Cairo Governorate
Nozha Directorate of Education
Nozha Language Schools
“Ismailia Road” Branch
Department : Maths
Form
: 2nd Prep.
Sheet
Sheet ( 1 )
Complete :1)
Z + Υ {0} = ……………
2) Z - {0} = ……………
3) a 2 = ……………..
4) 100 − 36 = 100 − .........
5) the S.S. of the equation x + 2 = − 4 in N = …………
6) the product of the rational no.
7) the sum of the rational no.
8) 310 + 310 + 3 10 = 3 ........
9) if a −1 =
a
by its additive inverse = ………..
b
a
with its additive inverse = ………….
b
2
then a = ………
3
0
2
10) the additive inverse of   is ………….
5
11) if x ∈ Z , x = 2 then x = ………..
25
+ − 5
12) −
=……….
13) the standard form of no. 0.00015 is ………..
14) the sum of two square roots of the no. 2
2
2
15)  3  ×
0
81  7 
× 
16  9  = ………
1
= ………….
4
16) the S.S. of inequality –x < 1 in N is ……..
17) the S.S. of equation –x -1 = 5 in Z is ……….
18) the S.S. of inequality 5 < x < 6 in N is ……….
19) the no. of solutions for inequality
1
2
<x<
is ………..
2
3
1
Sheet ( 2 )
1-Complete
3
1.
16 =
2.
..........
− 8 = ........
3
.......= 4 = ........
3
50 + ........ = 4
4.
5.
7.
3
3
3.
6.
a 3 =…………
3
( )
27 − 3 64 = − 25
...........
a vessel in the shape of cube of capacity 27 x3 cm its side length ……..
3
8.
3
9.
64 − 3 − 64 =
− 64 + 16 = ...........
10. x3 = 64 then
11.
………….
x4 =
3
x = …….
.........
12. if − 16 = 3 y , then y = ………
13. if
x
9
= 2 , then x -2 = …….
3 x
14. if the volume of share =
9
π then the length of radius = …… cm
16
15. the S.S. of equation x 3 + 27 = 0 in Q is …….
2
2- find the S.S. of each of the following equations in Q :1.
8x 3 + 7 = 8
2.
(x+3)
3.
( 5x -14 )
4.
2x 3 -5 = x 3 + 3
5.
( x 3 -14 ) 2 = 169
6.
(x
3
− 1)
3
2
= 343
3
+ 10 = 18
=
3
25
3- if the half of the cube of a no. equals 32 find this no.
4- find the length of a diameter of a shape whose
volume = 113.04 cm 3
5- if
3
( π = 3.14 )
x + 19 = 3 find the value of
3
x
3
Sheet 3
Complete
1.
The two consecutive integers which included the number 7 between
them are ……. and……..
2.
if x is an integer x < 13 < x + 1 then x = ……….
3.
( 3 − 3 )3 = ……
4.
if n ∈ z+ n< 26 < n + 1 then n = ……..
5.
the square whose area is 10 cm 2 its side length is …….cm
find the value of x in each of the following
1.
x < 3 5< x + 1
2.
( x – 5 )3 = 1
3.
10.001 x3 = - 8
4.
0.1 x2 = 10
5.
( x – 1)2 = 4
6.
5
x 3= - 2
4
7.
¼ x2 +2 =66
Prove that
11 is included between 3.31 and 3.32
1.
15 is included between 2.4 and 2.5
2.
3
3.
− 2 is included between -1.5 and -1.4
4
Sheet( 4)
complete :1-
Q Υ Q \ = ............
2-
R+ Ι R− = ...............
3-
R - {0} = ………….
4-
R – Q = ……
5-
R+ Υ R− = .........
6-
R + = ........ Υ .......... Υ .......... = ......... Υ {0}
7-
{x
8-
The S.S. of the equation x 2 +1 = 0 is ……….
9-
The S.S. of the equation x 2 + 2 = 0 is ……….
: x ∈ R , x < 0 } = .......... ..
10- The S.S. of the equation 0.008 x 3 + 1 = -7 in R is …….
solve each of the following equation to the nearest hundredth
given x ∈ R:1.
3
x
4
2
+ 2 = 11
2.
5x 2 + 3 = 2
3.
