MATHEMATICS (ICSE Paper 2012)
Two and Half Hour. Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper.
The time given at the head of this Paper is the time allowed for writing the answers. Attempt all questions form Section A and any four questions from Section B. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the Answer. Omission of essential working will result in the loss of marks.
The intended marks for questions or parts of questions are given in brackets [ ].
Mathematical tables are provided.
SECTION A [40 Marks]
(Answer all questions from this Section.)
Question 1:
(a) Given . Find . [3]
(b) The Monthly Pocket Money of Ravi and Sanjeev are in the ratio . There expenditures are in the ratio . If each saves every month, find their monthly pocket money. [3]
(c) Using the Reminder Theorem factories completely the following polynomial: [4]
Answers:
(a) Given
(b) Let monthly pocket money be Ravi is and Sanjeev is .
They both save per month.
Therefore, their expenditure would be and respectively.
Hence
Ravi’s pocket money
Sanjeev’s pocket money
(c) Given
Try
, therefore (x-1) is not a factor of the given function.
Try
Therefore is a factor of
To factories
Hence,
Question 2:
(a) On what sum of money will the difference between the compound interest and simple interest for years be equal if the rate of interest charged for both is p.a.? [3]
(b) is an is isosceles right-angled triangle with . A semi-circle is drawn with as the diameter. If find the area of the shaded region. . [3]
(c) Given a line segment joining the points and Find:
(i) the ratio in which is divided by the
(ii) find the coordinates of the point of intersection.
(iii) the length of . [4]
Answers:
(a) Let the sum be
Simple Interest for 2 years
Amount Compound Interest
Given difference = 25 Rs.
Therefore
(b) is a right angled triangle. Therefore
Area of semi circle
Area of
Area of the shaded region = Area of the semi circle – Area of
(c) Let the required ratio be and the point of intersection be
Since
Therefore the point intersection is
Length of .
Question 3:
(a) In the given figure is the central of the circle and is a tangent at . If and . Calculate the radius of the circle. [3]
(b) Evaluate without using trigonometric tables:
[3]
(c) Marks obtained by students in a short assessment is given below, where are two missing data:
| Marks | 5 | 6 | 7 | 8 | 9 |
| No. of Students | 6 | A | 16 | 13 | B |
If the mean of the distribution is find . [4]
Answers:
(a) Let the radius of the circle
Here we apply intercept theorem. Therefore:
(b)
=
=
(c) Given, the total number of students
Therefore
… … … (i)
Given mean
Therefore
… … … (ii)
Solving (i) and (ii) we get and
Question 4:
(a) Kiran deposited per month for months in a Bank’s recurring deposit account. If the bank pays interest at the rate of per annum, find the amount she gets on maturity. [3]
(b) Two coins are tossed once; Find the probability of getting:
(i) heads
(ii) At least tail [3]
(c) Using graph paper and taking along both and ;
(i) Plot the points and
(ii) Reflect in the origin to get the images respectively.
(iii) Write down the co-ordinates of .
(iv) Give the geometrical name for the figure .
(v) Draw and name its lines of symmetry. [4]
Answers:
(a)
(b) Let Heads – and Tails –
If two coins are tossed once, then the total number of possibilities would be as shown: Sample Space
(i.e. there are 4 possible outcomes)
(i) Event: getting two heads
Hence the probability
(ii) Events : At least one tail
Hence the probability
(c) (i) Please refer to the graph shown below
(ii) Please refer to the graph shown below
(iii) Reflection of in the origin are respectively.
(iv) Name of the geometrical figure in the graph show is Rhombus
(v) Two lines of symmetry: Both diagonal
SECTION B [40 Marks]
(Answer any four questions in this Section.)
Question 5:
(a) In the given figure, is the diameter of a circle with center . . Find (i) (ii) [3]
(b) Given Write (i) the order of the matrix (ii) the matrix . [3]
(c) A page from the savings Bank Account of Mr. Prateek is given below: [4]
| Date | Particular | Withdrawal | Deposit | Balance |
| Jan. 1st 2006 | B/F | – | – | 1,270 |
| Jan. 7th 2006 | By Cheque | – | 2310 | 3580 |
| March 9th 2006 | To Self | 2000 | – | 1580 |
| March 26th 2006 | By Cash | 6200 | 7780 | |
| June 10th 2006 | To Cheque | 4500 | – | 3280 |
| July 15th 2006 | By Clearing | – | 2630 | 5910 |
| October 18th 2006 | To Cheque | 530 | – | 5380 |
| October 27th 2006 | To Self | 2690 | – | 2690 |
| November 3rd 2006 | By Cash | – | 1500 | 4190 |
| December 6th 2006 | To Cheque | 950 | – | 3240 |
| December 23rd 2006 | By Transfer | – | 2920 | 6160 |
If he receives as interest on 1st January, 2007. Find the rate of interest paid by the bank.
Answers:
(a) (i) is a cyclic quadrilateral)
(ii) In
(b)
Therefore
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