TALENT & OLYMPIAD. 3.6 Million MATHEMATICS. SOLD Over. copies of this series since the 1st Edition Revised Edition EXAMS RESOURCE BOOK CL ASS VIII

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Must For Maths Taent Search Exams & Oympiads SLIENT FETURES ` 50 Must For Science Taent Search Exams & Oympiads M S UNIQUE FETURES Synopsis: To provide the essence of a chapter in a nutshe Previous

no. of questions Questions @ Stimuating Minds: Seected questions to chaenge your higher order thinking TLENT & OLYMPI EXMS RESOURE OOK SOLUTIONS E-ook SOL Over 3.

com TLENT & OLYMPI EXMS RESOURE OOK MTHEMTIS L SS VIII Strong Foundation for etter Resuts ` 130/- M s Taent & Oympiad Exams Resource ook - MTHEMTIS VIII Suitabe for curricua of major boards ike SE /

1 Must For Maths Taent Search Exams & Oympiads SLIENT FETURES ` 50 Must For Science Taent Search Exams & Oympiads M S UNIQUE FETURES Synopsis: To provide the essence of a chapter in a nutshe Previous ontest Probems: Probems appeared in various taent & oympiad exams rossord Puzzes: To stimuate the mind to think beyond reguar preparation & to offer fun Soutions: Soutions and expanations for maximum no. of questions Stimuating Minds: Seected questions to chaenge your higher order thinking TLENT & OLYMPI EXMS RESOURE OOK SOLUTIONS E-ook SOL Over 3.6 Miion rain Mapping cademy copies of this series since the 1st Edition Revised Edition etaied soutions to a probems in Taent & Oympiad Exams Resource ook are avaiabe as this e-book on.bmataent.com TLENT & OLYMPI EXMS RESOURE OOK MTHEMTIS L SS VIII Strong Foundation for etter Resuts ` 130/- M s Taent & Oympiad Exams Resource ook - MTHEMTIS VIII Suitabe for curricua of major boards ike SE / ISE / State oards. Fundamenta concepts are thoroughy revised Extensive range of questions that stimuate the interests of the students hie testing their knoedge ppication/ski/knoedge/understanding oriented questions Suitabe for Internationa/Nationa/Regiona Oympiads and Taent exams ike NSTSE, Maths Oympiad, RMO, NMO, IMO etc. Hundreds of objective questions (F.bm re a e ta Sa e n m t. p co e) m M S.bmataent.com YOUR SOL Over 3.6 Miion OH India s FIRST scientificay designed porta for Oympiad preparation Oympiad & Taent Exams preparation packages naysis Reports Previous question papers Free emo Packages Free ndroid Mobie pp Get 15% discount on a packages by using the discount coupon code: KR157N unique opportunity to take about 50 tests per subject. rain Mapping cademy copies of this series since the 1st Edition Revised Edition

2 M s LSS VIII Mathematics.bmataent.com (Free Sampe)

3 Pubished by: rain Mapping cademy # /1/, First Foor, Farhath Hospita Road, Saeem Nagar, Maakpet, Hyderabad , E mai: info@bmataent.com Website:.bmataent.com UNIFIE OUNIL RIN MPPING EMY LL RIGHTS RESERVE No part of this book may be reproduced, stored in a retrieva system or transmitted in any form or by any means, eectronic, mechanica, photocopying, recording or otherise ithout the prior ritten permission of the pubisher. ISN : iscaimer Every care has been taken by the compiers and pubishers to give correct, compete and updated information. In case there is any omission, printing mistake or any other error hich might have crept in inadvertenty, neither the compier / pubisher nor any of the distributors take any ega responsibiity. In case of any dispute, a matters are subjected to the excusive jurisdiction of the courts in Hyderabad ony..bmataent.com (Free Sampe) Printed at: Sri Vinayaka rt Printers, Hyderabad.

4 Pubisher s Note Sometimes the understanding of fundamenta concepts aone does not hep the students to crack the competitive exams as most of them are objective in structure. Students need rigorous training to famiiarize themseves to the stye of the exams they are attempting. The board exams hich are of quaifying, but not competitive, nature do not competey address the needs of students in testing them in objective type format. To bridge this gap and to enabe the students to face the reaity of competitive exams, rain Mapping cademy, brought out an a-objective questions reference book. crisp summary of the topics and usefu equations ere provided at the beginning of each chapter so that the students can memorize the important points. are has been taken to design thought-provoking questions. These shoud hep students to attain a deeper understanding of principes. The questions have been revieed to fi the gaps in probem coverage and to buid the confidence in the students. They have aso been expanded to impart reasoning/ogica/anaytica skis. This book i cater a the requirements of the students ho are approaching nationa/state eve taent search examinations and a Oympiad exams. This book aso compements the additiona preparation needs of the students for the reguar board exams..bmataent.com (Free Sampe) We took utmost care to make this the best resource book avaiabe for the taent / oympiad exams aspirants. We ecome criticism from the students, teacher community and educators, especiay concerning any errors and deficiencies hich may have remained in this edition and the suggestions for improvement for the next edition.

