CBSE Class 10 Algebra Previous Year Questions – Board Exam Solved Problems
Algebra is one of the most important sections of the CBSE Class 10 Mathematics syllabus. Every year, several questions in the board exam are asked from algebra chapters such as Quadratic Equations, Polynomials, Pair of Linear Equations in Two Variables, and Arithmetic Progressions.
Practicing previous year CBSE board exam questions helps students understand the exam pattern, identify frequently asked concepts, and improve speed and accuracy. In this article, we cover important algebra questions that have appeared in CBSE board exams along with detailed step-by-step solutions.
Why Practice Previous Year Algebra Questions?
Many questions in CBSE board exams follow similar concepts every year. If students practice questions asked in previous papers, they become familiar with the difficulty level and the expected method of solving.
- Understand CBSE exam pattern
- Identify frequently asked topics
- Improve time management
- Build confidence before the exam
Important Algebra Chapters in CBSE Class 10
- Polynomials
- Pair of Linear Equations in Two Variables
- Quadratic Equations
- Arithmetic Progressions
Previous Year Algebra Questions with Solutions
Question 1: Find the zeros of the polynomial 2x² − 7x + 3.
Solution:
Given polynomial = 2x² − 7x + 3
We factorize the polynomial.
2x² − 7x + 3
Split middle term:
2x² − 6x − x + 3
2x(x − 3) −1(x − 3)
(2x − 1)(x − 3) = 0
Therefore:
x = 1/2 and x = 3
Zeros of the polynomial = 1/2 and 3
Question 2: Find the sum and product of zeros of the polynomial x² − 5x + 6.
Solution:
Given polynomial: x² − 5x + 6
a = 1, b = −5, c = 6
Sum of zeros = −b/a
= −(−5)/1 = 5
Product of zeros = c/a
= 6/1 = 6
Sum = 5
Product = 6
Question 3: Solve the quadratic equation x² − 7x + 10 = 0.
Solution:
x² − 7x + 10 = 0
Factorization:
(x − 5)(x − 2) = 0
x − 5 = 0 → x = 5
x − 2 = 0 → x = 2
Roots = 5 and 2
Question 4: Solve 2x² − 5x − 3 = 0 using quadratic formula.
Solution:
a = 2, b = −5, c = −3
Quadratic Formula:
x = [-b ± √(b² − 4ac)] / 2a
D = b² − 4ac
= (-5)² − 4(2)(-3)
= 25 + 24
= 49
x = [5 ± √49] / 4
x = (5 ± 7)/4
x = 3 or x = −1/2
Question 5: Solve the system of equations:
2x + y = 7
x − y = 1
Solution:
From equation 2:
x − y = 1
x = y + 1
Substitute in equation 1:
2(y + 1) + y = 7
2y + 2 + y = 7
3y = 5
y = 5/3
x = y + 1
x = 5/3 + 1
x = 8/3
Solution = (8/3 , 5/3)
Question 6: Find the 15th term of the arithmetic progression 3, 7, 11…
Solution:
a = 3
d = 4
n = 15
aₙ = a + (n − 1)d
a₁₅ = 3 + (14 × 4)
a₁₅ = 3 + 56
a₁₅ = 59
15th term = 59
Question 7: Find the sum of first 20 terms of AP: 2, 5, 8…
Solution:
a = 2
d = 3
n = 20
Sₙ = n/2 [2a + (n − 1)d]
S₂₀ = 20/2 [4 + (19 × 3)]
S₂₀ = 10 [4 + 57]
S₂₀ = 10 × 61
S₂₀ = 610
Sum of first 20 terms = 610
Question 8: Find two numbers whose sum is 27 and product is 182.
Solution:
Let numbers be x and y.
x + y = 27
xy = 182
Form quadratic:
x² − 27x + 182 = 0
Factorization:
(x − 13)(x − 14) = 0
x = 13 or 14
Numbers = 13 and 14
Exam Tips for Algebra Questions
✔ Write all steps clearly for full marks
✔ Practice arithmetic progression formulas regularly
✔ Verify answers by substituting values in original equations
Common Mistakes Students Make
- Incorrect sign while using quadratic formula
- Forgetting to split middle term correctly
- Calculation mistakes in arithmetic progression
- Not writing final answer clearly
How to Prepare Algebra for CBSE Board Exam
To score high marks in the Class 10 board exam, students should focus on understanding the core concepts of algebra instead of memorizing steps. Practice at least 10 algebra questions daily and revise formulas regularly.
Solving previous year questions is one of the best strategies to prepare for the exam. It helps identify patterns and increases confidence before the board examination.
