ICSE MATHEMATICS MODEL PAPER 3

ICSE MATHEMATICS MODEL PAPER 3
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.	Part of a geometrical figure is given in each of the diagrams below. Complete the figures so that the dotted line in each case is the line of symmetry of the completed figures. (Recognisable free hand sketches would be awarded full marks  i.           ii                        iii                    iv [4]
2.	a)If P(x, x +3) is the center of a circle passing through (13,5) and (11,13) find x and hence the coordinates of P.bThe price of a T.V. set inclusive of sales tax is Rs. 13,530. If the rate of sales tax is 10%, find its basic price  [  4]
3.	State which of the following diagrams represents a function : (i) (ii)  (iii) (iv            [4]
4.	B and C have coordinates (3, 2) and (0, 3). Find the image B' of B under reflection in the x axis the image C' of C under reflection in line BB' Calculate the length B' C'           [4]
5.	The C.I on a certain sum of money at 5% p.a. for 2 years is Rs. 984. What will be the S.I. on the same sum for 3 years at 8% p.a.?    [4]
6.	[2]b                                  [2]
7.	A man invests Rs. 8208 in a company paying 8%, when a Rs. 100 share quotes at a premium of 8%. Find : The number of shares bought Annual income Percentage income                                                [4]
8.	ABCD is a parallelogram and P is any point on AB. PD cuts AC at Q. Prove that AP : AB = AQ : CQ                                           [4]
9.	In the adjoining figure, AB is the diameter of a circle with center O and CD || BA. If Ð CAB = xo, find the values of : РCOB РDOC РDAC РADC                     [4]
10.	a)What should be subtracted from 23, 30, 57 and 78 so that the remainders may be in proportion? b)The mean of 5 numbers is 15. If one number is excluded, the mean becomes 12.5, find the excluded number             [4]
SECTION - B [40 Marks] Answer any FOUR questions in this section
11a	A page from the passbook of Praveen Dhillon saving bank account in a particular year is given below: Date Particulars Withdrawals Rs. P. Deposits Rs. P. Balance Rs. P. 2000         Jan 1 By balance – -- 1,500.00 "  " 5 By cash – 1000.00 2,500.00 "  " 20 By cheque     500.00 – 2,000.00 Feb 15 By cash – 1,200.00 3,200.00 "  " 27 By cheque    700.00 – 2,500.00 May  8 By cheque 1,000.00 – 1,500.00 "  " 15 By cash – 700.00 2,200.00 June 3 By cash – 1,500.00 3,700.00 "  " 14 By cash – 700.00 4,400.00 "  " 28 By cheque 1,200.00 – 3,200.00 Aug 12 By cash – 2,000.00 5,200.00 "  " 30 By cheque 1,300.00 – 3,900.00 Nov 1 By cash – 600.00 4,500.00 Nov 20 By cash – 1,000.00 5,500.00 Dec 8 To cheque 1,200.00 – 4,300.00 "  " 20 By cash – 2,000.00 6,300.00 Calculate the interest earned by Praveen Dhillon at the end of the year, if the rate of interest is 6% p.a. payable in December       [5]
11b	At a shooting competition, the scores of a competitor were as given below : Score 0 1 2 3 4 5 No. of shots 0 3 6 4 7 5 What was his modal score? What was his median score? What was his total score? What was his mean score? [5]
12a. b	The coordinates of the center of a circle are (3x - 2, 3x + 1) and the circle passes through (-2, -1). Find x if the radius of the circle is 10 units and the center has coordinates that are both positive [5]
	A solid metal cartridge is fabricated out of a cone of height 24 cm and base radius 7 cm, mounted on a cylinder of the same radius and height 55 cm. If it weighs 97.02 kg, calculate the total volume of the cartridge and the density of the metal in gm/cm3 correct to the nearest gm.If the cartridge is melted and recast into a solid hemisphere, show that the radius of the hemisphere is equal to :cm  [5]
13a b	The angle of elevation of a flagpole in front of a school when observed from the base of the school is 45°. When the observer stands in front of the pole with the school in the background, he finds the tops of the pole and school at the same angle of elevation of 30°. If the observer is now standing at a distance of 30 m in front of the pole, calculate (to the nearest meter) : the height of the pole the height of the school   the distance between the pole and the school         [5]
	Mr Rohit Sharma is a school teacher whose annual income from salaries for the year 2000-2001 is Rs 96500. He contributes Rs 480 per month to provident fund and pays annually Rs 360 as group insurance and Rs 960 as LIC premium. Calculate his taxable income and the income tax to be paid by him.                            [5]Assume the following rates: 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
14a b	Find graphically, the vertices of the triangle whose sides have the equations 2y - x = 8, 5y - x = 14 and y - 2x = 1 respectively. Take 1 cm = 1 unit on both the axes       [5]
	Without using set squares or protractor, construct a triangle ABC in which AB = 4 cm, BC = 5 cm and ÐABC = Ð1200. Locate the point P such that ÐBAP = 900 and BP = CP. Measure the length of BP.                                                [5]
15a b	Find the length and area of the shaded portion in the adjoining figure. Given OA = OP = OB = OQ = 14 cm.  [5]
	16    Find x                                                             [5]
16a b	In PQR, T is the mid-point of QR and PS  QR. If QR = p, PT = a, PQ = r, PR = q and ST = x. Show that: q2 + r2 = 2a2  +                                                [5]
	D ABC has vertices A(4, 2), B(2, -2) and C(6, -4). AL, BM and CN are the medians through A, B and C touching opposite sides at L, M and N respectively. Find the coordinates of L, M and N, and the length of sides AL, BM and CN.  [5]
17a     b	Draw a quadrilateral ABCD with AB = 5 cm, BC = DC = 6 cm, AD = 3 cm and internal ÐA = 600. Draw the bisectors of ÐA and ÐB and let them intersect at P. Measure and note the lengths of PA and PB Prove that P is equidistant from AD and BC.   [5]
	Using factor theorem find whether (x + 2) and (x - 3) are factors of the polynomial x3 - 3x2 - 4x + 12. If yes, factorise the given polynomial.  [5]