[ Your School Name ] · Half-Yearly Examination 2026–27
MATHEMATICS (STANDARD) — Class X
Time Allowed: 3 HoursMaximum Marks: 80
General Instructions:
- This question paper contains 38 questions. All questions are compulsory.
- The paper is divided into five Sections — A, B, C, D and E.
- Section A has 20 questions of 1 mark each (MCQ & Assertion–Reason).
- Section B has 5 questions of 2 marks; Section C has 6 questions of 3 marks; Section D has 4 questions of 5 marks; Section E has 3 case-study questions of 4 marks each.
- Internal choice is provided in some questions. Use of a calculator is not permitted.
SECTION A (20 × 1 = 20 Marks)
- The HCF of the smallest two-digit composite number and the smallest composite number is:
(a) 2 (b) 4 (c) 6 (d) 8
- If one zero of the polynomial p(x) = x² − 6x + k is 2, then the value of k is:
(a) 6 (b) 8 (c) 4 (d) −8
- The pair of linear equations 3x + 2y = 5 and 6x + 4y = 9 is:
(a) consistent (b) inconsistent (c) dependent (d) has a unique solution
- Assertion (A): If two triangles are similar, the ratio of their areas equals the square of the ratio of their corresponding sides.
Reason (R): All equilateral triangles are similar.
(a) Both A and R true, R is the correct explanation of A (b) Both true, R not the correct explanation (c) A true, R false (d) A false, R true
- … Q5–Q20 continue (MCQ & Assertion–Reason) …
SECTION B (5 × 2 = 10 Marks)
- Find the LCM and HCF of 96 and 404 by the prime factorisation method, and verify that LCM × HCF = product of the two numbers. [2]
- In △ABC, DE ∥ BC and AD = 3 cm, DB = 5 cm, AE = 4 cm. Find the length of AC. [2]
- … Q23–Q25 continue …
SECTION C (6 × 3 = 18 Marks)
- Prove that √5 is an irrational number. [3]
- Solve for x and y: 2x + 3y = 11 and 2x − 4y = −24. Hence find the value of m if y = mx + 3. [3]
- … Q28–Q31 continue …
SECTION D (4 × 5 = 20 Marks)
- State and prove the Basic Proportionality Theorem (Thales’ Theorem). [5]
- The mean of the following frequency distribution is 54. Find the missing frequency f.
| Class | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 |
| Frequency | 5 | 8 | f | 12 | 7 |
[5]
- … Q34–Q35 continue …
SECTION E (3 × 4 = 12 Marks) — Case-Study Based
- Case Study: A shopkeeper buys two types of pens. The cost of 3 pens of type A and 2 of type B is ₹80, while 4 of type A and 1 of type B cost ₹85.
(i) Frame the pair of linear equations. [1]
(ii) Find the cost of one pen of type A. [1]
(iii) Find the total cost of 5 type-A and 5 type-B pens. [2]
- … Q37–Q38 continue …
Blueprint — Chapter-wise & Type-wise Weightage
| Chapter / Unit | MCQ (1m) | SA-I (2m) | SA-II (3m) | LA (5m) | Case (4m) | Total |
|---|
| Real Numbers | 3 | 1 | 1 | — | — | 8 |
| Polynomials | 3 | 1 | 1 | — | — | 8 |
| Linear Equations | 4 | 1 | 2 | 1 | 1 | 21 |
| Triangles | 5 | 1 | 1 | 2 | 1 | 24 |
| Statistics | 5 | 1 | 1 | 1 | 1 | 19 |
| Total (38 Q) | 20 | 5 | 6 | 4 | 3 | 80 |
Generated by Inforida Orbit · A separate marking scheme / step-wise answer key is produced alongside this paper · Edit any question before printing.
