10th Maths Revision Exam 9 Question Paper with Answer Key

Perfect your exam strategy and build ultimate confidence with the 10th Maths Revision Exam 9 Question Paper. As you approach the final stretch of your SSLC preparation, intensive revision through multiple mock series is the absolute key to achieving a perfect centum. This full-syllabus question paper is structured strictly according to the official public exam blueprint, offering targeted practice for high-yielding algebraic problems, complex geometry proofs, compulsory questions, and essential graph constructions. Use this test paper as a timed rehearsal to evaluate your accuracy, master your presentation, and eliminate exam anxiety!

CLASS: 10 EXAM NO: ______________ TIME: 3 hr

REVISION EXAMINATION – 9

MATHEMATICS MARKS: 100

SECTION - I (Choose the correct answer) [14 × 1 = 14]

1. Let n(A) = m and n(B) = n, then the total number of non-empty relations that can be defined from A to B is
(a) mⁿ (b) n^m (c) 2^mn - 1 (d) 2^mn

2. The function f: ℕ → ℤ is defined by f(x) = (-1)^x. Then the function is
(a) one-to-one function (b) many-one function (c) constant function (d) identity 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. An A.P. consists of 31 terms. If its 16th term is m, then the sum of all the terms of this A.P. is
(a) 16m (b) 62m (c) 31m (d) ^31m/₂

5. The square root of ^{(256x⁸y⁴z¹⁰)}/_{(25x⁶y⁶z⁶)} is equal to
(a) ¹⁶/₅ |^x²z⁴/_y²| (b) 16 |^y²/_x²z⁴| (c) ¹⁶/₅ |^xz²/_y| (d) ¹⁶/₅ |^xz/_y|

6. For the given matrix A =

, then the order of the matrix A^T is
(a) 0 × 0 (b) 1 × 3 (c) 3 × 1 (d) 1 × 0

7. In a ΔABC, AD is the bisector of ∠BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm, the length of the side AC is
(a) 6 cm (b) 4 cm (c) 3 cm (d) 8 cm

8. The slope of the line which is perpendicular to a line joining the points (0, 0) and (-8, 8) is
(a) -1 (b) 1 (c) ¹/₃ (d) -8

9. Which one of the following is the equation of a straight line passing through the origin?
(a) x = 2y + 5 (b) y = ¹/₂x (c) y = 7 (d) x = 4

10. If x = a tan θ and y = b sec θ, then
(a) ^y²/_b² - ^x²/_a² = 1 (b) ^x²/_a² - ^y²/_b² = 1 (c) ^x²/_a² + ^y²/_b² = 1 (d) ^x²/_a² - ^y²/_b² = 0

11. In a hollow cylinder, the sum of the external and internal radii is 14 cm and the width is 4 cm. If its height is 20 cm, the volume of the material in it is
(a) 5600π cm³ (b) 1120π cm³ (c) 56π cm³ (d) 3600π cm³

12. The CSA of a right circular cone whose height is equal to its radius is
(a) 2πr² (b) πrl (c) √2πr² (d) √2πr (sq. units)

13. Which of the following is not a measure of dispersion?
(a) Range (b) Standard deviation (c) Arithmetic mean (d) Variance

14. Which of the following values cannot be a probability of an event?
(a) ³/₁₀ (b) ⁴/₅ (c) 0 (d) ⁷/₄

SECTION – II (Answer 10 questions. Question Number 28 is compulsory) [10 × 2 = 20]

15. If B × A = {(-2, 3), (-2, 4), (0, 3), (0, 4), (3, 3), (3, 4)}, find A and B.

16. Find the value of k such that f ∘ g = g ∘ f if f(x) = 2x - k, g(x) = 4x + 5.

17. Find the 15th term of an A.P. given by 3, 15, 27, 39, ...

18. Find the sum of 8 terms of the G.P. 1, -3, 9, -27, ...

19. Find the square root of the following rational expression: ^{(400x⁴y¹²z¹⁶)}/_{(100x⁸y⁴z⁴)}.

20. If α and β are the roots of the equation x² + 7x + 10 = 0, find the value of α - β.

21. Construct a 3 × 3 matrix whose elements are given by a_ij = |i - 2j|.

22. If ΔABC ~ ΔDEF such that the area of ΔABC is 9 cm² and the area of ΔDEF is 16 cm², and BC = 2.1 cm, find the length of EF.

