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ICSE Class X Board Exam 2025 : Mathematics

6 pages, 39 questions, 0 questions with responses, 0 total responses,

Rakesh Raushan
Manipal university Jaipur, Jaipur
Ph.D Pursuing DIP

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Springfield School Pre-board-I Examination 2024-25 Class : X Max. Marks : 80 Subject : Mathematics Duration : 3 Hrs. Section A (Attempt all questions from this section) 1. Choose the correct answers to the questions from the given options : (i) On dividing 2 x3 6 x 2 (2k 7) x 5 by (15) ( x 3) , the remainder is (k 1) then the value of k is (a) (ii) 2 (b) 2 (c) 3 (d) 3 A lady deposited D 1800 per month for 15 months in recurring deposit account at 7% per annum simple interest. The interest earned by her at maturity is (a) (iii) D 900 (b) D 1080 (c) D 1260 (d) D 1500 Diagonals of a trapezium ABCD with AB | | DC intersect each other at the point O. If AB = 2 CD, then the ratio of the areas of triangle AOB and COD, equals (a) (iv) 1:4 (b) 4:1 (c) 2:1 (d) 1:2 In the adjoining diagram PA and PB are tangents to a circle with centre O . A If APB = 50 , then OAB equal to (v) (a) 25 (b) 50 (c) 100 (d) None of these 50 O B In ABC, A = 30 and B = 90 . If AC = 8 cm, then its area is (a) (vi) P 16 3 cm2 (b) 16 cm2 (c) 8 3 cm2 (d) 6 3 cm2 In the adjoining diagram, if AB | | ED Statement 1 : ABC ~ DEC E A Statement 2 : ABC DEC Which of the following is valid? (a) Both the statements are true. (b) Both the statements are false. (c) Statement 1 is true and statement 2 is false. (d) Statement 1 is false and statement 2 is true. C B D Page | 1 (vii) For the following distribution Class 0-5 5-10 10-15 15-20 20-25 Frequency 10 15 12 20 9 The sum of lower limit of median class and upper limit of modal class is (a) (viii) 35 (b) 30 (c) 25 (d) 15 A card is drawn from a well shuffled deck of 52 cards. Find the probability that the card drawn is spade or an ace is (a) (ix) 17 52 15 52 (b) (c) 4 13 (d) None of these 2 1 If C = 4 1 and D = 3 0 Assertion (A) : Product CD of the two matrices C and D is possible. Reason (R) : (x) Number of columns of matrix C is equal to the number of rows in matrix D. (a) A is true and R is false (b) A is false, R is true (c) Both A and R are true and R is the correct reason for A. (d) Both A and R are true and R is incorrect reason for A. An article which is marked at D 32000 is available at a discount of 25% and the rate of GST is 18%. The amount of SGST is (a) (xi) D 4320 (b) D 2160 (c) D 2880 (d) D 720 If Asha invests D 19200 on D 50 shares at a premium of 20%, then the number of shares she buys is : (a) (xii) (b) 384 (c) 320 (d) 160 If the equation kx( x 2) 6 0 has equal roots, then the values of k is (a) (xiii) 640 6 (b) 2 6 (c) 12 (d) 0, 12 If the line 3x 4 y 7 0 and 2 x ky 5 0 are perpendicular to each other, then the value of k is (a) (xiv) 3 2 (b) 3 2 (c) 2 3 (d) 2 3 An integer is such that one-third of next integer is atleast 2 more than one-fourth of the previous integer. The smallest value of the integer is (a) (xv) 15 (b) 16 (c) 17 (d) 18 (d) 162 The 5th term from the end of the GP 2, 6, 18, ., 13122 (a) 486 (b) 54 (c) 1458 Page | 2 2. (i) Show that (2x + 3) is a factor of 6 x 3 17 x 2 4 x 12 . Hence factorise the given expression completely, using the factor theorem. (ii) (4) Three vertices of a parallelogram ABCD taken in order are A(3, 6), B (5, 10) and C(3, 2), find (iii) (4) (a) The coordinates of the fourth vertex D. (b) Length of the diagonal BD. (c) Equation of side AB of the parallelogram ABCD. In the given figure PQRS is a cyclic quadrilateral. PQ and SR produced meet at T. (a) Prove that TPS ~ TRQ. (b) Find SP if TP = 18 cm, RQ = 4 cm and (4) S R TR = 6 cm. (c) Find the area of quadrilateral PQRS if area of P T Q PTS = 27 cm2. 3. (i) The product of first three terms of a GP is 1000. If 6 is added to its second term and 7 is added to its third term, the terms become in AP. Find the GP. (ii) (4) A circle is touching the side BC of a ABC at P and is touching AB and AC when produced at Q and R respectively. Prove that : AQ = (iii) (4) 1 (Perimeter of ABC) 2 Use graph paper to answer the following questions. (Take 1 unit = 2 cm on both axes) (5) (a) Plot the points A( 4, 2) and B(2, 4) (b) A' is the image of A when reflected in the y-axis. Plot it on the graph paper and write coordinates of A'. (c) B' is the image of B when reflected in the line AA'. Write the coordinates of B'. (d) Write the geometric name