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Maths
by Fuse Team
# Maths

## Numbers

### Number System

### Factor and Multiples

### Fractions

### Ration and Proportion

### Percentages

### Decimals

### Exponents and roots

### Advanced Numbers

### Applications of numbers

### Matrices

### Permutations and combinations

### Factors and Multiples

## Geometry

### Basic Geometrical Concepts

### Concept Of Polygons

### Triangles

### Circles

### Angles

### Mensuration

### Vectors

### Symmetry and Reflection

### Polynomials

### Similarity

### Three Dimensional Geometry

### Trigonometry

## Algebra

### Formulae

### Equations

### Number Patterns

### Indices

### Functions and Graphs

### Manipulating algebra

### Using Algebra

## Probability

### Probability concepts

### Sample space diagrams

### Probability Concepts

### Addition rule

### Probability outcomes

## Statistics

### Types of data

### Methods of collection

### Frequency tables

### Representing Data

### Data Analysis

## Mathematical Reasoning

### Sets

### Relation and Mapping

### Reasoning

## Advanced Concepts in Maths

### Limits and Derivatives

### Complex numbers and quadratic equations

## Applications of Maths

### Applications

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Types of numbers

Place values

Reading, Writing, and Expanding Numbers Using Place Value Table

Successors and Predecessors of Numbers

Number Line

Comparison and Ordering of Numbers

Formation of Numbers from Given Digits

Location of Integers on Number Line

Comparison and Order of Integers

Addition

Subtraction

Multiplication of positive numbers

Properties of Multiplication of Integers

Division

Division of negative numbers

Division Algorithm

Order of Performing Operations (BODMAS)

Closure Property of Whole Numbers over Addition and Multiplication

Commutativity and Associativity of Whole Numbers over Addition and Multiplication

Distributive Property of Whole Numbers for Multiplication over Addition

Additive and Multiplicative Identities for Whole Numbers

Rounding

Indices

Reading, Writing and Explanding

Types of Fractions

Mixed numbers and improper fractions

Fractions Represented by Given Figures

Fractions of a quantity

Equivalent fractions

Representation of Fractions on Number Line

Comparing and Ordering of Like and Unlike Fractions

Simplifying fractions

Multiplication of Fractions with Whole Numbers

Multiplication of Fractions with Fractions

Division of Fractions by Whole Numbers and Fractions

Division of Whole Numbers by Fractions

Adding and subtracting fractions

Adding and subtracting fractions with different denominators

Adding and subtracting improper fractions

What is a ratio?

Equivalent ratios

Direct proportion

Inverse proportion

Proportional division

Map scales

Application of Ratios in Solving Problems

Unitary Method and Its Applications

Time and Work

Speed, Distance and Time

Use of Ratios and Proportions to Compare Quantities

Unitary Method and Its Applications

Compounded ratios

Percentages of…

Fraction-percentage conversion

Decimal-percentage conversion

Percentage changes

Percentage discount

Profit Percent and Loss Percent

Comparing using %

Interest

Concept Of Simple Interest

Calculating Compound Interest Using the Concept of Simple Interest

Formula for Finding Compound Interest

Problems Where the Interest is not Compounded Annually

What are decimals

Rational and irrational numbers (surds)

Comparison, Standard Form and Equivalence of Rational Numbers

Representation of Decimals on a Number Line

Terminating and Non-Terminating Decimal Expansions of Rational Numbers

Converting decimals to fractions and fractions to decimals

Terminating Decimals

Recurring Decimals

Comparison, Arrangement, and Order of Decimal Numbers

Addition and Subtraction of Decimal Numbers

Multiplication of Decimals

Multiplication of Decimals by 10, 100, and 1000

Division of a Decimals by 10, 100, and 1000

Division of a Decimal Number by a Whole Number

Division of a Decimal Number by another Decimal Number

Estimation of Decimals

Calculations with standard form

Rounding

Significant Figures

Errors

Estimation

Addition and subtraction of decimals

Multiplication and division of decimals

Exponential Forms of Numbers

Comparison of Exponential Forms

Multiplication of Powers with the Same Base

Division of Powers with the Same Basede

Taking a Power of a Power

Multiplication of Powers with the Same Exponents

Division of Powers with the Same Exponents

Zero as an Exponent

Numbers with Negative Exponents

Expanding Decimals Using Exponents

Laws Of Exponents

Identification Of Perfect Squares

Properties of Perfect Squares

Square Root of a Number by Prime Factorisation Method

Identification of Perfect Cubes by Prime Factorization

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

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

Cube Root of a Perfect Cube by Method of Prime Factorisation

Identification of Perfect Squares and Their Roots by Prime Factorisation

Square Roots Of Numbers By Division Method

Index laws for exponents

Concepts Related To Rational Numbers

Comparison, Standard Form and Equivalence of Rational Numbers

Concepts Associated With Irrational Numbers

Operations on Irrational Numbers

Representation of Rational Numbers on the Number Line

Representation Of Rational Numbers On A Number Line Using Successive Magnification

