Alg. Exercise (1) Department : Math Form : 1 st prep. Sheet. [1] Complete : 1) Rational number is 2) The set of integer is.. 3) If. is rational if x.

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2 airo Governorate Nozha irectorate of Education Nozha Language Schools Ismailia Road epartment : Math Form : 1 st prep. Sheet [1] omplete : lg. Exercise (1) 1) Rational number is ) The set of integer is.. ) If b a is rational then b ) The number ) The number is rational if x. x x + x 6) The rational number is rational if x. x x = 0 if x =.. 7) The rational number b a is an integer if. 8) Express of 0.7 as rational number is simplest form. 9) The rational number x is negative if x..zero. 10) If b a is rational number and ab = zero then a =.. 11) Write the rational number 11 7 as decimals 1

3 Exercise () [1] Represent each of the following on number line : a) 7 b) 1 1 [] Write the correct sign ( <, >, = ) : c) - 1 a) Every positive rational number..zero. b) Every negative rational number.zero. c) d) e) f) g) 1 [] Write two rational number lying between : 1) 1 and. 1 ) and 1 ) 0. and [] omplete : 1) etween each two successive integers there is.. ) The opposite rational number 1 on number line.. ) The number of integers lying between 7 and 11 8 are. [] Write the rational number that equal and the sum of terms 8.

4 Exercise () [1] omplete : 1) The additive identity element in ϕ is ) The additive inverse of number is.. ) The additive inverse of ( ) zero is ) The additive inverse of is ) The additive inverse of number zero 6) The additive inverse of 0. is.. 7) The remainder of subtracting 1 from 6 =.. 1 8) The remainder of subtracting from 9) The remainder of subtracting from zero 10) = zero then =.. 11) If ( + 1 ) is additive inverse of number then =.. 1) If X =, Y = and Z = then Y X - X Z = [] Using the number line to find result : a) = b) =

5 [] Using the addition properties in : a) + ( ) b) ( ) c) [] If X =, Y =, Z = find : 6 a) X + Z b) X Y c) ( X + Z ) d) ( X + Y ) Z

6 [1] omplete : Exercise () 1) The multiplicative identity of the rational no. is.. ) The multiplicative inverse of no. 7 is. ) The multiplicative inverse ( ) zero is ) The rational no. a 1 has multiplicative inverse if a =.. ) The rational no. has multiplicative inverse is 6) ( ) = a a 7) If = 80 then b b X X 8) = then Y Y =. =. 0 9). = 1 10) 11) 7 ( ) = n, then n =. 7.. = ).. = 1 [] Using properties of following : 1) (-11)

7 ) ( ) + ( ) ) [] If X =, Y = and Z = - 1 a) XYZ b) Y X - Y Z [] Find the middle rational no. lying between : a) 8, 8 1 b), 6

8 c) zero, [] Find the rational number lying at : a) One fourth of way between, b) One tenth of way between, 7

9 [1] omplete : Unit Two 1) The degree of term X Y is its coefficient is ) The coefficient of algebraic term X Y Z is and its degree.. ) The degree of an absolute term in algebraic expression.. ) -a b number of terms..name is, degree is.. ) X 7 X + number of terms.name, degree is. 6) The coefficient of the algebraic term X is..and its degree is 7) If the degree of the algebraic term X n Y is then n =. 8) If the degree of algebraic term Y m+1 is the degree of a algebric term X Y then in =.. [1] Find the result of each of following : 1) X + X ) -a + a ) X X ) Subtract Y from Y ) - X Y + Y X 6) What is increase of a b than a b is? 7) What is decrease of ab than ab? Sheet (7) 8) Find the sum of : a) a b + 6c b) a 7b c + c) x + y z + a + 6b c -a + b + c 7x + y + -x y + z 1 8

10 [] Find the sum of following : 1) X Y, X + Y ) a b ab + b, - a b + b ) X X + X, X 6 X 6X +, 7 X + X [] Reduce each of the following : 1) X X + 7 X 6 X 1 ) 6 X Y XY + XY X Y + X Y ) X X X + X ) a ab + b a + ab b 7 Sheet (8) [1] Simplify : 1) ( X ) =.. ) a ( a ) = ) k ( k k 7 ) = ) -c ( 7 c ) =. ) X Y ( X XY + Y ) = 6) L m ( L m L m ) =. 7) (X + ) ( X + ) =.. 8) (X + 1) ( X + ) = 9) (X + Y ( X Y ) =. 10) (X ) ( X + ) = 11) ( X + Y ) =.. 1) ( X + Y ) =. 1) ( m ) ( m + ) =. 1) ( XY ) =.. 1) ( X + ) ( X ) ( X + ) =.. 9

