Cairo Governorate Department : Maths Nozha Directorate of Education Form : 1 st Prep Nozha Language Schools Revision Sheet Ismailia Road Branch 1) Complete : - Unit (1) Numbers 1) If x N then ( 2x + 1 ) is.( even or odd ) 2) If x N then 2 x is. 3) 3 2 x 3 3... = 3 5 3, 2 = 3... 3 4) a is the.inverse of.., ( - a ) = 5) 3 a Z if.. 6) ( 5a ) 0 =., 7a 0 =. 7) If y x = 2 3, x = 3n then y =, n 0, x + y x + 2y =. 8) 9 5... =... 9) If 2 3 x X = 1, then x = 10) If 9 7 + x = 0 then x =. 11) number of factors of 24 =. 12) The number lies at the half way between 3 1, 2 1 3...... 13) =. %, 0.7 =, 12.5 % = 8...... 14) If 1 5 1 x X = 0.6, then x =.. 15) Factors of 28 is.. 1
1 2 3 4 5 49... 16) x x x x x x = = 0... 2 3 4 5 6 50... 17) The multiplicative inverse of ( 2 3 3 2 ) is.. 18) The rational no that lies at the quarter way between a and b, a < b is. 19) a a + 2 Q if a. 1... 1 7... 5 20) < <, < < 8... 4 6... 4 21) 15 >. 22) 7127 x 125 = 7127 x... = 8 23) 44 x 0.55 = 44 x (...... + ) = 10 100 24) 0, 3, 8, 15, 24, 35,.,..,.. 2 4 8 16 25) 1,,,,,.,. 3 9 27 81 26) 1, 3 2, 5 3, 7 4, 9 5,., 27) a b +1 Q If b = II- Choose the correct answer :- 1 1 1 1) If 3 x = 27, xy = 1 then y =. [, 9,, ] 27 3 9 2) If 7 x = 42 then 3 5 x = [ 14, 18, 10, 20 ] x 3 5x 3) If = then y 2 5y... =... [ 9 4, 9, 2 3, 3 2 ] 4) 691 + 208 ~.. [ 800, 900, 1000, 1100 ] 5 5) If x > 5 then..the smallest no. [, 5 5,, x x x + 1 x 1 5 ] 2
6) If 13 7 = 52 x then x =. 7) 2 ( 1-2 1 ) + 3 ( 1-3 1 ) + 4 ( 1-4 1 ) + + 10 ( 1-10 1 ) = [ 50, 49, 45, 54 ] 8) The product of any two odd no. = no. [ even, odd, prime ] 9) The smallest prime no. is [ 1, 2, 3, 5 ] 10) 691 + 208 ~ [ 800, 900, 1000, 1100 ] III- Find :- 3 5 7 9 25 1)... =... 5 7 9 11 27 1 1 1 99 2) ( 1 ) ( 1 ) ( 1 ) ( ) = 2 3 4 100 2 3 3) If a =, b = 3 4 a b then,, a + b, a b, ( a + b) ( a b) b a 4) Five rational no. lying between 1 2, 7 8 7 23 17 23 23 5) + =... 12 45 12 45 45 a 6) Write 0.82 in form b 7) A rational no. lying at the third way between 8) A rational no. lying at the fifth way between 4 7 2, 3 2, 3 6 10 9) x ( 3 2 + ) = 5 3 1 3 1 2 + then x =.. 7 5 7 3 10) Arrange the following descendingly : 5 3,0.5,, 8 8 9 16, 0.75 3
Algebra Unit ( 2 ) I- Complete : 1) 5 x y its coefficient is..and of.degree. 2) If x 3 y m of ninth degree then m =.. 3) x + x y 3 of.. degree. 4) 3x 2 + 2x + 5 of.degree and its absolute term is.. 5) The result of subtracting x from x is.. 6) The result of subtracting Zero from 3x is. 7) The decrease of 7x than -2x 8) The increase of -2x than 2 x 9) 4b + + + 3a = 9a + 7b 10) 5 y + 4y y = 11) 5 x 2 + x 2 =.. 12) 7 x 2 X 3x = 13) 35 x 5 5 x = 14) 7 x 2 X 3x =... 7 y 15) 4 y + 7 y 3 =. y 0 16) 18x 2 + 6x 3x =. x 0 18a 2 b =... 17) 6ab b 0 2 7a 7a 18) 2 + 7 =.. 19) ab x a 2 b 2 x a b 2 =. 4
