CBSE Board Exams 2026: Mathematics is often considered one of the most challenging subjects for students. Those who are comfortable with the subject are generally viewed as having strong analytical and problem-solving abilities. Students who show interest and perform well in mathematics are believed to possess sharper reasoning skills, which often help them in both academic and professional settings.
Mathematics questions expand a student's thinking, strengthen their problem-solving abilities, encourage brainstorming for solutions, promote conceptual understanding, and help them think beyond conventional limits.
This year, CBSE has introduced a significant change in the question paper pattern by incorporating 50 per cent competency-based questions, including MCQs, case-based questions, source-based integrated questions, data-interpretation questions, and situational problems. Twenty per cent of the paper will include select-response (MCQ) questions, while the remaining 30 per cent will feature constructed-response questions, including short-answer and long-answer questions.
Over the years, the mathematics paper has consistently been perceived as challenging in terms of the difficulty level of questions.
Therefore, revising all key topics and maintaining a strong command over important formulas chapter-wise becomes essential. To help students understand the nature and level of questions, CBSE has released competency-focused practice questions to familiarise them with the exam pattern and expected question formats.
Here are some of the questions students can review to understand the expected level in the upcoming board examination:
Chapter - 1: Real Numbers
Free Response Questions
Q: 2 to the power n is not divisible by 6 where n is a positive integer. Is the above statement true or false? If true, give a valid reason and if false, give an example.
Q: For a positive integer n, m is a prime factor of n. Show that m is not a factor of (n + 1).
Q: A rectangular arrangement of pens has rows and columns. Rohan takes away 3 rows of pens and then Sarah takes away 2 columns of pens from the remaining pens. The remaining pens are rearranged in p rows and q columns where p is a prime number.
If Rohan takes 24 pens and Sarah takes 18 pens, find all possible value(s) of p. Show your work.
Answer the following questions based on the information given.
Sakshara International School organised a combined exhibition for Grade 10 students of its three branches. 345 students from the Mumbai branch, 405 from the Pune branch, and 270 from the Nagpur branch participated.
The following activities were planned:
Group projects: Students from each branch were divided into groups such that each group had an equal number of students, and the number of groups was minimum.
Individual project: Each of the 1,020 students had to submit an individual project. A fixed number of topics were allotted such that each topic had an equal number of students.
Inter-state model-making competition: A few equal numbers of students were selected from each branch to participate. Each branch had to submit between 3 to 7 models.
Chapter - 2: Polynomials
Multiple Choice Questions
At which point will the graph of the polynomial p(x) = (-x + 6x² - 1) intersect the negative x-axis?
- only -1/3
- only -1/2
- both -1/3 and -1/2
- none, it never intersects the negative x-axis
Free Response Question
State whether the following statement is true or false. Justify your answer.
If the graph of a polynomial has EXACTLY 2 zeroes, then the polynomial must be quadratic.
Chapter - Probability
Q: Pratik has blue and green coins of the same size in a bag. He has 50 coins each of blue and green.
He is randomly picking up one coin at a time without replacement. He does not see which coin he has picked.
What is the MINIMUM number of coins he would have to pick to definitely get a pair of blue or green coins?
Free Response Questions - Surface Areas and Volumes
State whether the following statement is true or false. Explain your answer.
If a cylinder and a cone have equal radii and equal volume, then the height of the cylinder is 3 times that of the cone.
CBSE Class 10 board exams 2026 are scheduled to begin on February 17 with the Mathematics papers (Standard and Basic). The examinations will be held from 10:30 AM to 01:30 PM.
Click the following links to access the complete set of competency-focused practice questions.
