Class 10 Maths Most Important Questions for Half Yearly Exam CBSE Board Exam 2026-27

Class 10 Maths Most Important Questions for Half Yearly Exam CBSE Board 2026-27
is an important milestone in the preparation for the CBSE Board Examination. A strong performance in the half-yearly examination helps students identify their strengths and understand the topics that need more practice before the final Board Exam.

To help students prepare effectively, we have selected a set of Class 10 Maths Most Important Questions for the Half Yearly Exam 2026-27. These questions are based on the Class 10 Mathematics curriculum prescribed by CBSE for the academic session 2026-27 and are intended for revision of the portion covered by schools for the half-yearly examination. CBSE offers Mathematics at two levels—Mathematics Basic and Mathematics Standard—so students should practise according to the level they have opted for. CBSE has also published separate Sample Question Papers and Marking Schemes for Mathematics Basic and Mathematics Standard for 2026-27.

Why Are These Questions Important?

The purpose of these questions is not to predict the exact questions that will appear in the examination. Rather, they have been selected to help students revise important concepts, formulas, mathematical reasoning, application-based problems and different question formats from the prescribed syllabus.

CBSE’s Mathematics curriculum places emphasis on conceptual understanding, logical reasoning, problem-solving, mathematical communication and the application of mathematical concepts. Therefore, students should not depend only on memorising answers. They should understand the method used to solve each question and practise presenting the solution step-by-step.

Questions Selected from the Class 10 Maths Half Yearly Syllabus

The questions in this post are selected from the Class 10 Mathematics syllabus prescribed for the 2026-27 academic session, limited to the portion generally covered for the Half Yearly Examination by schools.

The important areas may include chapters from:

Real Numbers
Polynomials
Pair of Linear Equations in Two Variables
Quadratic Equations
Arithmetic Progressions
Triangles
Coordinate Geometry
Introduction to Trigonometry
Some Applications of Trigonometry, wherever included in the school’s half-yearly portion.

Students should check their school’s latest half-yearly syllabus/portion before beginning final revision because the chapters included in a half-yearly examination may vary from one school to another.

The questions have been chosen to provide practice in MCQs, short-answer questions, application-based questions, competency-based questions, case-based questions, numerical problems and questions requiring proper mathematical reasoning.

Watch the Video: Class 10 Maths Most Important Questions 2026-27

Looking for the most important Class 10 Maths questions for the Half Yearly Exam 2026-27? In this video, we have discussed carefully selected questions from the Class 10 Maths syllabus and the portion relevant for Half Yearly Exam preparation.

Watch the complete video and try to solve each question yourself before seeing the solution. This will help you improve your conceptual understanding, calculation speed and exam confidence.

📌 Tip: Pause the video, solve the question on your own, and then check your answer and method.

Class 10 Maths Important Questions for Half Yearly Exam 2026-27

1.The graph of a quadratic polynomial p(x) passes through the points (-6,0),

(0, -30), (4,-20) and (6,0). The zeroes of the polynomial are

A) – 6,0 B) 4, 6 C) – 30,-20 D) – 6,6

2. The value of k for which the system of equations 3x-ky= 7 and 6x+ 10y =3 is inconsistent, is

A) -10 B) -5 C) 5 D) 7

3. If the system of equations 3x+y =1 and (2k-1)x +(k-1)y =2k+1 is inconsistent, then k =

(a) -1 (b) 0 (c) 1 (d) 2

4. If the vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2), then the coordinates of its fourth vertex S are

(a) (-2,-1) (b) (-2,-3) (c) (2,-1) (d) (1,2)

5. ∆ABC~∆PQR. If AM and PN are altitudes of ∆ABC and ∆PQR respectively and AB²: PQ² = 4 : 9, then AM: PN =

(a) 3:2 (b) 16:81 (c) 4:9 (d) 2:3

6.In the given figure, DE ∥ BC, AE = a units, EC = b units, DE = x units and BC = y units. Which of the following is true?

7.In the given figure, a tangent has been drawn at a point P on the circle centred at O.

•

8. The point on the x- axis nearest to the point (-4,-5) is

A) (0, 0) B) (-4, 0) C ) (-5, 0) D) (√41, 0)

9.For the following distribution,

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DIRECTION: In the question number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option

A)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

B)Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

C)Assertion (A) is true but reason (R) is false.

D)Assertion (A) is false but reason (R) is true.

10. Assertion (A): HCF of any two consecutive even natural numbers is always 2.

Reason (R): Even natural numbers are divisible by 2.

11. The H.C.F of 85 and 238 is expressible in the form 85m -238. Find the value of m.

12.

13. Find the point(s) on the x-axis which is at a distance of √41 units from the point (8, -5).

14. Given that √3 is irrational, prove that 5 + 2√3 is irrational.

15. The sum of two numbers is 18 and the sum of their reciprocals is 9/40. Find the numbers.

16. If cosθ + sinθ = 1 , then prove that cosθ – sinθ = ±1

17. Prove that √3 is an irrational number.

18.If the sum to first n terms of an A.P. is 3n² + 2n , find the A.P.

19.A boat goes 30 km upstream and 44 km downstream in 10hours. In 13 hours, it can go 40 km upstream and 55km downstream. Determine the speed of the stream and that of the boat in still water.

20.A manufacturer of laptop bags produced 600 bags in the 3 rd year and 700 bags in the 7 th year. Assuming that the production increases uniformly by a fixed number every year, find:

(i) the production in the 1st year,

(ii) the production in the 10 th year,

(iii) the total production in the first 7 years.

FAQs – Class 10 Maths Most Important Questions for Half Yearly Exam CBSE Board Exam 2026–27

1. Why are these Class 10 Maths important questions useful for the Half Yearly Exam 2026–27?

These questions are selected from the prescribed Class 10 Mathematics syllabus and focus on important concepts, common question patterns, and topics that students should revise before the Half Yearly Examination.

2. Are these questions based on the CBSE Class 10 Maths syllabus?

Yes. The questions are prepared according to the topics prescribed for the Class 10 CBSE Mathematics curriculum for the 2026–27 academic session.

3. Can these questions help in Half Yearly Exam preparation?

Yes. They can be used as a revision resource after completing the concepts and exercises from the NCERT textbook.

4. Which chapters should Class 10 students revise for the Half Yearly Exam?

Students should revise all chapters included in their school’s Half Yearly Exam syllabus. Special attention should be given to formulas, important concepts, NCERT questions, examples, and different question types.

5. Are these questions enough to score good marks?

No single question set can guarantee a particular score. Students should use these questions along with NCERT, class notes, previous questions, sample papers, and regular practice.

6. Should I solve the questions before watching the video solutions?

Yes. Try solving each question yourself first. If you are unable to solve it, watch the solution carefully and then attempt the question again without looking at the answer.

7. How should I revise Class 10 Maths before the Half Yearly Exam?

Revise concepts and formulas first, then solve important questions chapter-wise. Finally, practise a complete sample or question paper within the prescribed time limit.

8. Are these questions useful for CBSE Board Exam preparation too?

Yes, the practice of these important concepts and question types can also support preparation for the Class 10 Board Examination, although the Half Yearly and Board Exam syllabi may differ.

9. Where can I find more Class 10 Maths preparation videos?

You can explore Future Study Point for Class 10 Maths lessons, important questions, NCERT solutions, sample papers, and exam-preparation content.

10. What should I do if I make mistakes while solving these questions?

Do not simply check the answer. Identify the step where you made the mistake, revise the related concept, and solve the question again independently. This helps improve accuracy and confidence.