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ICSE MATHEMATICS MODEL PAPER 2

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 man borrows Rs. 6000 at 5% interest compounded yearly. If he repays
Rs. 500 at the end of each year, find his loan outstanding at the beginning of the fourth year       [4]
2. Mr Kumar opened a savings account in Punjab National Bank on 3rd January 1999 with Rs 5000. His transactions during the year 1999 were as under:
January 12, deposited Rs 3718·46 by cheque
February 7, deposited Rs 2000·00 by cash
May 16, withdrew Rs 4102·50 by cheque
June 3, withdrew Rs 1500·00
June 26, withdrew Rs 700·00
August 13, deposited Rs 6726·80 by cheque
September 10, deposited Rs 3000·00 by cash
November 4, withdrew Rs 2500·00
Write the entries in his passbook. He closed his account on 19th December, 1999. If the bank paid interest (computed annually) at 5·5%, find the amount he received on the day of closing his account.        [4]
3. A man invest Rs. 10780 in 2 companies by investing part in 7% Rs. 100 shares at Rs. 98 and the balance in 8% shares at par. If the dividend income received in both cases is equal, find his investments in each company [4]
4. Taking x as the variable, write an inequation from the following graphs:

a)
ima-linear07-3.gif (822 bytes)       

b)

Find the range of valus of x which satify the inequality

- 1/5 Ł 3x/10 + 1 < 2/5 ; x e R                         [4]
5. wpe13.gif (2035 bytes)                [4]   
6. a)If f(x) = x2 + 2x + 1,   find f(x + 1). If f(x) = f(x + 1), find x.

b)The mean of the numbers, 6, y, 7, x, 14 is 18. Express y in terms of x.    [4]
7. a)Given, 5 cos A - 12 sin A = 0, evaluate without using tables
    sin A + cos A   
   2 cos A - sin A

b)Prove that (1 + cotq - cosecq)(1 + tanq + secq) = 2      [4] 
8. a)If A = (8, 6) and B = (-2, 4) find the coordinates of a point C on the X-axis such that C is equidistant from A and B.

b)Find the equation of the right bisector of the line segment joining the points P(4, -3) and Q(6, -5).                                                [4]
9. In the adjoining figure, ABC is a right angled triangle with AB = 6 cm, and BC = 8 cm. A circle with center O has been inscribed inside the triangle. Calculate the value of x, the radius of the inscribed circle.

 

[4]

 ima-circles11.gif (1003 bytes)
10. State whether true or false :
  1. An angle having equal arms has two lines of symmetry which are the perpendicular bisectors of the equal arms that include the angle.
  2. An isosceles triangle has two lines of symmetry : one which is the perpendicular bisector of the unequal side, and the other which is the bisector of the angle included by the equal sides.
  3. An equilateral triangle has 3 lines of symmetry and one point of symmetry.
  4. An isosceles triangle has lines of symmetry which are the bisectors of the equal angles of the triangle.
  5. A parallelogram with all sides equal and no angle equal to 900, has two lines of symmetry.
  6. A parallelogram with two lines of symmetry has to have at least one internal angle equal to 900.[4]

SECTION - B [40 Marks]

Answer any FOUR questions in this section

 
11.a

  

b

 Draw a circle with radius 3 cm and centre O. Take a chord PQ = 4 cm. Draw a tangent to the circle at P. Measure [the acute angle between the tangent and chord PQ   [5]   
Find x from the following equations :
                      
(i) a +x +a -x   = c                                                       
   a + x -a - x      d
[5]
12a 

  

b

 Given (x - a) is a factor of  f(x) = x3 - 4x2 - x + a, find the value of a and hence the remaining factors of f(x).[5]
The two triangles shown in the adjoining figure are similar. If AB and PR are not parallel, and BR = 4, AQ = 3, AP = 12 and PR = 15, calculate :
  1. Length of QB
  2. Ratio of areas of D's ABQ and PQR.[5]

 

 prob18.gif (1747 bytes)
13a

   

 

b

 Draw a horizontal line AB = 6 cm. Locate a point C which is at a distance of 2 cm from A, towards B and 1 cm above the line AB. Similarly, locate a point D which is 3 cm away from B towards A and 2 cm above AB. Locate a point P which lies on AB and is equidistant from C and D. Measure and note the distance AP.[5]
  1. A furniture shop marks a dining room set at Rs. 35000.00.
    The present taxation structure is as follows :
    • Sales Tax @ 12%
    • A surcharge of 10% of the sales tax amount
    • A turnover tax @ 1% of the net bill value of Rs. 35000.00

Find the total value a customer would have to pay for the dining set.[5]
14a

    

 

 

 

 

b

 A gas tank is made by joining a cone to a hemisphere of radius 3 m as shown in the figure. If the volume of the hemisphere is one and a half times that of the cone, calculate the height of the cone and the surface area of the tank. Also, find the volume of gas that the tank can hold.

[5]

       cylinder09.GIF (2864 bytes)
IA point P moves in a plane such that its distance from another point Q is always 7 cm. If the point P moves from its starting position in the plane, say P1, a distance of 44 cms and halts at point P2, what is the distance between P1 and P2?    [5]    
15a  

 

 

 

 

b

 In the following figure, D and E are mid-points of the sides BC and CA respectively of a ABC, right angled at C. Prove that

4(ADČ +BEČ) = 5ABČ
[5]
From the table given below, derive the equation of the line and draw its graph. From the graph, find the values of p and q.                                                                                    
x 1 p 4 -1
y 1 7 10 q

[5]

16a

 

 

 

 

b

 The angle of elevation of the top of a tower from two points as shown in the figure are complimentary. Prove that the height of the tower equals the square root of the product of the distances of the two points from the tower.
[5]		 prob20.gif (1919 bytes)
The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hours and 30 minutes. Find the speed of the stream
[5]
17a In a public collection towards erection of a memorial, 1000 people contributed sums of money varying from Re. 1 to Rs. 103 (in units of Re. 1). The following table gives the frequency distribution of contribution :

 
Contribution No. of people
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100		 30
60
80
170
200
180
140
70
40
30

Using a suitable scale, draw on graph paper an ogive (cumulative frequency graph) and use it to answer the following questions :

  1. Estimate the median
  2. If it is agreed to allow only those who contributed Rs. 45 or more to attend the unveiling ceremony, what percentage would attend?  [5]
b Mr Raunak Singh is an administrative officer in LIC. His annual income (excluding HRA) in financial year 2000-2001 is Rs 191734. He contributes Rs 875 per month to provident fund, and pays Rs 260 per month as LIC premium. He buys National Savings Certificates worth Rs 40000 and contributes Rs 12000 in mutual fund. He donates Rs 2500 in Prime Minister relief fund (eligible for 100% deduction U/S 80G) and Rs 500 to a charitable trust (eligible for 50% deduction U/S 80G). If Rs 1000 per month has been deducted by the employer as income tax at source in the first 11 months, find his taxable income and the balance of the income tax he shall has to pay in the last month       (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

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