20) 48x 2 + 36x + 24... = 8 x 2 +. +.. 21) If the side length of a square is 3 x then its area =, its perimeter =.. 22) If a rectangle its length is 5 x and its width is 3x then its area =.., its perimeter =. 23) ( 3x 1 ) 2 =. 24) ( 3x + 4y ) 2 = 25) ( x 3 y ) ( x +. ) =.. 9 y 2 26) ( a 2b ) ( + ) = a 2 4 b 2 27) 5 a 3 b 10 a 4 b + 25 a 5 b 3 = (.. 2 a b +..) 28) 3x ( 5x + 7x.) =. +. 6 x 29) x ( a b ) y ( a b ) = (. ) (. ) 30) 7a ( 2a + b ) + 5b ( 2a + b ) = (. ) (. ) 31) ( b a ) ( - ) = ( 2a b ) ( b a ) 32) If 5x 3 y n+4 of 8 th degree then n =. 33) 18x 2 y... = 6 x y II- Find 1) Add 3 x 2 + 5 xy 8y 2, 2x 2 3x y 2 y 2 2) The decrease of 2 ( x 4 y ) Z than the sum of 3 ( x y ) + 2x 4 ( y + 2z ) 3) Add 2x + 3y + 4z, 2z x y and x 2y 6z 4) The increase 7x 3y + 7 z than 2x 3y + 3z 5) Subtract 8a 2 7 a + 12 from the quient of divide 28a 3 18a 2 + 8a over 2a then find its numerical value at a = 3 6) Find ( x 2 ) ( x 2 + 2x + 4 ) 7) ( a + b ) 2 2 a b 5
8)( 5a 2 7b 3 ) 2 + ( 5a 2 + 7b 3 ) 2 9) x 3 y 2 ( 2x 3 + 3x 2 y + y 3 ) 10) divide 8 x 3 y + 2y 3 x 2 over 2 x 2 y 11) divide 12a 3 b 2 + 6a 2 b 2 3a b over 3ab 12) Factorize by taking H.C. F 6 a 2 ( b c ) + 8 a ( b c ) 13) Factorize by taking H.C. F 32 a 3 b 3 16 a 2 b 2 + 8 a b 14) Factorize by taking H.C. F 3 x 2 y 6 x y 2 3y 15) Factorize by taking H.C. F 12 x 2 ( y + 1 ) + 8 x y ( y + 1 ) 16) If x + y = 5, a b = 4 then find a ( x + y ) b ( x + y ) 17) If x + y = 2 then find 3x ( x+ y ) + 3y ( x + y ) 18) Simplify ( 2x + y ) 2 ( 2x y ) ( 2x + y ) 19) 1 (2a + 1) 4 2 at a = 2 20) A rectangle its area 3xy + 2y 2 and its width is y, Find its length and its perimeter. 6
Statistics I- Complete : 1) The mode of the numbers 5, 6, 10, 13, 17, 17, 22 is.. 2) The mean of the numbers 2, 5, 8, 9, 14, 28 is 3) The median of the numbers 25, 32, 28, 40, 52, 58, 50 is 4) The median of values 7, 16, 3, 5 and 9 is 5) The mode of 2, 3, 8, 2, 10 is.. 6) The arithmetic mean of 3, 1, 9, 7, 6, 4 is. 7) If the order of the median of a no. of values is 3 rd then the no. of these values is 8) If the mode of values 2, x, 3 is 2 then x =.. 9) The arithmetic mean of the marks of 4 students equals 20 marks then the sum of the marks of these students is marks. 10) If the arithmetic mean of the values a + 1, a and a 1 is 5 then a = II- The following table shows the saved money by Ahmed, Hany, Samy and Samir in 4 months in L.E Jan. Feb. March April Ahmed 40 60 35 80 Samy 30 68 57 55 Represent it by bar charts graph. 7
III- The following table shows the marks of Mona in Math in 5 month. Month sep Oct Nov Dec Jan Mark 30 40 35 42 50 1) Represent the pervious data by broken line graph. 2) Find the greatest and the smallest mark obtained by Mona. IV- The following table shows the percentage of sport activities which are favourite to the pupils of a school. Sport Act. Football Handball Basket ball Swimming Percentage 40% 20% 10% Complete the table, then represent the data by pie charts 8
