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Final Revision sheets Prep. (1)
Name : …………………………………
Algebra and statistics
1) Complete:
a) The number 2.3 can be written in the form of as …………
b) The number 25.5% can be written in the form of as …………
c) The number 0.45 can be written in the form of as …………
d) The number
………
is a rational number, if x
 is a number
e) If Q , then a = …………
f) Between each two integer numbers there are infinite number of …………
g) The integer lying between
h) The rational number
and
is ………………
is an integer number if ………
i) The property used in: (
j) The additive inverse of (
)+
=
+ ( ) is ……………
) is ………..
k) The multiplicative identity of Q on the multiplication operation is ………
l) The rational number
has a multiplicative inverse if x
………
m) The multiplicative inverse of the number 0.25 is ………
n) The property used in :
×(
+
)=
o) The property used in :
+(
+
)=(
×
+
+
)+
×
is …………
is ………… – 3
2
= ……
p) The rational number which has no reciprocal is ………
q) ……… ×
r)
=1
+ ……… = 0
q) The degree of the algebraic expression 2
- 2xy + 4x + 1 is ……… , the number of
its terms is ……… and its absolute term is ………
u) The multiplicative inverse of 1 is ……………………
r) ( a + 7 ) (a  7 ) = a2 - ………
s) 0.
= ……………………… ( In the form of )
t)
(2+
)=
 ……… + ……. 
2-Complete :a) - 56
(-8
) = …………
b) ( a – 2b)(3a + 7b) = ……………………………
c) ( 2m – 3n)2 = ………………………….
d)6
y – 3x
e) (
b) X (
+ 2x
-5
a) X ( - 2
= …………… ( in the simplest form)
y+2
b) = …………
( in the simplest form)
f) (b – 4a)(b + 4a) = ……………………
g) (a – b)(a2 + 2ab +1) = ……………………………..
h) (9x3y4 + 12x2y3 – 3xy2) ÷ 3xy2 = ……………………………
i) If y = 2x + 5, then y = …… at x = 0
j) ( 5x )0 = …… , ( where x ≠ 0 )
k)
The multiplicative inverse of 32 = ……
l)
The variable in the term 7x is …… and the coefficient is ……
m)
4 , -8 , 16 , -54 , …… , ……
( the same pattern )
n) The additive inverse of the number -25 is ……
3-
Choose the correct answer :
1) The degree of the algebraic expression 3y + 22 x is ……
a)1
b)2
2) The rational number
a) a < b
c)3
d)4
is an integer number if ………
b) a > b
c) b is divisor of a
d) a is divisor
c) 1
d)zero
3) xy – yx = ………….
a) x
b) y
=…………
4)
4 y2
b) y2 – 4xy + 4x2
c) x2 + 4xy + 4
d) x2 + x-2y a) x2- 4xy2 +
5) 4 X 2Y 2  2XY 2 + 8 X 2Y = ……….. (2XY  Y + 4X )
a) 4X Y
b) 2X Y
c) 2X
d) 2Y
6) The median of the numbers 25 , 12 , 23 , 24 and 21 is …………………
a) 12
b) 21
c) 22
d) 23
2
3
7) The algebraic expression 3X Y + 2XYZ is of ………………… degree
a) 4th
b) 5th
c) 3rd
d) 2nd
8) (15X 4 + 5X 3 ) ÷ 5X 3 = ……………….. where X ≠ 0
a) 3X 2 + X
b) 5X 2 + 1
c) 3X +1
d) 4X 4
9) Which of the following is not rational number?
a) 0.8
b) 7
c) 20 %
d)
8) The median of the values : 6 , 5 , 9 ,8 is..........
a) 5
b) 6
c) 7
d) 7.5
9) The median of the values : 8 , 17 ,4 , 6, 10 is..........
a) 11
b) 10
c) 8
d) 6
10) The median of the values : 3 , 7 , 2 , 9 , 5 , l l i s ..........
a) 5
b) 6
c) 7
d) 12
(4) a) Find (X  1)(X 2+X +1)
b) Find two rational numbers between
and
c) The half of the way between  , 
d) Write
percentage form.
e) Find the value of the following in the simplest form If x =
a ) x -y
b)
c)
-
-
f) Use the property of distribution to find the value of
2) Factorize by taking the H.C.F:
a) 36a2b3 + 48a4b2 – 12b5a3
b) -35m3n4 - 21n3m2 -7mn3
c) 125x4y2 + 25x3y5 – 75y3x3
3) Find in the simplest form:
a) The sum of : (4ab – 6ac +3a2) and (-2ab + 4ca -2a)
b) The increase of : 7xy - 3
c) The decrease of : 4
f)
g) – 3
h) 6
2
+(-3
)
+ 9)
than
+ 2xy – 3 than -2
d) x ( 2x + 3 ) + 3x ( 2x – 4 )
e) (x – 3) (x + 3) (
+2
,z=3
-
+ 2xy
- 3xy + 5
×13 
×22+ 9×
,
y=
i) – 2
j)
×(-3
)
-
k)
+(-
)
l)
×
+
m)
×
+
×
×
+
n) The quotient of : (24a3 – 36a2 + 12a) by -6a
o) The quotient of : (-75x4 – 20x5 + 55x2 – 30x3) by 5x2
4) put the suitable sign " < , = , > "
a)36.5% ………
b) 1.2 ……… 0.3
……
d)
c) ……
…… 1
e) 1.
