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Maths by Mind Map: Maths

1. Numbers

1.1. Number System

1.1.1. Types of numbers

1.1.2. Place values

1.1.3. Reading, Writing, and Expanding Numbers Using Place Value Table

1.1.4. Successors and Predecessors of Numbers

1.1.5. Number Line

1.1.6. Comparison and Ordering of Numbers

1.1.7. Formation of Numbers from Given Digits

1.1.8. Location of Integers on Number Line

1.1.9. Comparison and Order of Integers

1.1.10. Addition

1.1.11. Subtraction

1.1.12. Multiplication of positive numbers

1.1.13. Properties of Multiplication of Integers

1.1.14. Division

1.1.15. Division of negative numbers

1.1.16. Division Algorithm

1.1.17. Order of Performing Operations (BODMAS)

1.1.18. Closure Property of Whole Numbers over Addition and Multiplication

1.1.19. Commutativity and Associativity of Whole Numbers over Addition and Multiplication

1.1.20. Distributive Property of Whole Numbers for Multiplication over Addition

1.1.21. Additive and Multiplicative Identities for Whole Numbers

1.1.22. Rounding

1.1.23. Indices

1.1.24. Reading, Writing and Explanding

1.2. Factor and Multiples

1.3. Fractions

1.3.1. Types of Fractions

1.3.2. Mixed numbers and improper fractions

1.3.3. Fractions Represented by Given Figures

1.3.4. Fractions of a quantity

1.3.5. Equivalent fractions

1.3.6. Representation of Fractions on Number Line

1.3.7. Comparing and Ordering of Like and Unlike Fractions

1.3.8. Simplifying fractions

1.3.9. Multiplication of Fractions with Whole Numbers

1.3.10. Multiplication of Fractions with Fractions

1.3.11. Division of Fractions by Whole Numbers and Fractions

1.3.12. Division of Whole Numbers by Fractions

1.3.13. Adding and subtracting fractions

1.3.14. Adding and subtracting fractions with different denominators

1.3.15. Adding and subtracting improper fractions

1.4. Ration and Proportion

1.4.1. What is a ratio?

1.4.2. Equivalent ratios

1.4.3. Direct proportion

1.4.4. Inverse proportion

1.4.5. Proportional division

1.4.6. Map scales

1.4.7. Application of Ratios in Solving Problems

1.4.8. Unitary Method and Its Applications

1.4.9. Time and Work

1.4.10. Speed, Distance and Time

1.4.11. Use of Ratios and Proportions to Compare Quantities

1.4.12. Unitary Method and Its Applications

1.4.13. Compounded ratios

1.5. Percentages

1.5.1. Percentages of…

1.5.2. Fraction-percentage conversion

1.5.3. Decimal-percentage conversion

1.5.4. Percentage changes

1.5.5. Percentage discount

1.5.6. Profit Percent and Loss Percent

1.5.7. Comparing using %

1.5.8. Interest

1.5.9. Concept Of Simple Interest

1.5.10. Calculating Compound Interest Using the Concept of Simple Interest

1.5.11. Formula for Finding Compound Interest

1.5.12. Problems Where the Interest is not Compounded Annually

1.6. Decimals

1.6.1. What are decimals

1.6.2. Rational and irrational numbers (surds)

1.6.3. Comparison, Standard Form and Equivalence of Rational Numbers

1.6.4. Representation of Decimals on a Number Line

1.6.5. Terminating and Non-Terminating Decimal Expansions of Rational Numbers

1.6.6. Converting decimals to fractions and fractions to decimals

1.6.7. Terminating Decimals

1.6.8. Recurring Decimals

1.6.9. Comparison, Arrangement, and Order of Decimal Numbers

1.6.10. Addition and Subtraction of Decimal Numbers

1.6.11. Multiplication of Decimals

1.6.12. Multiplication of Decimals by 10, 100, and 1000

1.6.13. Division of a Decimals by 10, 100, and 1000

1.6.14. Division of a Decimal Number by a Whole Number

1.6.15. Division of a Decimal Number by another Decimal Number

1.6.16. Estimation of Decimals

1.6.17. Calculations with standard form

1.6.18. Rounding

1.6.19. Significant Figures

1.6.20. Errors

1.6.21. Estimation

1.6.22. Addition and subtraction of decimals

1.6.23. Multiplication and division of decimals

1.7. Exponents and roots

1.7.1. Exponential Forms of Numbers

1.7.2. Comparison of Exponential Forms

1.7.3. Multiplication of Powers with the Same Base

1.7.4. Division of Powers with the Same Basede

1.7.5. Taking a Power of a Power

1.7.6. Multiplication of Powers with the Same Exponents

1.7.7. Division of Powers with the Same Exponents

1.7.8. Zero as an Exponent

1.7.9. Numbers with Negative Exponents

1.7.10. Expanding Decimals Using Exponents

1.7.11. Laws Of Exponents

1.7.12. Identification Of Perfect Squares

1.7.13. Properties of Perfect Squares

1.7.14. Square Root of a Number by Prime Factorisation Method

1.7.15. Identification of Perfect Cubes by Prime Factorization

1.7.16. Finding the Smallest Number by Which a Non-Perfect Cube Must be multiplied or divided by to convert it to a perfect cube

