Most Expected Questions for Half-Yearly Exams – Class 10 Maths

Half-yearly Maths exams are stressful. You open your book, see endless sums, and think: “Do I really need to practice all of this? What if the paper asks something totally different?”

Most students spend hours practicing, but still enter the exam hall feeling unsure. That’s because Maths isn’t about memorizing, it’s about knowing which type of problems repeat, which formulas matter, and how questions are usually framed.

This is where a curated list of the most expected questions helps. At this point, it’s not about covering the entire syllabus; it’s about being smart. You need to focus on the most expected and high-weightage questions that actually show up in exams. That way, you save time, reduce stress, and walk into the exam hall with confidence.

Why Class 10 Half-Yearly Maths Exams Matter?

Half-yearlies aren’t just “internal exams.” They:

• Act as a progress check for your board preparation.
• Highlight your weak chapters before it’s too late.
• Train you in time management and accuracy under exam conditions.

While the exact paper varies from school to school, the types of questions remain the same because they’re based on CBSE patterns. That’s why practicing these questions is a safe strategy to score well.

Most Expected Questions – Class 10 Maths Half-Yearly Exams

These questions are curated from repeated exam patterns, past CBSE trends, and high-weightage chapters. 

Section A – 1 Mark Questions (MCQs + Assertion-Reason)

1. If HCF of 65 and 117 is 13, what is their LCM?
2. Which of the following is irrational: √9, (2 + √5), 0.333...?
3. The sum of zeroes of the polynomial x² – 7x + 12 is __.
4. If 2x + 3y = 12, then the coordinates of intercept on y-axis are:
5. The nature of roots of 2x² + 3x + 5 = 0 is __.
6. nth term of an AP is an = 3n + 2. Find a5.
7. In ΔABC, DE || BC and AD/DB = 2/3. What is AE/EC?
8. Distance between points (–2, 3) and (4, 7) is __.
9. If sin²θ + cos²θ = 1, then value of (1 + tan²θ) is __.
10. The angle of elevation of the sun when the shadow of a pole is equal to its height is __.
11. A card is drawn from a well-shuffled deck. Probability of getting a king is __.
12. Mean of first 10 natural numbers is __.
13. Mode of the data: 2, 3, 4, 3, 6, 3, 7 is __.
14. A die is thrown. Probability of getting a prime number is __.
15. Which of the following is correct?
    Assertion (A): A tangent to a circle is perpendicular to the radius at the point of contact.
    Reason (R): The angle between tangent and chord is always 60°.
16. Assertion (A): In an AP, the difference between consecutive terms is constant.
    Reason (R): The nth term is given by a + (n–1)d.
17. Assertion (A): The probability of an impossible event is zero.
    Reason (R): Probability of any event always lies between 0 and 1.
18. The curved surface area of a cone is πrl. Here l represents __.
19. The distance between (7, –3) and (7, 9) is __.
20. If P(E) = 0.65, then probability of not E is __.

Section B – Very Short Answer Questions (2 Marks each)

1. Find the zeroes of the polynomial x² – 11x + 30 and verify the relationship between zeroes and coefficients.
2. Find the coordinates of the centroid of ΔABC with vertices A(–1, 2), B(3, 4), C(5, –6).
3. Find the probability of getting (i) 2 heads, (ii) at least 1 head, when 2 coins are tossed together.
4. Draw a histogram for the following distribution:

Section C – Short Answer Questions (3 Marks each)

1. A motorboat goes 12 km downstream in 3 hours and returns the same distance upstream in 4 hours. Find the speed of the boat in still water and of the stream.
2. The sum of the first n terms of an AP is 5n² + 3n. Find its 10th term.
3. Solve for x: (¹/_{x – 2}) + (²/_{x – 3}) = ⁶/_x, x ≠ 2, 3, 0.
4. Construct a pair of tangents to a circle of radius 4 cm inclined to each other at 60°.
5. A solid consists of a hemisphere surmounted by a cone. The radius of each is 3.5 cm and height of cone is 7 cm. Find its volume. (π = 22/7)
6. Find the median for the following distribution:

Section D – Long Answer Questions (5 Marks each)

1. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 48 minutes less. Find the speed of the train.
   
2. A bucket is in the form of a frustum of a cone. Its height is 28 cm, top diameter 40 cm and bottom diameter 20 cm. Find its capacity (use π = 3.1416).
   
3. The median of the following data is 525. Find the values of x and y, if total frequency is 100.

4. From the top of a building 60 m high, the angles of depression of the top and bottom of a vertical lamp post are 30° and 60°. Find the height of the lamp post.

Quick, High-Impact Tips to Boost your Class 10 Maths Preparation

• Show steps clearly. Even if you slip, examiners can award method marks.
• Draw neat diagrams for geometry/trigonometry problems and label lengths/angles.
• Write units (m, cm, km/h) — missing units sometimes cost marks.
• Box the final answer so evaluators can find it fast.
• Memorise common values: tan30° = 1/√3, tan60° = √3, sin30° = 1/2, etc.
• Keep a short formula sheet and revise it daily (AP,formulas for areas, volumes, trig identities).
• Time strategy: Spend ~50% time on Sections C & D, 30% on B, and finish A fast (A should be quick wins).
• Practice previous years’ papers and mark them strictly — that trains accuracy under pressure.

Final Thoughts

Half-yearly exams are a checkpoint, not the final judgment. These expected questions cover the high-probability topics and exam patterns you’ll face. Use this paper as a timed mock: practise, mark, fix weak spots, and repeat. Keep your work neat, show steps, and trust your practice.

You’ve prepared. Now go write clean solutions and build momentum; boards will feel easier because of this work. Good luck, you’ve got this!

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