Representation of an Irrational Number on a Number Line

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

Simplifying Expressions using Identities Related to Square Roots

Concept and Properties of Real Numbers

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

Use of a calculator

Tables

Money

Times and dates

Units of measurement

Calculating Compound Interest Using The Concept Of Simple Interest

Growth and Depreciation

Sales Tax

Value Added Tax (VAT)

Savings Bank Account

Recurring Deposit Account

Shares and Dividends

Finding upper and lower bounds for calculations

Matrix and its Various Types

Equality of Matrices and Transpose

Addition and Subtraction of Matrices

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

Multiplication of Matrices and its Related Properties

Fundamental Principle of Counting

Concept of Factorials

Concept of Permutations When All Objects Are Distinct

Concept of Permutations When All Objects Are Not Distinct

Concept of Combinations

Factors and Multiples of Numbers

Properties of Factors and Multiples of Numbers

Perfect Numbers

Prime and Composite Numbers

Common Factors and Common Multiples of Numbers

Co-Prime Numbers

Divisibility of Numbers by 5, and 10

Divisibility of Numbers by 2, 4, and 8

Divisibility Rule of Numbers by 3, and 9

Divisibility of Numbers by 6

Divisibility of a Number by 11

Special Cases of Divisibility

Concept Of Prime Factorization

HCF and LCM of Numbers

Factors And Multiples Of Numbers

Prime and Composite Numbers

Co-Prime Numbers

Concept of Prime Factorization

HCF and LCM of Numbers

Basic Geometrical Concepts

Identification and Construction of Perpendicular Lines and Perpendicular Bisectors

Identification of Arms and Vertices of Angles

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

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

Complementary and Supplementary Angles

Adjacent Angles, Linear Pair of Angles and Vertically Opposite Angles

Corresponding Angles Axiom and Alternate Interior Angles Aziom

Interior Angles On The Same Side Of The Transversal

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

Concept of Polygons

Classification Of Polygons On The Basis Of Their Sides

Regular And Irregular Polygons

Properties Of Triangles

Properties Of Squares

Properties Of Rectangles

Properties Of Rhombuses

Properties Of A Parallelogram

Trapeziums, Kites

Convex And Concave Polygons

Angle Sum Property Of Polygons

Exterior Angle Sum Property Of Polygons

Construction of a Regular Hexagon

Construction of Quadrilateral When One Angle and Four Sides are Given

Construction Of Quadrilaterals When One Diagonal And Four Sides Are Given

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

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

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

Construction Of Special Types Of Quadrilaterals

Circles and Construction of Cirles

Angle in a Semi-circle is a Right Angle

Construction of Circles On Given Line Segment as a Diameter

Construction of Circle of Given Radius and Passing Though Two Points

Construction of Circumcircle and Incircle of a Triangle

Loci/regions

Nets

Classification and Properties of Triangles

Median, Altitudes and Angles of a Triangle

Key Terms Associated With a Triangle

Properties Of Equilateral Triangles

Isosceles Triangles

Angle Sum Property of Triangles

Exterior-Angle Property of Triangles

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

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

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

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

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

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

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

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

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

Pythagoras Theorem

Identification Of Congruent Figures and Similar Figures

SSS Congruency Criterion

SAS Congruency Criterion

ASA Congruency Criterion

RHS (Right Angle-Hypotenuse-Side) Congruency Criterion

SAS Congruence Rule

ASA (Angle-Side-Angle) Congruence Rule

AAS (Angle-Angle-Side) Congruence Rule

SSS (Side-Side-Side) Congruence Rule

RHS (Right Angle-Hypotenuse-Side) Congruence Criterion

Angles Opposite To Equal Sides of an Isosceles Triangle Are Equal

Sides Opposite To Equal Angles of A Triangle Are Equal

Mid-Point Theorem And Its Converse

Angles Subtended By Chords At The Centre

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

Only One Circle Can Pass Through Three Non-Collinear Points

Distance Of Chords From The Centre Of The Circle

Relation Between The Lengths Of Chords And Their Corresponding Arcs

Angles Subtended By Congruent Arcs

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

Angles In The Same Segment Of A Circle

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

Concyclic Points

Properties Of Cyclic Quadrilaterals

Concept Of Tangent At Any Point Of The Circle

Tangents Drawn From An External Point To A Circle

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

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

Alternate Segment Theorem

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

Construction Of Circumcircle Of A Triangle

Construction Of Incircle Of A Triangle

Construction Of Circumcircle And Incircle Of A Given Regular Hexagon

Concept of Angles

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

Constructing Copy of Given Angles

Construction of Angles Using Ruler and Compasses and Set Squares

Complementary and Supplementary Angles

Adjacent Angles

Linear Pair of Angles

Vertically Opposite Angles

Transversal Lines and Angles Formed by them on Two Parallel Lines

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

Perimeters of Regular Shapes

Areas of triangles

Area of Triangles Using Heron's Formula

Areas of Squares and Rectangles

Areas of other polygons (rhombus, parallelograms, trapezium)

