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ICSE Class X Sample / Model Paper 2027 : Mathematics

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Adrika Banerjee
Queen Mary School (QMS), Mumbai

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ICSE-X Practice Test 7 Mathematics Date-31-05-2026 Quadratic Equation, Linear Inequations, Statistics, Matrices, Probability, Polynomial Prepared by Dr. Snehasis Banerjee, Associate Professor, Hooghly Mohsin College Maximum Marks-30 Time Allotted 1 hr 10 mints Section A (7 marks) (Attempt all questions from this Section.) Question 1 i) In an AP, if a7 + a13 = 60 ; then the value of a10 is a. 10 b. 20 c. 30 d. 40 ii) 20 tickets on which number 1 to 20 are written, are mixed thoroughly and then a ticket is drawn at random out of them. What is the probability that the number is multiple of 3 or 7? 1 5 a. b. 1 4 c. 2 5 d. 3 4 iii) If ( + ) term of an A.P. is and ( ) term is y then the term is equal to + . 2 2 iv) When 3 5 2 + 12 is divided by + 1, the remainder is 18, then the value of is . . ( )2 . . 2 . 12 . 18 . 0 . 2 v) The equation 12 + 4 + 3 = 0 has real and equal roots if k is: . vi) If = [ 3 . 9 . 4 0 0 2 5 4 ], = [ ]and = [ ] 0 1 1 3 1 vii) Which of the following statements are true? Statement I: ( + ) is not possible Statement II: + is possible both I and II . only I . . only II . neither I nor II viii) Assertion (A): If 2 1, 4 3, 4 + 1are three consecutive terms of an AP, then = 1 Reason (R): If , , are three consecutive terms of an AP then 2 = + (a) Both assertion (A) and reason (R) are true but 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) A is true, R is false (d) A is false, R is true Page 1 of 2 Question 2 If + is a factor of the polynomial 2 + + and 2 + + , prove that = [4] Question 3 If a, b, c, d are in continued proportion, prove that: [3] ( )2 + ( )2 + ( )2 = ( )2 Question 4 =[ 3 2 5 2 ] and = [ ]. If is the identity matrix of 2 2 order. Evaluate: 2 + 4 5 1 5 1 3 [3] Question 5 Solve the following inequation and represent the solution set on the number line: 3 5 + 2 < + 4 2 + 5, [3] Question 6 4sin30 4 5 If = [ ] and = [ sin90 5 4 2cos60 ], then find BA - 5I where I is the identity matrix of order 2 2. 2cos0 [3] Question 7 (a) The terms 6, 13, 20, 216 are in AP. Find the number of terms in the given AP.(b) the middle term(c) the sum of first 16 terms [3] Question 8 Five years ago, a woman s age was the square of her son s age. Ten years hence her age will be twice that of her son s age. Find: a) The age of the son five years ago.b) The present age of the woman. Page 2 of 2 [3]

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