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
Key Points: Some Important Results on Circles
-
Intersecting Circles (Collinearity):
If two circles with centres O and O′ intersect at two points and diameters are drawn through these points, then the given points lie on a straight line. -
Cyclic Parallelogram:
Every parallelogram inscribed in a circle is a rectangle. -
Isosceles Trapezium:
An isosceles trapezium is always a cyclic quadrilateral. -
Cyclic Trapezium Properties:
A cyclic trapezium is isosceles, and its diagonals are equal. -
Regular Polygon:
Any four vertices of a regular polygon lie on a circle. -
Chords Bisecting Each Other:
If two chords of a circle bisect each other, then both the chords are diameters of the circle. -
Angle Bisectors of a Cyclic Quadrilateral:
The quadrilateral formed by the angle bisectors of a cyclic quadrilateral is also cyclic. -
Mid-point of Hypotenuse:
The mid-point of the hypotenuse of a right-angled triangle is equidistant from all three vertices of the triangle. -
Equal Chords and Angles at the Centre:
In a circle, equal chords subtend equal angles at the centre. -
Converse of Equal Chords Theorem:
In a circle, chords which subtend equal angles at the centre are equal in length.
