degree is ……..

3) The degree of the absolute term in algebraic expression is …………

4) The coefficient of the algebraic term ( -2)3 is …………… and its degree is ………….

5) 5X2 + 3 is an algebraic expression of the ……………… degree …………

6) The number of terms of the algebraic expression : 5Y2 – 3 X Y + 2 X2 is ………….and

its degree is …………..

7) – 3 a5 b number of terms ………………… , name is ……………… , degree is ………

8) 5 X3 – 7 X + 4 number of terms …………. name ……………….. , degree is ……………

9) The coefficient of the algebraic term X is ……………. and its degree is ………….

10) The degree of algebraic expression 5 X3 – 3 XY + 2Y2 equal the degree of the algebraic

expression is …………………….

11) If the degree of the algebraic term 5 Xn Y2 is 5 , then n = …………

12) If the degree of the algebraic term Ym+1 is the degree of the algebraic term 5 X2Y4

then m = …………………….

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Sheet 5

1- Find the result of each of following :

1) 3 X + 2 X 2) – 5 a2 + 3 a 2

3) 7

3X - 7X 4) – 2 X2Y + 3 Y X2

5) Subtract Y2 from – 3 Y2 .

6) What is increase 3 a 2 b of a2 b is ?

7) What is decrease – 3 a b of 2 a b ?

8) 7 X increase – 3 X by …………..

9) The result of subtracting 2 m form zero is …………..

10) 2 X decreases 4 X by ………… while

2 X increase 4 X by ………..

11) a) 3 a – 4 b + 6 C b) 3 a – 7b – 5 C +2 5 a + 6 b – 2 C - a + 4 b + c – 5 c) 5 X + 2 Y – Z + 2 d) – 2 a3 + 3 a2 b 7 X + Y – 3 Z + 3 - 5 a2 b + 3 a b2 - 2 X – 5 Y + 4 Z – 1 5 a3 - 4ab2

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3) Find the sum of each of following :-

1) 3 X – 2 Y + 5 , X + 2 Y – 2 2) 5m2 + 2 lm , 4 m – 5 n-l

3) 2a2b – 3ab2 + b3 , - a2b + b3 4) 3a3 – 2ab2 + b3 , a3 + 4a2b – b3

5) Find the sum of each of following :-

1) 3a + 2b – 5 , 2a – 7 b + 4 , 5b – 4a + 3

2) 5 X2 – 3 X + a , X 2 + 2X – 5 , X – 3 – 6 X2

3) 3 X – 4 X2 + X3 , 2 X2 – 6 X2 – 6 X + 5 , 4 + 7 X – X3

4- Reduce each of the following :-

1) 5 X – 3 X2 + 4 – 7 X2 – 6 X – 1

2) 6 X2 Y – 4 XY2 + 2 XY2 – 5 X2Y + 2 X2Y2

3) 5 X2 – 2 X + 8 – 7 X – 3 + X2

4) – a2 – 5ab + 4 b2 – 2 – 3a2 + 2ab – 2b2 – 7

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Sheet 6

1- Find the sum of following :-

1) 3a – 4 b + 6 c 2) 3a – 6 b – 3 c + 2 5a + 6 b – 2 C -2 a + 5 b + 2 C – 6

3) 4 X – 2 Y + 6 , 3 X – 2 Y + 5

4) 3n2 + 5 n – 7 , -2n2 – 3n + 4

5) 5m2 + 3 lm , 2 l2 – 4 m2 – 4 lm

6) 3 X – 4 X2 + X3 , 2 X2 – 6 X + 5 , 4 + 7 X – X3

7) 2 X2 – 3 X Y + Y2 , XY + 2Y2 + X2 , 3 XY – 2 X2

8) 5 X2 – 3 X + 9 , X2 + 2 X + 5 , - 3 – 6 X2

2- Subtract :-

1) X – 3 from 3 X – 6

2) 3 a b2 – 4 a2 b – b3 form a3 – 2ba2 + 2 b3

3) 5 a + 7 b form 3 a – 2 b

4) 2 X + 6 Y – 7 from 2 X – 5 Y + 2

3- What is the increase of :

1) 3 X2 Y – 5 X than 3 X – 4 X2y

2) 2 X2 – 3 X + 1 than 5 X + 2 X2 – 1

4- What is the decrease of :

1) 2 a + 3 b than 5 b – 3 a

2) 3 Y2 – 2 XY + X2 than 3X2 – 5 X Y + Y2

3) 5 X2 + 2 X than 7 X2 – X + 3

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Sheet 7 1- Carry out the following operations :

1) 5 X × 3 Y

2) – 3 a × ( 4 C )

3) ( 2 X Y ) × ( - 3 X2 )

4) (2 X3 ) × ( -3 X2 ) × ( -5 X4 )

5) ( 4 X3 Y ) × ( -2 XY2 ) × ( -3 X2 Y5 )

2- Find the quotient of each of following :

1) 24 C5 ÷ ( - 24 C5 )

