Algebra Revision Notes Class 10 – Important Points & Formulas for Board Exams
Algebra is one of the most important sections of the CBSE Class 10 Mathematics syllabus. A large number of questions in the board examination come directly from algebra chapters such as polynomials, quadratic equations, pair of linear equations in two variables, and arithmetic progression.
These revision notes provide a quick yet comprehensive summary of Class 10 algebra concepts, formulas, identities, shortcuts, and solved examples. Students can use these notes for quick revision before exams and strengthen their problem-solving skills.
Why Algebra is Important for Class 10 Boards
In the CBSE Class 10 exam pattern, algebra contributes a significant portion of the mathematics paper. Mastering algebra concepts helps students solve problems faster and improve overall accuracy.
- Helps build logical and analytical thinking
- Important for higher mathematics and competitive exams
- Provides foundation for calculus and advanced algebra
- Several board exam questions are directly formula-based
1. Algebraic Identities – Quick Revision
Algebraic identities are expressions that remain true for all values of variables. They are widely used for expanding expressions and factorization.
Important Identities
- (a + b)² = a² + 2ab + b²
- (a − b)² = a² − 2ab + b²
- (a + b)(a − b) = a² − b²
- (x + a)(x + b) = x² + (a + b)x + ab
- (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
- a³ + b³ = (a + b)(a² − ab + b²)
- a³ − b³ = (a − b)(a² + ab + b²)
Solved Example 1
Expand: (3x − 5)²
= (3x)² − 2(3x)(5) + 5²
= 9x² − 30x + 25
2. Polynomials – Important Concepts
A polynomial is an algebraic expression consisting of variables and coefficients.
General form of quadratic polynomial:
ax² + bx + c
Key Formulas
- Sum of zeros = −b/a
- Product of zeros = c/a
Solved Example 2
Find the sum and product of zeros of the polynomial 3x² − 7x + 2.
a = 3, b = −7, c = 2
Sum of zeros = −b/a = 7/3
Product of zeros = c/a = 2/3
3. Pair of Linear Equations in Two Variables
A pair of linear equations in two variables can be written as:
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Methods to Solve
- Substitution Method
- Elimination Method
- Graphical Method
- Cross Multiplication Method
Solved Example 3
Solve the equations:
2x + y = 7
x − y = 1
Add both equations:
3x = 8
x = 8/3
Substitute in first equation:
2(8/3) + y = 7
16/3 + y = 7
y = 5/3
Solution: (8/3 , 5/3)
4. Quadratic Equations – Quick Revision
A quadratic equation is written as:
ax² + bx + c = 0
Quadratic Formula
x = [-b ± √(b² − 4ac)] / 2a
Discriminant
D = b² − 4ac
- D > 0 → Two real roots
- D = 0 → Equal roots
- D < 0 → No real roots
Solved Example 4
Solve x² − 7x + 10 = 0
Factorization:
(x − 5)(x − 2) = 0
Roots: x = 5, x = 2
5. Arithmetic Progression (AP)
An arithmetic progression is a sequence where the difference between consecutive terms is constant.
Important Formulas
- nth term: aₙ = a + (n − 1)d
- Sum of n terms: Sₙ = n/2 [2a + (n − 1)d]
- Sₙ = n/2 (a + l)
Solved Example 5
Find the 15th term of AP: 4, 7, 10, …
a = 4
d = 3
a₁₅ = 4 + 14 × 3
a₁₅ = 46
6. Board Exam Important Question Types
- Factorization using algebraic identities
- Finding zeros of polynomials
- Solving quadratic equations
- Word problems based on quadratic equations
- Finding nth term in arithmetic progression
- Solving simultaneous equations
Exam Preparation Tips
✔ Practice quadratic equations daily
✔ Revise AP formulas before exams
✔ Solve previous year board questions
✔ Avoid calculation mistakes
Common Mistakes Students Should Avoid
- Forgetting negative signs in quadratic formula
- Incorrect expansion of algebraic identities
- Confusing sum and product of zeros
- Wrong substitution of AP formula values
- Arithmetic mistakes during calculations
Final Quick Revision Summary
To perform well in the Class 10 mathematics board examination, students should revise algebra formulas regularly and practice solved examples. Algebra becomes easy once formulas are clear and problems are practiced consistently.
Use these revision notes as a quick guide before exams and solve practice problems from textbooks and previous board papers.