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CBSE Class 10 Sample / Model Paper : Mathematics

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THE INDIAN COMMUNITY SCHOOL KUWAIT FIRST MID TERM EXAMINATION 2025-2026 SAMPLE QUESTION PAPER CLASS 10 MATHEMATICS Time : 1 hours Max.Marks : 40 Section A(Each question carries 1 mark) If one zero of a quadratic polynomial (kx2 + + 3x+ k) is 2, then the value of k is (A) 5/6 (B) -5/6 (C) 6/5 (D) -6/5 2. The zeroes of the polynomial x2 3x m(m+3) are (A) m,m+3 (B) m,m+3 (C) m,-(m+3) (D) m,-(m+3) 3. The sum of exponents of prime factors in the prime-factorization of 196 is (A) 3 (B) 4 (C) 5 (D) 2 4. Graphically, a pair of equations 6x 3y + 10 = 0; 2x y + 9 = 0 represents two lines which are: (A) intersecting at exactly one point (B) intersecting at exactly two points (C) coincident (D) parallel 5. If p and q are positive integers such that p = ab2 and q = a2 b, where a and b are prime numbers, then the LCM (p, q) is (A) ab (B) a2b2 (C) a3b3 (D) a3 b2 6. The HCF and LCM of 378, 180 and 420 of will be (A) 6 and 3980 (B) 12 and 3780 (C) 6 and 3780 (D) 12 and 3980 2 7. The discriminant of the quadratic equation 4 6x + 3 = 0 is (A) -12 (B) 84 (C) 2 3 (D) 12 8. The pair of equations + 2 + 5 = 0 and 3 6 + 1 = 0 have (A) a unique solution (B) exactly two solutions (C) infinitely many solutions (D) no solution 9. Half the perimeter of a rectangular garden, whose length is 4 m more then its width, is 36 m. The dimensions of garden will be (A) 20 m by 16 m (B) 36 m by 10 m (C) 16 m by 30 m (D) 20 m by 16 m 2 2 10. Assertion: The equation x +3x+1= (x-2) is a quadratic equation. Reason: Any equation of the form ax2+bx+c=0 where a,b,c are real numbers and a 0 is called a quadratic equation. (A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (C) Assertion (A) is true but reason (R) is false. (D) Assertion (A) is false but reason (R) is true. 1. Section B(Each question carries 2 marks) 1 1 1 1 1 1 1 1 1 1 11. Find c if the system of equations cx + 3y + (3 c) = 0; 12x + cy c = 0 has infinitely many solutions. 12. Find the zeroes of the quadratic polynomial 5 2 8x - 4 and verify the relationship between the zeroes and the coefficient of the polynomial. 2 2 Section C(Each question carries 3 marks) 13. If and are the zeroes of the quadratic polynomial 3x2 + 8x + 2, find the value of 2+ 2. 14. Given that 5 is irrational, prove that 2+ 3 5 is irrational. 15. If one of the zeroes of a polynomial 3x2 8x + 2k + 1 is seven times the other, find the value of k. 16. Solve using factorisation method. 3 3 3 3 Section D(Each question carries 4 marks) 17. Aditya works as a librarian in Bright Children International school in Indore. He ordered for books on English, Hindi and mathematics. He received 96 English books, 240 Hindi books and 336 maths books. He wishes to arrange these books in stacks such that each stack consists of the books on only one subject; and the number of books in each stack is the same. He also wishes to keep the number of stacks minimum. (i) Find the number of books in each stack. (ii) Find the total number of stacks formed. (iii) How many stacks of mathematics books will be formed? (OR) If each Hindi book weighs 1.5 kg, then find the weight of books in a stack of Hindi books. 1 1 2 Section E(Each question carries 5 marks) 18. Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Find the numbers. 19. Draw the graphs of the equations x y + 1 = 0 and 3x+2y - 12 = 0. Determine the co-ordinates of the vertices of the triangle formed by these lines and the X-axis and shade the triangular region. 5 5

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