CBSE Class 10 Maths Topper Answer Sheet 2025: How To Score 100/100 (PDF Inside)

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We all know the concepts. We all practice the NCERT questions. Yet, some students score 95 while others score a perfect 100. What makes the difference?

After closely analyzing the official CBSE Class 10 Mathematics Topper’s Answer Sheet from the 2025 board exams, I realized that scoring full marks isn't just about getting the right answer—it's about the art of presentation.

The examiner doesn't know you; they only know what you put on that paper. A messy paper is stressful to check, while a neat paper puts the examiner in a good mood.

Whether you are preparing for Standard or Basic Mathematics, these insights will change the way you attempt your paper. Let’s break down the 12 presentation hacks that can guarantee you full marks in your upcoming board exams.

Part 1: The Psychology of Neatness (Presentation Matters!)

The overarching theme of the topper's paper was neatness. It was designed to be easy for the examiner to navigate.

1. The "Single Line Strike" Rule Mistakes happen, especially in Maths calculations. The topper didn't scribble aggressively over errors. If they made a mistake, they simply cut the incorrect part with a single, clean horizontal line. This keeps the answer sheet looking professional even when errors occur.

2. The Power of the Pencil Every single diagram—whether it was a complex geometry figure or a simple triangle—was drawn with a pencil. Why? Because if you make a mistake in proportion or labeling, it can be easily rectified without making the page messy.

3. Breathing Room Between Answers The topper didn't cram answers together. They left a generous gap of 3–4 lines between each answer. Furthermore, after finishing an answer, they drew a distinct line with a pencil. This clearly signals to the examiner that one thought process has ended and another has begun.

4. Smart Page Usage If an answer finished near the bottom of a page, leaving only 3–4 lines empty, the topper didn't try to squeeze the start of the next question in that small space. They moved to a fresh page. This approach keeps the paper looking organized.

Part 2: Mastering the Booklet Structure

How you utilize the physical answer booklet is just as important as what you write in it.

5. The "Page 2" Dilemma Solved Students often get confused about whether to start writing on Page 2 or leave it blank. The 2025 analysis shows flexibility: some toppers use Page 2 specifically for rough work, while others start answering directly. Both approaches are totally fine; choose what makes you comfortable.

CBSE Class 10 Maths Topper Answer Sheet 2025: How to Score 100/100 (PDF Inside)

6. Rough Work Strategy (Crucial!) Every page has two margin lines. The left margin is for the question number. The space after the right margin line is dedicated to rough work. Key Insight: Toppers do not cross out their rough calculations after they are done. The examiner will not evaluate the rough work column, so don't make your sheet dirty by scratching it out unnecessarily.

7. Strict Section Discipline Before beginning a new section (e.g., Section B, Section C), the topper clearly wrote the Section Name as a centered heading. More importantly, they answered all questions belonging to that section within that area only. They did not mix questions from different sections (an approach now strictly prohibited in subjects like Science and SST).

Part 3: The Technical Details that Secure the "Hidden Marks"

This is where average students lose half-marks here and there, while toppers secure them all.

8. Formula First, Always CBSE marking schemes clearly instruct examiners to award separate marks just for writing the correct formula. Even if a question seems simple, the topper always clearly stated the general formula used before substituting values. Never skip this step!

9. The "Why" in Geometry In chapters like Triangles and Circles, you cannot just make a statement. The topper clearly stated the reason for every geometric step in brackets (e.g., [Angles in the same segment] or [By BPT theorem]).

10. Graphs and Scales While solving graphical questions, the topper used a pencil to draw the lines. Most importantly, they clearly stated the Scale used on both the X and Y axes at the top corner of the graph paper—a step most commonly missed by students.

11. The Final "Box" To make the checking process effortless for the examiner, the topper highlighted their final numerical answer by enclosing it in a neat rectangular box. Remember: the happier the examiner is checking your paper, the better your chances of full marks.

CBSE Class 10 2025 Maths Topper's Answer Sheet

SECTION - A

This section consists of 20 multiple choice questions of 1 mark each.

1. The system of equations x + 5 = 0 and 2x - 1 = 0 has

(A) No solution

(B) Unique solution

(D) Infinite solutions

2. In a right triangle ABC, right-angled at A, if sin B = 1/4, then the value of sec B is

(A) 4

(B) √15/4

(D) 4/√15

3. √0.4 is a/an

(A) natural number

(B) integer

(D) irrational number

4. Which of the following cannot be the unit digit of 8ⁿ, where n is a natural number?

(A) 4

(B) 2

(D) 6

5. Which of the following quadratic equations has real and distinct roots?

(A) x² + 2x = 0

(B) x² + x + 1 = 0

(D) 2x² + x + 1 = 0

6. If the zeroes of the polynomial ax² + bx + 2a/b are reciprocal of each other, then the value of b is

(A) 2

(B) 1/2

(D) -1/2

7. The distance of point (a, -b) from x-axis is

(A) a

(B) -a

(D) -b

8. In the adjoining figure, PQ || XY || BC, AP = 2 cm, PX = 1.5 cm and BX = 4 cm. If QY = 0.75 cm, then AQ + CY =

(A) 6 cm

(B) 4.5 cm

(D) 5.25 cm

9. Given △ABC ~ △PQR, ∠A=30º and ∠Q=90º. The value of (∠R + ∠B) is

(A) 90º

(B) 120º

(D) 180º

10. Two coins are tossed simultaneously. The probability of getting atleast one head is

(A) 1/4

(B) 1/2

(D) 1

11. In the adjoining figure, PA and PB are tangents to a circle with centre O such that ∠ P = 90º. If AB = 3√2 cm, then the diameter of the circle is

(A) 3√2 cm

(B) 6√2 cm

(D) 6 cm

12. If x = cos 30º - sin 30º and y = tan 60º - cot 60º, then

(A) x = y

(B) x > y

(D) x > 1, y < 1

13. For a circle with centre O and radius 5 cm, which of the following statements is true?

(A) P: Distance between every pair of parallel tangents is 5 cm.

