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
- Definition: Linear lnequations
- Signs of Inequality
- Definition: Replacement Set / Domain of Variable
- Definition: Solution Set
- Properties
CISCE: Class 10
Definition: Inequation
An inequation is a relation showing inequality between two quantities.
Symbols used:
-
> greater than
-
< less than
-
≥ greater than or equal to
-
≤ less than or equal to
CISCE: Class 10
Definition: Linear Inequation in One Variable
An inequation involving one variable of degree 1 is called a linear inequation in one variable.
General forms:
-
ax + b > c
-
ax + b < c
-
ax + b
-
ax + b
(where a, b, c are real numbers and a ≠ 0)
CISCE: Class 10
Definition: Replacement Set / Domain
The set from which values of the variable are taken is called the
replacement set or domain.
CISCE: Class 10
Definition: Solution Set
The set of all values from the replacement set that satisfy the inequality is called the solution set.
CISCE: Class 6
Key Points: Properties of Inequation
| Operation on Both Sides | Inequality Sign | Example |
|---|---|---|
| Add the same number | No change | (x - 2 < 4 ⇒ x < 6) |
| Subtract the same number | No change | (x + 3 > 7 ⇒ x > 4) |
| × or ÷ by a positive number | No change | (x < 6 ⇒ 3x < 18) |
| × or ÷ by a negative number | Reverses | (-2x > 6 ⇒ x < -3) |