1.7.17. Relation between the Units Digit of a Number and That of Its Cube

1.7.18. Cube Root of a Perfect Cube by Method of Prime Factorisation

1.7.19. Identification of Perfect Squares and Their Roots by Prime Factorisation

1.7.20. Square Roots Of Numbers By Division Method

1.7.21. Index laws for exponents

1.8. Advanced Numbers

1.8.1. Concepts Related To Rational Numbers

1.8.2. Comparison, Standard Form and Equivalence of Rational Numbers

1.8.3. Concepts Associated With Irrational Numbers

1.8.4. Operations on Irrational Numbers

1.8.5. Representation of Rational Numbers on the Number Line

1.8.6. Representation Of Rational Numbers On A Number Line Using Successive Magnification

1.8.7. Representation of an Irrational Number on a Number Line

1.8.8. Representing Square Root of a Given Positive Real Number 'n' Geometrically

1.8.9. Simplifying Expressions using Identities Related to Square Roots

1.8.10. Concept and Properties of Real Numbers

1.8.11. If P Is a Prime Number Which Divides A2, Then P Divides A, Where A Is a Positive Integer

1.9. Applications of numbers

1.9.1. Use of a calculator

1.9.2. Tables

1.9.3. Money

1.9.4. Times and dates

1.9.5. Units of measurement

1.9.6. Calculating Compound Interest Using The Concept Of Simple Interest

1.9.7. Growth and Depreciation

1.9.8. Sales Tax

1.9.9. Value Added Tax (VAT)

1.9.10. Savings Bank Account

1.9.11. Recurring Deposit Account

1.9.12. Shares and Dividends

1.9.13. Finding upper and lower bounds for calculations

1.10. Matrices

1.10.1. Matrix and its Various Types

1.10.2. Equality of Matrices and Transpose

1.10.3. Addition and Subtraction of Matrices

1.10.4. Multiplication of a Matrix by a Non-zero rational Number and its Properties

1.10.5. Multiplication of Matrices and its Related Properties

1.11. Permutations and combinations

1.11.1. Fundamental Principle of Counting

1.11.2. Concept of Factorials

1.11.3. Concept of Permutations When All Objects Are Distinct

1.11.4. Concept of Permutations When All Objects Are Not Distinct

1.11.5. Concept of Combinations

1.12. Factors and Multiples

1.12.1. Factors and Multiples of Numbers

1.12.2. Properties of Factors and Multiples of Numbers

1.12.3. Perfect Numbers

1.12.4. Prime and Composite Numbers

1.12.5. Common Factors and Common Multiples of Numbers

1.12.6. Co-Prime Numbers

1.12.7. Divisibility of Numbers by 5, and 10

1.12.8. Divisibility of Numbers by 2, 4, and 8

1.12.9. Divisibility Rule of Numbers by 3, and 9

1.12.10. Divisibility of Numbers by 6

1.12.11. Divisibility of a Number by 11

1.12.12. Special Cases of Divisibility

1.12.13. Concept Of Prime Factorization

1.12.14. HCF and LCM of Numbers

1.12.15. Factors And Multiples Of Numbers

1.12.16. Prime and Composite Numbers

1.12.17. Co-Prime Numbers

1.12.18. Concept of Prime Factorization

1.12.19. HCF and LCM of Numbers

2. Geometry

2.1. Basic Geometrical Concepts

2.1.1. Basic Geometrical Concepts

2.1.2. Identification and Construction of Perpendicular Lines and Perpendicular Bisectors

2.1.3. Identification of Arms and Vertices of Angles

2.1.4. Identification of Points that Lie Inside, Outside, and On Given Angles

