Unit (1) Numbers. 1) Complete : - 1) If x N then ( 2x + 1 ) is.( even or odd ) 2) If x N then 2 x is. = 3 , 2 = 3. 3) 3 2 x
|
|
- Lilian Ginger Brown
- 5 years ago
- Views:
Transcription
1 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 5 3, 2 = ) 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) If 2 3 x X = 1, then x = 10) If x = 0 then x =. 11) number of factors of 24 =. 12) The number lies at the half way between 3 1, ) =. %, 0.7 =, 12.5 % = ) If x X = 0.6, then x =.. 15) Factors of 28 is.. 1
2 ) x x x x x x = = ) The multiplicative inverse of ( ) 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 ) < <, < < ) 15 >. 22) 7127 x 125 = 7127 x... = 8 23) 44 x 0.55 = 44 x ( ) = ) 0, 3, 8, 15, 24, 35,.,.., ) 1,,,,,., ) 1, 3 2, 5 3, 7 4, 9 5,., 27) a b +1 Q If b = II- Choose the correct answer : ) If 3 x = 27, xy = 1 then y =. [, 9,, ] ) 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) ~.. [ 800, 900, 1000, 1100 ] 5 5) If x > 5 then..the smallest no. [, 5 5,, x x x + 1 x 1 5 ] 2
3 6) If 13 7 = 52 x then x =. 7) 2 ( ) + 3 ( ) + 4 ( ) ( ) = [ 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) ~ [ 800, 900, 1000, 1100 ] III- Find : )... = ) ( 1 ) ( 1 ) ( 1 ) ( ) = ) 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, ) + = 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, ) x ( ) = then x = ) Arrange the following descendingly : 5 3,0.5,, ,
4 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 a = 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) =.. 19) ab x a 2 b 2 x a b 2 =. 4
5 20) 48x x = 8 x ) 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.) = 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 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
6 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 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
7 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 Samy Represent it by bar charts graph. 7
8 III- The following table shows the marks of Mona in Math in 5 month. Month sep Oct Nov Dec Jan Mark ) 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
9 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
10 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
11 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 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
12 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
13 3) In the opposite figure Prove that A, B, C on the same st. line Then Find m ( ABD ) D C 122 A B ) 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
14 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
15 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
16 Parallism Find the value of X in each of the following figures. 1) 120 x 2) A B // C D m ( Y M A ) = X 60 A B // C D m ( B ) = m ( C ) = 60 3) X A B C equilateral 16
17 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 ) = x 40 6) E C // B D B D bisect the right angle B m( A C B ) = 60 17
18 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) ?? 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 ) =
19 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
Nozha Directorate of Education Form : 2 nd Prep
Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep Nozha Language Schools Geometry Revision Sheet Ismailia Road Branch Sheet ( 1) 1-Complete 1. In the parallelogram, each
More informationNozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Ismailia Road Branch
Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch Sheet ( 1) 1-Complete 1. in the parallelogram, each two opposite
More informationAlg. 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.
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..
More informationAlg. (( Sheet 1 )) [1] Complete : 1) =.. 3) =. 4) 3 a 3 =.. 5) X 3 = 64 then X =. 6) 3 X 6 =... 7) 3
Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch [1] Complete : 1) 3 216 =.. Alg. (( Sheet 1 )) 1 8 2) 3 ( ) 2 =..
More informationQuestions. Exercise (1)
Questions Exercise (1) (1) hoose the correct answer: 1) The acute angle supplements. angle. a) acute b) obtuse c) right d) reflex 2) The right angle complements angle whose measure is. a) 0 b) 45 c) 90
More informationGeometry Honors Review for Midterm Exam
Geometry Honors Review for Midterm Exam Format of Midterm Exam: Scantron Sheet: Always/Sometimes/Never and Multiple Choice 40 Questions @ 1 point each = 40 pts. Free Response: Show all work and write answers
More informationClass : IX(CBSE) Worksheet - 1 Sub : Mathematics Topic : Number system
Class : IX(CBSE) Worksheet - Sub : Mathematics Topic : Number system I. Solve the following:. Insert rational numbers between. Epress 57 65 in the decimal form. 8 and.. Epress. as a fraction in the simplest
More information(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2
CIRCLE [STRAIGHT OBJECTIVE TYPE] Q. The line x y + = 0 is tangent to the circle at the point (, 5) and the centre of the circles lies on x y = 4. The radius of the circle is (A) 3 5 (B) 5 3 (C) 5 (D) 5
More information1. How many planes can be drawn through any three noncollinear points? a. 0 b. 1 c. 2 d. 3. a cm b cm c cm d. 21.