11 [] Find value of K : 1) (X + Y ) = X + K X Y + Y then K =.. ) If (X Y) (X + Y) = X + K X Y Y then K.. ) ( X ) ( X + ) = X + K then K =.. [] Find numerical value of following : If X = 1, Y = - 1) (Y + 7 ) ( Y + ) ) (X + ) (X + ) ) (X + Y) (X + Y) Sheet (8) [1] Find the quotient : a) 18 a a b) c) d) 18 m + 6 m - m 8 X - 80 mx 8 X X - X + 6 X 7 X e) X + 1 X + 1 by X + f) X 7 by X g) X X + 1 by X 1 h) If area of rectangle is ( X + 7 X 1 ) and length is ( X + ) find perimeter if X = cm. 10

12 Sheet (9) Factorize by identifying the H..F : a) X + 6 X b) a + 10 a c) X + 1 X 6 d) 8 Y X e) X ( a + b ) + 7 (a + b) f) X ( X ) + X ( X ) + ( X ) g) m ( X + Y ) m ( X + Y ) 6 ( X + Y ) h) i) Sheet (10) 1) The mode of set of values is.. ) The mode of values of,, 8,, 9 is. ) The mode of values, 6, 1, 19, 19, 1 is ) If the mode of values,,, is then X = X ) If the mode of values 1, 17, X 1, 7, 1 is 7 then X =. 6) If mode of values of a +, a + 1, a +, a + equal 1 then a =. 7) The median of values, 8, is. 8) The median of values 6,, 9, 8 is. 9) The median of values 8, 17,, 6, 10 is. 10) The median of values 6,,, is. 11) The mean of values, 1, 6, 17 is 1) The mean of values,, 8, 9, 1, 8 is.. 1) The mean of values a,, 1,, + a is 1) The mean of values X, X Y, Y X is.. 11

13 [] The following table shows the number of hours that. li and hmed study daily in a week. li hmed a) find mean of studying hour for each li, hmed b) Find median of each of them. c) Find mode of hours of each of them. 1

14 Model exam (lg.) [1] omplete : x a) = zero if χ =. x + b) The degree of the algebraic term 6 x y is.. c) The additive inverse of the number d) -8 X exceeds X by e) ( 1 x x ) = 6 x. [] hoose the correct answer : 1) a) n = 1 Then n =.. b) is.. c) ) The rational number.. lies in half way between 1 and 8 7 ) a) x + b) 8 is a rational number then c) x.. d) d) 1 a) zero b) - c) d) - ) Express 11 as a decimal.. a) 0.6 b) 0.6 c) 0.6 d) 0.06 x ) If = Then : x y = y a) b) c) 1 d) zero [] a) dd : x y 6 and y + x + b) Use distributive property to find : c) The length of a rectangle is x cm and its width is x cm. calculate its area. [] a) Subtract : 6 x + x from x x + b) If a =, b = - 1 find the value of ( a + b ) ( a b ) c) Find three rational numbers between 1, 1 1

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16 Geom. Sheet (1) [1] Mention the type of angle whose measure is as following : 1) 7 ) 117 ) 90 ) ) 6) ) [] omplete : 1) The angle is.. ) The measure of straight angle ) The measure of zero angle ) The measure of right angle ) The measure of acute angle is less than and more than.. 6) The measure of obtuse angle is less than more than.. 7) The two complement angles are two angles whose sum of their measure is.. 8) The two supplement angles are the two angles whose sum of their measure is.. 9) The two adjacent angles formed by straight line and ray with same stating point are. 10) If the two outer sides of two adjacent angles are perpendicular, then these two adjacent angles are. 11) If the two outer sides of two adjacent angles are on the same straight line, then these adjacent angles are 1) The measure of angle which complement with 8 is 1) The measure of angle which complement with 90 is. 1 1) The measure of angle which complement with 60 is 1) Measure of angle which supplementary with 90 is.angle. 16) Measure of angle which supplementary with 180 is..angle. 1

17 17) Measure of angle which supplementary with 8. 18) If two straight lines intersect then the measure of each two vertically opposite angle are 19) The sum of measure of accumulative angles at point 0) ngle bisector is. 1) If m () = 80 then ( reflex ) = ) In opposite figure : a) M is the point intersection of and, ME bisects M and m ( M) = 10. Find : m ( M), m ( M ), m ( ME) 10 M E b) In the figure : 1) m ( M) =. ).and lie on the same straight line. 1 M 80 c) If, m () = 1 and bisects E. find : m (), m (E), m ( E) 1 E d) If E = {M}, M E and M bisects ME. Find : m ( ME), m (ME), m ( M), m (ME) M 16 E

18 Sheet () [1] omplete : 1) The two line segment are congruent if.. ) The two angles are congruent if. ) The two square are congruent if. ) The two rectangle are congruent if [] In the opposite figure : The two pentagons shown are congruent K E S R L H O omplete : 1) correspond to.. ) The polygon LK is congruent the polygon.. ) K = cm. ) M ( E) = m ( ) ) = cm 6) M ( ) = m ( ) [] In the opposite figure : If, m (F) = 110, = cm and polygon F the polygon EF E E = 8 cm, EF = cm. omplete : M ( EF ) =.. F =..cm 110 =.. F = 17