For Your Information NTIONL LEVEL SIENE TLENT SERH EXMINTION im of this examination The focus on fundamentas is so important that ithout a firm understanding of them, a chid cannot be expected to

5 For Your Information NTIONL LEVEL SIENE TLENT SERH EXMINTION im of this examination The focus on fundamentas is so important that ithout a firm understanding of them, a chid cannot be expected to face the reaity of the competitive ord once he/she finishes the forma education. Even hie opting for higher studies the student has to go through a compete scan of hat he/she knos. Exams ike IIT-JEE, IEEE, IIMS, FM, T, ST, GRE, GMT, etc. are so designed to test the fundamenta strength of a student. Hence the need of the hour is buiding the fundamenta base as strong as possibe. successfu ife emerges out from heathy and sound competition. ompetition is the ony ay for the students to shake ethargy. It s the ony ay to get introduced for many orthiness. Firm standards in education and competition are the tonic for a promising and taented future. This exacty is the phiosophy behind the Unified ounci s NSTSE. Organisation Nationa Science Taent Search Examination is conducted by Unified ounci. Unified ounci is India s first ISO 9001 certified organisation in the educationa testing and assessment. Since its inception, Unified ounci has put together the best brains in an endeavour to make the younger generation fundamentay stronger and nourish their brains for a bright and enterprising future. Eigibiity : Students of casses 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 & 12 are eigibe to participate in this examination. Medium & Syabus: This exam is conducted in ony Engish medium and is suitabe for a the students fooing SE/ISE/State oard Syabi. Examination Pattern.bmataent.com (Free Sampe) There i be a separate question paper for each cass. questions are objective-type mutipe choice ith no negative marking for rong ansers. uration: 90 minutes ate : onducted every year on the ast Sunday of January. Test entres : Spread across the country.

6 Infrastructure The ounci makes use of utra-modern equipment such as Optica Mark Recognition (OMR) equipment to evauate the anser papers to proficienty assess students performance. The examination procedure is competey computerised. Unique Service from Unified ounci: Unique anaysis reports ike Student s Performance Report for students, Genera Schoo Report & Individua Schoo Report for schoos provided. These reports are very much hepfu for students & schoos to anayse their strengths and eaknesses. Genera Schoo Report (GSR) anayses the performance of students participating in the exam (subject-ise and cass-ise). The report, in graphica format i have Ogive and Histogram Graphs, hich are usefu to schoos that ish to improve their students performance by benchmarking the areas of eaknesses and buiding upon them. Individua Schoo Report (ISR) anayses the performance of a particuar schoo hen compared to the rest of the students participating in this examination (subject-ise, cass-ise and question-ise). This report acts as a too for the schoos to improve their students performance in the future by benchmarking the areas of eaknesses and buiding upon them. ards & Schoarships: FOR LSS I Mathematics : 25 marks Genera Science : 15 Marks FOR LSS II Mathematics : 25 marks Genera Science : 25 Marks FOR LSS III Mathematics : 40 marks Genera Science : 35 Marks FOR LSSES IV & V Mathematics : 45 marks Genera Science : 45 Marks Genera Questions : 10 marks IVISION OF MRKS FOR LSSES VI TO X Mathematics : 25 marks Physics : 25 marks hemistry : 20 marks ioogy : 20 marks Genera Questions : 10 marks FOR LSS XI & XII(PM) Mathematics : 40 marks Physics : 25 marks hemistry : 25 marks Genera Questions : 10 marks FOR LSS XI & XII(P) ioogy : 40 marks Physics : 25 marks hemistry : 25 marks Genera Questions : 10 marks.bmataent.com (Free Sampe) Top 100 members in each cass i be aarded ith ards & Medas etc. UNIFIE OUNIL n ISO 9001: 2008 ertified Organisation Foundation for success # /1/, Farhath Hospita Road, Saeem Nagar, Maakpet, Hyderabad Phones : , , E-mai: exam@unifiedcounci.com, Website:.unifiedcounci.com

