Master Fundamental Concepts of Math Olympiad: Maths, #1

By Subbalakshmi Devaki

Are you ready to unlock your full potential in math and conquer the world of Math Olympiad competitions? Look no further! "The Ultimate Guide to Study Math Olympiad: Grades 6 to 12" is here to equip you with the essential knowledge and techniques needed to excel in math competitions and enhance your mathematical prowess.

Whether you are a passionate student aiming to participate in the International Mathematical Olympiad (IMO) or seeking to enhance your math skills for other exams, this comprehensive guide has got you covered. From learning the basics to mastering advanced problem-solving strategies, this book is designed to guide you through every step of your journey.

With a focus on Grades 6 to 12, this guide provides a solid foundation by covering all the fundamental math concepts necessary for Olympiad-level success. You will explore various mathematical topics, including algebra, geometry, number theory, and combinatorics, each explained in a clear and concise manner. Each chapter presents the key principles, accompanied by practical examples and step-by-step solutions to help you grasp the concepts effortlessly.

"The Ultimate Guide to Study Math Olympiad" goes beyond mere theory and offers invaluable study tips and tricks specifically tailored for Math Olympiad participants. Learn how to enhance your calculation speed, improve problem-solving abilities, and develop a systematic approach to tackle even the most complex math problems. Discover effective techniques to manage time during exams and maximize your performance under pressure.

Written by experts in the field, this book is packed with practice problems of varying difficulty levels, allowing you to gradually build your skills and challenge yourself. The carefully selected exercises mirror the style and complexity of Math Olympiad questions, ensuring that you are well-prepared to face any test or competition.

Key Features of "The Ultimate Guide to Study Math Olympiad: Grades 6 to 12":

Comprehensive coverage of essential math topics for Olympiad-level competitions

Step-by-step explanations and examples to enhance understanding

Strategies to increase calculation speed and improve problem-solving skills

Effective study tips and tricks for Math Olympiad success

Practice problems with varying difficulty levels for comprehensive learning

Time management techniques for efficient exam performance

Suitable for students, teachers, and anyone passionate about math competitions

Prepare yourself for a remarkable journey through the world of math Olympiads. Whether you're a beginner or an experienced competitor, "The Ultimate Guide to Study Math Olympiad: Grades 6 to 12" will provide you with the tools and knowledge necessary to excel in any mathematical challenge. Take the first step towards becoming a math Olympiad champion and embark on your path to mathematical greatness today.

 

 

• Language: English
• Publisher: Subbalakshmi Devaki
• Release date: Jan 11, 2022
• ISBN: 9798223265993

Book preview

Structure of each topic

All the topics in this book are discussed from the root. Initially we teach all the basics associated with the particular topic then followed by relevant examples along with explanatory answers. So it will be easy for the students to solve the questions what they come across in the competitive exams.

Index

1. Numbers       Page 1- Page 14

Numbers Classification

a)  Real Numbers     

b)  Imaginary Numbers    

c)  Rational Numbers    

d)  Irrational Numbers

e)  Integers    

f)  Decimals

g)  Fractions

h)  Recurring Decimals

i)  Non-Recurring Decimals

j)  Proper Fractions

k)  Improper Fractions

l)  Mixed Fractions

Integers Classification:

a)  Even Numbers

b)  Odd Numbers

c)  Neutral Numbers

d)  Whole Numbers

e)  Prime Numbers

f)  Composite Numbers

g)  Even Prime

h)  Co-Prime

i)  Twin Prime

Perfect Number and Fibonacci Sequences

a)  Perfect Number

b)  Fibonacci Sequences

BODMAS

Decimals and Fractions

a)  Place value of Decimals

b)  Converting Decimals to Fractions

c)  Addition and Subtraction of  Fractions

d)  Multiplication and Division of  Fractions

e)  Conversion of  Proper fractions to Mixed Fractions

f)  Addition and Subtractions of Mixed Fractions

6. Factors and Multiples

7. L.C.M and H.C.F

a)  Method 1 to find L.C.M and H.C.F

b)  Method 2 to find L.C.M and H.C.F

c)  Method 3 to find L.C.M and H.C.F

d)  Points to be noted in L.C.M and H.C.F

Factorials

Divisibility Rules

2. Arithmetic  Page 15- Page 55

Percentages          16

a)  What is Percentage?

