Class 10 Maths Half Yearly Question Paper

Class 10 Mathematics Half Yearly Sample Paper 2025 (With Answers)

SECTION A (1 Mark Each)

1. Find the value of k for which the system of equations
$(k+1)x + 3y = 7$ and $2x + (k-1)y = 5$ has infinitely many solutions.

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

Ans. $k=2$

2. The quadratic equation $x^2 - 6x + 9 = 0$ has

(a) two distinct real roots (b) no real roots (c) two equal real roots (d) more than 2 roots

Ans. two equal real roots

3. ΔXYZ ~ ΔLMN. If $XY^2 : LM^2 = 49:64$ , and altitudes XP and LQ are drawn, then XP : LQ = (choose)

(a) 7:8 (b) 8:7 (c) 49:64 (d) 2:3

Ans. 7:8

4. The quadratic polynomial whose zeroes have sum = 4 and product = −21 is:

(a) $x^2 - 4x - 21$ (b) $x^2 + 4x + 21$ (c) $x^2 - 21x + 4$ (d) $x^2 + 21x - 4$

Ans. $x^2 - 4x - 21$

5. A circle touches the coordinate axes at (a,0) and (0,a). Its radius is:

(a) a (b) $\sqrt{2}a$ (c) a/2 (d) 2a

Ans. $\sqrt{2}a$

6. If A(2,3), B(4,1), C(6,5) are the vertices of a triangle, then the triangle is:

(a) Scalene (b) Isosceles (c) Right angled (d) Equilateral

Ans. Right angled

7. If -1 and 2 are the zeroes of $x^2 + px + q$ , then values of p and q are:

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

Ans. $p=-1,\ q=-2$

8. A point lies on a circle of radius 10 units with centre at origin. How many such points lie in the second quadrant?

(a) 0 (b) 1 (c) 2 (d) Infinitely many

Ans. Infinitely many

9. The system $3x + 2y = 5$ , $6x + 4y = k$ has no solution if:

(a) $k=10$ (b) $k \ne 10$ (c) $k=5$ (d) $k=0$

Ans. $k=10$

10. The 15^th term of the AP 2, 7, 12, … is:

(a) 70 (b) 72 (c) 75 (d) 77

Ans. $72$

11. If terms $2g-1,\ g,\ g+3$ are in A.P., then g =:

(a) 1 (b) 2 (c) 3 (d) 4

Ans. $g=3$

12. Simplify: $\dfrac{\sin\theta \cdot \cos\theta}{\tan\theta}$

(a) $\sin^2\theta$ (b) $\cos^2\theta$ (c) $\cos\theta$ (d) $\sin\theta$

Ans. $\sin\theta$

13. If the n-th term of an AP is $a_n = 7n - 4$ , then the sum of first 15 terms $S_{15}$ is:

(a) 735 (b) 735/2 (c) 750 (d) 800

Ans. 735

14. Last term of the A.P. 5, 11, 17, … up to 20 terms is:

(a) 125 (b) 123 (c) 120 (d) 115

Ans. 123

15. If $\tan A = \dfrac{3}{4}$ , then $\sec A = ?$

(a) $\dfrac{4}{3}$ (b) $\dfrac{5}{3}$ (c) $\dfrac{3}{5}$ (d) $\dfrac{5}{4}$

Ans. $\dfrac{5}{3}$

16. If ΔABC ≅ ΔDEF, then which is always true?

(a) Similar but not congruent (b) Congruent and similar (c) Neither (d) Congruent only

Ans. Congruent and similar

17. LCM of the smallest prime number and the smallest composite number is:

(a) 2 (b) 4 (c) 6 (d) 8

Ans. 6

18. Which of the following is NOT a prime factorization?

(a) 18 = 2 × 3² (b) 20 = 2² × 5 (c) 45 = 3 × 15 (d) 60 = 2² × 3 × 5

Ans. (c) 45 = 3 × 15

Directions: In Q.19 and Q.20, choose:
(A) Both Assertion (A) and Reason (R) true and R is correct explanation of A.
(B) Both A and R true but R is not correct explanation of A.
(C) A true, R false.
(D) A false, R true.

Q.19 Assertion (A): The decimal expansion of $\dfrac{7}{20}$ is terminating.
Reason (R): A fraction $\dfrac{p}{q}$ has a terminating decimal expansion if q has no prime factors other than 2 or 5.
Options: A/B/C/D

Ans. (A) Both A and R true, R correct explanation

Q.20 Assertion (A): Every irrational number is a real number.
Reason (R): The set of real numbers includes rationals and irrationals.
Options: A/B/C/D

Ans. (A) Both A and R true, R correct explanation

SECTION B (2 Marks Each)

21. Solve the system:

$5x + 7y = 35$
$3x - 2y = 4$

Ans. $x=3,\ y=2$

22. A line meets x-axis at A and y-axis at B. If C(2,3) is the midpoint of AB, find coordinates of A and B.

Ans. A(4,0), B(0,6)

23. Find HCF and LCM of 36 and 48 using prime factorization.

Ans. HCF = 12, LCM = 144

24. Find the ratio in which point P divides the line joining (−2, 6) and (4, −2) if P lies on the x-axis.

Ans. Ratio = 3 : 2

25. Find a quadratic polynomial whose zeroes are $5 + \sqrt{2}$ and $5 - \sqrt{2}$ .

Ans. $x^2 - 10x + 23$

Last-Minute Tips for Class 10 Maths Half Yearly Exam

Smart revision is the key to scoring well. Start with important formulas and theorems. Write them on a separate sheet and revise daily.

Solve sample papers and previous years’ papers. This will show you the exam pattern, marking scheme, and improve your speed. Always use a timer and try to finish on time.

Revise chapters with higher weightage and focus on weak areas. Do not start new topics at the last moment. While solving, write every step clearly, as marks are given for proper working.

Stay calm, avoid stress, and sleep well before the exam. A fresh mind, regular practice, and smart revision will boost your confidence and performance.

Importance of Practicing Sample Papers

- Understands exam pattern and marking scheme.
- Finds weak areas that need more practice.
- Improves speed and time management.
- Builds confidence and reduces exam fear.
- Gives practice with different types of questions.

News Feed

How to Reduce YouTube or TV

Kumbh Mela Quiz | History, UNESCO

“Haryana Heroes’ Martyrdom Day” Quiz for

Class 8 Science – Conservation of

Class 10 Mathematics Half Yearly Sample Paper 2025-26 (With Answers)

Class 10 Mathematics Half Yearly Sample Paper 2025 (With Answers)

SECTION A (1 Mark Each)

SECTION B (2 Marks Each)

Last-Minute Tips for Class 10 Maths Half Yearly Exam

Importance of Practicing Sample Papers

Leave A Comment Cancel reply

Details Info

How to Reduce YouTube or TV

Kumbh Mela Quiz | History, UNESCO

Contact Us

News Feed

Class 10 Mathematics Half Yearly Sample Paper 2025-26 (With Answers)

Class 10 Mathematics Half Yearly Sample Paper 2025 (With Answers)

SECTION A (1 Mark Each)

SECTION B (2 Marks Each)

Last-Minute Tips for Class 10 Maths Half Yearly Exam

Importance of Practicing Sample Papers

You may also read:

Leave A Comment Cancel reply