2.1.5. Reasoning Behind Construction Of Perpendicular Bisector Of A Line Segment, Bisector Of An Angle and Common Angles

2.1.6. Complementary and Supplementary Angles

2.1.7. Adjacent Angles, Linear Pair of Angles and Vertically Opposite Angles

2.1.8. Corresponding Angles Axiom and Alternate Interior Angles Aziom

2.1.9. Interior Angles On The Same Side Of The Transversal

2.1.10. Lines Which Are Parallel To The Same Line Are Parallel To Each Other

2.2. Concept Of Polygons

2.2.1. Concept of Polygons

2.2.2. Classification Of Polygons On The Basis Of Their Sides

2.2.3. Regular And Irregular Polygons

2.2.4. Properties Of Triangles

2.2.5. Properties Of Squares

2.2.6. Properties Of Rectangles

2.2.7. Properties Of Rhombuses

2.2.8. Properties Of A Parallelogram

2.2.9. Trapeziums, Kites

2.2.10. Convex And Concave Polygons

2.2.11. Angle Sum Property Of Polygons

2.2.12. Exterior Angle Sum Property Of Polygons

2.2.13. Construction of a Regular Hexagon

2.2.14. Construction of Quadrilateral When One Angle and Four Sides are Given

2.2.15. Construction Of Quadrilaterals When One Diagonal And Four Sides Are Given

2.2.16. Construction Of A Quadrilateral When Three Sides And Both Diagonals Are Given

2.2.17. Construction Of Quadrilaterals When Two Adjacent Sides And Three Angles Are Given

2.2.18. Construction Of Quadrilaterals When Three Sides And Two Included Angles Are Given

2.2.19. Construction Of Special Types Of Quadrilaterals

2.2.20. Circles and Construction of Cirles

2.2.21. Angle in a Semi-circle is a Right Angle

2.2.22. Construction of Circles On Given Line Segment as a Diameter

2.2.23. Construction of Circle of Given Radius and Passing Though Two Points

2.2.24. Construction of Circumcircle and Incircle of a Triangle

2.2.25. Loci/regions

2.2.26. Nets

2.3. Triangles

2.3.1. Classification and Properties of Triangles

2.3.2. Median, Altitudes and Angles of a Triangle

2.3.3. Key Terms Associated With a Triangle

2.3.4. Properties Of Equilateral Triangles

2.3.5. Isosceles Triangles

2.3.6. Angle Sum Property of Triangles

2.3.7. Exterior-Angle Property of Triangles

2.3.8. The Sum of Lengths of Any Two Sides of a Triangle Is Greater Than the Third Side

2.3.9. If Two Sides Of A Triangle Are Unequal, Then The Angle Opposite To The Longer Side Is Larger (Or Greater)

2.3.10. In Any Triangle, The Side Opposite To The Larger (Greater) Angle Is Longer

2.3.11. Construction of a Triangle When the Lengths of Its Sides Are Given

2.3.12. Construction of Triangles When the Lengths of Two Sides and the Measure of the Angle between Them Are Given

2.3.13. Construction of a Triangle When the Measure of Two Angles and the Length of the Included Side Is Given

2.3.14. Construction of a Right-Angled Triangle When the Length of One Arm and Its Hypotenuse Is Given

2.3.15. Construction of a Triangle Whose Base, Sum or Difference of Other Two Sides and Base Angle Are Given

2.3.16. Construction of a Triangle When Its Perimeter And Base Angles Are Given

2.3.17. Pythagoras Theorem

2.3.18. Identification Of Congruent Figures and Similar Figures

2.3.19. SSS Congruency Criterion

2.3.20. SAS Congruency Criterion

2.3.21. ASA Congruency Criterion