19 Sheet () 1) raw the line segment whose length 7 cm. then divid it into two equal parts in length using the compass and the an scaled ruler. ) raw where m ( ) = 80 using the ruler and compasses bisect by ) Use the ruler and compasses to draw the equilateral of side 6 cm. raw where = {}. what the length of. ) raw XYZ whose measure 70 use ruler and draw congruent equal to it. ) Using the protractor, draw with measure 70 and on the other side of, draw using ruler and compasses draw E //. 18

20 Sheet () [1] omplete the following : 1) ny two triangle s are congruent if two sides ) ny two triangles are congruent if two angles and in one of the triangles are congruent to their corresponding element in the other. ) ny two triangles are congruent if each.is congruent to its corresponding side in the other triangle. ) ny two right angled triangles are congruent if.. ) The diagonal of the rectangle divides its surface into two..triangles. 6) If XYZ, then = and m ( Z) = m (.) [] In the opposite figure : These triangles are congruent, then X =.. cm. 7 7 X cm. [] In the opposite figure : If =, = 7 cm., m ( ) = m ( ) = and m ( ) = 0 omplete the following : If 1) m ( ) = ) =.cm. 0 ) m ( ) =. 7 cm. [] In the opposite = {F}, F = F, F = F, m ( F) = 0 and m ( ) = 1, Then m ( ) =.. F

21 [] In the opposite figure : If bisects,, m ( ) = 100 nd = 6 cm. complete the following : 6 cm ). ) m ( ) = ) = cm. [6] In the opposite figure : =, m ( ) =, and, M Then m ( M) = [7] In the opposite figure : is the midpoint of,, = cm., and m ( ) = 7 Find : cm 1) The length of ) m ( ) 7 [8] In the opposite figure : =, = E E nd m ( ) = 7 Find the measures of the unknown angles in E 7 0

22 Sheet () [1] omplete the following : 1) If two straight lines are parallel to a third straight line, then they are ) If a straight line cuts two parallel straight lines, then each two corresponding angles are. ) If a straight line cuts two parallel straight lines, then each two interior angles in the same side of the transversal are [] In the opposite figure : O O // H // YX //, = X = X and = 18 cm. H Find the length of Y Y X [] In the opposite figure : //, EF //, m ( ) = and m ( ) = 117 etermine : m ( E) F E [] In the opposite figure : 117 m ( ) = 0, m ( E) = // EF and // Find : 0 M ( E) 1 F E

23 E [] In the opposite figure : //, E, 70 0 m ( E) 70 and m ( ) = 0 Find the measures of the triangle [6] In the opposite figure : // // EF, m ( ) = and 0 bisects E Find : 1) m ( E) ) m ( EF) E F [7] In the opposite figure : E //, //, F bisects E and m ( EF) = 6 Find : m ( ) E 6 F [8] In the opposite figure : XL // YZ, XY // LZ and m ( XYM) = 100 Where M ZY L X Find : 1) m ( X) ) m ( Z) ) m ( L) Z 100 Y M

24 Model exam - hoose the correct answer : 1) The angle whose measure 0 complements the angle whose measure a) 0 b) 10 c) 0 d) 180 ) The measure of the vertically opposite angle of an angle of measure 70 is a) 0 b) 70 c) 110 d) 90 ) is an aright angled triangle at, = cm, = cm then ( ) = cm a). b) 16 c) d) ) If L 1 / / L and L 1 L then a) L 1 / / L b) L L c) L 1 L d) L 1 intersects L ).. a) b) c) d) 10 6) In the opposite figure : / / then x = X a) 10 b) 100 c) 60 d) 0 - omplete : a) The angle whose measure is 70 supplementary the angle whose measure is. b) If m ( ) = 10 then m ( reflex ) = c) If X Y Z then =.. d) If a st. line intersects one of two parallel st. lines then.. e) The sum of measure of the accumulative angles at a point equals. f) In the opposite figure : then X =.. X X

25 - a) In the opposite figure : E 11 H E, E H //, m ( E ) = 11, m ( ) =, m ( ) = 6 (i) is E H //? Why? 6 (ii) Find : m ( ) b) In the opposite figure: 1 cm m ( ) = 90, m ( ) = 90 = 7 cm, = cm, = 1 cm 7 cm Find ( ) cm - a) Using the geometric instruments draw in which = = cm and = 6 cm draw to cut at. Find the length of and the area of b) In the opposite figure : Prove that : E F and find : m ( ) and F 16 cm 7 E. 8 cm. 8 cm F cm 16cm - a) In the opposite figure : m ( ) = 100, bisects ( ), 100 m ( ) = 1 find : m ( ) 1 b) In the opposite figure : = { M }, M = M and M = M is M M? Why? M

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