Geometry I- Choose the correct answer : 1- The sum of measures of a cumulative angles at a point is.. [ 360º 270 º 180 º 90 º ] 2- The right angle supplements angle of measure. [ Zero 90 º 180 º others ] 3- The sum of two a complementary angles is.. [ 90 º 180 º 270 º 360 º ] 4- The sum of two supplementary angle is. [ 90 º 180 º 270 º 360 º ] 5- If m ( ABC ) = 120 then m ( reflex ABC ) =.. [ 270 º 240 º 140 º 60 º ] 6- The acute angle complements..angle. [ right acute obtuse st. ] 7- The measure of right angle. [ 90 º 180 º 270 º 360 º ] 8- The angle whose measure bigger than 90º and smaller than 180º is.angle. [ right acute obtuse st.] 9. The two angle make from a st. line and ray its start point on st. are.. [ complementary supplementary equal in measure there sum 360 º ] 10. From the opposite figure B a) X [ AC, YC, AY, CY ] b) AX AB = [ XAB, YX, { A }, AB ] Y C A X c) AB CY = [ { A }, { C }, CY, Ø ] 9
11- AB.AB [,,, ] 12- In ABC...if ( AC ) 2 = (AB ) 2 + ( BC ) 2 then m.. = 90 º [ C, B, A ] 13- In right angled triangle the sum of areas of two squares on the side of right angles equals [ The length of hypotenuse, the area of square on hypotenuse, twice the length of hypotenuse] 14- In triangle ABC if ( AC ) 2 = ( AB ) 2 ( BC ) 2 then m ( ) = 90 º [ A, B, C ] 15- The set of number can be formed right angled triangle [ { 3, 4, 7 }, { 5, 12, 13 }, { 6, 7, 10 }, { 12, 16, 17 } ] 16- L 1, L 2, L 3 three st. line on the same plane and L 1 // L 2, L 1 // L 3 then [ L 2 // L 3, L 2 L 3, L 1 L 2, L 1 // L 2 // L 3 ] 17- If A supplements B, A B then m ( A ) [ 45 º, 60 º, 90 º, 180 º ] 18- The polygon ABCD The polygon AYZL then BC [ XY, YZ, ZL, LX ] 20- If the polygon ABCD The polygon LMNF then C [ L, M, N, F ] 10
II- Complete : 1) In the opposite figure F, B AD C a) AB FD b) FC AD c) FC FD d) FA FC D F B A 2) The angle of measure complements the angle of measure 40 and supplements the angle of measure 3) The angle of measure 65º supplements angle of measure.and complements angle of measure 4) The angle of measure 178 2 1 º is..angle 5) If m ( ABC ) = 100 º then m ( reflex ABC ) =.. 6) If the two adjacent angles are supplementary then the other outer sides of angles are.. 7) The sum of two supplementary angles equals.. 8) The sum of two complementary angles equals.. 9) The sum of measures of accumulative angles at a point equal. 11
10) In the opposite figure. if Y XZ, L M m ( XYL ) = 30 º, m ( MYZ ) = 45 º m ( LYM ) = º. X Y Z 11) In the opposite figure A BH AD bisects CAH, m ( BAC ) = 40 º D C a) AB AH =.. b) AB AC = c) BA HA = H A B III- 1) In the opposite figure find m ( ABC ), m( CBH ) = 116 m( AB D ) = 98, m( DBH ) = 42 A C 2) In the opposite figure FH bisect AFC AB CD = { F },FH bisects ( AFC) m ( AFH ) = 26º Find m ( CFB ), m ( BFD )? 98 D B 42 H C H B F A D 12