2.3.22. RHS (Right Angle-Hypotenuse-Side) Congruency Criterion

2.3.23. SAS Congruence Rule

2.3.24. ASA (Angle-Side-Angle) Congruence Rule

2.3.25. AAS (Angle-Angle-Side) Congruence Rule

2.3.26. SSS (Side-Side-Side) Congruence Rule

2.3.27. RHS (Right Angle-Hypotenuse-Side) Congruence Criterion

2.3.28. Angles Opposite To Equal Sides of an Isosceles Triangle Are Equal

2.3.29. Sides Opposite To Equal Angles of A Triangle Are Equal

2.3.30. Mid-Point Theorem And Its Converse

2.4. Circles

2.4.1. Angles Subtended By Chords At The Centre

2.4.2. Perpendicular From The Centre Of A Circle To A Chord Bisects The Chord

2.4.3. Only One Circle Can Pass Through Three Non-Collinear Points

2.4.4. Distance Of Chords From The Centre Of The Circle

2.4.5. Relation Between The Lengths Of Chords And Their Corresponding Arcs

2.4.6. Angles Subtended By Congruent Arcs

2.4.7. Relation Between Angles Subtended By An Arc At The Centre And At Any Point On The Remaining Part Of The Circle

2.4.8. Angles In The Same Segment Of A Circle

2.4.9. Relation Between Length Of Segments Of Two Chords When They Intersect Internally or Externally

2.4.10. Concyclic Points

2.4.11. Properties Of Cyclic Quadrilaterals

2.4.12. Concept Of Tangent At Any Point Of The Circle

2.4.13. Tangents Drawn From An External Point To A Circle

2.4.14. Relation Between The Centres Of A Circle And The Point Of Contact When They Touch Each Other

2.4.15. Relation Between The Length Of The Segments Of A Chord And A Tangent To A Circle Drawn From An Exterior Point

2.4.16. Alternate Segment Theorem

2.4.17. Construction Of Tangents To A Circle From A Point Outside The Circle

2.4.18. Construction Of Circumcircle Of A Triangle

2.4.19. Construction Of Incircle Of A Triangle

2.4.20. Construction Of Circumcircle And Incircle Of A Given Regular Hexagon

2.5. Angles

2.5.1. Concept of Angles

2.5.2. Measurement and Construction of Acute, Right, and Obtuse Angles Using a Protractor

2.5.3. Constructing Copy of Given Angles

2.5.4. Construction of Angles Using Ruler and Compasses and Set Squares

2.5.5. Complementary and Supplementary Angles

2.5.6. Adjacent Angles

2.5.7. Linear Pair of Angles

2.5.8. Vertically Opposite Angles

2.5.9. Transversal Lines and Angles Formed by them on Two Parallel Lines

2.5.10. Construction of Lines Parallel to a Given Line Through a Point Not on the Line

2.6. Mensuration

2.6.1. Perimeters of Regular Shapes

2.6.2. Areas of triangles

2.6.3. Area of Triangles Using Heron's Formula

2.6.4. Areas of Squares and Rectangles

2.6.5. Areas of other polygons (rhombus, parallelograms, trapezium)

2.6.6. Area of Quadrilaterals Using Heron's Formula

2.6.7. Perimeter of others

2.6.8. Area of others

2.6.9. Triangles on the Same Base and Between Same Parallel Lines

2.6.10. Parallelograms on the Same Base and Between Same Parallel Lines

2.6.11. Circumference (Perimeter) of A Circle

2.6.12. Area of A Circle

2.6.13. Areas of Sectors, Segments, and Combination of Circles with other Planes

2.6.14. Surface Areas of Cubes and Cuboids

2.6.15. Volumes of Cubes and Cuboids

2.6.16. Surface Areas and Volumes of Cylinders

2.6.17. Surface Areas and Volumes of Cones