5) Arrange the following rational numbers in descending order:
a)
,
b)
,
,
, 0.5 ,
,
,
6) Write:
a) 4 rational numbers between 2.5 and .
b) 2 integers number between
and
.
7) Simplify then find the numerical value:
a) ( 2a – 3)2 + (a + 2)(2a – 4)
at a = 1
b) (3x + 1)( 2x – 3) – (4x + 1)( 4x -1)
c) (a – 3)( a + 3)(a2 – 9)
at x = 0
at a = -1
8) (a) If y = 4x – 1 , and if ( 4 , a ) satisfy this relation , find the value of a.
(b) Solve each of the following equation : 4 ( x – 6 ) = 4 , x  Q
9) (a) If A = (b) If x = -
, find the value of A3 + B3
and B =
, y=
following:
and z = x4
y 2 z2
. Find the numerical value of each of the
10) Find:
a) The mean for the values: 3 , 2 , 6 , 5 , 4 , 9 , 1
b) The median for the values: 6 , 3 , 2 , 5 , 4 , 9 , 6
c) The mode for the values: 1 , 6 , 3 , 7 , 6 , 2 , 6 , 9
d) The mean for the values: 3 , 2 , 6 , 5 , 4 , 9 , 1
e) The median for the values: 6 , 3 , 2 , 5 , 4 , 9 , 6
f) The mode for the values: 1 , 6 , 3 , 7 , 6 , 2 , 6 , 9
11) The following frequency table represents the marks of 40 pupils in an
examination:
The marks
15
16
17 18 19
Number of pupils (frequency)
5
4
11
9
6
20
5
a) Represent these data by bar graph.
b) Find the mode mark.
12) The following frequency table represents the marks of 40 pupils in an
examination
The mark
15
16
17
18
19
20
Number of pupils (frequency)
4
5
8
12
7
4
Find the mode mark .
13)The following frequency table shows the number of study hours of 30 pupils in a week:
The number of study hours
25
The number of pupils (frequence)
3
a) Represent these data by bar charts graph
b)Find the mode number of study hours.
26
5
27
11
28
7
29
2
30
2
14) The following table shows the age of visitors to an exhibition within an hour of the day .
Visitors
Number of visitors
10-
20-
30-
40-
50-
6
9
12
10
8
Find the mode mark using the histogram of this distribution.
2- Geometry
1) Draw an angle of measure 80° and bisect it .
2) Draw an angle of measure 60° and draw a congruent angle to it.
3) Draw a triangle ABC whose sides are AB = 6cm , BC = 7cm and AC = 6cm then
draw a bisector for angle A.
4) [3] a) Draw ∆ XYZ which XY = YZ = 4 cm and XZ = 6 cm , Using the compasses
and
the ruler bisect  A
(don’t remove the arcs )
5) Complete:
a) The sum of measures of two complementary angles is ……………
b) The sum of measures of two supplementary angles is ……………
c) The sum of measures of accumulative angles about one point is…
d) Two adjacent angles are called complementary angles if
e) Two adjacent angles are called supplementary angles if they are drawn by a
straight line and ………………………………………
f) The complementary angle of the acute angle is ……………………
g) The supplementary angle of the acute angle is …………………….
h) If  A complements  B ,  A complements  C ,then  B,  C are …….
i) If m( A) = 2m( B) ,  A supplements  B then m( B) = ………….
j) If m( A) = 1500 then m (reflex  A ) = …………….
k) The angle whose measure is 150 supplements the angle whose measure is …..
l) The angle whose measure is 105, its type is ……………
m) If

,

n) If

, then m(
then
…….
) = …………
o) If m( X) = 2 m( Y) and  Y is an obtuse angle then  X is ………
p) The angle whose measure is 800 complements the angle whose measure is …..
6-complete:
1)The angle that its measure is complements an angle of measure ….
2) If a straight line intersects two parallel straight line, then any two alternate
angles are……….
3) If ΔABC  ΔXYZ, then BC =……
4) The two triangles are congruent if ………
5) The sum of measures of the accumulative angles at the point = ………..
6) If m( B) = 650 , then the measure of reflexive  B = ………………..
7) If ∆ ABC ∆ XYZ , then BC = …………
8) If M( X ) = ½ m( Y) and m( X ) =300 ,then the two angles X and Y are
……
9)The angle that its measure 72° is complements an angle of measure ….
10) If a straight line intersects two parallel straight line, then any two alternate
angles
are………….