7 ONTENTS Mathematics 1. Rationa Numbers Linear Equations in One Variabe Understanding Quadriateras ata Handing Squares and Square roots ubes and ube roots omparing Quantities gebraic Expressions and Identities Visuaising Soid Shapes Mensuration Exponents and Poers irect and Inverse Proportions Factorisation Introduction to Graphs bmataent.com (Free Sampe) 15. Paying ith Numbers Mode Test Paper Expanatory nsers rossord Soutions

8 M s Taent & Oympiad Exams Resource ook HPTER 3 ass VIII - Mathematics Understanding Quadriateras Quadriatera: cosed figure bounded by four ine segments is caed a quadriatera. It has four anges and four sides. assification of poygons Sampe Figure Number of sides, vertices, iagonas, Name of the shape 3, 3, 0 Triange 4, 4, 2 Quadriatera 5, 5, 5 Pentagon 6, 6, 9 Hexagon 7, 7, 14 Heptagon 8, 8, 20 Octagon iagonas: diagona is a ine segment connecting to non-consecutive vertices of a poygon. S P R Q E onvex poygon: poygon is said to be convex if no portion of its diagonas ies in its exterior..bmataent.com (Free Sampe) onvex poygons oncave poygon: poygon is said to be concave if some portion of its diagonas ies in its exterior. L K M N oncave poygons Understanding Quadriateras

9 M s Taent & Oympiad Exams Resource ook ass VIII - Mathematics Types of quadriateras: Property The diagonas are perpendicuar to each other. O y x x y Yes iagonas are equa and right bisectors of each other. Not aays.bmataent.com (Free Sampe) Understanding Quadriateras

10 M s Taent & Oympiad Exams Resource ook ass VIII - Mathematics 1 is a quadriatera. If and bisect each other, hat is? () square () paraeogram () rectange () the above 2 is a paraeogram. The ange bisectors of and meet at O. What is the measure of O? () 45º () 90º () 75º () 180º 3 The diagona of a rectange is 10 cm and its breadth is 6 cm. What is its ength? () 6 cm () 5 cm () 8 cm () 4 cm 4 and MNOP are quadriateras as shon in the figure. s p r q Which of the fooing is correct? () p + q + r + s = + x + y + z () p + q + r + s < + x + y + z () p + q + r + s > + x + y + z () Either () or () 5 What do you ca a paraeogram hich has equa diagonas? () trapezium () rectange () rhombus () kite 6 In a square, the diagonas bisect at O. What type of a triange is O? () n equiatera triange. () n isoscees but not a right anged triange. () right anged but not an isoscees triange. () n isoscees right anged triange. M P z x y N O 7 The perimeter of a paraeogram is 180 cm. If one side exceeds the other by 10 cm, hat are the sides of the paraeogram? () 40 cm, 50 cm () 45 cm each () 50 cm each () 45 cm, 50 cm 8 In the quadriatera, the diagonas and are equa and perpendicuar to each other. What type of a quadriatera is? () square () paraeogram () rhombus () trapezium 9 is a paraeogram as shon in the figure. If = 2 and P is the mid-point of, hat is the measure of P? () 90º () 60º () 45º () 135º 10 In a paraeogram, if = 2x + 5, = y + 1, = y + 5 and = 3x 4, hat is the ratio of and? () 71 : 21 () 12 : 11 () 31 : 35 () 4 : 7 11 If is an isoscees trapezium, hat is the measure of? () () () () 90º 12 diagona of a rectange is incined to one side of the rectange at 25º. What is the measure of the acute ange beteen the diagonas? () 25º () 40º () 50º () 55º 13 If anges P, Q, R and S of the quadriatera PQRS, taken in order, are in the ratio 3 : 7 : 6 : 4, hat is PQRS? () rhombus () paraeogram () trapezium () kite.bmataent.com (Free Sampe) P 3. Understanding Quadriateras 23

11 M s Taent & Oympiad Exams Resource ook ass VIII - Mathematics 22 Each interior ange of a reguar poygon is 150º. Ho many sides has the poygon? () 8 () 12 () 9 () In the figure, is a trapezium and = E. 4xº 85º 2xº xº E Find the vaue of x. () 30º () 40º () 60º () 50º 24 The figure shos a hexagon EF. = = 100º. The other anges are of the same size. E F 100 o 100 o Find. () 100º () 110º () 130º () 120º 25 Each interior ange of a reguar poygon is 162º. Ho many sides has the poygon? () 12 () 20 () 16 () is a quadriatera such that =, = 1 2 and = 1 4. If = 12 cm, hat is the measure of? () 6 cm () 4 cm () 12 cm ()3 cm 27 In the figure given, P E. If E = 3 cm, hat is the ength of? x x E () 4 () 3 3 () 3 () 5 28 Ho many measurements are required to construct a quadriatera? () 5 () 4 () 3 () 2 29 Ho many unique measurements are needed to construct a paraeogram? () 2 () 3 () 4 () 1 30 What is the minimum number of dimensions needed to construct a rectange? () 1 () 2 () 3 () 4 31 What is the minimum number of measurements needed to construct a square? () 1 () 2 () 3 () 4 32 In the diagram, KLMN is a constructed paraeogram. What is the measure of KLM? N M K L () 15 () 30 () 45 () The construction of hich figure is shon in the given figure? 3. Understanding Quadriateras 25 () trapezium () rhombus () rectange () kite 34 In the figure, is a rhombus. E and E are straight ines. s t.bmataent.com (Free Sampe) p E r q What is the vaue of p + q + r + s + t? () 200º () 270º () 360º () 540º