2) – 32 a3 b6 ÷ ( - 4 a3 b2 )

3) 8 m4 n3 ÷ ( - 4 mn2 )

4) -18 X3Y6 Z3 ÷ ( - 6 X3 Y3 Z3 )

5) 9 X5 Y4 ÷ 6 X3 Y

6) – 25 a6 ÷ ( - 5 a2 )

3- Simplify :-

1) 32 t4 ×

23 t4

2) 2

15 3ba × 10

8 2ab

3) 8 C2 × ( - d ) × ( 41− Cd2 )

4) 7

4 33Kh × 2

21 3hk

5) ( 3 X3 ) × ( 61 X2 )

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4- Choose the correct answer :-

1) 2 X × 5 X = ………..

a) 10 X b) 7 X c) 7 X2 d) 10 X2

2) If 2b is the edge length of a cube , then its volume = ………

a) 4b2 b) 2 b3 c) 4 b3 d) 8 b3 3) If the area of a rectangle is 24 X3 and length 8 X2 then its width = …………

a) 3 X5 b) 3 X c) 3 X2 d) 3

5- Complete :

1) 3Yy + Y2 = ……….

2) ( 6 X3 ÷ 2 X ) – 2 X = …………

3) ( 5 a ÷ a ) + ……………. = zero

4) 15 X2 Y3 ÷ …………… = 3 XY2

5) ………….. ÷ 7 a3 = 5a2

6) 42 X4 Y5 = 3 X2Y × 2 XY

7) XX

133152 3

= ………….

8) 32

42

54162

+

+

n

n

YY = ……………

9) nn

nn

YXYX

5

215

3624 +− = …………..

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Sheet 8

1- Find the following products :

1) -5 X ( 2 X + Y – 3 Z )

2) 3 X ( 2 X + Y + Y – 3 Z )

3) 31 X2 ( 6 X2 – 9 X Y – 3 Y2)

4) 3 X Y ( 2 X2 – 5 X2 – 4 Y2 )

5) lm2 ( l 2 – 3 ml – 4 m2 )

2- Complete :

1) X ( ……………. -2 X ) = 6 X - ………….

2) 3 X ( …………. + 5 Y ) = 6 X2 + ………….

3) 2 X ( 3 X …….. ) = …………… - 10 X

4) 3 XY ( …………. - …………. – 5 X2 ) = 6 X2 Y – 12 XY2 ……..

5) 9 XY2 ( ……….. - ………… -5 X2 ) = 36 X2 Y5 – 18 X Y2 - ……….

3- Put in simplest form :

1) 3 a ( a – b ) + 4 a ( 2 a + b )

2) 3a ( 4 a – 2 ) – 4 a ( 3a – 2 )

3) 2 X ( X + Y ) – Y ( 2 X – Y ) + 2 ( Y2 – X2 )

4) 3 a ( 4 a – 1 ) + 2 a ( a + 3 ) – 5 a ( 2a – 1 )

4- Simplify : 3 ( 1 – 2 X ) – ( X2 – 5 X + 3 ) + 2 X ( X + 3 )

then find numerical value if X = - 2

5- Simplify :

A b ( 3 a – 2 b ) – 2 a ( a b – b2 ) + b ( 4 a b – a2 ) find the numerical value of

the result when a = 1 , b = -3

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Sheet 9

1- Write the missing term in each of the following products :

1) ( X + 5 ) ( X + 3 ) = ………… + 8 X + ………..

2) ( X + 2 ) ( X – 4 ) = ………… - …………… - 8

3) ( a – 3 ) ( a – 7 ) = a2 - …………. + ………….

4) ( 3 X – 4 ) ( X + 7 ) = ………… + ……………. -28

5) ( 4 X – 3 Y ) ( 2 X + 6 Y ) = …………. + ………….. + ………

2- Find by direct product :

1) ( X + 3 ) ( X – 5 ) = …………..

2) ( 2 X – Y ) ( 3 X + 4 Y ) = ……….

3) ( 3 m2 + 8 ) ( 4 m2 – 4 ) = …………

4) ( b2 – 4 ) ( b2 + 2 )

5) ( 4 X + 1 ) ( 2 X + 3 )

6) ( 23 a – 6 b ) (

23 a + 2 b )

3- Find by inspection the expansion of each following :

1) ( a + 3 )2

2) (4 m – 7 )2

3) ( 2 X + 5 Y )2

4) ( - 4 a – 7)2

5) ( - l – m )2

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4- Find by direct product the result :

1) (a + 2 ) ( a – Z )

2) ( 4 m – 7 ) ( 4 m + 7 )

3) ( 2 X – 4 Y ) ( 4 Y – 2 X )

4) ( Y – 3 ) ( Y + 3 ) (Y2 + 9 )

5) ( lm + 6 n ) ( l m – 6 n )

6) ( X + 2 Y ) ( X – 2 Y ) ( X2 + 4 Y2 )

5- Choose the correct answer : 1) The middle term in the expansion of ( 3 X – 1 )2 is …………..