FALL SEMESTER EXAM REVIEW (Chapters 1-6) CHAPTER 1 1. How many planes can be drawn through any three noncollinear points? a. 0 b. 1 c. 2 d. 3 2. Find the length of PQ. a. 50.9 cm b. 46.3 cm c. 25.7 cm
More informationGeometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1
Name: Class: Date: Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1 Multiple Choice. Identify the choice that best completes the statement or answers the question. 1. Which statement(s)
More informationGrade 6 Math Circles March 22-23, 2016 Contest Prep - Geometry
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles March 22-23, 2016 Contest Prep - Geometry Today we will be focusing on how to solve
More information2. In ABC, the measure of angle B is twice the measure of angle A. Angle C measures three times the measure of angle A. If AC = 26, find AB.
2009 FGCU Mathematics Competition. Geometry Individual Test 1. You want to prove that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex. Which postulate/theorem
More information6 CHAPTER. Triangles. A plane figure bounded by three line segments is called a triangle.
6 CHAPTER We are Starting from a Point but want to Make it a Circle of Infinite Radius A plane figure bounded by three line segments is called a triangle We denote a triangle by the symbol In fig ABC has
More information4016/01 October/November 2011
ELEMENTARY MATHEMATICS Paper 1 Suggested Solutions 1. Topic: Arithmetic (Approximation & Estimation) 4.51 4016/01 October/November 2011 19.6.91 2 1.05 ( sig. fig.) Answer 1.05 [2] 2. Topic: Integers 2
More informationChapter 7. Geometric Inequalities
4. Let m S, then 3 2 m R. Since the angles are supplementary: 3 2580 4568 542 Therefore, m S 42 and m R 38. Part IV 5. Statements Reasons. ABC is not scalene.. Assumption. 2. ABC has at least 2. Definition
More informationGeometry. Midterm Review
Geometry Midterm Review Class: Date: Geometry Midterm Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1 A plumber knows that if you shut off the water
More informationSt. Fatima Language Schools
The Vision of the School: Distinct Environment for Refined Education St. Fatima Language Schools Work sheets (2018/ 2019) Primary (5) (First Term ) Name :.. Class :.. sup :Maha Ahmed -0- Sheet (1) 1) Approximate
More information1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle?
1 For all problems, NOTA stands for None of the Above. 1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle? (A) 40 (B) 60 (C) 80 (D) Cannot be determined
More informationThe vision of the school: Distinct Environment for Refined Education. Supervisor of Mathematics Mrs. Shereen Wahba -1-
The vision of the school: Distinct Environment for Refined Education Supervisor of Mathematics Mrs. Shereen Wahba -1- St. Fatima L. S. Primary [1] Complete:- Multiplying 10 a) 2 = =.. b) 10 + 10 + 10 +
More informationSOLUTIONS SECTION A [1] = 27(27 15)(27 25)(27 14) = 27(12)(2)(13) = cm. = s(s a)(s b)(s c)
1. (A) 1 1 1 11 1 + 6 6 5 30 5 5 5 5 6 = 6 6 SOLUTIONS SECTION A. (B) Let the angles be x and 3x respectively x+3x = 180 o (sum of angles on same side of transversal is 180 o ) x=36 0 So, larger angle=3x
More informationCONGRUENCE OF TRIANGLES
Congruence of Triangles 11 CONGRUENCE OF TRIANGLES You might have observed that leaves of different trees have different shapes, but leaves of the same tree have almost the same shape. Although they may
More informationSection 2-1. Chapter 2. Make Conjectures. Example 1. Reasoning and Proof. Inductive Reasoning and Conjecture
Chapter 2 Reasoning and Proof Section 2-1 Inductive Reasoning and Conjecture Make Conjectures Inductive reasoning - reasoning that uses a number of specific examples to arrive at a conclusion Conjecture
More informationMathematics Class X Past Year Paper Time: 2½ hour Total Marks: 80
Pas Year Paper Mathematics Class X Past Year Paper - 013 Time: ½ hour Total Marks: 80 Solution SECTION A (40 marks) Sol. 1 (a) A + X B + C 6 3 4 0 X 0 4 0 0 6 6 4 4 0 X 0 8 0 0 6 4 X 0 8 4 6 X 8 0 4 10
More information0114ge. Geometry Regents Exam 0114
0114ge 1 The midpoint of AB is M(4, 2). If the coordinates of A are (6, 4), what are the coordinates of B? 1) (1, 3) 2) (2, 8) 3) (5, 1) 4) (14, 0) 2 Which diagram shows the construction of a 45 angle?