3) In the opposite figure Prove that A, B, C on the same st. line Then Find m ( ABD ) D C 122 A B 45 135 4) In the opposite figure BA bisects DBH, m ( DBH ) = 70 º m ( DBC ) = 145º, prove that the point A, B, C are collinear. D C * A B * H 5) In the opposite figure AB CD = { M } m ( CMB ) = m ( BMH ) = m ( HMD ) Find : m ( A M C ) m ( A M D ) C B M A H D 6) By using geometrical tools, Draw the triangle ABC which AB = 6 cm, BC = 8 cm, AC = 10 cm, then draw BD bisect B and cut AC at D then find the length of BD 7) Draw ABC which A B = A C = 5 cm, B C = 6 cm draw from point A perpendicular on BC cut it at point D 13
8)In the opposite figure ABC is right angled triangle at B, ACD is right at C AB = 3 cm, BC = 4 cm, AD = 13 cm, D Find AC, DC A C B 9) In the opposite figure AB = AD, AC = 8 cm m ( BAC ) = m ( DAC ) = 30 º m ( D ) = 25. find the length of DC, m ( B ) A D C B 10) In the opposite figure the quadrilateral ABCD D m ( B ) = m ( D ) = 90 BC = DC, m ( ACD ) = 35 Find m ( DAB ) A C B 11) In the opposite figure the quadrilateral ABCD AC BD MD = MB D Prove that AB AD, BC DC A M C B 14
12) In the opposite figure m ( AMB ) = 45 º, m ( CMD ) = 120º C B m( BMC ) = 2 m ( AMB ), Complete: a) m ( BMC ) =.. b) m ( AMD ) =. M A c) m ( BMD ) =. D 13) In XYZ if ( XY ) 2 = (XZ ) 2 + (ZY ) 2 then m (..) = 90 º 14) The area of a square drawn on one side of right angled triangle equals 15) In XYZ ( YZ) 2 = (XZ ) 2 (XY 2 ) then the triangle is right angled at 16) The biggest side length in right angled is 17) If ABC DXF, m ( X ) = 87º, DF= 5cm C m ( D) = 35º, m ( C ) =.., AC =. A B E D F 18) In the opposite figure AB = DC, m ( ACB ) = 35 D A AB BC, DC BC M m ( BMC ) =..º C B 15
Parallism Find the value of X in each of the following figures. 1) 120 x 2) A B // C D m ( Y M A ) = 120 60 X 60 A B // C D m ( B ) = m ( C ) = 60 3) X A B C equilateral 16
4) B E bisect ( A B C ) A B // C D m ( C ) = 70 X * * 70 5) m ( L A B ) = 35 A B // C D m ( M C D ) = 40 35 x 40 6) E C // B D B D bisect the right angle B m( A C B ) = 60 17
Find the missing angles : 7) 8) 15 x * 120 m( B ) = 120 A B // C D A B // D C B C bisect ( B ) m ( E C F ) = 15 m ( A B F ) = 32 9) 10) 128 130?? 30 A B // C D m ( E C D ) = 90 m ( E C B ) = 130 A B // E D m ( A ) = 30, m ( E D C ) = 128 18
Complete : 1) If L and M are two parallel straight lines then L M = 2) If AB CD = φ then AB.CD 3) If L 1, L 2, L 3 are three straight lines such that L 1 // L 2, L 2 // L 3 then 4) If L 1, L 2, L 3 are three straight lines L 1 L 2 = φ, L 2 L 3 = φ then 5) From a point out side a given straight line there is exactly one and only straight line.. 6) If a straight line intersects two parallel straight lines then 1). 2). 3) Name the pairs of parallel straight lines, Give your reasons. H A * *60 D * * * E C B Prove that AH // CB H D 62 A 65 C 53 B 19