2.6.18. Surface Areas and Volumes of Pyramids

2.6.19. Heights, Distances And Trigonometric Ratios

2.6.20. Areas of Sectors, Segments, and Combination of Circles with other Planes

2.6.21. Surface Areas of Sphere and Hemi Sphere

2.6.22. Volume of Sphere and Hemisphere

2.6.23. Surface Areas of Combination of Solids

2.6.24. Volume of Combination of Solids

2.6.25. Conversion of Solids from One Shape into Another

2.6.26. Scale drawings

2.7. Vectors

2.7.1. Meaning of vectors

2.7.2. Algebra of vectors

2.7.3. Geometric proof

2.8. Symmetry and Reflection

2.8.1. Symmetrical Figures and Lines Of Symmetry

2.8.2. Symmetric Point and Its Construction

2.8.3. Construction of the Line of Symmetry when Two Given Points are Symmetric with Respect to the line of symmetry

2.8.4. Point Symmetry

2.8.5. Concept of Rotation and Rotational Symmetry of Figures

2.8.6. Reflections Or Mirror Image Of Figures

2.8.7. Symmetrical Figures and Lines of Symmetry

2.8.8. Concept of Rotation on Coordinate Plane

2.9. Polynomials

2.9.1. Degrees Of A Polynomial

2.9.2. The Values Of A Polynomial At Different Points

2.9.3. Zeroes Of Polynomials

2.9.4. Division Of Polynomials By Long Division Method

2.9.5. Remainder Theorem And Its Applications

2.9.6. Factor Theorem

2.9.7. Factorization Of Quadratic Polynomials

2.9.8. Factorisation Of A Cubic Polynomial

2.9.9. Introduction to Conic Sections

2.9.10. Circle (Polynomial)

2.9.11. Parabola (Polynomial)

2.9.12. Ellipse (Polynomial)

2.9.13. Hyperbola(Polynomial)

2.10. Similarity

2.10.1. Similar And Congruent Figures

2.10.2. Basic Proportionality Theorem

2.10.3. AAA Criterion Of Similarity Of Triangles

2.10.4. SSS Property Of Similarity Of Triangles

2.10.5. SAS Criterion Of Similarity Of Triangles

2.10.6. Pythagoras Theorem

2.10.7. Problems on Pythagoras Theorem

2.10.8. Similar And Congruent Figures

2.10.9. Areas Of Similar Triangles

2.11. Three Dimensional Geometry

2.11.1. Identification of Three-Dimensional Shapes

2.11.2. Attributes of Three-Dimensional Shapes

2.11.3. Rectangular Coordinate System

2.11.4. Distance between Two Points in Three-Dimensional Space

2.11.5. Section Formula

2.12. Trigonometry

2.12.1. Intro to trigonometric ratios

2.12.2. Identifying the sides in basic trigonometry

2.12.3. Introduction SOHCAHTOA

2.12.4. Introducing the sine ratio

2.12.5. Introducing the cosine ratio

2.12.6. Introducing the tangent ratio

2.12.7. Sin rule

2.12.8. Cosine rule

2.12.9. Decoding basic trigonometry

2.12.10. Use Trigonometric Ratios In Solving Problems

2.12.11. Trigonometric Ratios Of Some Specific Angles

2.12.12. Trigonometric Ratios Of Complementary Angles

2.12.13. Trigonometric Identities

2.12.14. Use Of Trigonometric Identities In Proving Relationships Involving Trigonometric Ratios

2.12.15. Trigonometric Tables

2.12.16. Heights, Distances And Trigonometric Ratios

2.12.17. Degree and Radian Measures

2.12.18. Sign of Trigonometric Functions

2.12.19. Trigonometric Equations

2.12.20. 1/2absinC

3. Algebra

3.1. Formulae

3.1.1. Concepts of Algebra, Patterns and Variables

3.1.2. Concepts of Expressions containing variables

3.1.3. Generating a formulae