11) If ∆ABC ≡∆XYZ, then BC =………
12) If m(A) =150° , then m(reflex A)= ………….
13) The two triangles are congruent if …………..
7- choose the correct answerer:
1)The straight line which is perpendicular to one of two parallel straight lines is
………
to the other straight line.
a) parallel
b)perpendicular
c) intersects and not perpendicular
d)does not intersect
2) The measure of the straight angle = ……….°
a)90
b)45
c)180
d)130
3)If ∆ABC ≡∆XYZ, m A) = 50° and m (B) = 60°, then m (Z) =……
a) 60°
c) 70°
b) 50°
d) 65°
4)
6) In the opposite figure:
If m( XYL)= 600 , YM bisects  LYZ , YZ  YX
,
Z
M
L
then Find m( LYM) = …………….
(a) 300
(b) 150
(c) 1200
(d) 600
Y
X
7) The acute angle complement ………….. angle
(a) acute
(b) right
(c) obtuse
(d) reflex
8) If  A supplements  B and  A   B ,then m( A) = …….
(a) 45°
(b) 60°
(c) 90°
(d) 180°
9) If m( X ) = 2 m( Y ) and Y is an obtuse angle , then  X is ……
(a) acute
(b) right
(c) obtuse
(d) reflex
10) If m(A) =150°, then m( reflex  A) =……
(a) 30°
(b) 210°
(c) 90°
(d) 180°
11) 1) If m( A ) + m( B)= 900 , then  A and  B are ………………
(a) Equal
(b) Complementary
(c) supplementary
(d) Adjacent
12) The sum of measures of the accumulative angles at a point = ………. 0
(a) 90
(b) 180
(c) 270
(d) 360
13) XY …….. XY
(a) 
(b) 
(c) 
(d) 
14) If the measure of an angle is 900,then the measure of its supplements is ….0
(a) 90
(b) 0
(c) 100
(d) 200
15)The angle of measure 650 complements an angle of measure...........
(a) 1800
(b) 250
(c) 900
(d) 1150
16) The sum of the measure of the accumulative angles at a point is ...........
(a) 1800
(b) 900
(c) 2700
(d) 3600
17) the measure of the vertically opposite angle of an angle of measure 700 is ...........
(a) 200
(b) 700
(c) 1100
(d) 2900
18) If A supplements B, and m (A) =2 m (B), so m (B) =.........
(a) 300
(b) 600
(c) 900
(d) 1200
19) if A supplements B , A supplements C , then B , C are .........
(a) Supplementary
(b) complementary
(c) equal in measure
(d) adjacent
20) the supplementary of the right angle is …........ angle
(a) an acute
(b) an obtuse
(c) a right
(d) a straight
(b)
(c) 
(d) 
21) AB............. AB
(a) 
22) The angle of measure 500 supplements an angle of measure….............
(a) 400
(b) 1300
(c) 300
(d) 1800
23) Which of the following lengths can be lengths of sides of a right angled triangle ?
(a) 3 , 4 & 6 cm.
(b) 3 , 4& 5 cm.
(c) 3 , 3 & 5 cm.
(d) 4 , 4 & 5 cm.
8- Find the measure of each of the following angles using the figures:
D
A
B
M 140
C
5XB X
C
A
If B  AC , then x =…………..
m( BMC ) = ……………………
10- In the figure shown :
E
D
AB  DF = {C} , m( ACE) = 90°, m( FCB) = 130° ,
Complete:
A
C
a) m( ACF)= ……………………..=……°
b) m(ECD) =……………………..=…… °
c) m(DCB) = ……………………..=……°
d) m(ACD) = …………………….=… .. °
e) m(ECF) = ……………………..=…… °
F
1300
B
11- In the opposite figure:
A
D
AB  CD = {E} , AE = DE and EC = EB
350
E
m(A) = 350 , m( AEC)=950
950
Complete the following:
C
B
a) ∆ EAC  ∆ ………..
b) m( D) = ………°
c) AC = ………
d) m( B) = ……….°
12- In the opposite figure:
C
AC=AD , CB=DB , m( DAB) =560and m( CBA) = 34°
Complete :
B
340
560
A
a) ∆ ACB  ∆ …………..
D
b) m( CAB) = m( …….) = ………°
c) m( DBA) = m( …….) = ………°
d) m( C) = m( ……) = ………………… = ………..
13- In the opposite figure: LM = OM , LN = ON ,
m( L)=700 , m( LMN)=500
1) Is ∆
LMN  ∆ OMN ? Why ?
2) Find m( LNO) ?
L
N
M
O
A
350
14- In the opposite figure:
D
BC=DC , AC=EC , m( ABC)=m( EDC)=90°, m( A)=35°
Complete: a) ∆ ABC  ∆ ………., because
E
1) AC= ………
b) AB  ……..
2) BC = ………
3) m( ABC)= ………
c) m( C) = …………………..= ……..°
d) m( E) = m( ……) = ………°
B
C