Formatting page ...
ICSE 2025 Examination Pre-Board Practice Paper-1 MATHEMATICS Max. Marks: 80 Time allowed: Three hours ____________________________________________________________________________________ SECTION A (Attempt all questions from this section) Question 1: Choose the correct answers to the questions from the given options: [15] (Do not copy the questions, write the correct answers only) (i) The solution set for the inequation -8 2x<8, x W is: (a) {0,1,2,3} (c) {-4,-3,-2,-1} (b) {-4,-3,-2,-1,0,1,2,3,4} (d) {-8,-7,-6,-5, .6,7,8} (ii) Biswas deposits 1000 every month in a recurring deposit account for 3 years at 8% interest p.a. Find the matured value: (a) 40400 (b) 40440 (c) 44400 (d) None of these (iii) For a hemisphere of radius 3.5 cm, what would be its total surface are? (a) 115.5 cm (b) 120.5 cm 2 (c) 130.5 cm2 (d) none of these (iv) For a frequency distribution, mean, median and mode are connected by the relation: (a) Mode = 2 Median 3 Mean (b) Mode = 3 Median 2 Mean (c) Mode = 3 Mean 2 Median (d) none of these (v) If x, 6, 18, y are in continued proportion, then the values of x and y would be: (a) 54 & 2 (b) 2 & 54 (c) 3 & 36 (d) none of these (vi) The sum of first 16 terms of the A.P. 10, 6,2,-2, is: (a) -320 (b) 320 (c) -350 (d) -300 (vii) In what ratio is the join of A(4,3) and B(2,-6) divided by the x-axis? (a) 1:2 (b) 2:1 (c) 2:3 (d) none of these (viii) If cosec A cot A = k, then the value of cosec A + cot A is: (a) 1(b) 1- k (c) 1+k (d) (ix) For 5 items being bought at the rate of 2000 each, discounted at 10% GST of 18% is levied, then what is the total amount paid including GST? (a) 10620 (b) 12620 (c) 14620 (d) None of these (x) The length of AB, from the given figure is: (a) 8 cm (b) 6 cm (c) 4 cm (d) 10 cm (xi) If ax2 + bx + c =0 has equal roots, then c = (a) (b) (c) - (d) (xii) If P(E) denotes the probability of an event E, then: (a) P(E) < 0 (b) P(E) > 0 (c) 0 P(E) 1 (d) -1 P(E) 1 (xiii) ABCD is a cyclic quadrilateral. If BAD = (2x+5)0 and BCD = (x+10)0, then x is equal to: (a) 650 (b) 450 (c) 550 (d) 50 (xiv) On dividing 2x3 +3x2 -ax +5 by x-2, it leaves a remainder 7, then what is the value of a? (a) -13 (b) 10 (c) 13 (d) None of these (xv) Directions: In the following question, a statement of Assertion (A) is given followed by a corresponding statement of Reason (R) just below it. Of the statement, mark the correct answer as: (a) A is true, R is false (b) A is false, R is true (c) both A and R are true (d) both A and R are false Assertion (A): 25th term of the A.P. 4, 9 ,14, 19, is 124. Reason (R): nth term of an A.P. is given by an = a + (n-1) d Question: 2 (i) From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and base radius 7 cm is carved out. Find the volume and the total surface area of the remaining solid. [4] (ii) Priyanka has a recurring deposit account of 1000 per month at 10% per annum. If she gets 55550 as interest at the time of maturity, find the total time for which the account was held. [4] (iii) From the top of a lighthouse 100m high the angles of depression of two ships on opposite sides of it are 450 and 300 respectively. Find the distance between the two ships to nearest metre. [4] Question: 3 (i) If x, y and z are in continued proportion, prove that ( ) ( ) = [4] (ii) In the given figure, PAT is tangent at A and BD is a diameter of the circle. If ABD = 280 & BDC=520. Find: (a) TAD (b) BAD (c) PAB (d) CBD [4] (iii) Using (a) Step Deviation Method (b) Short Cut Method calculate the mean marks of the following: Class Intervals 50-55 55-60 60-65 65-70 Frequency 5 24 37 40 70-75 42 75-80 48 85-90 77 [5] SECTION B (Attempt any four questions from this section) Question 4 + 2 3 (i) = find x and y. 2 1 2 80-85 70 [3] (ii) The sum of ages of Vivek and his younger brother Amit is 47 years. The product of their ages in years is 550. Find their ages. [3] (iii) In the given figure, ABC and CEF are two triangles where BA is parallel to CE and AF:AC=5:8 (a) Prove that: ADF ~ CEF (b) Find AD, if CE= 6 cm (c) If DF BC, find area ADF: area ABC [4] Question 5 (i) The daily wages of 80 workers in a project are given below: Wages (in ) 400-450 450-500 