3.1.4. Subject of a Formula

3.1.5. Substituting in a formula

3.1.6. Factors, Coefficients, and Terms of Algebraic Expressions

3.1.7. Changing the Subject of a formulae

3.2. Equations

3.2.1. Concept of Equations

3.2.2. Linear Expressions

3.2.3. Quadratic Expressions

3.2.4. Simultaneous Expressions

3.2.5. Equations Reducible To Linear Form

3.2.6. Other Algebraic Expressions

3.2.7. Linear Inequations and Their Classification

3.2.8. Inequalities and Their Classification

3.2.9. Expressing Given Situations Mathematically

3.2.10. Reducing Equations To Simpler Form

3.2.11. Equations Reducible To Linear Form

3.2.12. Identification Of Quadratic Equations

3.3. Number Patterns

3.3.1. Linear

3.3.2. Quadratic

3.3.3. Other

3.4. Indices

3.4.1. Rules

3.4.2. Negative Indices

3.4.3. Fraction Indices

3.4.4. Concept and Laws of Logarithms

3.5. Functions and Graphs

3.5.1. Cartesian plane and the Terms Associated With it

3.5.2. Read the Locations of Points Plotted on a Coordinate Plane

3.5.3. Plotting the Points on the Coordinate Plane

3.5.4. y= mx+c

3.5.5. Graphs of Linear Equations in Two Variables

3.5.6. Graphs of Linear Equations Parallel to Coordinate Axes

3.5.7. Graphical Solution Of A Pair Of Linear Equations In Two Variables

3.5.8. Other

3.6. Manipulating algebra

3.6.1. Algebraic Shorthand

3.6.2. Expanding brackets

3.6.3. Algebraic fractions

3.6.4. Addition and Subtraction of Algebraic Expressions

3.6.5. Simplification of Algebraic Fractions

3.6.6. Simplification of Algebraic Fractions Having Integral Denominators

3.6.7. Like Terms

3.6.8. Collecting Terms

3.6.9. Expanding Brackets and Factorising

3.6.10. Solution of Equations by Trial and Error Method

3.6.11. Solution of Equations by Performing Same Mathematical Operation on Both Sides

3.6.12. Solution of Equations by Transposing Terms

3.6.13. Use of the Identity a2 - b2

3.6.14. Use of the Identities (a + b)2 And (a − b)2

3.6.15. Use of the Identity (x + a) (x + b)

3.6.16. Use of the Identity (a + b) (a – b)

3.6.17. Factorising linear

3.6.18. Completing the square

3.6.19. Factorising quadratic

3.6.20. Factorization of Algebraic Expressions Using the Method of Common Factors

3.6.21. Factorization of Algebraic Expressions by Regrouping Terms

3.6.22. Factorisation of Algebraic Expressions Using Identities style (a + b)2, (a − b)2, and a

3.6.23. Factorization of Quadratic Polynomials

3.6.24. Factorisation of Algebraic Expressions Using Identities (a + b) 2, (a – b) 2, and a2 - b2

3.6.25. Using the Identity a3 - b3 and a3 + b3 To Factorise Algebraic Expressions

3.6.26. Simplification of Algebraic Fractions

3.6.27. Simplification of Algebraic Fractions Having Integral Denominators

3.6.28. Algebraic Shorthand

3.6.29. Like Terms

3.6.30. Expanding Brackets and Factorising

3.6.31. Multiplication of Monomials with Algebraic Expressions

3.6.32. Multiplication of Binomials with Binomials

3.6.33. Multiplication of Two Polynomials

3.6.34. Finding Values of Algebraic Expressions at Given Points

3.6.35. Problem solving - linear

3.7. Using Algebra

3.7.1. Solution of Linear Equations That Contain Linear Expressions on One Side and Numbers on the Other Side