of figure ABA'B'. (e) Name a line of symmetry of the figure formed. Section B (Attempt any four questions from this section) 4. (i) Mr. Manish invested D 8000 in 7% D 100 shares at D 80. After a year he sold these shares at D 75 each and invested the proceeds (including his dividend) in 18% D 25 shares at D 41. Find (3) (a) His dividend for the first year. (b) His annual income in the second year. (c) The percentage increase in his return on his original investment. Page | 3 (ii) Solve the following inequation, write the solution set and represent it on the real number line : (3) 5 x 21 (iii) 5x 3 6 3 x, x R 7 7 Prove the following trigonometric identity : (4) cos A sin A 1 1 cos A cos A sin A 1 sin A 5. (i) PQR is a triangle. S is a point on the QR of PQR such that PSR = QPR. Given QP = 8cm, P PR = 6 cm and SR = 3 cm. (b) Find the lengths of QR and PS. (c) Find area PQR : area SPR 8c m Prove that PQR ~ SPR. m 6c (ii) (a) Q S 3 cm R Mr. Amit deposits a certain sum of money each month in a Recurring Deposit Account of a bank. If the rate of interest is 8% per annum and Mr. Amit gets D 8088 from the bank after 3 years, find the value of his monthly instalment. (iii) (3) The mean of the following distribution is 50 and sum of all the frequencies is 120. Using stepdeviation method find f1 and f2. Class Interval Frequency 6. (i) (4) 0-20 20-40 40-60 60-80 80-100 17 f1 32 f2 19 A(a, b), B( 4, 3) and C(8, 6) are the vertices of a ABC. Point D is on BC such that BD : BC is 2 : 3 and M(6, 0) is mid-point of AD. Find : (ii) (3) (a) Coordinates of point D (b) Coordinates of point A (c) Equation of a line passing through M and parallel to line BC. In the given figure PT is a tangent to the circle. Chord BA produced meets the tangent PT at P. Given PT = 20 cm and PA = 16 cm. (a) Prove that PTB ~ PAT (b) Prove that PT BT = (AT) (PB) (c) Find the length of AB. (3) T B A P Page | 4 (iii) The following bill shows the GST rate and marked price of articles (4) Vidhyut Electronics S.No. Item Marked Price Quantity Rate of GST (a) LED TV Set D 12000 01 28% (b) MP4 Player D 5000 01 18% Find the total amount to be paid (including GST) for the above bill. 7. (i) The angle of elevation of an aeroplane from a point on the ground is 60 . After a flight of 30 seconds, the angle of elevation changes to 30 . If the aeroplane is flying at a constant height of 3600 (ii) 3 metre. Find the speed of the plane in km/hr. (5) The marks obtained by 200 students in an examination are given below : Marks 0-10 No of Students (5) 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 5 10 11 20 27 38 40 29 14 6 Using a graph paper, draw an ogive for the given data and use it to find the, 8. (i) (a) Median (b) Lower quartile (c) Number of students who obtained more than 80% marks in the examination (d) Number of students who did not pass, if the pass percentage was 35. A box contains cards bearing numbers from 6 to 70. If one card is drawn at random from the box, find the probability that it bears. (ii) (3) (a) a number divisible by 5. (b) An odd number less than 30. (c) A composite number between 50 and 70. (a) Using properties of proportion, find x : y (3) x2 2x y 2 3 y 2x 4 3y 9 (b) (iii) a 2 b2 c2 4 If b is the mean proportion between a and c, prove that : 2 2 2 b a b c In the given figure, O is the centre of the circle and AB is a tangent to the circle at B. If PQB = 50 , (a) Find the value of angles x, y and z. (b) Prove that RB is parallel to PQ. (4) P R x O y S 55 z A Q B Page | 5 9. (i) The table given below shows the ages of members of a society (3) Age (in years) Number of members of the society 25-35 5 35-45 32 45-55 69 55-65 80 65-75 61 75-85 13 Use graph sheet for this question Take 2 cm = 10 years along one axis and 2 cm = 10 members along the other axis. (a) Draw a histogram representing the above distribution. (b) Find the modal age of the members. (ii) If the sum of n terms of an AP is 3n2 + 5n and its mth term is 164, find the value of m. (3) (iii) Solve the following equation using quadratic formula. (4) abx 2 (b2 ac) x bc 0 10. (i) Two pipes running together can fill a cistern in 2 8 minutes. If one pipe takes one minute 11 more than to other to fill the cistern. Find the time in which each pipe can separately fill the tank. (3) (ii) 2 3 1 0 0 4 2 , B If A and C . Find the value of AC + B 10C. 5 7 1 7 1 4 (3) (iii) 2 4 Prove that : sec 2 sin 4 2 sin 2 1 (4) 2 cos cos ******* Page | 6

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