Topics
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
Commercial Mathematics
Goods and Services Tax (G.S.T.)
Banking
Algebra
Geometry
Shares and Dividends
Symmetry
Mensuration
Linear Inequations
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
Trigonometry
Statistics
Problems on Quadratic Equations
- Method for Solving a Quadratic Word Problem
- Problems Based on Numbers
- Problems on Ages
- Problems Based on Time and Work
- Problems Based on Distance, Speed and Time
- Problems Based on Geometrical Figures
- Problems on Mensuration
- Problems on C.P. and S.P.
- Miscellaneous Problems
Ratio and Proportion
Probability
Remainder Theorem and Factor Theorem
- Function and Polynomial
- Division Algorithm for Polynomials
- Remainder Theorem
- Factor Theorem
- Applications of Factor Theorem
Matrices
Arithmetic Progression
Geometric Progression
Reflection
- Co-ordinate Geometry
- Advanced Concept of Reflection in Mathematics
- Invariant Points
- Combination of Reflections
- Using Graph Paper for Reflection
Section and Mid-Point Formulae
Equation of a Line
Similarity
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
Angle and Cyclic Properties of a Circle
Tangent Properties of Circles
Constructions
Volume and Surface Area 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
Heights and Distances
- Angles of Elevation and Depression
- Problems based on Elevation and Depression
Graphical Representation of Statistical Data
Measures of Central Tendency (Mean, Median, Quartiles and Mode)
Probability
- Introduction
- Formation of Arcs
- Minor Arc
- Major Arc
- Key Points Summary
Introduction
An arc is defined as any continuous, curved part or segment of a circle’s circumference (its boundary).
When two points are placed on a circle, they inevitably divide the circumference into two arcs.
Understanding arcs is fundamental to measuring distances along curved paths in geometry and real-world design.
Formation of Arcs
-
Start with a circle having centre O
-
Mark two distinct points on the circumference (for example, points A and B)
-
These two points divide the circle into two parts
-
Each curved part is called an arc
-
One arc will be shorter (minor arc)
-
The other arc will be longer (major arc)
Minor Arc
The minor arc is the shorter of the two arcs formed between two points on a circle.
Characteristics:
-
Length is less than half the circumference
-
Angle subtended at the center is less than 180°
-
Appears as the "smaller curve"
-
Named using two letters
Major Arc
The major arc is the longer of the two arcs formed between two points on a circle.
Characteristics:
-
Length is greater than half the circumference
-
Angle subtended at the center is greater than 180°
-
Appears as the "larger curve"
-
Named using three letters with a middle point.
Key Points: Arc of the Circle
-
Arc Definition: An arc is a curved portion of a circle's circumference between two points.
-
Two Types: Minor arc (< 180°) and Major arc (> 180°).
-
Semicircle: When the arc angle is exactly 180°, it's called a semicircle.
-
Complete Circle: Minor arc + Major arc = 360° (complete circumference).