More informationNotes: Review of Algebra I skills
Notes: Review of Algebra I skills http://www.monroeps.org/honors_geometry.aspx http://www.parklandsd.org/wp-content/uploads/hrs_geometry.pdf Name: Date: Period: Algebra Review: Systems of Equations * If
More informationHANOI OPEN MATHEMATICS COMPETITON PROBLEMS
HANOI MATHEMATICAL SOCIETY NGUYEN VAN MAU HANOI OPEN MATHEMATICS COMPETITON PROBLEMS 2006-2013 HANOI - 2013 Contents 1 Hanoi Open Mathematics Competition 3 1.1 Hanoi Open Mathematics Competition 2006...
More informationGEO REVIEW TEST #1. 1. In which quadrilateral are the diagonals always congruent?
GEO REVIEW TEST #1 Name: Date: 1. In which quadrilateral are the diagonals always congruent? (1) rectangle (3) rhombus 4. In the accompanying diagram, lines AB and CD intersect at point E. If m AED = (x+10)
More informationMathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions
Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions Quiz #1. Tuesday, 17 January, 2012. [10 minutes] 1. Given a line segment AB, use (some of) Postulates I V,
More informationright angle an angle whose measure is exactly 90ᴼ
right angle an angle whose measure is exactly 90ᴼ m B = 90ᴼ B two angles that share a common ray A D C B Vertical Angles A D C B E two angles that are opposite of each other and share a common vertex two
More informationGeometry Unit 2 Review Show all work and follow the criteria for credit.
Competency 1: Angles and Angle Bisectors 1. What is the classification of an angle that has a measure of less than 90 o? 4. Given the diagram below where BD is an angle bisector. A D 2. Given the following
More informationANSWERS. CLASS: VIII TERM - 1 SUBJECT: Mathematics. Exercise: 1(A) Exercise: 1(B)
ANSWERS CLASS: VIII TERM - 1 SUBJECT: Mathematics TOPIC: 1. Rational Numbers Exercise: 1(A) 1. Fill in the blanks: (i) -21/24 (ii) -4/7 < -4/11 (iii)16/19 (iv)11/13 and -11/13 (v) 0 2. Answer True or False:
More informationPURPLE COMET MATH MEET April 2011 MIDDLE SCHOOL - SOLUTIONS. There are relatively prime positive integers m and n so that. = m n.
PURPLE COMET MATH MEET April 0 MIDDLE SCHOOL - SOLUTIONS Copyright c Titu Andreescu and Jonathan Kane Problem There are relatively prime positive integers m and n so that Find m + n. 4 + 4 + 4 + 4 + 4
More informationSMT 2018 Geometry Test Solutions February 17, 2018
SMT 018 Geometry Test Solutions February 17, 018 1. Consider a semi-circle with diameter AB. Let points C and D be on diameter AB such that CD forms the base of a square inscribed in the semicircle. Given
More informationchapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?
chapter vector geometry solutions V. Exercise A. For the shape shown, find a single vector which is equal to a)!!! " AB + BC AC b)! AD!!! " + DB AB c)! AC + CD AD d)! BC + CD!!! " + DA BA e) CD!!! " "
More informationPart (1) Second : Trigonometry. Tan
Part (1) Second : Trigonometry (1) Complete the following table : The angle Ratio 42 12 \ Sin 0.3214 Cas 0.5321 Tan 2.0625 (2) Complete the following : 1) 46 36 \ 24 \\ =. In degrees. 2) 44.125 = in degrees,
More informationBasic Trigonometry. Trigonometry deals with the relations between the sides and angles of triangles.
