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ICSE Prelims 2018 : Mathematics Set A (Smt. Sulochanadevi Singhania School, Thane)

4 pages, 51 questions, 43 questions with responses, 112 total responses,

Pandurang Pai
Smt. Sulochanadevi Singhania School, Thane

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SMT. SULOCHANADEVI SINGHANIA SCHOOL, THANE Class Subject Exam Date Marks Time 10 Mathematics Prelim 12.01.2018 80 2 Hrs. Total No. of printed sides 4 Set A General Instructions: 1. Attempt all questions from section A 2. Attempt any 4 complete questions from section B 3. All working, including rough work must be clearly shown and must be done on the same sheet as the rest of the answer. 4. Omission of essential working will result in loss of marks. 5. Mathematical tables are provided. SECTION A (40 MARKS) Attempt all questions from this section Question 1 A) Given A = [ ] find the value of m if A2 = 6A mI where I is an identity matrix of order 2 x 2. [4] B) Solve the following quadratic equation and give your answer correct to 2 significant figures: [3] C) Prove the following identity : [3] Question 2 A) A shopkeeper purchased an article for Rs.7500 and sold it to a customer. If the rate of VAT charged is 10% and the shopkeeper paid a VAT of Rs.150 to the Government. Find i) The price paid by the customer inclusive of tax ii) The profit % made by the shopkeeper. [3] B) Ms. Rita deposits Rs.500 every month in a cumulative deposit account and receives Rs.6455 at the end of one year. Find the rate of interest per annum. [3] C) If is a factor of , find the values of a and b.[4] Question 3 A) Solve the following linear inequation and represent the solution on the number line [3] B) The following numbers are arranged in ascending order. If their mean and median are the same find the value of p and the mean. 37, 41, p +2, p+8, 51, 55. [3] 2 C) The sum of n terms of an AP is 3n + 2n. Find the first term, common difference and the tenth term of the AP. [4] Question 4 A) In ABC, BAC = 90 also AD is perpendicular to BC. i) ii) iii) Prove that ADB CDA. If BD =18cm, CD = 8 cm find AD. Find the A( ADB) : A ( CDA) [3] B) A wooden toy is in the shape of a right-circular cone mounted on a hemisphere. If the radius of the cone is 1.5 cm and the volume of the toy is 28.26 cm3, find the height of the toy. (take = 3.14) [3] C) In the adjoining figure AB is the diameter of a circle with centre O. and . find , and . [4] SECTION B (Attempt any four complete questions from this section) Question 5 A) There are 2 dice, one red and the other black. Both are rolled simultaneously. Find the probability of the following: i) The number on the black dice is either 2 or 4 ii) Getting an even doublet iii) The product of the numbers in both the dice is at most 10. [3] B) Find matrices A and B if A + B = [ ] and A B = [ ] [3] C) Plot the points A (4,6); B (1,3) and D (7,3). Reflect A in the line BD to get an image C. i) Write the coordinates of C. ii) Assign a geometrical name for the figure ABCD. iii) Find the area of the figure ABCD. [4] Question 6 A) Given a GP with the first term 729 and the 7th term 64, find the common ratio and the sum of the first seven terms. [3] B) Eight solid iron spheres are dropped in to a cylindrical jar of diameter 24 cm containing water. If the water level rises by 2 cm, calculate the radius of the sphere. [3] C) Find the ratio in which the line divides the line segment joining the points P (2, -2 ) and Q (3, 7) and hence find the coordinates of point of intersection. [4] Question 7 A) If -5 is the root of the quadratic equation the value of m. Also find the value of if ( has equal roots. ) , find [3] B) In the adjoining figure a circle with centre O passes through A, B and C. AB is the diameter and PBT is the tangent at B. i) If = 35 , find ii) If AP = 15cm and the length of the tangent PB is 9 cm, find the radius of the circle. [3] C) If the mean of the 50 observations given below is 15.5, find the values of a and b . [4] Class Interval Frequency 0-5 5 -10 10 -15 15 20 20 25 25 - 30 2 7 18 a 8 b Question 8 A) Sanjay buys 120 Rs.50 shares at a premium of 30% i) What is his investment? ii) If the rate of dividend is 12.5%, find his annual income. iii) If he wants to increase his income by Rs.50, how many extra shares should he buy. [3] D C B) In a parallelogram ABCD, E is a point D on AD and CE produced meets BA produced at F. E If AE = 4cm, AF = 8cm and AB =12cm, find the perimeter of the Parallelogram ABCD. [3] F A B C) i) ii) iii) Construct a ABC with BC = 6cm = 45 and AB = 4.8cm. Construct a circumcircle for the ABC. Locate points X and Y on the circumcircle which are at a distance of 1.8 cm from BC. [4] Question 9 A) If a, b, c are in continued proportion, prove that ( )( ) . B) The Weights (in Kg) of the students in a class are as follows: Weight (In Kg) 50 53 46 54 48 No .of students 8 8 7 2 5 Find the median, upper quartile and the mode of the above data. [3] 55 1 52 9 [3] C) From the top of a tower AB of height 120 m , the angle of elevation of the top and the angle of depression of the bottom of another taller tower CD are 45 and 24 respectively. Find the distance between the two towers and the height of the tower CD. [4] Question 10. A) Train A travels a distance of 264 km at a certain speed. Train B travels 8Km/hr faster than train A and takes 22 minutes less. Find the speed of train B. [4] B) The following table shows the monthly income (in thousands) of a certain number of workers in a factory. Monthly income 20-25 (in thousands) No. of workers 40 25 -30 30 -35 35 -40 40 -45 45 50 50 -55 68 86 90 40 26 120 Draw an Ogive and estimate the following: i) Median income ii) The number of employees earning more than Rs.42000 iii) Find the number of workers who belong to the lower quartile income group. [6] Question 11 A. If the line through A ( 3, -7) and B ( 4, 2) is perpendicular to the line value of B. Using properties of proportion solve for C. In the given figure, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. IF CD = 3.5 cm, DP = 4.5 cm, BP = 3 cm, find the radius of the circle and the length of the tangent PT. [3] = find the [3] [4]

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