10th Maths Full Portion Test Question Papers with Answers

Rehearse for the main stage and evaluate your overall board readiness with our definitive collection of 10th Maths Full Portion Test Question Papers. Simulating a 100-mark exam under the official 3-hour time constraint is the ultimate way to convert your hard work into a perfect centum. This comprehensive resource portal hosts full-syllabus mock papers designed strictly according to the latest Samacheer Kalvi blueprint. From initial one-mark choices and compulsory 2-mark/5-mark challenges to the final 8-mark practical geometry and graph constructions, these papers provide the comprehensive practice you need to perfect your time management, eliminate exam fear, and present your steps flawlessly.

COMMON FULL PORTION EXAMINATION - 2026

Standard X Reg No: ______________ MATHEMATICS

Time: 3.00 hours Marks: 100

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

1. The range of the relation R = {(x, x²) / x is a prime number less than 13} is
a) {2, 3, 5, 7} b) {2, 3, 5, 7, 11} c) {4, 9, 25, 49, 121} d) {1, 4, 9, 25, 49, 121}

2. Let f(x) = √(1 + x²) then
a) f(xy) = f(x) · f(y) b) f(xy) ≥ f(x) · f(y) c) f(xy) ≤ f(x) · f(y) d) none of these

3. If 6 times the 6th term of an A.P. is equal to 7 times the 7th term, then the 13th term of the A.P. is
a) 0 b) 7 c) 13 d) -7

4. The sum of first n terms of a G.P., when r = 1 is
a) aⁿ b) n c) na d) a

5. Which of the following should be added to x⁴ + 64 to make it a perfect square
a) 4x² b) 16x² c) 8x² d) -8x²

6. The square root of 4m² - 24m + 36 is
a) 4(m - 3) b) 2|m - 3| c) 2(m - 3)² d) 4(m + 3)

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 point of intersection of 3x - y = 4 and x + y = 8 is
a) (5, 3) b) (2, 4) c) (3, 5) d) (4, 4)

9. A straight line PQ cuts X-axis at A and Y-axis at B. If the mid point of AB is (2a, 2b), then the co-ordinates of A and B are
a) (a, 0), (0, b) b) (2a, 0), (0, 2b) c) (4a, 0), (0, 4b) d) (0, 2b), (2a, 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. If two solid hemispheres of same base radius r units are joined together along their bases, the curved surface area of this new solid is
a) 4πr² sq. units b) 6πr² sq. units c) 3πr² sq. units d) 8πr² sq. units

12. The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is
a) 60π cm² b) 66π cm² c) 120π cm² d) 136π cm²

13. The range of the data 8, 8, 8, 8, 8, ... 8 is
a) 0 b) 1 c) 8 d) 3

14. A page is selected at random from a book. The probability that the digit at units place of the page number chosen is less than 7 is
a) ³/₁₀ b) ⁷/₁₀ c) ³/₉ d) ⁷/₉

PART - II: Answer any 10 questions (Q.No. 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 k if f(k) = 5 where f(x) = 2x - 1.

17. Find the number of terms in the A.P. 3, 6, 9, 12, ..., 111.

18. If 1³ + 2³ + 3³ + ... + k³ = 44100 then find 1 + 2 + 3 + ... + k.

19. Find the excluded values of the following expression: ^{(x² + 6x + 8)}/_{(x² + x - 2)}.

20. What length of ladder is needed to reach a height of 7 ft along the wall when the base of the ladder is 4 ft from the wall? Round off your answer to the next tenth place.

21. If the three points (3, -1), (a, 3) and (1, -3) are collinear, find the value of a.

22. Find the equation of a line through the given pair of points (2, 3) and (-7, -1).

23. Prove that ^{sec θ}/_{sin θ} - ^{sin θ}/_{cos θ} = cot θ.

24. A right circular cylinder just encloses a sphere of radius r units. Calculate:
i) the surface area of the sphere
ii) the curved surface area of the cylinder.

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

26. A coin is tossed thrice. What is the probability of getting two consecutive tails?

27. Find the slope of the line which is parallel to 3x - 7y = 11.

28. If (5 x 1)

-1

= (20), find the value of x. (Compulsory)

PART - III: Answer any 10 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 f(x) = x - 1, g(x) = 3x + 1 and h(x) = x², show that (f ∘ g) ∘ h = f ∘ (g ∘ h).

31. The product of three consecutive terms of a geometric progression is 343 and their sum is ⁹¹/₃. Find the three terms.

32. Rekha has 15 square colour papers of sizes 10 cm, 11 cm, 12 cm, ..., 24 cm. How much area can be decorated with these colour papers?

33. If ax⁴ + bx³ + 361x² + 220x + 100 is a perfect square, find the values of a and b.

34. If α, β are roots of the equation 2x² - x - 1 = 0 then form the equation whose roots are
i) ¹/_α, ¹/_β
ii) 2α + β, 2β + α

35. If A =

1	2	1
2	-1	1

, B =

2	-1
-1	4
0	2

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

36. State and prove the angle bisector theorem.

37. Find the area of the quadrilateral whose vertices are (-9, 0), (-8, 6), (-1, -2) and (-6, -3).

38. Find the equation of a straight line parallel to y-axis and passing through the point of intersection of the lines 4x + 5y = 13, x - 8y + 9 = 0.

39. A man is watching a boat speeding away from the top of a tower. The boat makes an angle of depression of 60° with the man's eyes when at a distance of 200 m from the tower. After 10 seconds, the angle of depression becomes 45°. What is the approximate speed of the boat (in km/hr), assuming that it is sailing in still water?

40. A conical container is fully filled with petrol. The radius is 10 m and the height is 15 m. If the container releases the petrol through its bottom at the rate of 25 cu. metre per min, in how many minutes will the container be emptied? Round off your answer to the nearest minute.

41. Two dice are rolled together. Find the probability of getting a doublet or sum of faces as 4.

42. A chess board contains 64 equal squares and the area of each square is 6.25 cm². A border around the board is 2 cm wide. Find the length of the side of the chess board. (Compulsory)

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

43. (a) Graph the following linear function: y = ¹/₂x. Identify the constant of variation and verify it by the graph. Also find y when x = 9.

(b) A two-wheeler parking zone near bus stand charges as below:

Time (hr) (X)	4	8	12	24
Amount (Y)	60	120	180	360

Check if the amount charged are in direct variation or in inverse variation to the parking time. Graph the data. Also:
i) Find the amount to be paid when parking time is 6 hrs.
ii) Find the parking duration when the amount paid is ₹150.

44. (a) Construct ΔABC of base BC = 8 cm, ∠A = 60° and the angle bisector of ∠A meets BC at D such that BD = 6 cm.

(b) Take a point which is 11 cm away from the center of a circle of radius 4 cm and draw the two tangents to the circle from that point.