ICSE MATHEMATICS MODEL PAPER 2

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ICSE MATHEMATICS
Cambrian Hall Dehradun
December Examination2001

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 : 100)

SECTION - A [52 Marks]

Answer ALL questions in this Section

A sum of Rs9600 is invested for 3 years at 10%per annum at compound intrest.
A) what is the sum due at the end of the first year?
B)what is the sum due at the end of the second year?C)
C)Find the compound intrest earned in 2 years?
D)Find the differnce between the answers in(ii)and (i) and find the intrest on this sum for one year
E)Hence find the compound intrest for the 3rd year. ( 8)

Mohan has a recurring bank account of Rs 250 per month for a period of one year at the rate of 10%p.a. .Find the amount he willreceive at the time of maturity if intrest is calculated at the end of each month. (4)

Points A (5 ,0) & B (-2, 0) are invariant under reflection in line L1 points C (-5,0 ) & D ( 0,2) are invariant under reflection in line L2

. a ) Name & write the equations of the lines L1 & L2.

b) write the images of P1 (5,8)and Q1 (-3,-4)On reflection in L1 and
L2

c)write down the images of Pand Q on reflectionIsIs L2. .Name the
images as P2 and O2 respectively
d)State a single transformation that Maps P2 onto Q2 ( 8)

a)If a = c,
      b   d        Prove that (2a+ 3b):(2c-3d)=(2a-3b)(2a+3d)     (4)
                   3        2
b When kx    +9x    +4x -10 is divided by x+1 .the remainder is 2 .find the value of k
(4)

In the adjoining figure, DE is parallel to BC
and divided tringle ABC into two parts of equal area. Find DB:AB

(8)

Ramesh bought a VCR a t the list price of Rs 13500.The shopkeeper gave a discount of 5%on the list price .There is another discount of 2%,after allowing the discounts a sales tax of 10%is charged ,find the amount Ramesh had to pay( 8)

Two cicles touchintrnally .The sum of their areas is116 p cm² and the distance beween their cntres is 6 cm .Find the redii of two circlees (8)

SECTION - B [42 Marks]

Answer any FOUR questions in this section

A)If xÎR solve
-5>3x+1£10 and represent the solution on the nuber line (4)
B)Given that A={ 0, 1, 2,3} and a relation R is defined on set A as
R:{ (x,y) ÎA xA: x=y} then

i List the element of R
ii list the domain of R
iii List the range of r(4)
C) A funcion f is defined by f(x)=cos x -sin x . Evaluate
i ) f( 0) ( ii ) f( 30 ) -f( 60 ) ( iii) x if f(x) =0 (4)

a) Solve for x using the formula 4x²- 2x + 1/ (4)

b)Prove that^1-sinA =(secA-tanA)²(4)^{1+sinA

c)Find the value of p if the lines whose equaions are 2x-3y+5=0 and
px+6y+7 are parallel to each other}(4)

A)Use graph paperfor this question.fraw the graph of x+y=3 and 2x+5y=12 on the same axes.Use 2cm=1 unit on both axis and plot only 3 ponits for each line (4)
B) Matric18.gif (1756 bytes)

(4)

C) In the adjoining figure two chordesAB andCD
of a circle intersect each other at point P
outside the circle .If AB=5cm BP=3cm and PD=2 cm then find CD

(4)

a)How much should a man invest in Rs 20share selling at Rs 25 to obtain an income of
     Rs 400 , if the divident declared by 10 %p.a.?Also find rate of income .(4)
b)Calculate the ratio in which the line joining A(6,5) and B(4-3) is divided y line
   y=2. write down the equation of the line passing through the points Aand B(4)
c)The sum of two numbers is 9 and the sum of their squares are 41.taking one number
      as x from a quadratric equation in x and solve it to find them            (4)

12a

Find the mean and mode of the following data
4,7,4,3,2,7,7,6,4,7,8, (4)

In the adjacent figure find (i) BC(ii)CD(Given that tringle ABC is right angled at B

(4)

A sphere of diameter 14 cm is dropped into a cylinder of base radius 10.5 cm containg water . Calculate the rise in the lavel of water in the cylinder if the sphere is comleatly submerged and no water over flow(4)

Date	Particulars	Withdrawals Rs. P.	Deposits Rs. P.	Balance Rs. P.
2000
Jan 1	By balance	–	--	1200.00
" " 5	By cash	–	500.00	1700.00
" " 20	By cheque	-	700.00	2,400.00
Feb 15	To cash	500.00		1900.00
May 8	By cheque		1,000.00	2900.00
July12	By cheque		1500.00	4400.00
July20	To cheque	1000.00		3400.00
sep1	By cash	–	1,200.00	4600.00
Oct5	To cheque	2000.00		2600.00
Dec15	By cheque		500.00	3,100.00

This is a page from pass book of Mr X"s saving Bank account in particular year is given above .Assuming that the intrest rate is 5% p.a. and intrest is paid once in a year at the end of December . calculate the interest earned by Mr x at the end of the year13(6)

13b

use ruler and campass to construct the tringle ABC in which BC=7cm and angle ABC =60 and AC-AB=1.5 cm .Construct a circle of radius 2cm to touch the angle ACB(6)

14a

ABC is a tringle in which AB=Ac and Dis any point onBC .Prove that
AB²-AD²= BDxDC(6)

^{The following table shows the distribution of height of a
group of factory workrs}

Height in cm	No. of workers
150 - 155 155 - 160 160- 165 165 - 170 170 - 175 175 - 180 180- 185	6 12 18 20 13 8 6

(i) Detrrmine the cummulative frequencies
( ii) Draw the cummulative curve on the graph (use 2cm =5cm heighton one axis and
2cm =workers on other (6)

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