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1st EDITION

I SBN SYLLABUS COVERED

YEAR 2021 978-93-5423-515-3

Covers Syllabus of CBSE, CISCE, State Board & International Boards

PUBLISHED BY

COPYRIG HT

RESERVED BY THE PUBLISHERS

All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without written permission from the publishers. The author and publisher will gladly receive information enabling them to rectify any error or omission in subsequent editions.

OSWAAL BOOKS & LEARNING PVT. LTD. 1/11, Sahitya Kunj, M.G. Road, Agra - 282002, (UP) India

1/1, Cambourne Business Centre Cambridge, Cambridgeshire CB 236DP, United kingdom

0562-2857671 0562-2527781

[email protected]

www.OswaalBooks.com

DI SCL A IM ER

Oswaal Books has exercised due care and caution in collecting all the data before publishing this book. In spite of this, if any omission, inaccuracy or printing error occurs with regard to the data contained in this book, Oswaal Books will not be held responsible or liable. Oswaal Books will be grateful if you could point out any such error or offer your suggestions which will be of great help for other readers. Printed at Alankar ( 2 )Graphics, Agra

TABLE OF CONTENTS g

Latest Syllabus for Academic year 2021

1.

Roman Numerals

2.

7 - 7 9 -

18

Large Numbers

19 -

36

3.

Addition and Subtraction

37 -

53

4.

Multiplication and Division

54 -

74

5.

Factors and Multiples

75 -

92

6.

Fractions and Decimals

93 -

121

7.

Geometry

122 -

141

8.

Measurement

142 -

155

9.

Money, Time and Calender

156 -

172

10.

Perimeter and Area

173 -

191

11.

Data Handling

192 -

211

12.

Symmetry and Patterns

212 -

232

l

Sample Question Paper, Level-1

233 -

237

l

Sample Question Paper, Level-2

238 -

247

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HOW TO IMPROVE YOUR CHILD’S MENTAL CALCULATION?

Do you want your child to calculate 305*650 at a lightning speed?

Mathematics is the most useful and fundamental aspect of our lives. Therefore, preparing the children to deal with difficult Math problems from an early age can significantly improve the quality of their lives & support them in their future endeavors.

1. Practice Every Day

Practice

Get your children excited about Math! Don’t restrict learning Math lessons or concepts to just 45 mins of classroom session. For instance: Ask your children to compute the cost of some everyday grocery items.

2. Technology Today’s children are technology lovers. Show them some fun Math riddles on YouTube or introduce them to Apps like My Math App that have some really fun practice exercises to increase calculation

3. Cognitive Learning Tools Try out games or innovative teaching tools like Abacus, Flashcards or Sudoku. These methods have a greater impact on students’ comprehension and retention.

4. Math Tricks Making children learn just the core principles of the subject can put them down or they might lose interest. Teach them some speed math tricks like quick calculation of squares, addition & subtraction of large numbers etc.

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LET THE FUN RIDE BEGIN!

Want to make your child future ready? Olympiad exams can be considered a special avenue of personal growth in a student’s life. children in India get the



opportunity to sit for these unique exams every year from a very early age. Olympiads allow parents to understand their child’s potential as compared to lakhs of students from all over the country, or even all over the globe. Olympiads

Classroom is like a pond in which kids learn to swim. But one day they will outgrow this pond and will have to swim in the ocean – the real world. As parents you have the onus of preparing them for this real world. Gone are the days when a child’s knowledge or intelligence was judged by their scores in classroom tests. The motive behind Olympiads is to prepare the children for the competition they will be facing beyond the four walls of the classrooms. Olympiads test children’s logical and reasoning abilities – two of the most vital and helpful life skills. Oswaal Books has carefully designed this special edition; Olympiad Previous Years’ Solved Papers. The book aims to bring out the best in a child by honing their concepts and sharpening their minds. The book covers syllabi of all leading boards like CBSE, CISCE, State & International Boards.

Learning beyond the regular!

test logical thinking and scientific reasoning. They demand a deeper understanding of concepts and help sharpen analytical skills. They nurture curiosity and push students to go the extra mile. Studying diligently for Olympiads is bound to improve a student’s grades in school as well. Moreover, these exams train students for other future competitive exams and boost their confidence.