3.7.2. Solving Linear Inequalities in One Variable

3.7.3. Solving a System of Linear Inequalities in Two Variables

3.7.4. Solution of Linear Equations That Contains Linear Expressions on Both Sides

3.7.5. Solution of Linear Equations That Contain Linear Expressions on One Side and Numbers on the Other Side

3.7.6. Problem solving simultaneous

3.7.7. Solution of Linear Equations That Contain Linear Expressions on One Side and Numbers on the Other Side

3.7.8. Solving Problems Using The Algebraic Identities (x + y)3 and (x - y)3

3.7.9. Solving Problems Using the Algebraic Identity (x + y + z) 2

3.7.10. Solving Problems Using the Identity (x + y + z) (x2 + y2 + z2 - xy - yz - zx) = x3 + y3 + z3 - 3xyz

3.7.11. Mathematical Expressions of Word Problems

4. Probability

4.1. Probability concepts

4.1.1. Intro to probability

4.2. Sample space diagrams

4.2.1. Tree Diagrams of independent events

4.2.2. Tree Diagrams of dependent events PROB_003_p1_Tree Diagrams and "at least"

4.2.3. Venn diagrams

4.3. Probability Concepts

4.3.1. Calculating a probability

4.3.2. Complementary events

4.3.3. Probability with listings

4.3.4. Conditional probability

4.3.5. Relative frequency

4.4. Addition rule

4.4.1. Mutually exclusive events

4.4.2. General addition rule

4.5. Probability outcomes

4.5.1. Outcome of a single event

4.5.2. Outcome of multiple events

4.5.3. Experimental Probability

4.5.4. Experimental and Theoretical Probability

5. Statistics

5.1. Types of data

5.1.1. Grouped data

5.1.2. Continuous data

5.1.3. Qualitative

5.1.4. Discrete data

5.1.5. Quantitative

5.2. Methods of collection

5.2.1. Surveys and questionnaires

5.2.2. Sampling

5.2.3. Frequency Tables

5.2.4. Primary and secondary sources

5.2.5. Mean

5.2.6. Mode

5.2.7. Median

5.2.8. Range

5.2.9. Modal class

5.2.10. Quartile and interquartile range

5.2.11. Estimating the mean

5.2.12. Estimating the median

5.2.13. Estimating the range

5.2.14. Modal class

5.3. Frequency tables

5.3.1. FT- Mean

5.3.2. FT- Median

5.3.3. FT- Mode

5.3.4. FT- Moving averages

5.3.5. Frequency, Class Limits, Class Size, Tally Marks With Respect To Frequency Distribution Table

5.3.6. Frequency Distribution Tables For Given Data Set

5.3.7. Mean of Ungrouped Data and Data Given in the Form of Frequency Distribution Table

5.4. Representing Data

5.4.1. Statistical Charts and Graphs

5.4.2. Pie charts

5.4.3. Line graphs

5.4.4. Bar charts

5.4.5. Pictograms

5.4.6. Histograms

5.4.7. Construction of Histograms

5.4.8. Interpretation of Histograms

5.4.9. Scatter diagrams

5.4.10. Line of best fit

5.4.11. Correlation

5.4.12. Interpretation of Tally Charts

5.4.13. Interpretation of Bar Graphs

5.4.14. Interpretation of Circle Graphs

5.4.15. Interpretation of Line Graphs

5.4.16. Cumulative Frequency Diagrams

5.4.17. Drawing Frequency Diagrams

5.4.18. Frequency density

5.4.19. Stem and leaf

5.4.20. Box and whisker plots

5.4.21. Stem and Leaf Diagrams

5.4.22. Two-way tables

5.4.23. Constructing frequency polygons

5.4.24. Reading and Interpreting Frequency Polygons

5.4.25. Time Series Graphs

5.4.26. Two-way Tables

5.5. Data Analysis