b)  Why do we need Percentage?

c)  Finding Percentage

d)  Percentage Changes

e)  Percentages to Fraction Conversions

f)  Example problems

Profit and Loss    24

g)  Basic Terms

h)  Relationship between basic terms

i)  Examples

Simple Interest and Compound Interest   28

a)  Simple Interest

b)  Compound interest

c)  Formulas

d)  Examples

Ratio and Proportion    30

a)  Difference b/w Ratios and Fractions

b)  Why Ratio?

c)  Divisions of values as per ratio

d)  Combining ratio

e)  Proportion

1)  Mean Proportion

2)  Third Proportion

3)  Fourth Proportion

f)  Direct and inverse Proportion

1)  Direct Proportion

2)  Inverse Proportion

Averages    33

a)  Linear Data

b)  Non-Linear Data

c)  Weighted Average

Mixture and Alligations      37

a)  Mixture

b)  Alligations

c)  Example Problems

Time and Work      44

a)  Model -1 (questions based on proportions)

b)  Model -2 

c)  Model -3

d)  Model -4 (Based on Capacities)

e)  Model -4 (Pipes and Cisterns)

Time, Speed and Distance51

a)  Speed

b)  Average Speed

c)  Relative Speed

d)  Example Problems

3. Geometry    Page 56- Page 82

Lines and Angles

a)  Line

b)  Ray

c)  Line Segment

d)  Parallel Lines

e)  Perpendicular Lines

f)  Supplementary Angles

g)  Complementary angles

h)  Vertical opposite Angles

i)  Parallel Line properties

j)  Perpendicular

k)  Bisector

l)  Perpendicular Bisector

Triangles

a)  Property 1

b)  Property 2

c)  Property 3

d)  Property 4

e)  Area of Triangles

f)  Pythagorean Theorem

g)  Similar Triangles

h)  Congruent Triangles

i)  Types of Triangles

1)  Scalen Triangle

2)  Right angle Triangle

3)  Acute angle Triangle

4)  Obtuse angle Triangle

5)  Isosceles Triangle

6)  Equivalent Triangle

7)  Isosceles Right-angle Triangle

j)  Centers:

1)  In center

2)  Circum center

3)  Ex-center

4)  Centroid

5)  Ortho-center

k)  Mid-point Theorem:

l)  Special Triangles:

1)  30-60-90- triangle

2)  45-45-90-triangle

Quadrilaterals

a)  Parallelogram

b)  Square

c)  Rectangle

d)  Rhombus

e)  Trapezium

f)  Quadrilateral

Polygons

a)  Sum of Interior angles

b)  Sum of Exterior angles

c)  Numbers of Diagonals

d)  Regular Polygons

Circle

a)  Circle

b)  Arc

c)  Sector

d)  Semi-circle

e)  Important result in circle

3-D Geometry

a)  Cuboid

b)  Cube

c)  Cylinder

d)  Cone

e)  Sphere

f)  Hemi-Sphere

Co-ordinate Geometry

a)  Distance between two points

b)  Slope

c)  Mid-point

d)  m:n ratio division

e)  Perpendicular line slope

f)  Intercepts

g)  Line equation

h)  Line equation parallel to x-axis

4. Algebra    Page 83- Page 95

1. Algebraic Expression   

2. Algebraic Equation   

3. Roots of an Equation

4. Exponents

5. Basic Formulas

6. Functions

a)  Special Functions

7. Simple Equations

8. Inequalities and Absolute Values

a)  Arithmetic Operations on Inequalities

b)  Absolute values

c)  Solving a Quadratic Inequality

d)  Graphical Representation

5. Counting    Page 96- Page 118

Permutations and Combinations    97

a)  Difference between Permutations and combinations

b)  Basic Approach

c)  Conditional Slots

Probability          101

a)  Basic Formulas

b)  Independent Event