What’s so unique about Oswaal One for All Olympiad for your child? (1) 100% Updated: Based on the latest exam pattern issued by: IMO, SEAMO, ISTSE, UIMO, NMITO and SZF (2) Thorough Practice: Solved Previous Years’ Papers from 2011 to 2019 (3) Competency Evaluation: Better assessment through 3 Levels of Questions: Level 1, Level 2 & Achievers (4) Valuable Insights: Find Amazing Facts, Fun Trivia & Did You Know, inside (5) Revise & Remember: Complete concept review with

Our Heartfelt Gratitude!

examples

We have taken due care in

This book aims to make the children exam-ready, boost their confidence and improve their problem-solving ability. With the moto of ‘Learning Made Simple’, Oswaal Books is constantly striving to make learning simple & accessible for students across

developing this book. There have been a lot of people who have helped us in our journey. We would like to offer heartfelt

the globe.

With Best Wishes!

gratitude to them- our authors,

Team Oswaal Books

editors, reviewers

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NAVIGATION MADE SIMPLE!

Learning Outcomes

Concept Review

Amazing Facts

Did you Know

Fun Trivia

Multiple Choice Questions

Answer Keys

Answers with Explanations

Where to report any plausible content or technical error?

Write to us on: [email protected] Full name of the book with its ISBN Mention the page number and specify the error You may also upload an image with the error marked, with a little detail of the error.

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SYLLABUS

There are so many platforms based on National and International level who are conducting OLYMPIAD Exams from class 1 to 12.



Students are able to face the Most Popular below listed exam;



•

International Maths Olympiad (IMO)



•

Maths Olympiad (MO)



•

Unified International Mathematics Olympiad (UIMO)



•

Southeast Asian Mathematical Olympiad (SEAMO)



•

International Olympiad of Science (IOS)



•

National Level Science Talent Search Examination (NSTSE)



•

National Science Olympiad (NSO)



•

Science Olympiad (SO)



•

International General Knowledge Olympiad (IGKO)



•

International Reasoning & Aptitude Olympiad (IRAO)



•

International Talent Hunt Olympiad (ITHO)



•

International English Olympiad (IEO)



•

Unified International English Olympiad (UIEO)



•

International English Language Olympiad (IOEL)



•

International Society for Olympiad (ISO)



Since in the race of Olympiad Exam, students are participating from India and Abroad via different channels, so we Oswaal has published a unique book for these exams wherein we have covered the latest syllabus of CBSE, CISCE, IGCSE, IB, and All Indian and International recognised Boards. Based on the above Boards Curriculum, we have extracted & refined below syllabus:

Syllabus: Mathematics

Section – 1 : Patterns, Alphabet Test, Coding-Decoding, Ranking Test, Mirror Images, Geometrical Shapes and Solids, Embedded Figures, Direction Sense Test, Days and Dates & Possible Combinations, Analogy and Classification.



Section – 2 : Numerals and Number Names, Number Sense (more than 4-digit numbers), Computation Operations, Fractions, Length, Weight, Capacity, Time, Money, Geometry, Perimeter of Various Shapes, Symmetry, Conversions, Data Handling.



Section – 3 : The Syllabus of this section will be based on the Syllabus of Mathematical Reasoning.



Section – 4 : Higher Order Thinking Questions – Syllabus as per Section–2 qq

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Roman Numerals

9

1

CHAPTER

ROMAN NUMERALS

Learning Outcomes

 Understand how to read and write Roman numerals.  Learn how to convert Hindu-Arabic numbers to Roman numerals.  Learn how to convert Roman numerals to Hindu-Arabic numbers.

Concept Review INTRODUCTION Have you ever noticed a clock or a wrist watch that has symbols (numerals) I, II, III, IV,…, XII instead of 1, 2, 3,…,12?

AMAZING FACT



What do these symbols (numerals) represent? How they are different from the numbers we use?

Roman Numerals Well, these are Roman numerals. Roman numerals were developed by the Romans many years ago. However, we still use them in our daily life. The Romans used seven letters of the English alphabet to represent numeric (Hindu-Arabic numbers). Hindu-Arabic Numbers Roman Numerals

1

5

10

50

100

500

1000

I

V

X

L

C

D

M

The history of Roman numerals began back in the 8th to 9th century BC, approximately the same time as the founding of ancient Rome around Palantine Hill. The numeric system of ancient Rome prevailed longer than the empire itself, remaining in common use until the 14th century.

