ICSE MATHEMATICS MODEL PAPER 4

ICSE MATHEMATICS MODEL PAPER 4
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 will result in loss of marks. Time: 21/2 Hours] (max. Marks : 80)
SECTION - A [40 Marks] Answer ALL questions in this Section
1.a b	(3 Marks)
	If f(x) = 3x + 2 and the domain D = {-2, -1, 0, 1, 2}, then : find the range classify the function giving reasons for your answe      (  3 marks)
2	y + 2x = 0 is the equation of a line in the coordinate plane. Write the equation of the image of this line in the x axis the y axis the origin.                                                                                      (  4 marks
3ab	The area enclosed between two concentric circles is 770 cm2. Given that the    radius of the outer circle is 21 cm, calculate the radius of the inner circle.                 (  3 marks)
	Which is a better investment :   7% Rs. 100 shares @ Rs. 120 or 8% Rs. 10 shares @ Rs. 13.50 ?                                                      (  3 marks)
4.a b	, prove that x2 – 4ax + 1 =                                         (  3 marks)
	(  3 marks)
5	A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 m/sec. Calculate in minutes the time it takes to fill the tank                          (  4 marks)
6.	In the diagram, PR and QA are parallel.Prove that : PS : QR = SQ : QA PO : SO = OQ : OR  (  4 marks)
7	n the adjoining figure, ABCD is a cyclic quadrilateral in which ÐBAD = 75o, Ð ABD = 580,and ÐADC = 770. Find РBDC РBCD РBCA  (  4 marks)
8ab	If 3, 8, 10, x, 14, 16, 18, 20 are in ascending order and their median is 13, calculate the numerical value of x.                                                                               (  2marks)
	List the solution set of 30 - 4(2x - 1) < 30, given that x is a posititive integer.                                                                                                                (  2marks)
SECTION - B [40 Marks] Answer any FOUR questions in this section
9a	In DABC, point P lies on the intersection of bisectors of angles A and B. Prove that if a circle is drawn with center P and radius equal to the distance of P from side AB, the circle will touch sides AB, AC and BC tangentially                                              (  5marks)
9 b	The following is a set of marks obtained by 100 pupils in an examination (with maximum marks 100) : Marks Group Frequency 1 - 10 11 - 20 21 - 30 31 - 40 41 - 50 51 - 60 61 - 70 71 - 80 81 - 90 91 - 100 4 6 7 16 25 21 12 5 3 1 Using a suitable scale on graph paper draw a cumulative frequency curve to represent the given data and use it to estimate the following : the median the lower quartile the upper quartile                                                                        (  5 marks)
10.a   b	A sum of Rs. 36000 is lent out for 2 years at compound interest, the rate being 10% for the first year and 12% for the second year. A part of the loan is returned at the end of the first year and on making a payment of Rs. 22400 at the end of the second year the complete loan is repaid. What was the amount repaid at the end of the first year?(  5 marks)
	In the adjoining figure a surveyor standing at point A on a river bank observes the angles between B and E on the opposite bank to be 60°. He then walks to point C 50 m upriver and observes angle DCE to be 45°. Calculate the width of the river and the distance between B and E.(  5 marks)
11a	Mrs. Ram is a teacher in a public school. Her annual salaried income is Rs 1,16,760. She donates Rs 1,001 to the Prime Minister's Relief Fund, which has 100% tax exemption. She contributes Rs 2,562 per month to her P.F. account, pays an annual premium of Rs 7,376 towards her Life Insurance Policy. Calculate the income tax paid by Mrs. Ram if her earlier deductions for the first eleven months of income tax were at the rate of Rs 145 per month.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                                                                                                              (5 marks)
11b	A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8 : 5, show that the ratio of radius of cylinder to height of cylinder is 3 : 4.(  5 marks)
12ab	Mr. Jacob has a 5 year R.D. A/c in the Bank of Baroda and deposits Rs.2,400 per month. If he receives Rs.1,82,090 at the time of maturity, find the rate of interest.   (  5 marks)
	he cost of manufacturing x articles is Rs. 20 + 2x. The selling price of x articles is Rs. 2.5 x. On a graph sheet, with the same axes, draw two graphs, first for the cost of manufacture against number of articles and the second for the selling price against number of articles. Take 2 cm = 10 articles on one axis and 2 cm = Rs. 20 on the other axis. Provide for x upto x = 80. Use the graph to determine : Number of articles to be manufactured and sold at break-even (No profit no loss) ; The profit made when 60 articles are manufactured and sold(  5 marks)
13a b	Construct  ABC such that AXB = 116o, AB = 7.8 cm, CF = 5 cm, CF  AB. X is the point of intersection of the altitudes                        ( 5 marks)
	Marks obtained by 70 students are given below: Marks 20 70 50 60 75 90 40 No. of students 8 12 18 6 9 5 12 Find: (i) the median marks, (ii) the modal marks                                                                                         (   5 marks)
14a    b     c	A rectangle with one side 4 cm is inscribed in a circle of radius 2.5 cm. Find the area of the rectangle                                                                              (   3marks)
	A music shop has a sound system marked at Rs. 14000 on which a sales tax of 12% is chargeable. What discount must be offered on the marked price such that a customer finally pays Rs. 14000 including sales tax.                                           (   2marks)
	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.                                                                               (   5marks)