10th Maths Second Revision Test Question Paper 1 with Answers

Step up your board exam preparation with the 10th Maths Second Revision Test Question Paper 1. As the public examinations approach, the second revision phase is critical for moving beyond basic concepts and mastering advanced application problems. This full-syllabus question paper is structured strictly according to the official SSLC blueprint, featuring highly repeated 2-mark sums, complex 5-mark algebra and trigonometry proofs, and high-scoring 8-mark graph and geometry constructions. Use this test paper as a timed home mock exam to sharpen your critical thinking, minimize step errors, and build full confidence for the main boards!

CLASS: X EXAM NO: ______________ TIME: 3 hr

SECOND REVISION EXAMINATION 2025-26

MATHEMATICS MARKS: 100

PART - I: Choose the correct answer 14 × 1 = 14

1. A = {a, b, p}, B = {2, 3}, C = {p, q, r, s} then n[(A ∪ C) × B] is
a) 8 b) 20 c) 12 d) 16

2. Let A = {1, 2, 3, 4}, B = {4, 8, 9, 10}. A function f: A → B given by f = {(1, 4), (2, 8), (3, 9), (4, 10)} is a
a) Many-one function b) Identity function c) One-to-one function d) Into function

3. Using Euclid's division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are
a) 0, 1, 8 b) 1, 4, 8 c) 0, 1, 3 d) 1, 3, 5

4. If A = 2⁶⁵ and B = 2⁶⁴ + 2⁶³ + 2⁶² + ... + 2⁰ which of the following is true?
a) B is 2⁶⁴ more than A b) A and B are equal
c) B is larger than A by 1 d) A is larger than B by 1

5. A system of three linear equations in three variables is inconsistent if their planes
a) intersect only at a point b) intersect in a line
c) coincide with each other d) do not intersect

6. ^{(3y - 3)}/_y ÷ ^{(7y - 7)}/_3y² is
a) ^9y/₇ b) ^9y³/_{(21y - 21)} c) ^{(21y² - 42y + 21)}/_3y³ d) ^{7(y² - 2y + 1)}/_y²

7. The matrix

1	0	0
0	2	0
0	0	3

is a
a) unit matrix b) zero matrix c) diagonal matrix d) scalar matrix

8. In the adjacent figure ∠BAC = 90° and AD ⊥ BC then

[Figure: Right-angled triangle ABC at A with AD perpendicular to hypotenuse BC]

a) BD · CD = BC² b) AB · AC = BC² c) BD · CD = AD² d) AB · AC = AD²

9. If A is a point on the y-axis whose ordinate is 8 and B is a point on the x-axis whose abscissa is 5 then the equation of the line AB is
a) 8x + 5y = 40 b) 8x - 5y = 40 c) x = 8 d) y = 5

10. The distance of the point P(-6, -8) from the origin is
a) 10 b) 5√2 c) √10 d) 100

11. If a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p² - q² is equal to
a) a² - b² b) b² - a² c) a² + b² d) b - a

12. A spherical ball of radius r₁ units is melted to make 8 new identical balls each of radius r₂. Then r₁ : r₂ is
a) 2:1 b) 1:2 c) 4:1 d) 1:4

13. If the standard deviation of x, y, z is p then the standard deviation of 3x + 5, 3y + 5, 3z + 5 is
a) 3p + 5 b) 3p c) p + 5 d) 9p + 15

14. If P(A ∩ B) = 0.3, P(A ∪ B) = 0.45 and P(A) = 0.45 then P(B) is
a) 0.14 b) 0.30 c) 0.75 d) 1

PART - II: Answer any 10 questions (Question number 28 is compulsory) 10 × 2 = 20

15. Let A = {1, 2, 3} and B = {x / x is a prime number less than 10}. Find A × B and B × A.

16. Define real valued function.

17. Solve: 3x - 2 ≡ 0 (mod 11).

18. Find the excluded values of the expression ^{(7p + 2)}/_{(8p² + 13p + 5)}.

19. Find the quadratic equations whose sum and product of roots are (-2 - a)², (a + 5)².

20. Form a 2 × 2 matrix using your classroom situation.

21. In the figure, AD is the bisector of ∠A. If BD = 4 cm, DC = 3 cm and AB = 6 cm, find AC.

22. Find the equation of a straight line which has slope -⁵/₄ and passes through the point (-1, 2).

23. Find the equation of a straight line which is parallel to the line 3x - 7y = 12 and passing through the point (6, 4).