2
+ 5 = 21
x3
2-
a square of side length 6 cm find its diagonal length
3-
the square of area 32 cm 3 find its side length and the length of its diagonal
4-
the area of square equal the area of ∆ with base = 6 cm long and its height
equals 6 cm find the side length of the square
5
Sheet ( 5)
1) Find:1) ] 0.4[∩] 2.6]
2) [1, 5[-] 3, 5[
3) [-1, 5] ∩ [2, 7]
4) [-3, 2] – [0, 4[
5) [-1, 4[∩] 2, 6]
6) ]-1, 7[ - [-4, 3[
7) ]-3, 4[∩ [1,3 [
8) [-5, 2[ U ]-3, 5 [
9) [-3, 7] U [2, 9]
10) ]-4, 3[ U]-1, 7[
11) ]-4, 3[ -]-1, 7[
12) ]- 3, 4] ∩ [-1, 6 [
13) N ∩ [-2, 3[
14) ]- 2 , 1] U ]-1, 4 [
15) Z ∩ [-2, 2[
16) R + U [0, 3[
17) R + U ]-2, 0]
18) R − U [0, 1]
19) [1, 6[- [1, 6]
20) [3, 8] –] 3, 8]
21) [-5, 7[ - {-5, 8}
22) [1, 4] -]1, 4[
23) [2, 5] U [2, 5[
24) ]-2, 2[ - [2, 2]
25) ]2, 5] ∩ [2, 5[
6
2) If X =] - 4 , 5], Y = [-2,6 [,find:1) X U Y
2) X ∩ Y
3) X – Y
4) Y – X
3) If [-5. a] ∩ [b. 4] = [0.3]
Then a = ……………. and b = ………………
3) Complete
1- [1, 5] -] 1, 2 [= …….
2- If 8 x 3 + 1 = 7 then x = ……………
3- R = ………..
(In the form of interval)
4- [ -3 , 4 ] - ] 2 , 5 [ = …….
5- R + ∩ [- 1, 3] = ………….
4) If x =] - 3 , 1] and
y = [-2, 4[
Then find
1- x
Υ
y
2- x ∩ y
3- x − y
4-Y
Sheet ( 6 )
1. find each of the following in simplest form :1.
7 −
3 + 2
7 +
3
2. 2 2 − 3 3 3 + 5 2 + 3 2
3. 8
1
+ 23 3 −
4
3
64 − 5 3 3
7
4.
1
2
2+
4
7
5+
3
4
2
7
2_
5
5. ( 3 5 ) 3 x 3 3
6. ( 2 + 1 ) ( 2 _ 1)
7. (5 _ 3 ) 2 _ 28
2. Complete
1)
2 3 + 3 3 =........
2)
– 2 3 x 3 =.........
3)
(2 3 7 ) 3 =............
4)
The additive inverse of the number
5)
The additive inverse of ( 2 _ 5 ) is .............
6)
The multiplicative inverse of the number
7)
If x= 2 + 5
8)
The multiplicative inverse of the no.
9)
If x 2 - y 2 = 16 , x – y = 2 then x + y = ...........
10)
(
3−2
3. If x
)
2
y= 2 _ 5
6
5
is..............
2
is.............
6
then ( x + y ) 2 =...............
2 3
is .............
5
= 7 - .....................
5−2
y=
1-
x+y
2-
x–y
3-
xy
4-
x2 - y2
5-
x 2 - 2xy + y 2
5+2
find the value of each of the following :-
8
Sheet (7 )
4. simplify
1-
45 + 20 − 4 5
2-
50 − 18 − 2
3-
98 − 128 − 18 + 4 2
1
1
− 12 − 5
3
5
4-
2 5+6
5-
(− 5)2
6-
2
7
×
7
2
7-
(
2
)
6 3− 2
(
6
2
× 54
3
12
89-
+ 18 −
)
2
3 + 5 − 60
5. complete :1-
63
2-
1
1
+
= ..........
2
2
7
=
.........
= ............
........
3-
The multiplicative inverse of the no. 50 is ………….
4-
If x =
5-
The next no. in the pattern 3 , 12 , 27 , 48 ,........
6-
6
2
then x −1 = ……..
3 × 6 = 3 × .........
7-
If x 2 = 5 then (x + 5 ) =…….. or ……….
8-
If 2 27 − 2 48 = x 3 then x = ……….
1-
if x = 7 +
2-
a x = 6 , a − y = 3 , find the value of a x + y
2
1
1
12 , y =
63 − 3 then prove that x 2 y 2 = 16
2
3
9
Sheet ( 8 )
1-
complete :-
1-
if x = 3 + 2 then
2-
the conjugate no. of the no. 1 +
3-
if x = 2 + 5 and y is the conjugate no. of x then ( x – y ) 2 = ……
4-
(
2 +
5-
If
1
= 3 − 2 then the value of x in the simplest form = ……..
y
2-
if x =
5+ 2 ,y=
3-
if x =
5− 2 ,y=
3
) (
−9
the value of x
4-
if x =
2
2 −
the product of multiplicative x by its conjugate is ……..
3
)
−9
3− 2
7
is ………
= ………….
5 − 2 then find the value of
3
5− 2
− 2 xy + y
1
7
x+ y
xy − 1
then prove that x, y are conjugate no. then find
2
, and y is the multiplicative inverse of x then find y then prove
that ( x + y ) 2 = 12
10
Sheet ( 9 )
5-
find the result :-
1-
3
16 + 3 54 − 3 128
2-
3
54 + 3 16 − 3 250
3-
3
16 + 3 10 × 3 25
4-
3
5-
3
6-
− 6
24
1
9
81 + 3 − 24 − 33
27 +
1
3
3
8
9
13
3
27 − 9
1
−1
3
complete :1-
3
2-
3
− 64 + 16 = ......
54 −
16 =
3
3-
If x = 2 , y =
3
4-
7
13
= ...........