a) 3 X b) – 6 X c) 6 X d) 6 X2

2) The middle term in the expansion of ( 2 a + 3 b )2 is …………..

a) 12 a b b) - 12 a b c) 6 a b d) – 6 a b

3) If X = - 1 , then the numerical value of expression ( X2 + 1 )2 is …….

a) zero b) 1 c) 2 d) 3

4) If X = 34 , then ( X – 2 ) ( X + 2 ) = …………

a) 34 – 2 b) (

34 )2 – 2 c) (

34 )2 – 4 d) (

34 )2 + 4

5) X – Y = 3 and X + Y = 5 then X2 – Y2 = …………

a) 2 b) – 2 c) 8 d) 15

6) If X + Y = 7 then the numerical value of the expression X2 + 2 X Y + Y2 = ………

a) 7 b) 14 c) 49 d) 28

7) If ( X – 3 ) ( X + 3 ) = X2 + k then K = ………………

a) 9 b) 6 c) -9 d) -6

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6- Reduce of he following :

1) ( X – 3 )2 – 9

2) 3 ( m – 5 ) ( m + 2 )

3) ( X – 2 ) ( X + 2 ) – X ( X + 1 )

4) ( 2 X – Y ( 2 X + Y ) – ( X – 2 Y ) 2

5) ( 5 X – 2 Y)2 – ( 5 X + 2 Y )2

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Sheet 10

1- Find the quotient in each of following :

1) 5 a – 10 by 5

2) 12 X + 15 Y by – 3

3) 12 a2 b + 20 ab2 by 4 a b

4) 3 a2 b – 6 a b2 + 12 a b by – 3 a b

5) 32 X5 – 48 X3 + 72 X7 by – 8 X3

6) X

XX3

912 2 − = …………

7) XY

YXXY2124 2

−− = …………

8) 22

564524

6304218

YXYXYXYX

−+− = …………..

9) Multiply 4 X2 by ( 3 X3 Y3 – 6 X2 Y3 ) then divide the result by 12 X4Y2

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Sheet 11

1- Factorize each of following by H.C. F :

1) 5 a + 5 b 2) 5 Y – 10

3) 35 a + 10 a2 4) 15 a3 b – 5 a2 b2

5) 49 b2 – 7 b3 6) 6 a3 – 4a2 b2

7) 3 X2 + 6 X 8) 18 a2 b c – 6 a b c + 30 abc2 – 24 a b2 c2

9) 15 a3 b4 + 6 a5 b3 – 3 a2 b2 10) 32 X3 Y3 + 16 X2 Y2 + 8 X Y

11) a ( a+ 3 ) + b ( a + 3 ) 12) 6 a2 ( X – 1 ) – 8 a ( X – 1 )

13) 24 a2 b3 ( a – 2 ) – 3 6 a3 b2 ( 2 – a )

14) 3 X2 ( X – 7 ) + 2 X ( X – 7 ) + 5 ( X – 7 )

15) 16 a2 b2 ( a + b + 2 ) – 8 a2 b ( a + b + 2 )

2- Find the result by the H.C. F :

1) 7 × 123 + 7 × 35 – 7 ×18

2) 6 × ( 15)2 + 18 ×15 – 8 ×15

3) 5 X (48)2 + 7 X 48 + 53 X 48

4) (31)2 + 31 × 23 – 3 1 × 54

5) ( 51 × 17 + 51 × 33 ) + (49 × 21 + 49 × 29 )

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Sheet 12

Complete :

1) The mode of set of value is …………..

2) The mode of value of 2 , 3 , 8 , 2 , 9 is ………….

3) The mode of value 3 , 6 , 13 , 19 , 19 , 12 is …………..

4) If the mode of value 31 ,

71 ,

51 ,

71 is

X1 then X = ………

5) If the mode of value 12 , 17 , X + 1 , 7 , 12 is 7 then X is …………

6) If the mode of value of a + 2 , a + 1 , a + 3 a + 2 equal 12 then a = ………..

7) The median of the value : 4 , 8 , 3 is ……………

8) The median of the value : 6 , 5 , 9 , 8 is ………………

9) The median of value : 8 , 17 , 4 , 6 , 10 is …………..

10) The order of median of value 6 , 2 , 5 , 4 1 is ……………..

11) Write the median :

2.9 , 2.3 , 1.6 , 9.1 , 2.8 , 0.7 , 8.1 , 7.3 , 6.2 , 5.3 , 12.2 , 4.3 , 8.5

12) The mean of the value 5 , 12 , 6 , 17 is ……………..

13) The mean of these numbers 2 , 5 , 8 , 9 , 14 , 28 is …………..

14) The mean of the value 2-a , 4 ,1 , 5 , 3 + a is ……………..

15) The mean of the values X , X-Y , Y – X is ………………

16) If mean of numbers 9 , 4 , 5 X is 5 the X is ……………..

17) If the mean of value X – 1 , X , X + 1 is 6 then X = ……………

18) If mean of side length of triangle is 8 then premonitory triangle is ………

Good Luck