500-550 550-600 600-650 650-700 700-750 No. of Workers 2 6 12 18 24 13 5 Use a graph sheet to draw an ogive for the above distribution. (Use a scale of 2 cm = 50 on x-axis and 2cm = 10 workers on y-axis). Use your ogive to estimate: (a) the median wage of the workers (b) The lower quartile wage of the workers. (c) The number of workers who earn more than 625 daily. [5] (ii) A shopkeeper in Dehradun buys an article at the marked price of 24000 from a wholesaler in Delhi. The shopkeeper sells the article to a consumer in Dehradun at a profit of 15% on the basic cost price. If the rate of GST is 12%, find: (a) the price of the article (inclusive of tax, under GST) at which the shopkeeper bought it. (b) the amount of tax, under GST, paid by the shopkeeper to the Govt. (c) the amount of tax, under GST, received by Delhi Govt. (d) the amount of tax, under GST, received by Govt. of Uttarakhand. (e) the amount which the consumer pays for the article. [5] Question 6 (i) If 5th, 8th and 11th terms of G.P. are p, q and s respectively. Show that q2 = ps. [3] (ii) The line joining the points A (2,1) and B (5, -8) is trisected at the points P and Q such that P is nearer to A. If point P lies on the line 2x y + k =0, find the value of k. Also, find the co-ordinates of point Q. [3] (iii) A solid cylinder of silver 9 cm high and 4 cm in diameter is melted and recast into a right circular cone of diameter 6 cm. find the height and the total surface area of the cone. Give your answer correct to one decimal place. (Take =3.14) [4] Question 7 (i) A(-1,3), B(4,2) and C(3,-2) are the vertices of a triangle. (a) Find the co-ordinates of the centroid G of the triangle. (b) Find the equation of the line through G and parallel to AC. [3] (ii) Prove that: [3] + = 1+ sec cosec (iii) Mr. Ram Gopal invested 8000 in 7%, 100 shares at 80. After a year, he sold these shares at 75 each and invested the proceeds (including his dividend) in 18%, 25 shares at 41. Find: (a) his dividend for the first year. (b) his annual dividend in the second year. (c) the percentage increase in his return on his original investment. [4] Question 8 (i) Solve the inequation: -2 + 10x 13 + 10 < 24+10x, x Z Write down the solution set and represent it on the real number line. [3] (ii) When the polynomial x3 + 2x2 5ax 7 is divided by x + 1, the remainder is A and when the polynomial x3 + ax2 12x + 6 is divided by x 2, the remainder is B. Find the values of a , if 2A + B =6 [3] (iii) A 1.4 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 91.4 m from the ground. The angle of elevation of the balloon from the eyes of the girl at that instant is 60 0. After sometime, the angle of elevation reduces to 30 0. Find the distance travelled by the balloon during the interval. Take 3 = 1.732 [4] Question 9 (i) Using the properties of proportion, find the values of x, when = [3] (ii) A motor boat whose speed is 15 km/h in still water goes 36 km upstream and comes back to the starting point in 5 hours. Find the speed of the stream. [3] (iii) Draw a circle of radius 4 cm. Take a point P outside the circle. Without using the centre of the circle, draw two tangents to the circle from, point P. [4] Question 10 (i) Using remainder theorem, factorise the 3x3+2x2-19x+6 completely. [3] (ii) Cards marked with the numbers from 2 to 101 are placed in a box and mixed thoroughly. On ecard is drawn from this box. Find the probability that the number on the card is: (a) an odd number. (b) a number less than 24. (c) a number which is not a perfect square. (d) a prime number less than 15. [3] (iii) Use graph paper to answer the following questions: (Take 2 cm = 1 unit on both axes) (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 the coordinates of A . (c) B is the image of B when reflected in the line AA . Write the co-ordinates of B . (d) Write the geometric name of the figure ABA B . (e) Name the line of symmetry of the figure formed. [4] -------------------------------------------------------------------------------------------------------------------------------------------------------Prepared by: Tr. M.R. Sachdeva (Maths Master) (www.mangatsir75.blogspot.com)
|
