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ICSE Class X Prelims 2025 : Mathematics (Wisdom World School, Hadapsar, Pune) : Mathematics Mid-Term

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Wisdom World School, Hadapsar, Pune

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WISDOM WORLD SCHOOL Kumar Picasso, Hadapsar First Preliminary Assessment 2024-25 Date: 18.12.2024 Reading Time: 10 min Std: X Max. Marks: 80 Writing Time: 3 hours SUBJECT: MATHEMATICS General Instructions: Answers to this Paper must be written on the answer sheet provided by the school. You will not be allowed to write in the first 10 minutes. This time is to be spent in reading the Question Paper. SECTION A (Attempt all questions from this section) Question 1 [15] Choose the correct answer from the options given below: (Do not copy the questions, write answers only) i) The probability of getting a sum of 13, when a pair of dice is rolled is: a. 0 b. c. 1 12 1 13 1 d. 11 ii) If 5 4 a. b. c. d. 4 1 3 > 1, , then largest value of x is: -6 -8 -9 -7 Page 1 of 11 iii) The point (3,5) on reflection in the line = 1 is mapped onto P , the coordinates of P is: a. b. c. d. (2,1) ( 3,1) (3, 6) (3, 7) iv) If 2 , + 10 and 3 + 2 are in AP, then = a. 0 b. 2 c. 4 d. 6 v) The point of intersection of the perpendicular bisectors of the sides of a triangle is called: a. b. c. d. vi) The centroid of triangle ABC is ( 1,4). If A is (5, 6) , B is ( 2,3). Then coordinate of C is: a. b. c. d. vii) Orthocentre Incentre Circumcentre Median ( 6,15) (6, 15) ( 6,5) (6, 5) Which among the following cannot be determined graphically for a grouped frequency distribution? a. Median b. Mode c. Interquartile d. Mean Page 2 of 11 viii) For an intrastate sale, the CGST paid by a dealer to the central government is Rs.120. If the marked price of the article is Rs.2000, the rate of GST is: a. b. c. d. ix) 6% 10% 12% 16.67% A rectangular sheet of size 11 cm X 7 cm is first rotated about the side 11 cm and then about the side 7 cm to form a cylinder, as shown in the diagram. The ratio of their curved surface areas is: a. 1:1 b. 7:11 c. 11:7 d. x) 11 7 7 : 11 Construction of cumulative frequency distribution table is useful in determining the: a. b. c. d. Mean Median Mode All the three measures. Page 3 of 11 xi) ABCD is a cyclic quadrilateral such that AB is a diameter of the circle cicumscribing it and angle ADC= 1400, then angle BAC is equal to: a. b. c. d. xii) 800 400 500 300 Which of the following is/are a quadratic equation? 1. ( + 2)( + 3) = 2 2 3 2. 2 + 3 = ( 1)(1 3 ) 3. ( + 2)2 = 2( + 3) a. b. c. d. xiii) Only 1 Only 3 Only 2 and 3 All 1,2 and 3 Assertion (A): 5, 5 2 5 , 0, 2, is an Arithmetic Progression. Reason (R): the terms of an AP cannot have both negative and positive terms. a. Both assertion and reason are correct, and Reason is the correct explanation of Assertion. b. Both assertion and reason are correct, and Reason is not the correct explanation of Assertion. c. Assertion is correct but reason is incorrect. d. Assertion is incorrect but reason is correct. Page 4 of 11 xiv) Assertion (A): The curved surface area of a cylinder with radius 2cm and height 10 cm is 40 cm2. Reason (R): The volume of cone is one third of the volume of the cylinder if their height and radius have same measure. 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 xv) ( + )(1 ) is equal to: a. secA b. sinA c. cosecA d. cosA Question 2 i) ii) iii) In the adjoining diagram, a tilted right circular cylindrical vessel with bas diameter 7 cm contains a liquid. When placed vertically, the height of the liquid in the vessel is the mean of two heights shown in the diagram. Find the area of wet surface, when the cylinder is placed vertically on a horizontal surface. If + = , then prove that 2 1 2 +1 = If a, b,c and d are in continued proportion, prove that: + = ( + )( + ) Page 5 of 11 [4] [4] [4] Question 3 i) The sum of the three numbers in G.P. is 39 10 and their product is 1. Find the [4] numbers. ii) The following bill shows the GST rate and the marked price of items: [4] S.No Item Marked Price (Rs.) Quantity (kg) Rate of GST 1 Flour 35 5 x% 2 Rice 180 5 5% 3 Surf Excel 220 y 18 % Find: a. the value of x if the total GST on flour and rice is Rs.45 b. the value of y, if CGST paid for detergent powder is Rs. 39.60. c. total amount to be paid including GST for the above bill. iii) Use graph paper for this question: a. Plot the points (0,5), (2,5), (5,2), (5, 2), (2, 5) (0, 5). b. Reflect the points B, C, D and E on the Y axis and name them respectively as B , C , D and E . c. Write the co-ordinates of B , C , D and E . d. Name the figure formed by BCDEE D C B . [5] Section B Attempt only four questions from this Section Question 4 i) Solve the linear inequation, 1 1 1 5 3 3 2 2 2 where x is a positive odd integer. a. Find the minimum value of . b. Write the solution set. c. Draw the number line representing the solution set. Page 6 of 11 [3] ii) Determine whether the following quaratic equation has real roots. 