Topics
Goods and Services Tax (G.S.T.)
Commercial Mathematics
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
Algebra
Shares and Dividends
Geometry
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
Ratio and Proportion
Statistics
Probability
Factorisation of Polynomials
- Function and Polynomial
- Division Algorithm for Polynomials
- Remainder Theorem
- Factor Theorem
- Applications of Factor Theorem
Matrices
Arithmetic and Geometric 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
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
Tangent and Secant Properties
Constructions
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
Heights and Distances
- Angles of Elevation and Depression
- Problems based on Elevation and Depression
Statistics : basic concepts, Mean, Median, Mode. Histograms and Ogive
Probability
- Theorem
CISCE: Class 10
Basic Proportionality Theorem
Statement:
If a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio.
To Prove:
\[\frac{\mathrm{AD}}{\mathrm{DB}}=\frac{\mathrm{AE}}{\mathrm{EC}}\]
Proof:
-
A line parallel to a side of a triangle forms equal corresponding angles.
-
Hence, the two triangles formed are similar (AAA similarity).
-
In similar triangles, corresponding sides are proportional.
Therefore, the line divides the two sides in the same ratio.
\[\frac{\mathrm{AD}}{\mathrm{DB}}=\frac{\mathrm{AE}}{\mathrm{EC}}\]
CISCE: Class 10
Converse of Basic Proportionality Theorem
Statement:
If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.
To Prove:
-
Assume a line through point D parallel to BC meets AC at F.
-
By BPT, \[\frac{\mathrm{AD}}{\mathrm{DB}}=\frac{\mathrm{AF}}{\mathrm{FC}}\]
- Given, \[\frac{\mathrm{AD}}{\mathrm{DB}}=\frac{\mathrm{AE}}{\mathrm{EC}}\]
-
Hence,\[\frac{AF}{FC}=\frac{AE}{EC}\]
-
⇒ Points E and F coincide.
Therefore,
