ICSE MATHEMATICS MODEL PAPER 5

ICSE MATHEMATICS MODEL PAPER 5
Answer all quetions in Section A and any four question from Section B. You will NOT be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. All working, including rough work, must be clearly shown and must be done on the same sheet as the right of the answer. Omission of essential working wilresult in loss of marks . Time: 21/2 Hours] (max. Marks : 80)
SECTION - A [40 Marks] Answer ALL questions in this Section
1.	A sum of Rs. 69,300 is to be divided between two boys A and B, 21 and 22 years old respectively, in such away that, if their portions be invested at 10% per annum compound interest; they shall receive equal amounts on reaching 24 years of age. i) What is the share of each in the money ? ii) What will each receive, when 24 years old              (3 marks)
2.	a)A triangle whose area is 12 square cm is transformed under enlarged about a point in space.The area of its image is 108 cm2 Find the scale factor of enlargement. b)If a matrix has 12 elements what are the possible order it can have c)Construct  a 3X4matrix  whose elements are aij=i+j                               (   5 marks
3.	Find the allitude of a right cirular cone ,diameter of this cone is 1.5  times of radious of sphere and this circularcone is inscribedin a sphere of  radious r      (4marks)
4.	Points A (O, - 4) & B (O, 2) are invariant under reflection in line L1 points C (2,0 ) & D ( -3, o) are invariant under reflection in line L2. i ) Name & write the equations of the lines L1 & L2. i i ) Name & write co-ordinates of the point which is invariant under reflection in both the lines L1 & L2 iii) Reflect A in the line y=x & write the co-ordinates of the inage A1. iv) Reflect B in y=x & write co-ordinates of B1 the image. v) Name figure so formed by joining AB A1 B1 vi ) Does it have any line symmetry. If yes, then draw & state how many.      ( 6 marks)
5.	Complete the above given figure in such a way that, both the x-axis and y-axis are lines of symmetry. (3marks)
6.	Solve the following equations graphically : x - y =  -1 ; 2x - 3y = 1. Measure and note the distance of the point of intersection from the origin Verify your answer in (ii) above with a proof.        ( 3marks)
7.	a)Evaluate the following (without using tables) 2 cos 67°     -      tan 40°       -      sin 90°     sin 23°              cot 50°         b)Prove that (1 + cotq - cosecq)(1 + tanq + secq) = 2. c)The mean of 1, 7, 5, 3, 4 and 4 is m. The numbers 3, 2, 4, 2, 3, 3 and p have mean m - 1 and median q. Find p and q.                     ( 6 marks)
8.	Radius of a circle is 20m. By drawing three concentric circles inside this circle, its area is divided into 4 equal parts. Find the radius of each of the new circles drawn ( = 3.14)                                          (   3 marks)
9.	In the adjoining figure, O is the center of a circle. Chord CD is parallel to the diameter AB. If РABC = 25o, calculate Ð CED. (3marks)
10.	A set of rectangles is such that each rectangle has a width of 5 cm.The lengths vary and are represented by x cm, where x Î R. The largest rectangle has an area of 25 cm2 . Define completely the relation between the area A of the rectangle and its length x State the domain of the relation State the range of the relation Is the relation a function.                     ( 4 marks)
SECTION - B [40 Marks] Answer any FOUR questions in this section
11a	A page from a saving bank passbook for the year 2000 is given below. Calculate the interest at the end of the year at the rate of 5% p.a. Date Particulars Amount withdrawn Rs. P. Amount deposited Rs. P. Balance Rs. P.           2000         Jan 1 By balance – 1,120.00 1,120.00 11 By cash –    800.00 1,920.00 Feb 2 To cheque 300.00 – 1,620.00 Mar 10 By cash – 1,400.00 3,020.00 June 28 To cheque 500.00 – 2,520.00 Sept 5 By cash –    480.00 3,000.00 Dec 13 By cash – 1,200.00 4,200.00
11b	A man invests Rs. 48000 in 20% Rs.100 shares at Rs. 120. When the shares rise to Rs. 140 he sells enough shares to purchase a washing machine for Rs. 7000. Find (a) his original number of shares (b) Shares remaining (c) original annual income.
12a. b	A circle with centre O. AB and CD are two parallel chords on the same side of the centre. If the radius of the circle is 65 cm and the length of the chords are 112 cm and 126 cm respectively, find area of rectangle ABCD.
	A rectangular block of granite, 1 m x 4 m leans against a vertical wall forming an angle of 300 with the horizontal as shown in the figure. Find the height of the highest point of the block from the ground.
13a b c	The number of match sticks in 40 boxes, on counting was found as given below : 44 41 42 43 47 50 51 49 43 42 40 42 44 45 49 42 46 49 45 49 45 47 48 43 43 44 48 43 46 50 43 52 46 49 52 51 47 43 43 45 Taking classes 40 - 41, 42 - 43, etc, construct the frequency distribution table for the above data. Draw a histogram to represent the above distribution.
	The length of a line AB is 10 units. If the coordinates of A are (0, -1) find the coordinates of point B if its abscissa is 12.
	Mrs. Basu paid Rs 650 for a locket including sales tax at 4%. What was the list price of the locket?   (Marks 2)
14a b	A cone with base radius 15 cm and height 8 cm is inverted and filled to the brim with water. Spherical steel balls each of radius 0.5 cm are dropped into the water. It is found that one-fourth of the water flows out. Find the quantity of steel balls dropped into the water.
	If the bisector of an angle of a triangle bisects the opposite side,prove that the triangle is isosceles.
15a	Given  f(x) = x3 + ax2 + bx + c. When f(x) is divided by (x + 2), the remainder is 8; (x+ 1) is a factor of f(x) and f(0) = - a. Find the expression and hence factorise it completely
	Miss Shubh Lakshmi is a bank employee. She gets Rs 8200 per month as salary. She contributes Rs 350 per month towards provident fund and pays Rs 1200 annually as LIC premium. If she deposits Rs 3000 in 10 years CTD account of post office, calculate her taxable income and the income tax to be paid by her for the assessment year 2000-2001. Assume the following rates:                                              (   5 marks) a) Standard deduction: 1/3rd of total income subject to a maximum of Rs. 20,000. (Rs. 25,000 if income is less than Rs. 1 lakh.) b) Rate of tax SLAB i) Up to Rs. 50,000 ii) from Rs. 50,001 to Rs. 60,000 iii) from Rs. 60,001 to Rs. 1,50,000 iv) from Rs. 1,50,001 onwards INCOME - TAX Nil (10% of the amount exceeding Rs. 50,000) Rs. 1,000 + 20% of the amount exceeding Rs. 60,000 Rs. 19,000 + 30% of the amount exceeding Rs. 1,50,000 c) Rebate in tax 20% of the total savings subject to a maximum of Rs. 12,000 d) Surcharge 10% of the tax payable
16a b	the adjoining figure, РPQR = Ð PRS. Prove that the triangles PQR and PRS are similar. If PR = 8 cm, PS = 4 cm, calculate PQ.
	For the following frequency distribution, calculate (i) the mean; (ii) the median; (iii) the mode : Class Frequency 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 2 7 18 10 8 5
17a b	In the adjoining figure, chords AB and CD of a circle intersect at E.Prove that the triangles ADE and CBE are similar Given that DC = 12 cm, DE = 4 cm and AE = 16 cm, calculate BE.
	If x/a = y/b = z/c, prove that