CBSE Board Mathematics Exam Questions 2026: With the CBSE Class 10 board exams set to begin in just ten days, students will appear for Basic Mathematics and Mathematics Standard on February 17 in the morning shift from 10:30 am to 1:30 pm. Mathematics remains one of the most challenging subjects across classes, often becoming the deciding factor in overall scores.
This trend was evident even in JEE Main Session 1 this year, where Mathematics emerged as the toughest section compared to Physics and Chemistry.
To secure high marks, consistent practice and strong conceptual clarity are essential. Below are some of the questions (by CBSE Centre for Excellence in Assessment and Education Initiatives) that students should practise to assess their readiness and strengthen their preparation ahead of the 2026 board exams.
1. p ( x ) = ( x + 5) 2 - 7( x - k ); where k is a constant.
If p ( x ) is divisible by x , find the value of k . Show your steps.
2. p and q are zeroes of the polynomial 3 x 2 + 4 x - 4.
Without finding the actual values of p and q , evaluate (1 - p )(1 - q ). Show your steps
3. f ( x ) = x 2 + 10 x + 21
Find the zeroes of the above polynomial. Show your work.
4. ( -2/5 ) is one of the zeroes of the polynomial 5 x 2 + 2 x - 7. (T/F). Justify your answer.
5. CASE STUDY
Answer the questions based on the given information.
The revenue (in Rs) of a firm is represented by the polynomial R( x ) = 5x 3 + 4x 2 + 7, and
the expenditure (in Rs) by the firm is represented by the polynomial E( x ) = 3 x 3 + 2 x - 1
where x is the number of items produced by the firm in a year.
Q1) Find the profit polynomial P( x ). Show your work.
If the firm produces 100 products in a year, find the revenue and profit (in Rs) for the firm using the polynomials. Show your work.
Q2) Tax is calculated on the profit using the polynomial T( y ) = 0.3 y + 100, where y represents the profit earned.
Q3) Determine the tax amount (in Rs) to be paid on the profit generated from 10 items. Show your work.
6. Finds the value of f (2) as: 1
(2) 3 + 7(2) 2 + 3(2) - 12 = 30
7. Writes that P( x ) = 0 at x = 6 or P(6) = 0 and hence ( x - 6) is a factor of the 1 polynomial. (Award 0.5 marks if only the factor is written.)
8. Expands (1 - p )(1 - q ) to get 1 - ( p + q ) + pq.
Finds the sum of the zeroes i.e. p + q = ( -4/3 ).
Finds the product of the zeroes i.e. pq = ( -4/3 ).
Uses the above steps to find the value of (1 - p )(1 - q ) as 1 - ( -4/ 3 ) +( -4/3 ) = 1.
9. Finds the revenue made by the company from 100 products as: 1
R(100) = 5(100) 3 + 4(100) 2 + 7
=> R(100) = 5000000 + 40000 + 7 = Rs 50,40,007.
Finds the profit made by the company from 100 products as: 1
P(100) = 2(100) 3 + 4(100) 2 - 2(100) + 8
=> P(100) = 2000000 + 40000 - 200 + 8 = Rs 20,39,808
10. Finds tax as: 1
T(2388) = 0.3(2388) + 100 = Rs 816.4.
11. For a positive integer n , m is a prime factor of n .
Show that m is not a factor of ( n + 1).
12. 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.
13. Writes the prime factorisation of 10 k2 as (2 * 32 * 53 * p2 )
14. Finds HCF of 345, 405 and 270 using Euclid's Division Algorithm as follows: 1
405 = 345 * 1 + 60
345 = 60 * 5 + 45
60 = 45 * 1 + 15
45 = 15 * 3 + 0
Finds HCF of 405 and 345 as 15.
Finds HCF of 270 and 15 as follows: 0.5
270 = 15 * 18 + 0
Concludes that HCF of 345, 405 and 240 is 15, hence there were 15 students in each
group.
15. g ( x ) = px 2 + qx + 152 is a polynomial where p and q are real numbers. The zeroes of
g ( x ) are distinct prime numbers. Find the:
i) zeroes of g ( x ).
ii) values of p and q .
Show your work and give valid reasons.
16. Anisha lives 15 km away from her school. She walks to the bus stop and takes a bus to school everyday. If she goes to the nearest bus stop, she needs to walk for 3 km and cover the rest by bus. This takes her 1.5 hours. If she walks to a bus stop further away, she needs to walk for 5 km and cover the rest by bus. This takes her 2 hours.
Frame equations and solve them to find the average speed Anisha walks at, as well as the average speed of the bus. Show your steps.
17. Gate 3 has been placed exactly opposite to gate 1 on the boundary of the park. The distance between gate 3 and gate 2 is 1 m more than the distance between gate 3 and gate 2. The shortest distance between gates 1 and 2 is 29 m, find the width of the park. Show your work.
18. Determine whether the following sequence is an arithmetic progression or not. (-12 + 12 a ), (-11 + 11 a ), (-10 + 10 a ),... where a is any rational number. Show your work.