Algebra – Grade 10 CBSE

There are 4 courses under Grade 10 Algebra for CBSE:

  1. Arithmetic Progression
  2. Quadratic Equations
  3. Polynomials
  4. Linear Equations in 2 variables

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Arithmetic Progression
Key topics include:

  • Introduction
    • Sequence
    • Progression
  • Arithmetic Progression
    • Arithmetic Progression
    • Arithmetic Series
  • nth Term of an Arithmetic Progression
    • nth Term
    • Counting the Terms from the End of an AP
  • Arithmetic Mean of Two Numbers
    • Arithmetic Mean (AM) Between Two Numbers
  • How To Select Few Terms in AP
    • Three Terms in AP
    • Four Terms in AP
    • Five Terms in AP
  • Sum of First n Terms of an AP
  • Sum of First n Natural Numbers
    • Sum of First n Natural Numbers
    • Sum of Squares of First n Natural Numbers
    • Sum of Cubes of First n Natural Numbers

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Quadratic Equations
Key topics include:
1. Quadratic Equations

a) Definition
b) Roots of a Quadratic Equation
c) Checking a Root of a Quadratic Equation By Substitution
d) Solving a Quadratic Equation by Factorization
e) Solving Quadratic Equation by Perfect Square Method
f) Solving Quadratic Equation by Formula

2. Nature of Roots

a) Discriminant of a Quadratic Equation

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Key topics include:

  • Polynomials
    1. Definition
    2. Degree of a Polynomial
    3. Constant Polynomial
    4. Linear Polynomial
    5. Quadratic Polynomial
    6. Cubic Polynomial
    7. Bi-quadratic Polynomial
    8. Multinomial Polynomial
  • Value of a Polynomial at a Given Point
  • Graph of Polynomial
    1. Graph of a Constant Polynomial
    2. Graph of a Linear Polynomial
    3. Properties of Linear Graph (Increasing & Decreasing Lines)
    4. Graph of a Quadratic Polynomial
    5. Properties of Quadratic Graph
    6. Graph of a Cubic Polynomial
    7. Properties of Cubic Graph
  • Zeros of a Polynomial
  • Formation of a Polynomial if its Zeros are given
    1. One Zero Given
    2. Two Zeros Given
    3. Three Zeros Given
    4. Four Zeros Given
  • Zeros of a Polynomial and its Factors
    1. Zero as a Factor
    2. Properties of Zero for Rational Coefficients
  • Relation Between the Zeros and Coefficient of a Polynomial
    1. Linear Polynomial
    2. Quadratic Polynomial
    3. Cubic Polynomial
  • Division Algorithm for Polynomial

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Linear Equations in 2 variables
Key topics include
1. Linear Equation in Two Variables

a) 1. Definition
a) 2. Simultaneously Linear Equation In Two Variables
b) 3. Consistent System of Linear Equation
c) 4. Inconsistent System of Linear Equations

2. Types of Solutions (Condition for Solvability)

a) 1. Unique Solution
b) 2. Infinitely Many Solutions
c) 3. No Solutions

3. Methods to Solve Linear Equations by Graph

a) 1. Case 1 : Lines Intersect at one Point
b) 2. Case 2 : Lines are Coincident
c) 3. Case 3 : Lines are Parallel

4. Method to Solve Linear Equations By Substitution
5. Method to Solve Linear Equation by Elimination
6. Method to Solve Linear Equation by Cross Multiplication

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