10th Maths Public Exam 2027 Expected 5 Mark Questions

Stay ahead of the curve and kickstart your advanced preparation with this definitive list of 10th Maths Public Exam 2027 Expected 5 Mark Questions. Long-answer questions form the core scoring section of the SSLC mathematics blueprint, making them crucial for securing a centum. This targeted guide analyzes previous years' trends and structural blueprints to predict the most important 5-mark problems across all eight chapters—from complex matrices and progressive sequences to critical trigonometry proofs and statistical calculations. Master these high-yield problems early to perfect your step-by-step working, clear up conceptual hurdles, and build absolute confidence for your upcoming 2027 board exams!

10TH STD — MATHEMATICS

Board exam Expected 5Marks Questions:

1. A function f is defined by f(x) = 2x - 3, then find:
(i) ^{[f(0) + f(1)]}/₂
(ii) find x such that f(x) = 0
(iii) find x such that f(x) = x
(iv) find x such that f(x) = f(1 - x)

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

3. If f(x) = x - 4, g(x) = x² and h(x) = 3x - 5, show that (f ∘ g) ∘ h = f ∘ (g ∘ h).

4. Find x if gff(x) = fgg(x), given f(x) = 3x + 1, g(x) = x + 3.

5. Find the largest number which divides 1230 and 1926 leaving remainder 12 in each case.

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

7. In a Geometric progression the 4^th term is ⁸/₉ and 7^th term is ⁶⁴/₂₄₃. Find the Geometric Progression.

8. A man repays a loan of Rs.65,000 by paying Rs.400 in the first month and then increasing the payment by Rs.300 every month. How long will it take for him to clear the loan?

9. Find the sum to n terms of the series: 5 + 55 + 555 + ... to n terms.

10. Find the sum of the series: 10³ + 11³ + ... + 20³.

11. Find the GCD of 3x⁴ + 6x³ - 12x² - 24x and 4x⁴ + 14x³ + 8x² - 8x.

12. If x = ^{(a² + 3a - 4)}/_{(3a² - 3)} and y = ^{(a² + 2a - 8)}/_{(2a² - 2a - 4)}, find the value of x²y^-2.

13. Simplify: ¹/_{(x² - 5x + 6)} + ¹/_{(x² - 3x + 2)} - ¹/_{(x² - 8x + 12)}.

14. What rational expression should be subtracted from ^{(x² + 6x + 8)}/_{(x³ + 8)} to get ³/_{(x² - 2x + 4)}?

15. If 9x⁴ + 12x³ + 28x² + ax + b is a perfect square, find the value of a and b.

16. Find the square root of 289x⁴ - 198x³ - 183x² + 216x + 144.

17. If one root of the equation 2y² - ay + 64 = 0 is twice the other, find the value of a.

18. If the roots of the equation (c² - ab)x² - 2(a² - bc)x + b² - ac = 0 are real and equal, prove that either a = 0 (or) a³ + b³ + c³ = 3abc.

19. Find X and Y, if X + Y =

7	0
3	5

and X - Y =

3	0
0	4

20. If A =

1	1
-1	3

, B =

1	2
-4	2

and C =

-7	6
3	2

, verify that A(B + C) = AB + AC.

21. State and Prove Thales Theorem.

22. Two poles of height a and b metres are p metres apart. Prove that the height of the point of intersection of the lines joining the top of each pole to the foot of the opposite pole is given by ^ab/_{(a + b)} metres.

23. The hypotenuse of a right triangle is 6 m more than twice of the shortest side. If the 3^rd side is 2 m less than the hypotenuse, find the sides of the triangle.

24. Prove that 8AE² = 3AC² + 5AD². In ΔABC is a right angled triangle with right angle at B and points D, E trisect BC.

25. PQ is a chord of length 8 cm to a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length of the tangent TP.

26. Show that in a triangle, the medians are concurrent.

27. Find the area of the quadrilateral (8, 6), (5, 11), (-5, 12) and (-4, 3).

28. A line makes positive (+ve) intercepts on coordinate axes whose sum is 7 and it passes through (-3, 8). Find its equation.

29. Find the equation of the ⊥^r bisector of the line joining A(-4, 2) and B(6, -4).

30. 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 A(5, -4) and B(-7, 6).

33. Find the mean and variance of the first n natural numbers.

33. For a group of 100 candidates the mean and standard deviation of their marks were found to be 60 and 15 respectively. Later on it was found that the scores 45 and 72 were wrongly entered as 40 and 27. Find the correct mean and standard deviation.

34. The marks scored by 10 students in a class test are 25, 29, 30, 33, 35, 37, 38, 40, 44, 48. Find the standard deviation.

35. Marks of the students in a particular subject of a class are given below. Find its standard deviation:

Marks	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Number of students	8	12	17	14	9	7	4

36. In a study about viral fever, the numbers of people affected in a town were noted. Find its standard deviation:

Age in years	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Number of people affected	3	5	16	18	12	7	4

37. Find the coefficient of variation of 24, 26, 33, 37, 29, 31.

38. The time taken (in minutes) to complete a homework by 8 students in a day are given by 38, 40, 47, 44, 46, 43, 49, 53. Find the coefficient of variation.

39. A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers 1, 2, 3, ... 12. What is the probability that it will point to (i) 7 (ii) a prime number (iii) a composite number?

40. Three fair coins are tossed together. Find the probability of getting (i) all heads (ii) atleast one tail (iii) atmost one head (iv) atmost two tails.

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

42. A box contains cards numbered 3, 5, 7, 9, ... 35, 37. A card is drawn at random from the box. Find the probability that the drawn card have either multiples of 7 or a prime number.

43. Three unbiased coins are tossed once. Find the probability of getting atmost 2 tails or atleast 2 heads.

44. In a town of 8000 people, 1300 are over 50 years and 3000 are females. It is known that 30% of the females are over 50 years. What is the probability that a chosen individual from the town is either a female or over 50 years?