Important Questions for Algebra CBSE Class 10 Maths Exam 2025: You Can’t Miss!

CBSE Class 10 2025 Algebra: Chapter-wise weightage

According to the official CBSE circular regarding subject-wise marks bifurcation for Class X Examination 2025 CBSE, the chapter-wise weightage for Algebra in the Class 10 Mathematics exam is as follows:

Polynomials

Find the zeroes of the quadratic polynomial $x^2-2 x-8 x^2-2 x-8 x^2-2 x-8$ and verify the relationship between the zeroes and coefficients.

General Approach to Solve:

Find the zeroes of the quadratic polynomial $x^2-2 x-8$ and verify the relationship between the zeroes and coefficients.

1. Factorization: Factorize the polynomial $\left(x^2-2 x-8=(x-4)(x+2)\right.$ ).
2. Find Zeros: Equate each factor to zero ( $x-4=0, x+2=0$ ), giving $x=4,-2$.
3. Verification: Verify by checking:

- Sum of zeros $=-$ coefficient of $x /$ coefficient of $x^2$

- Product of zeros $=$ constant term/coefficient of $x^2$

Pair of Linear Equations in Two Variables

Q. Solve the pair of equations: $2 x+y=5$ and $3 x-y=5$ using the elimination method.

General Approach to Solve:

1. Align Equations: Arrange both equations in standard form:

$2 x+y=5$

$3 x-y=5$

2. Eliminate a Variable: Add the two equations to eliminate $y$ :

$(2 x+y)+(3 x-y)=5+5 \rightarrow 5 x=10$, sо $x=2$.

3. Substitute: Substitute $x=2$ into one of the original equations:

$2(2)+y=5 \rightarrow y=1$.

4. Verify Solution: Substitute $x=2, y=1$ into both equations to ensure they are satisfied.

Quadratic Equations

Q. Solve $2 x^2+x-6=0$ using the quadratic formula.

General Approach to Solve:

1. Identify Coefficients: Compare with $a x^2+b x+c=0$ : $a=2, b=1, c=-6$.
2. Quadratic Formula: Use the formula $x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}$ :

Discriminant $=b^2-4 a c=1-4(2)(-6)=1+48=49$.

Roots $=\frac{-1 \pm \sqrt{49}}{4}=\frac{-1 \pm 7}{4}$.

Roots: $x=\frac{6}{4}=\frac{3}{2}$ and $x=\frac{-8}{4}=-2$.

3. Verification: Substitute $x=\frac{3}{2}$ and $x=-2$ into the equation to ensure they satisfy it.

Arithmetic Progressions (AP)

Q. Find the sum of the first 15 terms of the AP: $7,10,13, \ldots$

General Approach to Solve:

1. Identify Parameters: The AP is $7,10,13, \ldots$ so:

First term $(a)=7$,

Common difference $(d)=10-7=3$,

Number of terms $(n)=15$.

2. Sum Formula: Use the formula for the sum of an AP:

$S_n=\frac{n}{2}[2 a+(n-1) d]$

3. Substitute values:

$S_{15}=\frac{15}{2}[2(7)+(15-1) \cdot 3]$

4. Verification: Confirm calculations for any errors.

CBSE Class 10 Maths 2025: Exam Paper Structure and Marks Distribution

There are five sections in the question paper in which there lies a definite type of question and a definite number of marks allotted. To make student’s preparation more effective, here is the detailed division of the exam:

General Tips to Prepare for Algebra Chapters

• Focus on different types of polynomials (linear, quadratic, cubic) and their degree. Revise the Remainder Theorem and Factorization techniques thoroughly.
• Solve problems related to splitting the middle term, long division of polynomials, and finding zeros.
• Learn how to plot polynomials and interpret their graphs. This will help in understanding the behaviour of polynomials.
• Practice all methods to solve linear equations—Substitution, Elimination, and Cross Multiplication.
• Focus on real-life applications, such as problems of age, time and work, and mixtures. Convert word problems into equations for easier solving.
• Understand the standard form of quadratic equations and how to find roots using the Factorization Method, Completing the Square, and the Quadratic Formula.
• Learn to calculate the discriminant to determine the nature of roots (real, equal, or imaginary).
• Learn the formulas for the nth term and the sum of n terms (Sn=n/2[2a+(n−1)d])(S_n = n/2[2a + (n-1)d])
• Solve application-based problems such as finding missing terms, sums, or term positions in real-life situations.
• Create a formula and concept sheet for quick revision before exams.
• Solve CBSE Class 10 Sample paper 2024-25 for practice.