56 − 3
27
2
5-
3
3
..........
3
3 ×
3
9 =
if x = 3 +
x
− 16 then   = ..........
 y
..........
3
6 , y = 3-
3
x− y

6 then find the value of 
x+ y
11
3
sheet (10 )
the cube whose edge length 2L then its volume = …. cm3
the volume of the cube is L3 cm 3 then its total area = ..cm 2
if the volume of cube =64 cm3 then the length of diagonal of one face
=……………cm
4.
a right circular cylinder with volume 40 ╥ cm 3 and height =10 cm then the
base radius length =….cm
5.
a right circular cylinder with volume ╥ r 3 cm 3 then its height =………………
6.
if L.S.A of right circular cylinder 2╥ r 2 cm 2 then its height = ……………cm
7.
the sphere whose radius length ……its volume =….cm 3
8.
if the volume of a sphere =9/16 ╥ cm 3 then its radius length =……cm
9.
if the surface area of sphere is 9 ╥ then its diameter length =…….cm
10.
the circle whose radius length = ….cm its surface area =…….cm 2
1.
2.
3.
• the dimensions of the base of cuboid are 3 cm and ( 3 − 1 ) cm and height (
3 + 3 ) cm calculate its volume
• find the T.S.A of cuboid whose volume 720 cm 2 and height 5 cm with a squared
shape base
• the circle whose area is 64 ╥cm 2 find the length of its radius then find its
circumference (╥ = 3.14 )
• Find L.S.A of right circular cylinder of volume 924 cm 3 and the height 6cm
• Find the height of a right circular cylinder whose height is equal to its base radius
length and its volume is 72 ╥ cm 3
• The volume of sphere is 562.5╥ cm 3 find the area in terms of ╥
• A lead cuboid in which the length of its dimension are 77 cm ,24 cm ,21 cm it
was melted to make a sphere find the radius length of that sphere
12
Sheet ( 11)
Find the S.S.in R :1.
2x + 5≥3
2.
1-5x < 6
3.
3 <x +2 ≤ 6
4.
− 3 < 2x-1 < 5
5.
3
6.
0≤ 3 – 2 x < 9
7.
0 ≤
8.
1 - x ≥ -2x - 3
9.
5x -3 < 2x + 9
10.
4x < 5x +2 < 4x +3
11.
1 –x ≤ 1 -2x < 3-x
12.
x+1 > 3x -2 > x
− 8 ≤ x+1 ≤
9
− 2x + 6
<4
3
complete
1.
if 5x <15 then x ……..
2.
if 2 x ≤ 4 then x…….
3.
the S.S. of the inequality -5 ≤ - x < 2 in R is ……..
4.
if -3 < x < 3 where x …..R THEN 2X ∈ ] -6 , …… [
5.
IF -2 <X <3 then ……< 2x +3 < ………
6.
if x >5 then – x ……..
7.
if -2x ≤ 3 then x ……
8.
the S.S. of inequality 2x +3 ≤ x - 4 in R is ……..
13
Sheet ( 12)
Complete
....... + ........
2
1.
the centre of the set =
2.
if the lower limit of a set is 8 and the upper limit of the same set is 14 then its
centre is ………….
3.
if the mean of a frequency distribution is 39.4 and the total of the
frequencies is 100 then the total of the products of the sets by their centers =
……….
4.
if the mean of marks of 5 pupils is 20 then the total of their marks = ………..
5.
if the upper limit of a set is 14 and if its center is 10 then its lower limit = …..
Answer
1. the following table shows the frequency distribution of no. of daily study hrs
of 5 pupils in a class :
No. of hrs
No. of pupils
12
23
35
412
515
67
76
total
50
1. calculate the mean of the number of hours of study per day
2. find the number of pupils who study less than 4 hours darly
using the following set frequency table
Find 1- the value of each x and k
2- the mean of this distribution
Complete
Sets
10-
20-
x-
40-
50-
60-
total
frequency
10
17
20
32
K+2
4
100
14
1. the median of a set of the values 9,4,8,1 and 3 is …………………
2. the point of intersection of the ascending and descending cumulative frequency
curves determines………………on the set axis
3. the mode of the values 5 , 3 , 8, 5 , 9 is ……………….
4. if the mode of the values 4,a , 5, 3 is 3 then a =………………………….
5. if the mode of the values 12 ,7 , x+1 , 7 ,12 is 7 then x =…………….
• The following table shows the frequency distribution with equal range sets for
the weekly wages of 100 workers in a factory
Set of wage inl.E
70-
Number of works
80-
10
13
90-
100-
k-4
20
x
120-
130-
14
11
16
.find 1- the value of x and k
2-the mode of wages in L.E
The following table shows the frequency distribution for the weights of 50
students in k.g :
Weight in k.g
Number of
307
35-
40-
45-
50-
55-
total
3k
4k
10
8
4
50
student
1.
Find the value of k
2.
calculate the mean
3.
draw the ascending cumulative frequency curve
4.
draw the histogram and find the mode
5.
find the median
15