Basic Trigonometry Trigonometry deals with the relations between the sides and angles of triangles. A triangle has three sides and three angles. Depending on the size of the angles, triangles can be: -
More informationGeometry Chapter 3 3-6: PROVE THEOREMS ABOUT PERPENDICULAR LINES
Geometry Chapter 3 3-6: PROVE THEOREMS ABOUT PERPENDICULAR LINES Warm-Up 1.) What is the distance between the points (2, 3) and (5, 7). 2.) If < 1 and < 2 are complements, and m < 1 = 49, then what is
More informationQuestion 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD?
Class IX - NCERT Maths Exercise (7.1) Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? Solution 1: In ABC and ABD,
More informationGCSE style questions arranged by topic
Write your name here Surname ther names In the style of: Pearson Edexcel Level 1/Level 2 GCSE (9-1) Centre Number Mathematics Circle Theorems GCSE style questions arranged by topic Candidate Number Higher
More informationClass IX Chapter 7 Triangles Maths
Class IX Chapter 7 Triangles Maths 1: Exercise 7.1 Question In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? In ABC and ABD,
More information*Please do not write on these worksheets. Show all diagrams, work, and answers on your own piece of paper*
Geometry Homework Worksheets: Chapter 1 *Please do not write on these worksheets. Show all diagrams, work, and answers on your own piece of paper* HW#1: Problems #1-10 For #1-4, choose the best answer
More informationHW Set #1: Problems #1-8 For #1-4, choose the best answer for each multiple choice question.
Geometry Homework Worksheets: Chapter 2 HW Set #1: Problems #1-8 For #1-4, choose the best answer for each multiple choice question. 1. Which of the following statements is/are always true? I. adjacent
More information0809ge. Geometry Regents Exam Based on the diagram below, which statement is true?
0809ge 1 Based on the diagram below, which statement is true? 3 In the diagram of ABC below, AB AC. The measure of B is 40. 1) a b ) a c 3) b c 4) d e What is the measure of A? 1) 40 ) 50 3) 70 4) 100
More informationProperties of the Circle
9 Properties of the Circle TERMINOLOGY Arc: Part of a curve, most commonly a portion of the distance around the circumference of a circle Chord: A straight line joining two points on the circumference
More informationHonors Geometry Mid-Term Exam Review
Class: Date: Honors Geometry Mid-Term Exam Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. Classify the triangle by its sides. The
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 27, 2011 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name
More information9 th CBSE Mega Test - II
9 th CBSE Mega Test - II Time: 3 hours Max. Marks: 90 General Instructions All questions are compulsory. The question paper consists of 34 questions divided into four sections A, B, C and D. Section A
More informationHOLIDAY HOMEWORK - CLASS VIII MATH
HOLIDAY HOMEWORK - CLASS VIII MATH Assignment I ( Unit: Squares and Square Roots) 1. Which of the following numbers are perfect squares? Justify your answer by prime factorisation method. (a) 1764 (b)
More informationKENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION
KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 01 F PERIODIC TEST III EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS IX Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks)
More informationTriangle Congruence and Similarity Review. Show all work for full credit. 5. In the drawing, what is the measure of angle y?
Triangle Congruence and Similarity Review Score Name: Date: Show all work for full credit. 1. In a plane, lines that never meet are called. 5. In the drawing, what is the measure of angle y? A. parallel
More information1.) Determine whether the following numbers could be the sides of a right triangle. Show your work.
4Unit 2 review Version 1 Name: Date: 1.) Determine whether the following numbers could be the sides of a right triangle. Show your work. a. 7, 25, 19 b. 17, 15, 8 2.) What is the approximate length of
More informationClass IX Chapter 7 Triangles Maths. Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure).
Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? In ABC and ABD, AC = AD (Given) CAB = DAB (AB bisects
More informationG.CO.6-9 ONLY COMMON CORE QUESTIONS
Class: Date: G.CO.6-9 ONLY COMMON CORE QUESTIONS Multiple Choice Identify the choice that best completes the statement or answers the question. 1 The image of ABC after a rotation of 90º clockwise about
More informationPre RMO Exam Paper Solution:
Paper Solution:. How many positive integers less than 000 have the property that the sum of the digits of each such number is divisible by 7 and the number itself is divisible by 3? Sum of Digits Drivable
More informationMathematics. A basic Course for beginers in G.C.E. (Advanced Level) Mathematics
Mathematics A basic Course for beginers in G.C.E. (Advanced Level) Mathematics Department of Mathematics Faculty of Science and Technology National Institute of Education Maharagama Sri Lanka 2009 Director
More information1. The sides of a triangle are in the ratio 3 : 5 : 9. Which of the following words best describes the triangle?