24. Prove that ^{cos θ}/_{(1 + sin θ)} = sec θ - tan θ.

25. The ratio of the volumes of two cones is 2 : 3. Find the ratio of their radii if the height of the second cone is double the height of the first.

26. Find the standard deviation of the first 21 natural numbers.

27. A die is rolled and a coin is tossed simultaneously. Find the probability that the die shows an odd number and the coin shows a head.

28. Find the G.P. in which the 2nd term is √6 and the 6th term is 9√6. (Compulsory)

PART - III: Answer any 10 questions (Question number 42 is compulsory) 10 × 5 = 50

29. Let A = {x ∈ W | x < 2}, B = {x ∈ ℕ | 1 < x ≤ 4} and C = {3, 5}. Verify that A × (B ∩ C) = (A × B) ∩ (A × C).

30. Let A = {1, 2, 3, 4}, B = {2, 5, 8, 11, 14}. Let f: A → B, f(x) = 3x - 1. Represent this function:
i) by arrow diagram
ii) in a table form
iii) as a set of ordered pairs
iv) in graphical form

31. Find the HCF of 252525 and 363636.

32. The sum of first n, 2n and 3n terms of an A.P are S₁, S₂, S₃ respectively. Prove that S₃ = 3(S₂ - S₁).

33. If A =

3	1
-1	2

, show that A² - 5A + 7I₂ = 0.

34. The hypotenuse of a right-angled triangle is 25 cm and its perimeter is 56 cm. Find the length of the smallest side.

35. State and prove the Basic Proportionality Theorem.

36. Find the area of the quadrilateral formed by the points (8, 6), (5, 11), (-5, 12), (-4, 3).

37. A circular garden is bounded by East Avenue and Cross Road. Cross Road intersects North Street at D and East Avenue at E. AD is tangential to the circular garden at A(3, 10). Center of garden is M(7, 7) and it passes through B(7, 2). Using the figure, find the equation of:
(i) East Avenue
(ii) North Street
(iii) Cross Road

38. If the angle of elevation of a cloud from a point h metres above a lake is θ₁ and the angle of depression of its reflection in the lake is θ₂, prove that the height of the cloud from the ground is ^{h(tan θ₁ + tan θ₂)}/_{(tan θ₂ - tan θ₁)}.

39. A funnel consists of a frustum of a cone attached to a cylindrical portion 12 cm long at the bottom. If total height = 20 cm, diameter of cylindrical portion = 12 cm, and diameter of the top of the funnel = 24 cm, find the outer surface area of the funnel.

40. The mean and variance of seven observations are 8 and 16 respectively. If five of these are 2, 4, 10, 12, 14, find the remaining two observations.

41. A card is drawn from a pack of 52 cards. Find the probability of getting a king or a heart or a red card.

42. A metallic sheet in the form of a sector of a circle of radius 21 cm has central angle 216°. The sector is made into a cone by bringing the bounding radii together. Find the volume of the cone formed.

(OR)

Prove analytically that the line segment joining the mid-points of two sides of a triangle is parallel to the third side and is equal to half of its length. (Compulsory)

PART - IV: Answer all the questions 2 × 8 = 16

43. a) Draw a circle of radius 4 cm. At a point L on it draw a tangent to the circle using the alternate segment theorem.

(OR)

b) Construct ΔPQR in which PQ = 4.5 cm, ∠R = 35° and median RG from R to PQ is 6 cm.

44. a) Varshika drew 6 circles with different sizes. Draw a graph showing the relationship between diameter and circumference and use it to find the circumference when diameter is 6 cm.