Roman Numerals

Various combinations of these seven numerals are used to create Hindu-Arabic numbers. Let us learn to form Roman numerals of numbers by following some basic rules: Rule 1 : The symbols I, X and C can be used to three times in a number and the values are added. Examples : II =1+1 =2 III =1+1+1 =3 DID YOU KNOW? XX = 10 + 10 = 20 There is no symbol XXX = 10 + 10 + 10 = 30 Rule 2 : A symbol of smaller value before a symbol of greater for zero in the Roman numerals. value means ‘subtract smaller from greater’. The symbols V, L and Remember that : D are never repeated. 1. V, L and D can never be subtracted from any other roman numeral 2. I can be subtracted only from V and X. 3. X can be subtracted only from L and C. 4. C an be subtracted only form D and M. Examples : DID YOU KNOW?

IV =5–1 =4 IX = 10 – 1 =9 XL = 50 – 10 = 40 XC = 100 – 10 = 90 Rule 3 : A symbol of smaller value after a symbol of greater value means ‘add smaller to greater’. Examples :

There is no concept of place value system in Roman numerals.

VI =5+1 =6 XI = 10 + 1 = 11 LX = 50 + 10 = 60 CX = 100 + 10 = 110 Rule 4 : When a Roman numeral of smaller value is placed between two Roman numerals of greater values, its value is always subtracted from the value of the symbol on its right. Examples : XIV XIX XXIV XXIX

= 10 + (5 – 1) = 10 + (10 – 1) = 20 + (5 – 1) = 20 + (10 – 1)

= 14 = 19 = 24 = 29

Some Basic Combinations of Roman Numerals 1 I

2 II

3 III

4 IV

5 V

6 VI

7 VII 11

8 VIII

9 IX

MATHEMATICS One For All Olympiads Solved Papers, Class-4

10 X

20 XX

30 XXX

40 XL

50 L

60 LX

70 LXX

80 LXXX

90 XC

100 200 300 400 500 600 700 800 900 C CC CCC CD D DC DCC DCCC CM How to convert Hindu-Arabic Number in Roman Numerals ? Break the number into Thousands, Hundreds, Tens and Ones, and write down each in turn. Example: Convert 1984 to Roman Numerals. Solution: Break 1984 into 1000, 900, 80 and 4, then do each conversion • 1000 = M • 900 = CM • 80 = LXXX • 4 = IV 1000 + 900 + 80 + 4 = 1984 So, 1984 = MCMLXXXIV. Example: Convert MMXVII to Hindu-Arabic Number. Solution: MMXVII = MM + XVII = 2000 + 17 = 2017 Thus, MMXVII = 2017.

Multiple Choice Questions LEVEL 1 1. Compare and fill the box. VI IV (a) > (b) < (c) = (d) None of these  [2019] 2. Compare and fill the box. CCCXXIV + CCLXIX DCCLII – CLVI (a) > (b) < (c) = (d) None of these  [2018] 3. Roman numeral for 18 is : (a) XVII (b) XVIII (c) XIX (d) XV

4. 39 is written as : (a) XXXVIIII (b) XXXXI (c) XXXIX (d) XXIX 5. XXII represents : (a) 22 (b) 32 (c) 11 (d) 33 6. XXX XXV (a) > (b) < (c) = (d) None of these 7. XXIV XXXIV (a) > (b) < (c) = (d) None of these 8. XXXIX XXXVIII 12

Roman Numerals

(a) > (b) < (c) = (d) None of these 9. XXII XII (a) > (b) < (c) = (d) None of these 10. VI + VI = ......... (a) X (b) XI (c) XII (d) VII 11. V + VII = .......... (a) X (b) XI (c) XII (d) VII 12. XIII – VI = ....... (a) X (b) XI (c) XII (d) VII 13. XXV – ........... = XXIV (a) V (b) IV (c) I (d) II 14. X + ........ = XVI (a) VI (b) IV (c) III (d) II 15. XX + III = ...... (a) 23 (b) 12 (c) 32 (d) 20 16. XIX – IX = ...... (a) XII (b) X (c) XX (d) XIII 17. How many basic numerals are there in Roman numeration system ? (a) 10 (b) 9 (c) 8 (d) 7

18. Which basic Roman numeral can never be subtracted ? (a) X (b) I (c) V (d) C 19. What is the equivalent Hindu-Arabic numeral for XV ? (a) 10 (b) 51 (c) 15 (d) 50 20. Find the first basic Roman numeral. (a) 0 (b) I (c) V (d) X 21. Sheena shows her fingers as shown in figure. Which Roman numeral does it represent ? (a) III (b) II (c) IV (d) V 22. Which of the following is the largest number ? (a) CD (b) CM (c) DC (d) MC 23. L ÷ V X (a) < (b) > (c) = (d) None of these 24. VII × IV XXX (a) < (b) > (c) = (d) None of these 25. 99 is same as : (a) IC (b) IXIX (c) XCIX (d) CIX

LEVEL 2 1. Arrange the following from the greatest to the smallest.