Area of Quadrilaterals Using Heron's Formula

Perimeter of others

Area of others

Triangles on the Same Base and Between Same Parallel Lines

Parallelograms on the Same Base and Between Same Parallel Lines

Circumference (Perimeter) of A Circle

Area of A Circle

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

Surface Areas of Cubes and Cuboids

Volumes of Cubes and Cuboids

Surface Areas and Volumes of Cylinders

Surface Areas and Volumes of Cones

Surface Areas and Volumes of Pyramids

Heights, Distances And Trigonometric Ratios

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

Surface Areas of Sphere and Hemi Sphere

Volume of Sphere and Hemisphere

Surface Areas of Combination of Solids

Volume of Combination of Solids

Conversion of Solids from One Shape into Another

Scale drawings

Meaning of vectors

Algebra of vectors

Geometric proof

Symmetrical Figures and Lines Of Symmetry

Symmetric Point and Its Construction

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

Point Symmetry

Concept of Rotation and Rotational Symmetry of Figures

Reflections Or Mirror Image Of Figures

Symmetrical Figures and Lines of Symmetry

Concept of Rotation on Coordinate Plane

Degrees Of A Polynomial

The Values Of A Polynomial At Different Points

Zeroes Of Polynomials

Division Of Polynomials By Long Division Method

Remainder Theorem And Its Applications

Factor Theorem

Factorization Of Quadratic Polynomials

Factorisation Of A Cubic Polynomial

Introduction to Conic Sections

Circle (Polynomial)

Parabola (Polynomial)

Ellipse (Polynomial)

Hyperbola(Polynomial)

Similar And Congruent Figures

Basic Proportionality Theorem

AAA Criterion Of Similarity Of Triangles

SSS Property Of Similarity Of Triangles

SAS Criterion Of Similarity Of Triangles

Pythagoras Theorem

Problems on Pythagoras Theorem

Similar And Congruent Figures

Areas Of Similar Triangles

Identification of Three-Dimensional Shapes

Attributes of Three-Dimensional Shapes

Rectangular Coordinate System

Distance between Two Points in Three-Dimensional Space

Section Formula

Intro to trigonometric ratios

Identifying the sides in basic trigonometry

Introduction SOHCAHTOA

Introducing the sine ratio

Introducing the cosine ratio

Introducing the tangent ratio

Sin rule

Cosine rule

Decoding basic trigonometry

Use Trigonometric Ratios In Solving Problems

Trigonometric Ratios Of Some Specific Angles

Trigonometric Ratios Of Complementary Angles

Trigonometric Identities

Use Of Trigonometric Identities In Proving Relationships Involving Trigonometric Ratios

Trigonometric Tables

Heights, Distances And Trigonometric Ratios

Degree and Radian Measures

Sign of Trigonometric Functions

Trigonometric Equations

1/2absinC

Concepts of Algebra, Patterns and Variables

Concepts of Expressions containing variables

Generating a formulae

Subject of a Formula

Substituting in a formula

Factors, Coefficients, and Terms of Algebraic Expressions

Changing the Subject of a formulae

Concept of Equations

Linear Expressions

Quadratic Expressions

Simultaneous Expressions

Equations Reducible To Linear Form

Other Algebraic Expressions

Linear Inequations and Their Classification

Inequalities and Their Classification

Expressing Given Situations Mathematically

Reducing Equations To Simpler Form

Equations Reducible To Linear Form

Identification Of Quadratic Equations

Linear

Quadratic

Other

Rules

Negative Indices

Fraction Indices

Concept and Laws of Logarithms

Cartesian plane and the Terms Associated With it

Read the Locations of Points Plotted on a Coordinate Plane

Plotting the Points on the Coordinate Plane

y= mx+c

Graphs of Linear Equations in Two Variables

Graphs of Linear Equations Parallel to Coordinate Axes

Graphical Solution Of A Pair Of Linear Equations In Two Variables

Other

Algebraic Shorthand

Expanding brackets

Algebraic fractions

Addition and Subtraction of Algebraic Expressions

Simplification of Algebraic Fractions

Simplification of Algebraic Fractions Having Integral Denominators

Like Terms

Collecting Terms

Expanding Brackets and Factorising

Solution of Equations by Trial and Error Method

Solution of Equations by Performing Same Mathematical Operation on Both Sides

Solution of Equations by Transposing Terms

Use of the Identity a2 - b2

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

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

Use of the Identity (a + b) (a – b)