5 2 9 + 4 = 0 a. Give reasons for your answer. b. If the equation has real roots, identify them. [3] iii) In the given figure, O is the centre of the circle and AB is a tangent to the circle at B. If = 550 . a. Find the value of the angles x, y and z. b. Prove that RB is parallel to PQ. [4] Question 5 i) The mean of the following distribution is 62.8 and the sum of all frequencies is 50. Find the missing frequencies a and b. C.I. 0-20 20-40 40-60 60-80 80-100 100-120 Frequencies 5 a 10 b 7 8 Page 7 of 11 [3] ii) A man deposits Rs.200 per month in a recurring deposit account at 9% p.a. and earned a total interest of Rs. 1764. How many instalments did he pay? [3] iii) A bag contains 13 red cards, 13 black cards and 13 green cards. Each set of cards are numbered from 1 to 13. From these cards a card is drawn at random. What is the probability that the card drawn is a : a. green card b. a card with even number c. a red or black card with a number which is multiple of three? d. A prime number card. [4] Question 6 i) Using Remainder Theorem factorize the following polynomial: 2 3 + 2 13 + 6 [3] ii) Draw histogram from the given distribution table. Estimate the mode graphically. [3] Class Interval 11-20 21-30 31-40 41-50 51-60 iii) Frequency 5 8 13 10 6 In the adjoining figure, AC is the diameter of a circle with centre O. If CD//BE, = 800 , = 100 , find : i. ii. iii. Page 8 of 11 [4] Question 7 i) A solid metallic cylinder is cut into two identical halves along its height (as shown in the diagram). The diameter of the cylinder is 7cm and the height is 10 cm. Find : a. The total surface area (both the halves). b. The total cost of paining the two halves at the rate of R. 30 per cm2. [4] ii) Using a graph paper, draw an ogive for the following distribution which shows a record of the weight in kilograms of 200 students. [6] Weight Frequency 40-45 5 45-50 17 50-55 22 55-60 45 60-65 51 65-70 31 70-75 20 75-80 9 Use ogive to estimate the following. i. Median ii. The percentage of students weighing 55 kg or more. iii. The weight above which the heaviest 30 % of the students fall. iv. Interquartile range. Page 9 of 11 Question 8 i) The scale map is 1: 50,000. In the map, a triangular plot ABC of land has the following dimensions: = 2 , = 3.5 and the angle = 900 . [3] Calculate: i. the actual length of side BC, in km of the land. ii. The area of the plot in sq. km. ii) Find a point P which divides internally the line segment joining the points ( 3,9) and (1, 3) in the ratio 1: 3. [3] [4] iii) 0 Use ruler and compass to answer the question. Construct = 90 , where = 6 , = 8 . a. Construct the locus of points equidistant from B and C. b. Construct the locus of points equidistant from A and B. c. Mark the point which satisfies both the conditions of (a) and (b) as O. Construct the locus of the points keeping a fixed distance OA from the fixed point O. d. Construct the locus of points which are equidistant from BA and BC Question 9 i) (0,0), (3,5) and ( 5, 3) are the vertices of triangle OAB. i. The equation of median of triangle OAB through vertex O. ii. The equation of altitude of a triangle OAB through vertex B. [3] ii) 5 11 9 5 If + = [ ] and = [ ], find the matrices X and Y. 10 4 2 14 [3] Page 10 of 11 iii) The sequence 2,9,16, is given. a. Identify if the given sequence is an AP or GP. Give reasons to support your answer. b. Find 20th term of the sequence. c. Find the difference between the sum of its first 22 and 25 terms. d. Is the term 102 belong to this sequence? [4] Question 10 i) In the given figure, P is a point on AB such that : = 4: 3 and // . [4] i. Calculate : ii. If = 900 , = 900 and = 6 , calculate the length of . ii) The age of a grandmother is square of her granddaughter s age. Four years ago, she was 15 times the child s age. Find their present ages. iii) Aman has 500, Rs 100 shares of a company quoted at Rs.120, paying a 10% [4] dividend. When the share price rises to Rs.200 each, he sells all his shares. He invests half of the sale proceeds in Rs.10, 12% shares at Rs.25 and the remaining sale proceeds in Rs.400, 9% shares at Rs. 500. Find his: a. sale proceeds b. investment in Rs10, 12% shares at RS.25 c. original income d. change in income. Page 11 of 11 [3]

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