(B) Q: Distance between every pair of parallel tangents is 10 cm.

(D) S: There does not exist a point outside the circle from where length of tangent is 5 cm.

14. In the adjoining figure, TS is a tangent to a circle with centre O. The value of 2xº is

(A) 22.5

(B) 45

(D) 90

15. A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is 10√3 m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is

(A) 30º

(B) 45º

(D) 90º

16. If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of remaining wood to the volume of cone hollowed out is

(A) 1 : 1

(B) 1 : 3

(D) 3 : 1

17. If the mode of some observations is 10 and sum of mean and median is 25, then the mean and median respectively are

(A) 12 and 13

(B) 13 and 12

(D) 15 and 10

18. If the maximum number of students has obtained 52 marks out of 80, then

(A) 52 is the mean of the data.

(B) 52 is the median of the data.

(D) 52 is the range of the data.

Directions: In Question Numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option from the following:

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

(D) Assertion (A) is false, but Reason (R) is true.

19. Assertion (A): For two prime numbers x and y (x < y), HCF(x, y) = x and LCM(x, y) = y.

Reason (R): HCF(x, y) ≤ LCM(x, y), where x, y are any two natural numbers.

20. In an experiment of throwing a die,

Assertion (A): Event E₁: getting a number less than 3 and Event E₂: getting a number greater than 3 are complementary events.

Reason (R): If two events E and F are complementary events, then P(E) + P(F) = 1.

SECTION - B

This section has 5 very short answer type questions of 2 marks each.

21. In the adjoining figure, AD/BD = = AE/EC and ∠BDE = ∠CED, prove that △ ABC is an isosceles triangle.

22. A bag contains cards which are numbered from 5 to 100 such that each card bears a different number. A card is drawn at random. Find the probability that number on the card is

(i) a perfect square

(ii) a 2-digit number

23. Solve the following pair of equations algebraically:

101x + 102y = 304

102x + 101y = 305

24. If a sec θ + b tanθ = m and b secθ + a tanθ = n, prove that a² + n² = b² + m².

25. Prove that abscissa of a point P which is equidistant from points with coordinates A(7, 1) and B(3, 5) is 2 more than its ordinate.

SECTION - C

This section has 6 short answer type questions of 3 marks each.

26. Given that sinθ + cosθ = x, prove that sin⁴θ + cos⁴θ = [2 - {(x² - 1)²}]/2.

27. In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If ∠OPQ = 15º and ∠PTQ = θ, then find the value of sin 2θ.

28. Prove that √5 is an irrational number.

29. Find the zeroes of the polynomial q(x) = 8x² - 2x - 3. Hence, find a polynomial whose zeroes are 2 less than the zeroes of q(x).

30. Check whether the following system of equations is consistent or not. If consistent, solve graphically:

x - 2y + 4 = 0, 2x - y - 4 = 0

31. If the points A(6, 1), B(p, 2), C(9, 4) and D(7, q) are the vertices of a parallelogram ABCD, then find the values of p and q. Hence, check whether ABCD is a rectangle or not.

SECTION - D

This section has 4 long answer questions of 5 marks each.

32. Following data shows the number of family members living in different bungalows of a locality:

Number of Members	0-2	2-4	4-6	6-8	8-10	Total
Number of Bungalows	10	p	60	q	5	120

If the median number of members is found to be 5, find the values of p and q.

33. Find the smallest value of p for which the quadratic equation x²- 2(p + 1)x + p² = 0 has real roots. Hence, find the roots of the equation so obtained.

34. On the day of her examination, Riya sharpened her pencil from both ends as shown below:

The diameter of the cylindrical and conical part of the pencil is 4.2 mm. If the height of each conical part is 2.8 mm and length of entire pencil is 105.6 mm, find the total surface area of the pencil.

35. From one face of a solid cube of side 14 cm, the largest possible cone is carved out. Find the volume and surface area of the remaining solid. (Use ⫪ = 22/7, √5 = 2.2)

SECTION - E

This section has 3 case study based questions of 4 marks each.

36. In order to organise, Annual Sports Day, a school prepared an eight lane running track with an integrated football field inside the track area as shown below:

The length of innermost lane of the track is 400 m and each subsequent lane is 7.6 m longer than the preceding lane.

Based on given information, answer the following questions, using concept of Arithmetic Progression.

(i) What is the length of the 6th lane? (1)

(ii) How long is the 8th lane than that of 4th lane? (1)

(iii) While practicing for a race, a student took one round each in first six lanes. Find the total distance covered by the student. (2)

37. The Statue of Unity situated in Gujarat is the world's largest Statue which stands over a 58 m high base. As part of the project, a student constructed an inclinometer and wishes to find the height of Statue of Unity using it. He noted following observations from two places:

Situation - I: The angle of elevation of the top of Statue from Place A which is 80√3 m away from the base of the Statue is found to be 60º.

Situation - II: The angle of elevation of the top of Statue from a Place B which is 40 m above the ground is found to be 30º and entire height of the Statue including the base is found to be 240 m.

Based on given information, answer the following questions:

(i) Represent the Situation - I with the help of a diagram. (1)

(ii) Represent the Situation - II with the help of a diagram. (1)

(iii) Calculate the height of Statue excluding the base and also find the height including the base with the help of Situation - I. (2)

38. Anurag purchased a farmhouse which is in the form of a semicircle of diameter 70 m. He divides it into three parts by taking a point P on the semicircle in such a way that ∠ PAB = 30º as shown in the following figure, where O is the centre of semicircle.