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Shishya Model Paper 1: SSLC Mathematics

Shishya model paper — not official, not leaked

12 questions, 30 marks, about 1 hour, written by Shishya on chapters of the Tamil Nadu SSLC Class 10 Mathematics textbook: Relations and Functions, Numbers and Sequences, Algebra, Coordinate Geometry, Mensuration, Statistics and Probability. It is for revision before term exams (quarterly, half-yearly, mid-term, preparatory or prelim). It is not the board's paper, not a past paper and not a guess at any exam; your school sets its own term-exam portion.

How it was made: the questions and answers were drafted with AI, then every final number was recomputed by a calculator check from the question's own numbers (re-run before each release, last on 27 Oct 2026), and a second, independent AI solve had to reach the same number. Try each question first, then open the worked answer.

  1. Q1

    2 marksRelations and Functions

    If a set A has 3 elements and a set B has 4 elements, find the total number of relations from A to B.

    Worked answer
    1. Total elements in A x B = 3 * 4 = 12
    2. Number of relations = 2^(number of elements in A x B)
    3. Number of relations = 2^12
    4. 2^12 = 4096

    Answer: 4096 relations

  2. Q2

    2 marksRelations and Functions

    Given f(x) = 2x + 1 and g(x) = x^2, find the value of the composite function f(g(2)).

    Worked answer
    1. Calculate g(2) = 2^2 = 4
    2. Substitute g(2) into f(x): f(4) = 2(4) + 1
    3. Calculate 2(4) + 1 = 8 + 1
    4. Final value = 9

    Answer: 9

  3. Q3

    2 marksNumbers and Sequences

    Find the HCF of 135 and 225 using Euclid's division lemma.

    Worked answer
    1. 225 = 135 x 1 + 90
    2. 135 = 90 x 1 + 45
    3. 90 = 45 x 2 + 0
    4. The last non-zero remainder is the HCF

    Answer: HCF = 45

  4. Q4

    2 marksNumbers and Sequences

    Find the sum of the first 20 terms of the arithmetic progression 3, 7, 11, ...

    Worked answer
    1. a = 3, d = 4, n = 20
    2. S = n/2 [2a + (n-1)d]
    3. S = 20/2 [2(3) + (20-1)4]
    4. S = 10 [6 + 76]
    5. S = 10 x 82 = 820

    Answer: 820

  5. Q5

    3 marksAlgebra

    Solve the pair of linear equations 3x + 2y = 13 and x - y = 1. Find the value of x.

    Worked answer
    1. From x - y = 1, y = x - 1
    2. Substitute in the first equation: 3x + 2(x - 1) = 13
    3. 3x + 2x - 2 = 13, so 5x = 15
    4. x = 15/5 = 3 (and y = 3 - 1 = 2)

    Answer: x = 3 (y = 2)

  6. Q6

    3 marksAlgebra

    Find the product of the roots of the quadratic equation x^2 - 9x + 20 = 0.

    Worked answer
    1. a = 1, b = -9, c = 20
    2. Product of roots = c/a
    3. Product = 20/1 = 20

    Answer: The product of the roots is 20.

  7. Q7

    3 marksCoordinate Geometry

    Find the area of the triangle whose vertices are A(2, 3), B(5, 7), and C(8, 1).

    Worked answer
    1. Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
    2. Area = 1/2 * |2(7 - 1) + 5(1 - 3) + 8(3 - 7)|
    3. Area = 1/2 * |2(6) + 5(-2) + 8(-4)|
    4. Area = 1/2 * |12 - 10 - 32|
    5. Area = 1/2 * |-30|
    6. Area = 15

    Answer: 15 square units

  8. Q8

    3 marksCoordinate Geometry

    Find the slope of the line passing through the points P(1, 4) and Q(3, 10).

    Worked answer
    1. Slope m = (y2 - y1) / (x2 - x1)
    2. m = (10 - 4) / (3 - 1)
    3. m = 6 / 2
    4. m = 3

    Answer: 3

  9. Q9

    3 marksMensuration

    A cylindrical water tank has a radius of 14 cm and a height of 20 cm. Find the curved surface area of the tank in square centimeters, taking pi as 22/7.

    Worked answer
    1. Formula for curved surface area is 2 * pi * r * h
    2. Substitute values: 2 * (22/7) * 14 * 20
    3. Simplify: 2 * 22 * 2 * 20
    4. Calculate: 44 * 40
    5. Result: 1760

    Answer: 1760 square centimeters

  10. Q10

    3 marksMensuration

    A solid cone has a base radius of 7 cm and a height of 24 cm. Find the volume of the cone in cubic centimeters, taking pi as 22/7.

    Worked answer
    1. Formula for volume of a cone is (1/3) * pi * r^2 * h
    2. Substitute values: (1/3) * (22/7) * 7^2 * 24
    3. Simplify: (1/3) * (22/7) * 49 * 24
    4. Calculate: (1/3) * 22 * 7 * 24
    5. Calculate: 22 * 7 * 8
    6. Result: 1232

    Answer: 1232 cubic centimeters

  11. Q11

    2 marksStatistics and Probability

    The marks of 5 students in a Mathematics test are 45, 50, 65, 70, and 85. Find the range of this data set.

    Worked answer
    1. Highest mark = 85
    2. Lowest mark = 45
    3. Range = Highest - Lowest
    4. Range = 85 - 45
    5. Range = 40

    Answer: 40 marks

  12. Q12

    2 marksStatistics and Probability

    A fair die is thrown once. Find the probability that the number obtained is even. Express the answer as a decimal.

    Worked answer
    1. Total outcomes = 6
    2. Even numbers = 2, 4, 6
    3. Number of favorable outcomes = 3
    4. Probability = Favorable / Total
    5. Probability = 3 / 6 = 0.5

    Answer: 0.5

Tamil Nadu SSLC 2027: exam dates and papers →Official papers of earlier years →