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

5 pages, 53 questions, 39 questions with responses, 81 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 19.01.2018 80 2 Total No. of printed sides 4 Set B 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) The marked price of an article is Rs. 4500 and the rate of tax is 8% . A shopkeeper buys it at a discount and sells it to a customer at marked price. If the shopkeeper pays a VAT of Rs. 72 to the Government. Find the following: i) The price paid by the shopkeeper inclusive of tax ii) The % of discount received by the shopkeeper. [3] B) Mr. Sham opened a cumulative deposit scheme with a bank for 3 years. If the rate of interest is 8 % per annum and the bank pays Rs. 1776 as interest at the time of maturity, find the money deposited monthly and the maturity value he receives at the end of 3 years. [3] ) is a factor of the polynomial C) If ( ) find the value of a and 30 when divided by ( and it leaves a remainder [4] Question 2 A) Solve the following quadratic equation and give your answer correct up to two decimal places : [3] B) Prove the following identity : [3] C) If A = [ ] and B = [ ] find the values of a and b if BA = [ ] [4] Question 3 A) The internal diameter of a hollow wooden hemispherical bowl is 16cm and it is uniformly 1 cm thick. Find the volume of wood used in making the bowl [3] B) In the adjoining figure, chords AB and CD are produced to meet at O. i) Prove ODB OAC ii) Given CD = 2 cm, DO = 6 cm, BO = 3 cm calculate AB. iii) Find the ratio of A (Quadrilateral CABD) to the A ( CAO) [3] C) The age of 10 boys in a group 17, 16, 18, 19, 15, 17, 16, 15, 17 and 18. Find the mean age. If one more boy joins the group, the mean age becomes 17 years. Find the age of the newly joined boy and also find the mode the new group. [4] Question 4 A) Solve the following inequality and represent the solution on a real line : [3] B) The sum of the third and the eleventh term of an AP is 34. Find the sum of its 13 terms. [4] C) In the adjoining circle with center O, AB is the diameter and find and . and [3] SECTION B (Attempt any four complete questions from this section) Question 5 A) A dividend of 9 % was declared on Rs.100 shares selling at a certain price. If the rate of return is 7.5 % calculate : i) The market value of each share ii) The amount to be invested to obtain an annual income of Rs.1260. [3] B) Find the value of m for which the given equation real and equal roots. C) ( ) has [3] photo frames were bought for Rs.6000. Ten of them were damaged during transporting. The remaining were sold for a total profit of Rs.1200 by selling each for Rs.60 more than the cost price. Find the number of frames sold. [4] Question 6 A) A line AB meets x- axis at A and Y- axis at B. The point P (4, -1) divides AB in the ratio 1:2. Find the coordinates of A and B. [3] B) Calculate the mean of the following data by short-cut method: Class Frequency 40-45 5 45-50 12 50-55 20 55-60 16 60-65 10 65-70 8 [3] 70-75 5 75-80 4 C) In the adjoining figure TP and TR are the tangents to the circle with centre O. If and , calculate and [4] Question 7 A) A game of numbers has cards numbered 10, 11, 12, 13, .49, 50. A card is drawn at random, find the probability that the number on the card is i) a perfect square ii) has one of the digit as 3 iii) a number divisible by 3 and 4. [3] B) Given A = [ ] B=[ ] and C = [ A + 2D = 3B + C ] find matrix D such that [3] C) Use ruler and compasses only for the following question : i) Construct ABC in which BC = 6.5cm and AB = 5 cm. ii) Construct the locus of points at a distance of 3.5 cm from A. iii) Construct the locus of the points which are equidistant from AC and BC. iv) Mark two points X and Y which satisfies the above two loci (ii) and (iii) and measure XY. [4] Question 8 A) Sum of how many terms of the GP [3] B) The surface area of a solid sphere is 1256 cm2. It is melted and recast in to cones of radius 2.5 cm and height 8 cm. Calculate : i) The radius of the sphere (Take = 3.14) ii) The number of cones recast. [3] C) Using graph sheet, plot the point P (3, 4) and reflect it to P1 in x - axis. O1 is the image of O (origin) when reflected in the line PP1. i) ii) iii) 1 Write the coordinates of P and O1. Geometrical name and the area of the figure POP1O1 Write the coordinates of a point which is invariant about both the lines PP1 and y = 0. [4] Question 9 A) Prove the following identity : ( [3] ) B) Using properties of proportion solve for : = [3] C) Check whether the line passing through the points A (-2, 3) and B (4, 1) is perpendicular to the line 3x y = 1. Does the line 3x y = 1 bisect the join of A (-2, 3) and B (4, 1). [4] Question 10 A) From the top of a tower 80m high, the angles of depression of two cars standing on the ground in a straight line in the same side of the tower are 32 and 45. Find the distance between the cars. [4] B) The following data is the marks scored by 80 students in an examination: Marks No. of students 0-10 3 10-20 7 20-30 15 30-40 24 40-50 16 50-60 8 60-70 5 70-80 2 Use a graph sheet and draw an Ogive using a scale of 2 cm = 10 units on both the axes. Use the Ogive and estimate the following: i) Median marks ii) Number of students who scored more than 60% of marks iii) Number of students who did not clear the examination if the passing marks were 30 marks. [6] Question 11 A) i) In the given ABC, D and E are points on AB and AC respectively. If AD = 5.6cm, AB = 8.4 cm, AE = 3.8 cm and AC = 5.7 cm. Show that DE BC. ii) Find the measure of BC if DE = 4.8 cm. B) [3] If b is the mean proportion between a and c prove that [3] C) Find the mean of the following data: Marks No. of students Less than 10 7 Less than 20 19 [4] Less than 30 32 Less than 40 Less than 50 42 50

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