Are these official JKBOSE Mathematics questions?

No. They are original practice questions selected for concept coverage and learning value. They are not leaked questions, official model-paper items or claimed previous-year questions.

Are these questions enough for the Class 10 examination?

No. Use them as a diagnostic set, then cover the complete current syllabus, prescribed material, teacher assignments and verified model or previous papers.

How should I use the worked solutions?

Attempt each question independently, mark the exact step where you became unsure, then compare methods. Close the solution and solve the question again later without copying.

JKBOSE Class 10 Maths Important Questions

These are original practice questions, not official JKBOSE items or predictions. No responsible teacher can guarantee which questions will appear. The set is designed to reveal whether a student can choose a method, show steps, manage signs and units, and check an answer.

Confirm every topic against the current Class 10 syllabus guide and the official document applicable to your session. Attempt the question before reading its solution.

Number systems and algebra

1. Find the HCF using Euclid's algorithm

Question: Find the HCF of 225 and 135.

Solution: 225 = 135 × 1 + 90. Then 135 = 90 × 1 + 45, and 90 = 45 × 2 + 0. The last non-zero remainder is 45, so the HCF is 45.

2. Build a quadratic polynomial from its zeroes

Question: Form a monic quadratic polynomial whose zeroes are 2 and -3.

Solution: The polynomial is (x - 2)(x + 3) = x² + x - 6. Check: the sum of zeroes is -1, equal to -b/a, and their product is -6, equal to c/a.

3. Solve a pair of linear equations

Question: Solve 2x + y = 11 and x - y = 1.

Solution: Add the equations: 3x = 12, so x = 4. Substitute in x - y = 1: 4 - y = 1, so y = 3. Check in the first equation: 2(4) + 3 = 11.

4. Factor a quadratic equation

Question: Solve x² - 7x + 12 = 0.

Solution: We need two numbers with product 12 and sum -7: -3 and -4. Therefore (x - 3)(x - 4) = 0, giving x = 3 or x = 4.

5. Work with an arithmetic progression

Question: For the AP 5, 9, 13, ... find the 20th term and the sum of the first 20 terms.

Solution: Here a = 5 and d = 4. The 20th term is a + 19d = 5 + 76 = 81. The sum is 20/2[2(5) + 19(4)] = 10(86) = 860.

Geometry and coordinate geometry

6. Use similarity ratios

Question: Two triangles are similar. A side of 6 cm in the smaller triangle corresponds to 9 cm in the larger, and a side of 8 cm corresponds to 12 cm. If the third side of the larger triangle is 15 cm, find the corresponding smaller side.

Solution: The smaller-to-larger scale factor is 6/9 = 8/12 = 2/3. The required side is 15 × 2/3 = 10 cm.

7. Distance and midpoint

Question: For A(-2, 3) and B(4, -5), find AB and the midpoint.

Solution: AB = √[(4 + 2)² + (-5 - 3)²] = √(36 + 64) = 10 units. The midpoint is ((-2 + 4)/2, (3 - 5)/2) = (1, -1).

8. Apply a tangent property

Question: From an external point P, tangents PA and PB touch a circle at A and B. If PA = 7.5 cm, find PB and state the radius-tangent angle at A.

Solution: Tangents from the same external point are equal, so PB = 7.5 cm. The radius to the point of contact is perpendicular to the tangent, so angle OAP is 90 degrees.

Trigonometry and mensuration

9. Recover sine and cosine from tangent

Question: If tan θ = 3/4 for an acute angle, find sin θ and cos θ.

Solution: Represent opposite and adjacent sides as 3 and 4. The hypotenuse is √(3² + 4²) = 5. Therefore sin θ = 3/5 and cos θ = 4/5.

10. Area and arc length of a sector

Question: Find the area and arc length of a 90-degree sector of radius 7 cm. Use π = 22/7.

Solution: Area = 90/360 × πr² = 1/4 × 22/7 × 49 = 38.5 cm². Arc length = 90/360 × 2πr = 1/4 × 44 = 11 cm.

11. Cylinder measures

Question: A cylinder has radius 3 cm and height 10 cm. Find its volume and curved surface area.

Solution: Volume = πr²h = π(9)(10) = 90π cm³. Curved surface area = 2πrh = 2π(3)(10) = 60π cm². Keep square and cubic units distinct.

Statistics and probability

12. Mean and simple probability

Question: Find the mean of 4, 6, 8, 10 and 12. Separately, find the probability of obtaining an even number on a fair six-sided die.

Solution: Mean = (4 + 6 + 8 + 10 + 12)/5 = 40/5 = 8. The even outcomes are 2, 4 and 6, so probability = 3/6 = 1/2.

How to turn twelve questions into real improvement

Attempt the full set without notes and record start and finish time.
Classify each error as concept, method, sign, arithmetic, diagram, unit or presentation.
Write one correction rule beside every error, such as "substitute into both equations" or "convert sector angle to a fraction of 360".
Redo the missed question after 48 hours without viewing the solution.
Find two more questions that require the same method but use different values.

Continue with the model-paper practice guide after the full syllabus is covered. Students seeking a structured live plan can review Jhelum Alpha.

Sources and verification

Official JKBOSE Class 10 syllabus - topic relevance
JKBOSE official website - current documents and notices

JKBOSE Class 10 Maths Important Questions with Solutions: Original Practice Set