10th Maths First Revision Test 1 Question Paper with Answers

Kickstart your final board exam countdown with the official 10th Maths First Revision Test 1 Question Paper. The first major revision test is a critical milestone for SSLC students, specifically designed to test your mastery over the initial halves of the syllabus—including foundational chapters like Relations and Functions, Numbers and Sequences, and Algebra. This complete question paper adheres strictly to the official public exam blueprint, providing a perfect blend of standard textbook exercises, compulsory sums, and high-scoring graph and geometry problems. Use this paper as a timed mock test to evaluate your conceptual clarity and set a strong benchmark for your board prep!

FIRST REVISION TEST - 1

Standard: X Reg no: ______________ MATHEMATICS

Time: 2.30 hrs Marks: 100

Instructions: (1) Check the question paper for fairness of printing. If there is any lack of fairness, inform the Hall Supervisor immediately.

(2) Use Blue or Black ink to write and underline.

Notes: (i) This question paper contains four parts.

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. If the ordered pairs (a + 2, 4) and (5, 2a + b) are equal then (a, b) is
a) (2, -2) b) (5, 1) c) (2, 3) d) (3, -2)

3. If f(x) = 2x² and g(x) = ¹/_3x, then f ∘ g is
a) ³/_2x² b) ²/_3x² c) ²/_9x² d) ¹/_6x²

4. The least number that is divisible by all the numbers from 1 to 10 is
a) 2025 b) 5220 c) 5025 d) 2520

5. 7^4k ≡ _______ (mod 100)
a) 1 b) 2 c) 3 d) 4

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

7. The solution of the system x + y - 3z = -6, -7y + 7z = 7, 3z = 9 is
a) x = 1, y = 2, z = 3 b) x = -1, y = 2, z = 3
c) x = -1, y = -2, z = 3 d) x = 1, y = -2, z = 3

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

9. In ΔLMN, ∠L = 60°, ∠M = 50°. If ΔLMN ~ ΔPQR then the value of ∠R is
a) 40° b) 70° c) 30° d) 110°

10. If in ΔABC, DE || BC, AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm then the length of AE is
a) 1.4 cm b) 1.8 cm c) 1.2 cm d) 1.05 cm

11. If (5, 7), (3, p) and (6, 6) are collinear, then the value of p is
a) 3 b) 6 c) 9 d) 12

12. 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

13. tan θ cosec²θ - tan θ is equal to
a) sec θ b) cot²θ c) sin θ d) cot θ

14. If sin θ = cos θ then 2 tan²θ + sin²θ - 1 is equal to
a) -¹/₂ b) ³/₂ c) ²/₃ d) -²/₃

Part - II: Answer the following questions (Q.No 28 is compulsory) 10 × 2 = 20

15. If A × B = {(3, 2), (3, 4), (5, 2), (5, 4)} then find A and B.

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

17. If 13824 = 2^a × 3^b then find a and b.

18. Find the sum of infinity of 9 + 3 + 1 + ...

19. Find the excluded value of p in ^{(7p + 2)}/_{(8p² + 13p + 5)}.

20. Simplify: ^5t³/_{(4t - 8)} × ^{(6t - 12)}/_10t.

21. Determine the nature of the roots for √2 t² - 3t + 3√2 = 0.

22. In ΔABC, if DE || BC, AD = x, DB = x - 2, AE = x + 2 and EC = x - 1 then find the lengths of the sides AB and AC.

23. Show that the points P(-1.5, 3), Q(6, -2), R(-3, 4) are collinear.

24. What is the inclination of a line whose slope is 1?

25. A cat is located at the point (-6, -4) in xy-plane. A bottle of milk is kept at (5, 11). The cat wishes to consume the milk travelling through shortest possible distance. Find the equation of the path it needs to take its milk.

26. Prove that sec θ - cos θ = tan θ sin θ.

27. Show that √[^{(1 + sin θ)}/_{(1 - sin θ)}] = sec θ + tan θ.

28. When the positive integers a, b and c are divided by 13 the respective remainders are 9, 7 and 10. Find the remainder when a + 2b + 3c is divided by 13. (Compulsory)

Part - III: Answer the following questions (Q.No 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. If the function f: ℝ → ℝ is defined by

f(x) =
  • 2x + 7, x < -2
  • x² - 2, -2 ≤ x < 3
  • 3x - 2, x ≥ 3

then find the values:
i) f(4) ii) f(-2) iii) f(4) + 2f(1) iv) ^{[f(1) - 3f(4)]}/_f(-3)

31. If f(x) = x - 1, g(x) = 3x + 1 and h(x) = x² then show that (f ∘ g) ∘ h = f ∘ (g ∘ h).

32. Find the HCF of 396, 504, 636.

33. In an A.P., sum of four consecutive terms is 28 and the sum of their squares is 276. Find the four numbers.

34. If a, b, c are three consecutive terms of an A.P. and x, y, z are consecutive terms of a G.P. then prove that x^{b - c} × y^{c - a} × z^{a - b} = 1.

35. Find the GCD of the polynomials 2x³ - 5x² + 5x - 3 and x³ + x² - x + 2.

36. If 4x⁴ - 12x³ + 37x² + bx + a is a perfect square then find the values of a and b.

37. If the difference between a number and its reciprocal is ²⁴/₅, find the number.

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

39. Without using Pythagoras theorem, show that the points (1, -4), (2, -3) and (4, -7) form a right-angled triangle.

40. Find the equation of the perpendicular bisector of the line joining the points A(-4, 2) and B(6, -4).

41. If cosec θ + cot θ = p then prove that cos θ = ^{(p² - 1)}/_{(p² + 1)}.

42. Find the equation of the line passing through (22, -6) and having intercept on x-axis exceeds the intercept on y-axis by 5 units. (Compulsory)

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

43. (A) Construct a triangle similar to a given triangle PQR with its sides equal to ⁷/₄ of the corresponding sides of triangle PQR (Scale factor ⁷/₄ > 1).

(OR)

(B) Construct a ΔPQR with the base PQ = 4.5 cm, ∠R = 35° and the median RG from R to PQ is 6 cm.

44. (A) Draw the graph of y = x² - 3x - 6 and hence solve x² - x - 6 = 0.

(OR)

(B) Draw the graph of y = x² - 2x - 4 and hence solve x² - x - 5 = 0.