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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 Karnataka SSLC Class 10 Mathematics textbook: Real Numbers, Polynomials and Quadratic Equations, Arithmetic Progressions, Coordinate Geometry, Surface Areas and Volumes, 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 marksReal Numbers

    Find the HCF of 180 and 252 using prime factorisation.

    Worked answer
    1. 180 = 2^2 * 3^2 * 5
    2. 252 = 2^2 * 3^2 * 7
    3. Common factors are 2^2 and 3^2
    4. HCF = 2^2 * 3^2
    5. HCF = 4 * 9
    6. HCF = 36

    Answer: 36

  2. Q2

    2 marksReal Numbers

    The product of two numbers is 4320. If their HCF is 12, find their LCM.

    Worked answer
    1. Product = HCF * LCM
    2. 4320 = 12 * LCM
    3. LCM = 4320 / 12
    4. LCM = 360

    Answer: 360

  3. Q3

    2 marksPolynomials and Quadratic Equations

    If the zeroes of the quadratic polynomial 2x^2 - 8x + 6 are alpha and beta, find the value of alpha + beta.

    Worked answer
    1. a = 2
    2. b = -8
    3. Sum of zeroes = -b/a
    4. Sum = -(-8)/2
    5. Sum = 8/2
    6. Sum = 4

    Answer: 4

  4. Q4

    2 marksPolynomials and Quadratic Equations

    Find the smaller root of the quadratic equation x^2 - 11x + 30 = 0.

    Worked answer
    1. x^2 - 11x + 30 = 0
    2. x^2 - 5x - 6x + 30 = 0
    3. x(x - 5) - 6(x - 5) = 0
    4. (x - 5)(x - 6) = 0
    5. x = 5 or x = 6
    6. Smaller root = 5

    Answer: 5

  5. Q5

    3 marksArithmetic Progressions

    An arithmetic progression has a first term of 5 and a common difference of 3. Find the sum of the first 12 terms of this progression.

    Worked answer
    1. a = 5, d = 3, n = 12
    2. S_n = n/2 * [2a + (n-1)d]
    3. S_12 = 12/2 * [2(5) + 11(3)]
    4. S_12 = 6 * [10 + 33]
    5. S_12 = 6 * 43
    6. S_12 = 258

    Answer: 258

  6. Q6

    3 marksArithmetic Progressions

    Find the 20th term of an arithmetic progression where the first term is 2 and the common difference is 4.

    Worked answer
    1. a = 2, d = 4, n = 20
    2. a_n = a + (n-1)d
    3. a_20 = 2 + (20-1)4
    4. a_20 = 2 + 19*4
    5. a_20 = 2 + 76
    6. a_20 = 78

    Answer: 78

  7. Q7

    2 marksCoordinate Geometry

    Find the distance between the points A(3, 4) and B(0, 0).

    Worked answer
    1. Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
    2. Substitute values: sqrt((0 - 3)^2 + (0 - 4)^2)
    3. Simplify squares: sqrt((-3)^2 + (-4)^2)
    4. Calculate squares: sqrt(9 + 16)
    5. Add terms: sqrt(25)
    6. Final value: 5

    Answer: 5 units

  8. Q8

    2 marksCoordinate Geometry

    Find the x-coordinate of the midpoint of the line segment joining the points P(-2, 5) and Q(6, 3).

    Worked answer
    1. Midpoint formula x-coordinate = (x1 + x2) / 2
    2. Substitute x-values: (-2 + 6) / 2
    3. Add numerator: 4 / 2
    4. Divide: 2

    Answer: 2

  9. Q9

    3 marksSurface Areas and Volumes

    A cylindrical water tank has a base diameter of 14 m and a height of 21 m. Find the volume of the tank in cubic metres, taking pi as 22/7.

    Worked answer
    1. r = 14/2 = 7
    2. V = pi * r^2 * h
    3. V = (22/7) * 7 * 7 * 21
    4. V = 22 * 7 * 21
    5. V = 3234

    Answer: 3234 cubic metres

  10. Q10

    3 marksSurface Areas and Volumes

    A conical tent has a base radius of 7 m and a height of 24 m. Find the curved surface area of the tent in square metres, taking pi as 22/7.

    Worked answer
    1. l = sqrt(7^2 + 24^2)
    2. l = sqrt(49 + 576)
    3. l = sqrt(625) = 25
    4. CSA = pi * r * l
    5. CSA = (22/7) * 7 * 25
    6. CSA = 22 * 25 = 550

    Answer: 550 square metres

  11. Q11

    3 marksStatistics and Probability

    The following table shows the marks obtained by 18 students in a mathematics test. Find the mean marks of the students. Marks: 0-10, 10-20, 20-30, 30-40, 40-50 Frequency: 2, 4, 6, 4, 2

    Worked answer
    1. Midpoints: 5, 15, 25, 35, 45
    2. Sum of fx: 2*5 + 4*15 + 6*25 + 4*35 + 2*45 = 10 + 60 + 150 + 140 + 90 = 450
    3. Total frequency: 2 + 4 + 6 + 4 + 2 = 18
    4. Mean = 450 / 18 = 25

    Answer: 25 marks

  12. Q12

    3 marksStatistics and Probability

    A die is thrown once. Find the probability that the number obtained is greater than 3. Express the answer as a decimal.

    Worked answer
    1. Total outcomes = 6 (1, 2, 3, 4, 5, 6)
    2. Favorable outcomes = 3 (4, 5, 6)
    3. Probability = Favorable / Total = 3 / 6
    4. Probability = 0.5

    Answer: 0.5

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