CDXXII DX DXXV DCII P Q R S LXIX CDXXII DCVI DXXV (a) P, Q, R, S (b) P, R, S, Q P Q R S (c) P, R, Q, S (d) P, Q, S, R  [2014] (a) P, Q, R, S (b) P, R, S, Q 3. From which Roman numeral apart from V (c) R, S, Q, P (d) R, Q, S, P can I be subtracted ?  [2014] (a) I (b) X 2. Arrange the following from the smallest (c) L (d) C to the greatest. 13

MATHEMATICS One For All Olympiads Solved Papers, Class-4

4. Find the ascending order of XX, XXXVI and V. (a) V, XXXVI, XX (b) XX, V, XXXVI (c) V, XX, XXXVI (d) XXXVI, XX, V 5. Find the descending order of IX, IV and VI. (a) IV, IX, VI (b) IX, VI, IV (c) VI, IX, IV (d) IV, VI, IX 6. Which of the following number can be written using Roman numerals M, V, X, D and L : (a) 2555 (b) 1565 (c) 1568 (d) 3549 7. Which of the following is the set of Roman numerals used to write the equivalent of 1656 ? (a) M, C, X, L, V, I (b) I, V, X, C, M, L (c) M, L, X, V, D, I (d) I, L, V, D, C, M 8. Observe the pattern of numbers given :

(a) XV (b) XIX (c) IXIV (d) XXIV 11. Five students wrote the Roman numerals on the black board as shown below : Class IV ↔ 15 VVV ↔ 25 XVX ↔ 29 IXXX ↔ 19 XIX ↔ 32 XXVVII Pick the correct match. (a) 15 ↔ VVV (b) 19 ↔ XIX (c) 32 ↔ XXVVII (d) 25 ↔ XVX 12. How many “X” symbols are needed to represent the sum 15 + 14 = 29 in Roman system ? (a) 5 (b) 6 (c) 4 (d) 3 13. Which of the following has no Roman numeral ? (a) 0 (b) 13 (c) 25 (d) 29 14. 10 less than 100 is written as : (a) XV (b) XC (c) CX (d) LX 15. Number 75 is written as : (a) LXV (b) LXXV (c) CXV (d) LVV

Which Roman numerals must fill the blank

spaces ? (a) C, M (b) C, X (c) D, C (d) C, L 9. Identify the correct combination from the following : (a) {DC, 200} (b) {CXV, 512} (c) {CV, 105} (d) {CLVI, 256} 10. Which of the following Roman numeral is meaningless ?

16. Find the Roman number equivalent to the difference 500 and 200. (a) C (b) CCC (c) MMM (d) D 17. Find the Roman numeral for 3721 ÷ 61 ? (a) LC (b) LXI (c) XLI (d) CM 18. IX + XV + XX = ........ (a) 45 (b) 35 (c) 44 (d) 40 14

Roman Numerals

19. Which Roman numeral is greatest ? (a) DCLX (b) CDXL (c) DCXL (d) CDXX

20. What is Roman numeral for the greatest three digit number ? (a) IXIXIX (b) CMIXIX (c) CMXCIX (d) CMIIC

ACHIEVERS SECTION 1. Which of the following is the correct Roman numerals used to write the equivalent of the given numbers ?

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(a) 2. What is the Hindu Arabic numeral of MMMCCCXXXIII ? (a) 333 (b) 30303 (c) 3330 (d) 3333 3. What is the difference between the greatest and the least three digit numbers formed by using X, L, C and D ? (a) DCXL (b) DCLX (c) CDXL (d) CCXX 4. Find the incorrect statement from the following : (a) C – X = XC (b) XI – IX = XX (c) DC – C = D (d) LXI – LIX = II 5. Which of the following is correct statement ? (a) 516 < DCVI (b) 256 = CCLVII (c) 408 ≠ CDVIII (d) 1005 < MD



(b)

(c)





Answer-Key LEVEL 1 1. (a) 6. (a) 11. (c) 16. (b) 21. (a)

2. (b) 7. (b) 12. (d) 17. (d) 22. (d)

3. (b) 8. (a) 13. (c) 18. (c) 23. (c)

15

4. (c) 9. (a) 14. (a) 19. (c) 24. (a)

5. (a) 10. (c) 15. (a) 20. (b) 25. (c)