10th Maths First Revision Test 2026 Question Paper with Answers

Begin your final board countdown with the official 10th Maths First Revision Test 2026 Question Paper. This crucial revision test is a major milestone for SSLC students, specifically structured to evaluate your mastery over the core chapters under strict public exam conditions. This 2026 question paper features a comprehensive mix of foundational 2-mark problems, highly predicted 5-mark long answers, and vital 8-mark graph and geometry constructions aligned with the latest curriculum trends. Use this authentic test paper as a timed rehearsal to sharpen your problem-solving speed, perfect your step-by-step presentation, and lock in your path toward a perfect centum!

COMMON FIRST REVISION EXAMINATION - 2026

Standard X Reg No: ______________ MATHEMATICS

Time: 3.00 hours Marks: 100

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

1. Let A = {1, 2, 3, 4} and 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

2. If f: A → B is a bijective function and n(B) = 7 then n(A) is equal to
a) 7 b) 49 c) 1 d) 14

3. 7^4k ≡ _______ (mod 100)
a) 1 b) 2 c) 3 d) 4

4. The value of (1³ + 2³ + 3³ + ... + 15³) - (1 + 2 + 3 + ... + 15) is
a) 14400 b) 14200 c) 14280 d) 14520

5. ^{(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

6. Find the matrix X if 2X +

1	3
5	7

5	7
9	5

-2	-2
2	-1

2	2
2	-1

1	2
2	2

2	1
2	2

7. The solution of (2x - 1)² = 9 is equal to
a) -1 b) 2 c) -1, 2 d) None of these

8. If slope of the line PQ is ¹/_√3 then slope of the perpendicular bisector of PQ is
a) √3 b) -√3 c) ¹/_√3 d) 0

9. (2, 1) is the point of intersection of two lines:
a) x - y - 3 = 0; 3x - y - 7 = 0 b) x + y = 3; 3x + y = 7
c) 3x + y = 3; x + y = 7 d) x + 3y - 3 = 0; x - y - 7 = 0

10. If sin θ + cos θ = a and sec θ + cosec θ = b, then the value of b(a² - 1) is equal to
a) 2a b) 3a c) 0 d) 2ab

11. The total surface area of a cylinder whose radius is ¹/₃ of its height is
a) ^9πh²/₈ sq. units b) 24πh² sq. units c) ^8πh²/₉ sq. units d) ^56πh²/₉ sq. units

12. If the radius and height of the cylinder and cone are same then the volume of the cone will be _______ times the volume of the cylinder
a) 3 b) 2 c) ¹/₃ d) ¹/₂

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 a letter is chosen at random from the English alphabets {a, b, ..., z}, then the probability that the letter chosen precedes x
a) ¹²/₁₃ b) ¹/₁₃ c) ²³/₂₆ d) ³/₂₆

PART - II: Answer any 10 questions (Q.No. 28 is compulsory) 10 × 2 = 20

15. Find k if f(k) = 5, where f(k) = 2k - 1.

16. Let f(x) = 2x + 5, if x ≠ 0 then find ^{[f(x + 2) - f(2)]}/_x.

17. Find the HCF of 252525 and 363636.

18. Find the sum 3 + 1 + ¹/₃ + ... ∞

19. Find the excluded value of the following expression: ^{(x² + 1)}/_{(x² - 1)}.

20. Determine the nature of the roots for the following quadratic equation: √2 t² - 3t + 3√2 = 0.

21. In figure ΔABC is circumscribing a circle. Find the length of BC.

[Given: Triangle ABC circumscribing a circle with contact points L, M, N on sides AB, BC, CA respectively, with AN = 3 cm, AL = 3 cm, BL = 4 cm, AC = 9 cm]

22. The line p passes through the points (3, -2), (12, 4) and the line q passes through the points (6, -2) and (12, 2). Is p parallel to q?

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

24. A kite is flying at a height of 75 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.

25. Find the diameter of a sphere whose surface area is 154 m².

26. The slant height of a frustum of a cone is 5 cm and the radii of its ends are 4 cm and 1 cm. Find its curved surface area.

27. Find the range of the following distribution:

Age (in years)	16-18	18-20	20-22	22-24	24-26	26-28
No. of students	0	4	6	8	2	2

28. Construct a 3 × 3 matrix whose elements are given by a_ij = ^{(i + j)³}/₃. (Compulsory)

PART - III: Answer any 10 questions (Q.No. 42 is compulsory) 10 × 5 = 50

29. Let A = {1, 2, 3, 4} and B = {2, 5, 8, 11, 14} be two sets. Let f: A → B be a function given by 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 a graphical form

30. Find x if g(f(x)) = f(g(x)) given f(x) = 3x + 1 and g(x) = x + 3.

31. The ratio of 6th and 8th term of an A.P. is 7:9. Find the ratio of 9th term to 13th term.

32. Find the sum to n terms of the series 7 + 77 + 777 + ... to n terms.

33. Find the square root of the following polynomial by division method: 37x² - 28x³ + 4x⁴ + 42x + 9.

34. If α, β are the roots of the equation 3x² + 7x - 2 = 0, find the values of:
i) ^α/_β + ^β/_α
ii) ^α²/_β + ^β²/_α

35. If A =

5	2	9
1	2	8

, B =

1	7
1	2
5	-1

, verify that (AB)^T = B^TA^T.

36. State and prove Pythagoras theorem.

37. Find the value of k, if the area of a quadrilateral is 28 sq. units, whose vertices are taken in order (-4, -2), (-3, k), (3, -2) and (2, 3).

38. If ^{cos α}/_{cos β} = m and ^{cos α}/_{sin β} = n then prove that (m² + n²) cos²β = n².

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

40. The internal and external diameter of a hollow hemispherical shell are 6 cm and 10 cm respectively. If it is melted and recast into a solid cylinder of diameter 14 cm then find the height of the cylinder.

41. Two unbiased dice are rolled once. Find the probability of getting:
i) a doublet (equal numbers on both dice)
ii) the product as a prime number
iii) the sum as a prime number
iv) the sum as 1

42. If the vertices of ΔABC are A(6, 2), B(-5, -1) and C(1, 9): (Compulsory)
i) Find the equation of median
ii) Find the equation of altitude.

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

43. (a) Construct a triangle similar to a given triangle LMN with its side equal to ⁴/₅ of the corresponding sides of the triangle LMN (scale factor ⁴/₅ < 1).

(b) Draw a circle of diameter 6 cm from a point P, which is 8 cm away from its centre. Draw the two tangents PA and PB to the circle and measure their lengths.

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, Jayanth, Sathya and Swetha with their respective speed of 6 km/hr, 4 km/hr, 3 km/hr and 2 km/hr. And, they covered the distance in 2 hours, 3 hours, 4 hours and 6 hours respectively.
Draw the speed-time graph and use it to find the time taken of Kaushik with his speed of 2.4 km/hr.

(b) Draw the graph of y = x² + 3x - 4 and hence use it to solve x² + 2x - 4 = 0.