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ICSE Class X Prelims 2026 : Mathematics (Lawrence High School, HSR Layout, Bangalore)

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Suhasan K
AMC Cambridge Public School, Bangalore
9th to 10th Science Maths Social Kannada English

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LAWRENCE HIGH SCHOOL, ICSE FIRST PREPARATORY EXAMINATION 2025 2026 SUBJECT: MATHEMATICS Class: X Marks: 80 Time: 3 hours Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this Paper is the time allowed for writing the answers. Attempt all questions from Section A and any four questions from Section B. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the paper. Omission of essential working will result in loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables are provided. SECTION A ( 40 Marks) ( Attempt all questions from this section ) Question 1 Choose the correct answers to the questions from the given options. [ 15 ] ( Do not copy the question, write the correct answers only. ) i) Dev bought an electrical fan which has a marked price of 800. If the GST on the goods is 7%, then the SGST is: a) 24 b) 28 c) 56 ii) The 7th term of the given Arithmetic Progression a) +6 b) +7 c) +5 d) 80 , + 1, d) +4 + 2 , ..is : iii) Assertion ( A ): If PA and PB are two tangents to a circle with centre O, such that AOB = 110 , then APB = 90 . Reason ( R ) : The length of two tangents drawn from the external point are equal. a) A is true and R is true. A b) A is false and R is false. c) A is true and R is false O P d) A is false and R is true. B iv) Which among the following cannot be the probability of an event? a) 0.1 b) c) Page 1 of 7 d) 3% = v) In the triangles ABC and PQR, = , then a) PQR ~ CAB b) PQR ~ ABC c) CBA ~ PQR d) BCA ~ PQR vi) 50 shares of a company are bought by John at 20% discount and sold at a gain of 25%. Assertion ( A ) : The net gain on each share is 5% Reason ( R ) : The selling price of each share = 50 ( 80 /100 ) ( 125 /100 ) a) A is true and R is false b) A is false and R is true c) Both A and R are true d) Both A and R are false vii) Bisector of angle B of triangle ABC intersects side AC at point P, then point P is : a) equidistant from vertices A and C. b) PA = PB c) equidistant from sides AB and BC d) PB = PC viii) The length of PQ is : a) 9 m b) 15 m c) 21 m d) 45 m P S 3m 45 R 12m Q ix) Rams deposited 400 per month in a recurring deposit account for 18 months. The qualifying sum of money for the calculation of interest is a) 68,400 b) 3,600 c) 7,200 d) 1,36,800 x) The inclination of line of a line y = 3 x 5 is a) 60 b) 45 c) 30 d ) 90 xi) If x = 2 is one of the solutions of the quadratic equation 2 + 3 = 0, then the value of a is: a) 8 b) 3 xii) The third proportional to 6 a) 3 c) 1/ 3 d) 2 and 5 is b) 7 c) 4 d) xiii) The value of the polynomial 2 x3 3 x2 + 2 at x = 2 is : a) 2 2 b) 0 c ) 2 xiv) d)1 The mode for the given frequency distribution is: Number a) 17 8 9 10 11 12 13 14 Frequency 3 8 12 15 14 17 12 b) 15 c) 13 Page 2 of 7 d) 14 xv) If = [ ] = then a) only matrix AB is possible. b) only matrix BA is possible. c) both matrices AB and BA are possible, AB = BA. d) both matrices AB and BA are possible. Question 2 i) Use the remainder theorem to factorise the following expression: [4] 2 x3 + x2 13 x + 6. ii) Using componendo and dividendo , find the value of x . [4] = 5 iii) Using a ruler and compass only, construct a ABC such that BC = 5 cm, AB = 6.5 cm and ABC = 120 . a) Construct a circum-circle of ABC. [4] b) Construct a cyclic quadrilateral ABCD, such that D is equidistant from AB and BC. Question 3 i) In the given figure, DBC = 58 . BD is a diameter of the circle. Calculate a) BDC b) BEC c) BAC A [4] D B C E ii) [4] Page 3 of 7 iii) The following table shows the distribution of marks in an examination. Marks No: of students 0 10 5 10 20 11 20 30 10 30 40 20 40 50 28 50 60 37 60 70 40 70 80 29 80 90 14 90 100 06 [5] Using a graph paper, draw an ogive for the given distribution. Use scale as 2 cm = 10 marks on one axis and 2cm = 20 students on the other axis. Use your ogive to estimate: a) the median marks b) the number of students who failed if the maximum marks required to pass is 40. c) if scoring 85 and more than 85 is considered as grade one, then find the number of students who secured grade one in the examination. SECTION