UNIVERSITY OF NORTH CAROLINA CHARLOTTE 999 HIGH SCHOOL MATHEMATICS CONTEST March 8, 999 The sides of a triangle are in the ratio : 5 : 9 Which of the following words best describes the triangle? (A) obtuse
More informationTHEOREMS WE KNOW PROJECT
1 This is a list of all of the theorems that you know and that will be helpful when working on proofs for the rest of the unit. In the Notes section I would like you to write anything that will help you
More information1) Complete : 25 1) =. ( as a mixed no.) 6
Revision sheet ) Complete : 25 ) =. ( as a mixed no.) 6 9 2) =.. ( as an improper fraction ) ) 6 = ( as a decimal form) ) The place value of the digit 5 in 67. 58 is 5) Five hundred thirty two and five
More information(b) Follow-up visits: December, May, October, March. (c ) 10, 4, -2, -8,..
Geometry Honors - Chapter 2 Reasoning and Proof Section 2-1 Inductive Reasoning and Conjecture I can explore inductive and deductive reasoning. I can find counterexamples to disprove conjectures. I can
More informationCLASS IX : CHAPTER - 1 NUMBER SYSTEM
MCQ WORKSHEET-I CLASS IX : CHAPTER - 1 NUMBER SYSTEM 1. Rational number 3 40 is equal to: (a) 0.75 (b) 0.1 (c) 0.01 (d) 0.075. A rational number between 3 and 4 is: (a) 3 (b) 4 3 (c) 7 (d) 7 4 3. A rational
More informationAnswers. Chapter 9 A92. Angles Theorem (Thm. 5.6) then XZY. Base Angles Theorem (Thm. 5.6) 5, 2. then WV WZ;
9 9. M, 0. M ( 9, 4) 7. If WZ XZ, then ZWX ZXW ; Base Angles Theorem (Thm..6). M 9,. M ( 4, ) 74. If XZ XY, then XZY Y; Base Angles Theorem (Thm..6). M, 4. M ( 9, ) 7. If V WZV, then WV WZ; Converse of
More information+ 10 then give the value
1. Match each vocabulary word to the picture. A. Linear Pair B. Vertical Angles P1 C. Angle Bisector D. Parallel Lines E. Orthocenter F. Centroid For questions 3 4 use the diagram below. Y Z X U W V A
More informationLesson. Warm Up deductive 2. D. 3. I will go to the store; Law of Detachment. Lesson Practice 31
Warm Up 1. deductive 2. D b. a and b intersect 1 and 2 are supplementary 2 and 3 are supplementary 3. I will go to the store; Law of Detachment Lesson Practice a. 1. 1 and 2 are. 2. 1 and 3 are. 3. m 1
More informationArithmetic with Whole Numbers and Money Variables and Evaluation (page 6)
LESSON Name 1 Arithmetic with Whole Numbers and Money Variables and Evaluation (page 6) Counting numbers or natural numbers are the numbers we use to count: {1, 2, 3, 4, 5, ) Whole numbers are the counting
More informationMathematics. Mock Paper. With. Blue Print of Original Paper. on Latest Pattern. Solution Visits:
10 th CBSE{SA I} Mathematics Mock Paper With Blue Print of Original Paper on Latest Pattern Solution Visits: www.pioneermathematics.com/latest_updates www.pioneermathematics.com S.C.O. - 36, Sector 40
More informationGeometry Final Review. Chapter 1. Name: Per: Vocab. Example Problems
Geometry Final Review Name: Per: Vocab Word Acute angle Adjacent angles Angle bisector Collinear Line Linear pair Midpoint Obtuse angle Plane Pythagorean theorem Ray Right angle Supplementary angles Complementary
More information81-E 2. Ans. : 2. Universal set U = { 2, 3, 5, 6, 10 }, subset A = { 5, 6 }. The diagram which represents A / is. Ans. : ( SPACE FOR ROUGH WORK )
81-E 2 General Instructions : i) The question-cum-answer booklet contains two Parts, Part A & Part B. ii) iii) iv) Part A consists of 60 questions and Part B consists of 16 questions. Space has been provided
More informationPre-Regional Mathematical Olympiad Solution 2017
Pre-Regional Mathematical Olympiad Solution 07 Time:.5 hours. Maximum Marks: 50 [Each Question carries 5 marks]. How many positive integers less than 000 have the property that the sum of the digits of
More informationGeometry. Unit 2- Reasoning and Proof. Name:
Geometry Unit 2- Reasoning and Proof Name: 1 Geometry Chapter 2 Reasoning and Proof ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** 1. (2-1)
More informationPlease allow yourself one to two hours to complete the following sections of the packet. College Integrated Geometry Honors Integrated Geometry
