Nature of Roots of a Quadratic Equation

Goods and Services Tax (G.S.T.)

• Tax and Its Computation
• Mathematical Study of GST (Goods and Services Tax)
• GST Structure for Calculations
• Computational Mechanisms under GST
• Input Tax Credit (ITC) in Mathematics
• E-way Bill in GST Sums
• Examples based on GST Calculations

Compound Interest

• Compound Interest as a Repeated Simple Interest Computation with a Growing Principal
• Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years
• Use of Formula
• Finding CI from the Relation CI = A – P

Banking

• Money and Banking in Arithmetic
• Mathematics of Recurring Deposit (R.D.)

Shares and Dividends

• Shares
• Formulae for Shares and Dividends
• Examples based on Shares and Dividends

Linear Inequations

• Linear Inequations
• Method of Solving a Linear Inequality
• Representation of Inequalities
• Combining Inequalities
• Product of Two Linear Expressions

Quadratic Equations

• Quadratic Equations
• Method of Solving a Quadratic Equation
• Factorisation Method
• Quadratic Formula (Shreedharacharya's Rule)
• Nature of Roots of a Quadratic Equation
• Equations Reducible to Quadratic Equations

Ratio and Proportion

• Ratio
• Ratio in Lowest Terms
• All About Ratios: Dividing, Comparing, and Modifying Quantities
• Commensurable and Incommensurable Quantities
• Composition of Ratios
• Proportion
• Concept of Continued Proportion
• Properties of Proportion
• Direct Applications of Ratio and Proportion

Factorisation of Polynomials

• Function and Polynomial
• Division Algorithm for Polynomials
• Remainder Theorem
• Factor Theorem
• Applications of Factor Theorem

Matrices

• Concept of Matrices
• Types of Matrices
• Equality of Matrices
• Compatibility of Matrices
• Transpose of a Matrix
• Operations on Matrices> Addition and Subtraction of Matrices
• Operations on Matrices> Matrix Multiplication
• Operations on Matrices>Scalar Multiplication

Arithmetic and Geometric Progression

• Sequence, Series, and Progression
• Arithmetic Progression (A.P.)
• General Term of an Arithmetic Progression
• Sum of First ‘n’ Terms of an Arithmetic Progressions
• Three or More Terms in Arithmetic Progression (A.P.)
• Arithmetic Mean in A.P.
• Properties of an Arithmetic Progression

Co-ordinate Geometry

• Co-ordinate Geometry
• Advanced Concept of Reflection in Mathematics
• Invariant Points
• Combination of Reflections
• Using Graph Paper for Reflection

Symmetry

Similarity

• Similarity and Congruency of Figures
• Similarity as a Size Transformation
• Applications to Maps and Models
• Similarity of Triangles (Corresponding Sides & Angles)
• Criteria for Similarity of Triangles
• Basic Proportionality Theorem
• Relation Between the Areas of Two Triangles

Loci

• Locus
• Points Equidistant from Two Given Points
• Points Equidistant from Two Intersecting Lines
• Summary of Important Results on Locus
• Important Points on Concurrency in a Triangle

Circles

• Geometrical Concepts Related to a Circle
• Chord
• Arc of the Circle
• Segment of a Circle
• Theorems on Angles in a Circle
• Cyclic Quadrilateral and Concyclic Points
• Some Important Results on Circles
• Advanced Theorems Related to Circles

Tangent and Secant Properties

• Secant and Tangent
• Tangent and Secant Properties
• Intersecting Chords and Tangents
• Alternate Segment Property

Constructions

• Construction of Tangents to a Circle
• Construction of Two Tangents to a Circle
• Circumcircle of a Triangle
• Incircle of a Triangle
• Circumscribed Circle of a Regular Polygon
• Inscribed Circle of a Regular Polygon

Area and Volume of Solids (Cylinder, Cone and Sphere)

• Mensuration of Cylinder
• Hollow Cylinder
• Mensuration of Cones
• Mensuration of a Sphere
• Hemisphere
• Conversion of Solids
• Solid Figures
• Problems on Mensuration

Trigonometrical Identities

• Trigonometric Ratios
• Relation Among Trigonometric Ratios
• Trigonometric Identities (Square Relations)
• Elimination of Trigonometrical Ratios
• Trigonometric Ratios of Complementary Angles
• Application of Trigonometric Tables

Heights and Distances

• Angles of Elevation and Depression
• Problems based on Elevation and Depression

Statistics : basic concepts, Mean, Median, Mode. Histograms and Ogive

• Frequency Distribution and Its Applications
• Concepts of Statistics
• Histograms
• Frequency Polygon
• Cumulative Frequency and Cumulative Frequency Table
• Ogives (Cumulative Frequency Curve)

Probability

• Concept of Probability
• Elementary Types of Events and Properties of Probability
• Measurement of Probability
• Standard Results for Outcomes in Probability
• Problems based on Probability