Download Class 10 Half Yearly Mathematics Solved Paper (2024-25)
⬇️ Download PDFClass 10 – Half Yearly Examination 2024-25 (Mathematics)
Paper Code: 1003 Maximum Marks: 70 Time: 3 hrs 15 min
Section A – Objective Type Questions (1 mark each)
1 (i) LCM of 12, 15 and 21 = 420.
(ii) Zeros of x² – 2x – 8 = 0 → 4 and –2.
(iii) x + y = 4 and x – y = 2 → (3, 1).
(iv) 2x² + x + 4 = 0 → Discriminant < 0 → No real roots.
(v) 10th term of AP 3, 7, 11,… = a₁ + 9d = 3 + 9×4 = 39.
(vi) In triangle ABC, right angle at C → AC and BC are perpendicular.
(vii) Midpoint of A(2, 4), B(–2, 4) = (0, 4).
(viii) tan 60° = √3.
(ix) Height = shadow → angle = 45°.
(x) Longest chord of circle → Diameter.
(xi) Area of circle r = 5 cm → πr² = 78.5 cm².
(xii) Surface area of sphere = 4πr².
(xiii) Volume of cylinder = πr²h.
(xiv) Mean of 4, 10, 5, 9, 12 = 8.
(xv) Probability of getting a queen = 1/13.
Section B – Fill in the Blanks (1 mark each)
(i) If x + 2y = 4 and 2x + ky = 3 have no solution, then k = 4.
(ii) All circles are similar.
(iii) A tangent to a circle intersects at one point.
(iv) Area of circle (r = 7 cm) = 49π cm².
(v) Volume of cone = (1/3) πr²h.
(vi) If P(A)=1/2 then P(Ā)= 1/2.
Very Short Answer Type (1 mark each)
(i) HCF of 26 and 91 = 13.
(ii) Zeros of x² + 5x + 6 = –2, –3.
(iii) 13th term of AP 2, 7, 12,… = 62.
(iv) If sin A = 3/5, then tan A = 3/4.
(v) Ladder 5 m, angle 30° → height = 5 sin 30° = 2.5 m.
Short Answer Type (2 marks each)
4. HCF = 6, LCM = 360 for 6, 72, 120.
5. Zeros of x² – 3 = ±√3.
6. x + y = 5, 2x – 3y = 4 → (19/5, 6/5).
7. If DE || BC, then ΔADE ∼ ΔABC; use ratio AE/AC = AD/AB to find EC.
8. Distance A(1, 2), B(4, 5) = 3√2.
9. Height of tower = 30 tan 60° = 30√3 m.
10. Area of sector (r = 6 cm, θ = 60°) = 6π cm².
11. TSA of cylinder (r = 5 cm, h = 14 cm) = 190π cm² ≈ 596.9 cm².
Medium Questions (2 marks each)
12. Given median = 28.5 ⇒ y = x – 1 (relationship between x and y).
13. Die thrown once:
- (i) Prime number → 1/2
- (ii) Number between 2 and 6 → 1/2
- (iii) Odd number → 1/2
Long Answer Type (3 marks each)
14. Sum of first 15 multiples of 8 = 960.
15. Points dividing A(–2, 2) and B(2, 8) into four equal parts:
(–1, 7/2), (0, 5), (1, 13/2).
16. Tangent = 4 cm, distance to centre = 5 cm → r = 3 cm.
17. Median weight of 30 students = ≈ 56.67 kg.
Section C – Essay Type (4 marks each)
18 (a) Solve 3x² – 2√6 x + 2 = 0.
D = 0 → x = √6 / 3 (double root).
OR Two consecutive integers whose squares sum to 365 → 13 and 14.
19 (a) tan A = 4/3 ⇒ sin A = 4/5, cos A = 3/5, tan A = 4/3, cot A = 3/4, sec A = 5/3, cosec A = 5/4.
OR If sin B = sin Q (for acute angles), then B = Q.
20 (a) Modal class = 3–5 → Mode = 3 + [(8–7)/(16–9)] × 2 = 3.29 members.
OR Mean literacy rate of 35 cities = ≈ 69.43 %.