5.5.1. Comparing Two or More Sets of Data

5.5.2. Mean Of Grouped Data Using the Direct Method

5.5.3. Mean Of Grouped Data Using Assumed Mean Method

5.5.4. Mean Of Grouped Data Using Step Deviation Method

5.5.5. Finding Mode Of Grouped Data From Its Histogram

5.5.6. Upper Quartiles, Lower Quartiles, and Median of a Grouped Data by Constructing Ogive

5.5.7. Relation between Mean, Median, and Mode

5.5.8. Mean Deviation for Ungrouped Data

5.5.9. Mean Deviation for Discrete Frequency Distribution

5.5.10. Mean Deviation for Continuous Frequency Distribution

5.5.11. Variance and Standard Deviation of Ungrouped Data

5.5.12. Variance and Standard Deviation of a Discrete Frequency Distribution

5.5.13. Variance and Standard Deviation for a Continuous Frequency Distribution

5.5.14. Coefficient of Variation

5.5.15. Arithmetic Progression and Arithmetic Mean

5.5.16. Geometric Progressions

5.5.17. nth Term and Sum of n-Terms of a Geometric Progression

5.5.18. Geometric Mean and Its Relation with Arithmetic Mean

5.5.19. Sum of n Terms of Special Series

6. Mathematical Reasoning

6.1. Sets

6.1.1. Sets

6.1.2. Types of Sets

6.1.3. Equal Sets and Equivalence Sets

6.1.4. Union and Intersection of Sets

6.1.5. Complement of a set

6.1.6. Venn diagrams

6.1.7. Equal Sets and Equivalent Sets

6.1.8. Concept of Subset

6.1.9. Union and Intersection of Sets

6.1.10. Difference between Sets

6.1.11. Complement of a set

6.1.12. Venn diagrams

6.1.13. Subsets

6.1.14. Union and Intersection of Sets

6.1.15. Difference of Sets

6.1.16. Application of Union and Intersection

6.1.17. Complement of a Set

6.2. Relation and Mapping

6.2.1. Relation

6.2.2. Mapping

6.2.3. Concept of Functions

6.3. Reasoning

6.3.1. Statement

6.3.2. Negation of a Statement

6.3.3. Compound Sentence and its Components

6.3.4. Role of Connectives "And" and "Or"

6.3.5. Role of Quantifiers in a Compound Statement

6.3.6. Implications

6.3.7. Validity of "If-then" and "If and only if" Statements

6.3.8. Validation of a Statement by the Method of Contradiction and by Giving a Counter Example

6.3.9. Principle of Mathematical Induction

7. Advanced Concepts in Maths

7.1. Limits and Derivatives

7.1.1. Limit of a Function Using Intuitive Approach

7.1.2. Limit of a Polynomial and a Rational Function

7.1.3. Limits of Trigonometric Functions

7.1.4. Derivative of a Function

7.1.5. Derivatives of Trigonometric and Polynomial Functions

7.2. Complex numbers and quadratic equations

7.2.1. Complex Numbers

7.2.2. Addition and Subtraction of Complex Numbers

7.2.3. Multiplication of Complex Numbers

7.2.4. Division of Complex Numbers

7.2.5. Identities of Complex Numbers

7.2.6. Modulus and Conjugate of a Complex Number

7.2.7. Quadratic Equations with Complex Roots

7.2.8. Concept of Argand Plane

8. Applications of Maths

8.1. Applications

8.1.1. Calculating Compound Interest Using The Concept Of Simple Interest

8.1.2. Formula for Finding Compound Interest

8.1.3. Problems Where the Interest is not Compounded Annually

8.1.4. Growth and Depreciation

8.1.5. Sales Tax

8.1.6. Value Added Tax (VAT)

8.1.7. Savings Bank Account

8.1.8. Recurring Deposit Account