Factorising linear

Completing the square

Factorising quadratic

Factorization of Algebraic Expressions Using the Method of Common Factors

Factorization of Algebraic Expressions by Regrouping Terms

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

Factorization of Quadratic Polynomials

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

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

Simplification of Algebraic Fractions

Simplification of Algebraic Fractions Having Integral Denominators

Algebraic Shorthand

Like Terms

Expanding Brackets and Factorising

Multiplication of Monomials with Algebraic Expressions

Multiplication of Binomials with Binomials

Multiplication of Two Polynomials

Finding Values of Algebraic Expressions at Given Points

Problem solving - linear

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

Solving Linear Inequalities in One Variable

Solving a System of Linear Inequalities in Two Variables

Solution of Linear Equations That Contains Linear Expressions on Both Sides

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

Problem solving simultaneous

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

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

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

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

Mathematical Expressions of Word Problems

Intro to probability

Tree Diagrams of independent events

Tree Diagrams of dependent events, PROB_003_p1_Tree Diagrams and "at least"

Venn diagrams

Calculating a probability

Complementary events

Probability with listings

Conditional probability

Relative frequency

Mutually exclusive events

General addition rule

Outcome of a single event

Outcome of multiple events

Experimental Probability

Experimental and Theoretical Probability

Grouped data

Continuous data

Qualitative

Discrete data

Quantitative

Surveys and questionnaires

Sampling

Frequency Tables

Primary and secondary sources

Mean

Mode

Median

Range

Modal class

Quartile and interquartile range

Estimating the mean

Estimating the median

Estimating the range

Modal class

FT- Mean

FT- Median

FT- Mode

FT- Moving averages

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

Frequency Distribution Tables For Given Data Set

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

Statistical Charts and Graphs

Pie charts

Line graphs

Bar charts

Pictograms

Histograms

Construction of Histograms

Interpretation of Histograms

Scatter diagrams

Line of best fit

Correlation

Interpretation of Tally Charts

Interpretation of Bar Graphs

Interpretation of Circle Graphs

Interpretation of Line Graphs

Cumulative Frequency Diagrams

Drawing Frequency Diagrams

Frequency density

Stem and leaf

Box and whisker plots

Stem and Leaf Diagrams

Two-way tables

Constructing frequency polygons

Reading and Interpreting Frequency Polygons

Time Series Graphs

Two-way Tables

Comparing Two or More Sets of Data

Mean Of Grouped Data Using the Direct Method

Mean Of Grouped Data Using Assumed Mean Method

Mean Of Grouped Data Using Step Deviation Method

Finding Mode Of Grouped Data From Its Histogram

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

Relation between Mean, Median, and Mode

Mean Deviation for Ungrouped Data

Mean Deviation for Discrete Frequency Distribution

Mean Deviation for Continuous Frequency Distribution

Variance and Standard Deviation of Ungrouped Data

Variance and Standard Deviation of a Discrete Frequency Distribution

Variance and Standard Deviation for a Continuous Frequency Distribution

Coefficient of Variation

Arithmetic Progression and Arithmetic Mean

Geometric Progressions

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

Geometric Mean and Its Relation with Arithmetic Mean

Sum of n Terms of Special Series

Sets

Types of Sets

Equal Sets and Equivalence Sets

Union and Intersection of Sets

Complement of a set

Venn diagrams

Equal Sets and Equivalent Sets

Concept of Subset

Union and Intersection of Sets

Difference between Sets

Complement of a set

Venn diagrams

Subsets

Union and Intersection of Sets

Difference of Sets

Application of Union and Intersection

Complement of a Set

Relation

Mapping

Concept of Functions

Statement

Negation of a Statement

Compound Sentence and its Components

Role of Connectives "And" and "Or"

Role of Quantifiers in a Compound Statement

Implications

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

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

Principle of Mathematical Induction

Limit of a Function Using Intuitive Approach

Limit of a Polynomial and a Rational Function

Limits of Trigonometric Functions

Derivative of a Function

Derivatives of Trigonometric and Polynomial Functions

Complex Numbers

Addition and Subtraction of Complex Numbers

Multiplication of Complex Numbers

Division of Complex Numbers

Identities of Complex Numbers

Modulus and Conjugate of a Complex Number

Quadratic Equations with Complex Roots

Concept of Argand Plane

Calculating Compound Interest Using The Concept Of Simple Interest

Formula for Finding Compound Interest

Problems Where the Interest is not Compounded Annually

Growth and Depreciation

Sales Tax

Value Added Tax (VAT)

Savings Bank Account

Recurring Deposit Account