12 M s Taent & Oympiad Exams Resource ook ass VIII - Mathematics 35 In a trapezium, is parae to and the diagonas intersect each other at O. What is the ratio of O and O? () O O () () () Previous ontest Questions 1 In, P and Q are the midpoints of and. If PQ is produced to R such that PQ = QR, hat is PR? () rectange () square () rhombus () paraeogram 2 Three anges of a quadriatera are equa and the measure of the fourth ange is 120º. Find the measure of each of these equa anges. () 80º () 120º () 60º () 140º 3 quadriatera has three acute anges, each measuring 75º. Find the measure of the fourth ange. () 65º () 135º () 140º () 225º 4 In the figure given, PTU is a straight ine. R x Q S 125º 130º 85º T U What is the vaue of x? () 100º () 110º () 120º () 130º 5 Equiatera is dran on the side of square, E. P Find the measure of x shon in the figure. () 45 o () 135 o () 255 o () 225 o 6 What is the measure of XYW of the trapezium WXYZ given in the figure? W Z 35 o0 Y () 28 o () 33 o () 55 o () 37 o 7 In the given rectange PQRS, find the measure of POQ. P X 108 o O 66 o S R () 47 o () 24 o () 67 o () 58 o 8 The figure given is made up of a square and to isoscees trianges. What is the measure of the ange marked m? () 105 o () 95 o () 135 o () 85 o.bmataent.com (Free Sampe) 9 EF and FE are to isoscees trianges in the square. 70 F? m Q x E What is the measure of FE? E () 85 o () 65 o () 50 o () 130 o Understanding Quadriateras

13 Must For Maths Taent Search Exams & Oympiads SLIENT FETURES (F.bm re a e ta Sa e n m t. p co e) m Must For Science Taent Search Exams & Oympiads M S UNIQUE FETURES Synopsis: To provide the essence of a chapter in a nutshe Previous ontest Probems: Probems appeared in various taent & oympiad exams rossord Puzzes: To stimuate the mind to think beyond reguar preparation & to offer fun Soutions: Soutions and expanations for maximum no. of questions Stimuating Minds: Seected questions to chaenge your higher order thinking.bmataent.com YOUR TLENT & OLYMPI EXMS RESOURE OOK SOLUTIONS E-ook SOL Over 3.6 Miion rain Mapping cademy copies of this series since the 1st Edition Revised Edition etaied soutions to a probems in Taent & Oympiad Exams Resource ook are avaiabe as this e-book on.bmataent.com M s Taent & Oympiad Exams Resource ook - MTHEMTIS Suitabe for curricua of major boards ike SE / ISE / State oards. Fundamenta concepts are thoroughy revised Extensive range of questions that stimuate the interests of the students hie testing their knoedge ppication/ski/knoedge/understanding oriented questions Suitabe for Internationa/Nationa/Regiona Oympiads and Taent exams ike NSTSE, Maths Oympiad, RMO, NMO, IMO etc. Hundreds of objective questions VIII M S TLENT & OLYMPI EXMS RESOURE OOK MTHEMTIS Strong Foundation for etter Resuts SOL Over 3.6 Miion OH India s FIRST scientificay designed porta for Oympiad preparation Oympiad & Taent Exams preparation packages naysis Reports Previous question papers Free emo Packages Free ndroid Mobie pp Get 15% discount on a packages by using the discount coupon code: KR157N unique opportunity to take about 50 tests per subject. L SS VIII rain Mapping cademy copies of this series since the 1st Edition Revised Edition

SYMMETRY AND PRACTICAL GEOMETRY

SYMMETRY AND PRACTICAL GEOMETRY MTHEMTIS UNIT 9 SYMMETRY N RTIL GEOMETRY () Main oncepts and Resuts figure is said to have ine symmetry, if by foding the figure aong a ine, the eft and right parts of it coincide exacty. The ine is caed