23. Find the value of 'a', if the line through (-2, 3) and (8, 5) is perpendicular to y = ax + 2.

24. Prove that tan²θ - sin²θ = tan²θ · sin²θ.

25. The external radius and the length of a hollow wooden log are 16 cm and 13 cm respectively. If its thickness is 4 cm, then find its T.S.A.

26. Find the range and coefficient of range of the following data: 25, 67, 48, 53, 18, 39, 44.

27. If A and B are two mutually exclusive events of a random experiment and P(not A) = 0.45, P(A ∪ B) = 0.65 then find P(B).

28. The hill in the form of a right triangle has its foot at (5, 0). The inclination of the hill to the ground is 30°. Find the equation of the hill joining the foot and the top. (Compulsory)

SECTION - III (Answer 10 questions. Question Number 42 is compulsory) [10 × 5 = 50]

29. Let A = the set of all natural numbers less than 8, B = the set of all prime numbers less than 8, C = the set of even prime numbers. Verify that A × (B - C) = (A × B) - (A × C).

30. If the function f: [-5, 9] → ℝ is defined as follows:

f(x) =
  • 6x + 1, -5 ≤ x < 2
  • 5x² - 1, 2 ≤ x < 6
  • 3x - 4, 6 ≤ x ≤ 9

Find the values of: (i) f(-3) + f(2) (ii) f(7) - f(1) (iii) 2f(4) + f(8) (iv) ^{[2f(-2) - f(6)]}/_{[f(4) + f(-2)]}

31. The 104^th term and 4^th term of an A.P. are 125 and 0 respectively. Find the sum of first 35 terms.

32. In a geometric progression, the 4th term is ⁸/₉ and the 7th term is ⁶⁴/₂₄₃. Find the geometric progression.

33. Simplify: ¹/_{(x² - 5x + 6)} + ¹/_{(x² - 3x + 2)} - ¹/_{(x² - 8x + 15)}.

34. A bus covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more, it would have taken 30 minutes less for the journey. Find the original speed of the bus.

35. Let A =

1	2
1	3

, B =

4	0
1	5

, C =

2	0
1	2

. Show that (A - B)C = AC - BC.

36. State and prove Thales' theorem.

37. A quadrilateral has vertices at A(-4, -2), B(5, -1), C(6, 5), and D(-7, 6). Show that the midpoints of its sides form a parallelogram.

38. Find the equation of a straight line through the point of intersection of the lines 8x + 3y = 18, 4x + 5y = 9 and bisecting the line segment joining the points (5, -4) and (-7, 6).

39. From the top of a 12 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 30°. Determine the height of the tower.

40. Nathan, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of the model that Nathan made.

41. The number of televisions sold in each day of a week are 13, 8, 4, 9, 7, 12, 10. Find its standard deviation.

42. Two dice are rolled once. Find the probability of getting a composite number on the first die or a prime number on the second die. (Compulsory)

SECTION – IV (Answer both questions) [2 × 8 = 16]

43. (a) Take a point which is 11 cm away from the centre of a circle of radius 4 cm and draw the two tangents to the circle from that point. Also measure the length of the tangents.

(OR)

(b) Construct a ΔPQR in which PQ = 8 cm, ∠R = 60° and the median RG from R to PQ is 5.8 cm. Find the length of the altitude from R to PQ.

44. (a) Nishanth is the winner in a marathon race of 12 km distance. He ran at a uniform speed of 12 km/hr and reached the destination in 1 hour. He was followed by Aradhana, Ponmozhi, Jeyanth, Sathya and Swetha with their respective speeds of 6 km/hr, 4 km/hr, 3 km/hr and 2 km/hr. They covered the distance in 2 hrs, 3 hrs, 4 hrs and 6 hrs respectively. Draw the speed-time graph and use it to find the time taken by Kaushik with his speed of 2.4 km/hr.

(OR)

(b) Draw the graph of y = 2x² and hence solve 2x² - x - 6 = 0.