MATHEMATICS (ICSE – Class X Board Paper 2017)
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.)
(a) If is the mean proportion between , show that; 
(b) Solve the equation and give your answer correct to two decimal. 
(c) are two parallel chords of a circle such that . If the radius of the circle is , find the distance between the two chords. 
(b) The equation is
Substituting, we get
(a) Evaluate without using trigonometric tables,
(c) Jaya borrowed Rs. 50000 for 2 years . The rates of interest for two successive years are 12% and 15% respectively. She repays Rs. 33000 at the end of the first year. Find the amount she must pay at the end of the second year to clear her debt. 
is the amount and is the principal.
For first year:
For second year:
(a) The catalog price of a computer set is Rs. 42000. The Shopkeeper gives a discount of 10% on the listed price. He further gives an off-season discount of 5% on the discounted price. However, sales tax at 8% is charged on the remaining price after the two successive discounts. Find:
(i) The amount of sales tax a customer has to pay
(ii) The total price to be paid by the customer for the computer set. 
(b) is a point on the line segment such that is equal to . Find the coordinates of . 
(c) The marks of 10 students of a class in an examination arranged in ascending order is as follows: . If the median marks is 48, find the value of . Find the mode of the given data. 
(a) Cost Price
Price after discount
Price after discount
(ii) Price to be paid by the customer
Hence the coordinate of
Looking at all the terms, we see that 46 is repeated twice and hence the mode is 46.
(a) What must be subtracted from the resulting expressing has as a factor? 
(b) In the given figure ABCD is a rectangle. It consists of a circle and two semi circles each of which are of radius 5 cm. Find the area of the shaded region. Give your answer correct to three significant figures. 
(c) Solve the following in equation and represent the solution set on a number line.
Therefore has to be subtracted from the given polynomial.
(b) Radius of the circle
Therefore, as shown in the diagram: Breadth of the rectangle and Length of the rectangle
Area of the circles and semi circles
Therefore the shaded area
Therefore we have two equations:
Since , the values of
Section B (40 Marks)
Attempt any four questions from this Section:
(b) How much should a man invest in Rs. 50 shares selling at Rs. 60 to obtain an income of Rs. 450, if the rate of dividend declared is 10%. Also find his yield percent, to the nearest whole number. 
(c) Sixteen cards are labeled as . They are put in a box and shuffled. A boy is asked to draw a card from the box. What is the probability that the card draw is:
(i) A Vowel
(ii) A Consonant
(iii) None of the letters of the word median 
(b) Face Value
(i) Let the number of shares bought
Therefore yield nearest to a whole number is
(c) No of cards
(i) No of vowels:
(ii) No of consonants:
(iii) Letters other than ‘median’
(a) Using a ruler and a compass construct a in which , . Construct the locus of:
(i) Points equidistant from
(ii) Point equidistant from
Hence construct a circle touching the three sides of the triangles internally. 
(b) A conical tent is to accommodate 77 persons. Each person must have of air to breathe. Given the radius of the tent as 7 m find the height of the tent and also its curved surface area. 
(b) Radius of the cone
No of people
Volume per person
Therefore the volume of the tent
(ii) Curved surface area of a cone
(i) Applying componendo and dividendo
(a) A page from a Saving Bank Account Passbook is given below:
|Date||Particular||Amount Withdrawal||Amount Deposited||Balance|
|Jan 07, 2016||B/F||–||–||3000.00|
|Jan 10, 2016||By Cheque||–||2600.00||5600.00|
|Feb 08, 2016||To Self||1500.00||–||4100.00|
|Apr 06, 2016||By Cheque||2100.00||–||2000.00|
|May 04, 2016||By Cash||–||6500.00||8500.00|
|May 27, 2016||By Cheque||–||1500.00||10,000.00|
(i) Calculate the interest for the 6 months from January to June 2016, at 6% per annum.
(ii) If the account is closed on 1st July 2016, find the amount received by the account holder. 
(b) Use a graph for this question (Take unit on both axis)
(i) Plot the following points :
(ii) Reflect points on the and write down their coordinates. Name the images as respectively.
(iii) Join the points in order, so as to form a closed figure, Write down the equation of the line of symmetry of the figure formed. 
(a) Qualifying principal for various months:
(ii) Amount received by the holder on 1st July
(i) Please refer to the diagram above.
(iii) The enclosed figure is a kite. The line of symmetry is:
(a) Calculate the mean of the following distribution using step deviation method: 
|No. of Students||10||9||25||30||16||10|
(b) In the given figure is a tangent to the circle at are bisectors of , if prove that:
is a diameter of the circle
is an isosceles triangle. 
(c) The printed price of an air conditioner is Rs. 45000. The wholesaler allows a discount of10% to the shopkeeper. The shopkeeper sells the article to customer at a discount of 5% of the marked price. Sales tax (under VAT) is changed at the rate of 12% at every stage. Find:
VAT paid by the shopkeeper to the government;
The total amount paid by the customer inclusive of tax. 
(a) Table as follows:
|Marks||Mid Term||No. of Students|
(b) Consider the diagram as shown:
(i) (since DB is the diameter)
(ii) (angles subtended by the cord CB on the circumference of the circle)
(iii) (angles subtended by the cord DC on the circumference of the circle)
When the chord bisects the tangent…
is an isosceles triangle.
Wholesaler to Shopkeeper
Therefore discounted price
Shopkeeper to Customer
(i) VAT paid by the shopkeeper
(ii) Total price for the customer
(a) In the figure given, is the center of the circle. . Find giving suitable reasons, the measure of: 
(b) are the vertices of a triangle.
(i) Find the coordinates of the centroid of the triangle.
(ii) Find the equation of the line through and parallel to . 
(c) Prove that:
(radius of the same circles)
(i) ( is a cyclic quadrilateral)
(ii) (angle subtended by a chord at the center is twice that subtended on the circumference)
(iii) ( is isosceles)
(b) are the given coordinates of the three vertices of the triangle
(i) Let the centroid be
Hence centroid is
Therefore the slope of the line passing through and parallel to
Hence the equation of the line passing through and parallel to is:
RHS. Hence proved.
(a) The sum of the ages of Vivek and his younger brother Amit is 47 years. The product of their ages is a year is 550. Find their ages. 
(b) The Daily wages of 80 workers in a project are given below. 
|Wages in Rs.||400-450||450-500||500-550||550-600||600-650||650-700||700-750|
|No. of workers||2||6||12||18||24||13||5|
Use a graph paper to draw an ogive for the above distribution. (Use a scale of on workers on ). Use your ogive to estimate:
(i) The medium wage of the workers.
(ii) The lower quartile wage of workers.
(iii) The number of workers who can more than Rs. 625 daily;
(a) Let the age of Vivek
and Let the age of Amit
Hence the age of the two is years.
|Wages||No. workers||Cumulative Frequency (c.f)|
On the graph paper, we plot the following points:
From the graph
From the graph
(iii) The number of workers earning more that 625 per day students
(a) The angles of depression of two ships as observed from the top of a light house 60m high are respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships, Give your answer correct to the nearest whole number. 
(b) is a triangle, is a point on the side of triangle such that Given ,
(ii) Find the length of
(c) Richard has a recurring deposit account in a bank for 3 years at 7.5% p.a. simple interest. If he gets Rs. 8325 as interest at the time of maturity, find;
(i) The monthly deposit
(ii) The maturity Value 
Rounding off the the nearest whole number, we get
Therefore by AAA postulate,
(ii) Maturity Value