B ( 40 Marks) ( Attempt any four questions from this section ) Question 4 i) Ram opened a Recurring Deposit Account in a bank and deposited 800 per month [ 3 ] for 1 years. If he received 15,084 at the time of maturity, find the rate of interest per annum. ii) The first term of an A.P. is 5, the last term is 45 and the sum of its terms is 1000. Find: a) the number of terms b) common difference of the A.P. iii) P is a point on the x- axis which divides the line joining A (- 6, 2) and B (9, - 4). Find: a) the ratio in which P divides the line segment AB. b) the coordinates of the point P. c) equation of a line parallel to AB and passing through (-3, -2). Page 4 of 7 [3] [4] Question 5 i) [3] Aaayu Farms sells tinned rasgullas. The tin container is cylindrical in shape with diameter 14cm, height 16cm and it can hold 20 spherical rasgullas of diameter 6cm and sweetened liquid such that the can is filled and then sealed. Find how much sweetened liquid the can contains. (Take = 3.14 ) ii) The fourth term, the seventh term and the last term of the geometric progression are 10, 80 and 2560 respectively. Find its first term, common ratio and the number of terms . iii) In the given figure, O is the centre of the circle. DAE = 70 . Find [3] [4] Question 6 i) Lucky invests 4,500 in 8% , 10 shares at 15. He sells the shares when the price rises to 30 and invests the proceeds in 12% 100 shares at 125. Calculate: a) the sale proceeds. b) the number of 125 shares he buys. c) the change in his annual income from dividend. [3] ii) Using graph paper draw a histogram for the given distribution showing the number [3] of runs scored by 50 batsmen. Estimate the mode of the data: Runs Scored ( in thousands) No. of Batsmen 3 4 4 5 5 6 6 7 7 8 8 9 9 10 4 18 9 6 7 2 4 1 0 6 0 and B = . Find matrix M, if M = A 2 B + 5 I, 1 3 4 2 where I is the identity matrix. iii) A = Page 5 of 7 [4] Question 7 i) Use a graph sheet for this question. Take 1 cm = 1 unit along both x and y-axis. [5] a) Plot points A ( 0, 3 ) , B ( 4, 0 ) , C ( 6, 2 ) and D ( 5, 0 ). b) Reflect A on x-axis to A . Reflect B on y- axis to B . Reflect C on x-axis to C . c) Join the points A, B, C, D, C , B, A , B and A to form a closed figure. Name the closed figure BCDC . d) Determine the equation of the line such that D remains invariant when reflected in it. ii) Cards marked with numbers 1, 2, 3, 4 .20 are well shuffled and a card is drawn [ 5 ] at random. What is the probability that the number on the card is a) a prime number b) divisible by 3 c) a perfect square d) a number 22 e) multiples of 5 Question 8 i) PQR is a triangle. S is a point on the side QR of PQR such that PSR = QPR. = ii) Show that . [3] iii) Akshay visited an electrical goods store to buy appliances. The details of the items and their prices are given below. Items Quantity Rate per piece Discount ( % ) G.S.T ( % ) Wall fan 01 4,000 20% 18% L.E.D bulbs 10 300 Nil 12% Find : a) Discounted price of the wall fan. b) Total G.S.T paid on the two items. c) Total bill amount including G.S.T Page 6 of 7 [3] [4] Question 9 i) In the given figure, diameter AB and chord CD of a circle meet at P. [3] PT is a tangent to the circle at T. CD = 7.8cm, PD = 5 cm, PB = 4 cm. Find: a) AB b) the length of tangent PT. T A B C D ii) A shopkeeper purchases a certain number of books for was P 960. If the cost per book 8 less , the number of books that could be purchased for Write an equation , taking the original cost of each book to be the original cost of the books. iii) The weights of 50 oranges were recorded as given below. [3] 960 would be 4 more. x and solve it to find [4] Calculate the mean weight, to the nearest gram, by step deviation method. Weight in grams No: of oranges 80 85 85 90 5 90 95 95 100 100 105 105 110 110 115 10 12 8 4 3 8 Question 10 i) Solve the following equation : 18 x [3] = 6. Give your answer correct to two significant figures. ii) In the given figure, line APB meets the x-axis at point A and y-axis at point B. P is the point ( 4, 2 ) and AP : PB = 1 : 2. Find the coordinates of A and B. [3] B P A iii) Solve the following inequation, write the solution set and represent it on the number line: 1 < 1 6 [4] , R ----------------------------------------------------------------------------------------------------------Page 7 of 7

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