Incoming Integrated Geometry Summer Work Dear Incoming Integrated Geometry Students, To better prepare for your high school mathematics entry process, summer work is assigned to ensure an easier transition
More information7.5 Proportionality Relationships
www.ck12.org Chapter 7. Similarity 7.5 Proportionality Relationships Learning Objectives Identify proportional segments when two sides of a triangle are cut by a segment parallel to the third side. Extend
More information0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 2) 8 3) 3 4) 6 2 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
More informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Pearson Edexcel International GCSE Centre Number Mathematics B Paper 1 Candidate Number Tuesday 6 January 2015 Afternoon Time: 1 hour 30 minutes Paper Reference
More informationTERMWISE SYLLABUS SESSION CLASS-IX SUBJECT : MATHEMATICS. Course Structure. Schedule for Periodic Assessments and CASExam. of Session
TERMWISE SYLLABUS SESSION-2018-19 CLASS-IX SUBJECT : MATHEMATICS Course Structure Units Unit Name Marks I NUMBER SYSTEMS 08 II ALGEBRA 17 III COORDINATE GEOMETRY 04 IV GEOMETRY 28 V MENSURATION 13 VI STATISTICS
More informationTriangles. Chapter Flowchart. The Chapter Flowcharts give you the gist of the chapter flow in a single glance.
Triangles Chapter Flowchart The Chapter Flowcharts give you the gist of the chapter flow in a single glance. Triangle A plane figure bounded by three line segments is called a triangle. Types of Triangles
More informationGEOMETRY CHAPTER 2: Deductive Reasoning
GEOMETRY CHAPTER 2: Deductive Reasoning NAME Page 1 of 34 Section 2-1: If-Then Statements; Converses Conditional Statement: If hypothesis, then conclusion. hypothesis conclusion converse conditional statement
More informationFill in the blanks Chapter 10 Circles Exercise 10.1 Question 1: (i) The centre of a circle lies in of the circle. (exterior/ interior) (ii) A point, whose distance from the centre of a circle is greater
More informationDownloaded from
MODEL TEST PAPER SUMMATIVE ASSESSMENT-I SOLVED Time : 3 hrs. Maximum Marks: 80 General Instructions. Section-A consists of 8 parts carrying 1 mark each Section-B Q2 to Q11 carry 2 marks each Section-C
More informationThe matrix: "Is an organization of some elements written in rows
st term st Sec. Algebra. The matrix: "Is an organization of some elements written in rows Ex: and columns between brackets in the form ( ) ". st column nd rd - st row - nd row 7 rd row * The order of any
More informationNon-standard MMC problems
Non-standard MMC problems Carl Joshua Quines 1 Algebra 1. (15S/9B/E6) A quadratic function f(x) satisfies f(0) = 30 and f(2) = 0. Determine all the zeros of f(x). [2 and 15] 2. (15S/IVB/E6) What is the
More informationADARSHA VIDYALAYA HUNASHYAL P.B
ADARSHA VIDYALAYA HUNASHYAL P.B SUBJECT : MATHEMATICS MATHEMATICS FA 1 SL.N O CONTENTS TOPIC FA 1 PLYING WITH-NUMBERS ARITHMETIC FA - 1 2 SQUARE,SQUARE ROOTS CUBES AND CUBE ROOTS ARITHMETIC FA - 1 3 RATIONAL
More information1966 IMO Shortlist. IMO Shortlist 1966
IMO Shortlist 1966 1 Given n > 3 points in the plane such that no three of the points are collinear. Does there exist a circle passing through (at least) 3 of the given points and not containing any other
More informationSimilarity of Triangle
Similarity of Triangle 95 17 Similarity of Triangle 17.1 INTRODUCTION Looking around you will see many objects which are of the same shape but of same or different sizes. For examples, leaves of a tree
More informationGeometry Problem Solving Drill 08: Congruent Triangles
Geometry Problem Solving Drill 08: Congruent Triangles Question No. 1 of 10 Question 1. The following triangles are congruent. What is the value of x? Question #01 (A) 13.33 (B) 10 (C) 31 (D) 18 You set
More informationTRIANGLES CHAPTER 7. (A) Main Concepts and Results. (B) Multiple Choice Questions
CHAPTER 7 TRIANGLES (A) Main Concepts and Results Triangles and their parts, Congruence of triangles, Congruence and correspondence of vertices, Criteria for Congruence of triangles: (i) SAS (ii) ASA (iii)
More informationMath 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper.
Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper. 12. What angle has the same measure as its complement? How do you know? 12. What is the
More informationProofs. by Bill Hanlon
Proofs by Bill Hanlon Future Reference To prove congruence, it is important that you remember not only your congruence theorems, but know your parallel line theorems, and theorems concerning triangles.
More informationKENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION
KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 01 F SESSING ENDING EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS IX Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA
More informationHigher Geometry Problems
Higher Geometry Problems (1 Look up Eucidean Geometry on Wikipedia, and write down the English translation given of each of the first four postulates of Euclid. Rewrite each postulate as a clear statement
More informationName :. Class :.. Homework Rubric : ( 10 marks )
Name :. Class :.. Homework Rubric : ( 10 marks ) 8 marks for accuracy.( To be complete and correct ) 1 mark for punctuality. ( To be delivered on time ) 1 mark for organization ( To be clean, neat and
More informationQUESTION BANK ON STRAIGHT LINE AND CIRCLE
QUESTION BANK ON STRAIGHT LINE AND CIRCLE Select the correct alternative : (Only one is correct) Q. If the lines x + y + = 0 ; 4x + y + 4 = 0 and x + αy + β = 0, where α + β =, are concurrent then α =,
More informationCAREER POINT PRE FOUNDATION DIVISON CLASS-9. IMO Stage-II Exam MATHEMATICS Date :
CAREER POINT PRE FOUNDATION DIVISON IMO Stage-II Exam.-07 CLASS-9 MATHEMATICS Date : -0-07 Q. In the given figure, PQR is a right angled triangle, right angled at Q. If QRST is a square on side QR and
More informationHonors Geometry Midterm Questions
2015-16 Honors Geometry Midterm Questions Name 1. What is the midpoint of a line that has endpoints at (0, 3) and (6, -1)? A. (12, 2) B. (3, 1) C. (12, -5) D. (3, 2) 2. 3. If X is the midpoint of CN and
More informationImportant Instructions for the School Principal. (Not to be printed with the question paper)
Important Instructions for the School Principal (Not to be printed with the question paper) 1) This question paper is strictly meant for use in school based SA-II, March-2012 only. This question paper
More informationArchdiocese of Washington Catholic Schools Academic Standards Mathematics
6 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students compare and order positive and negative integers*, decimals, fractions, and mixed numbers. They find multiples*
More information[STRAIGHT OBJECTIVE TYPE] Q.4 The expression cot 9 + cot 27 + cot 63 + cot 81 is equal to (A) 16 (B) 64 (C) 80 (D) none of these
Q. Given a + a + cosec [STRAIGHT OBJECTIVE TYPE] F HG ( a x) I K J = 0 then, which of the following holds good? (A) a = ; x I a = ; x I a R ; x a, x are finite but not possible to find Q. The minimum value
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 17, 2011 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of
More informationMath Contest, Fall 2017 BC EXAM , z =
Math Contest, Fall 017 BC EXAM 1. List x, y, z in order from smallest to largest fraction: x = 111110 111111, y = 1 3, z = 333331 333334 Consider 1 x = 1 111111, 1 y = thus 1 x > 1 z > 1 y, and so x
More informationHanoi Open Mathematical Competition 2017
Hanoi Open Mathematical Competition 2017 Junior Section Saturday, 4 March 2017 08h30-11h30 Important: Answer to all 15 questions. Write your answers on the answer sheets provided. For the multiple choice
More information0811ge. Geometry Regents Exam
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 ) 8 3) 3 4) 6 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
More information