Other Solved Mathematics Board Papers
MATHEMATICS (ICSE – Class X Board Paper 2018)
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) Find the value of if
(b) Sonia had a recurring deposit in a bank and deposited Rs. 600 per month for 2.5 years. If the rate of interest was 10% per annum, find the maturity value of this account. [3]
(c) Cards bearing numbers 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20 are kept in a bag. A card is drawn at random from this bag. Find a probability of getting a card which is:
(i) a prime number
(ii) a number divisible by 4
(iii) a number that is multiple of 6
(iv) an odd number [4]
Answers:
and
Hence,
(b) Monthly investments
Maturity value
(c) Cards:
(i) Prime numbers:
(ii) Numbers divisible by
(iii) Numbers multiple of
(iv) Odd numbers: None
Question 2:
(a) The circumference of the base of a cylindrical vessel is and its height is . Find the
(i) radius of the cylinder
(b) If are three consecutive terms of an A.P., find the value of . [3]
(c) is a cyclic quadrilateral. Given that , calculate
(i)
(ii)
(iii) [4]
Answers:
(a) Circumference
Height
Circumference
Volume
(b) are in AP
Therefore the terms are and the common difference is
(c) Join
(i)
(opposite angles of a cyclic quadrilateral)
(ii)
(iii) (angles in the same segment)
Therefore
Question 3:
(a) If ) and are factors of , find the values of . [3]
(b) Prove that [3]
(c) Using a graph paper draw a histogram for the given distribution showing the number of runs scored by 50 batsman. Estimate the mode of the data. [4]
Runs Scored  30004000  40005000  50006000  60007000  70008000  80009000  900010000 
No. of Batsman  4  18  9  6  7  2  4 
Answers:
(a)
Factors:
Solving (i) and (ii)
Substituting in (ii)
(b)
. Hence proved.
(c)
Mode
Question 4:
(a) Solve the following inequation, write down the solution set and represent it on a real number line.
(b) If the straight lines are perpendicular to one another, find the value of . [3]
(c) Solve and give your answer correct to two decimal places. [4]
Answers:
(a)
First equation:
Second equation:
Hence the solution set
(b) Two equations are:
Since the two lines are perpendicular to each other
(c)
SECTION B [40 Marks]
(Attempt any four questions from this Section.)
Question 5:
(a) The term of a G.P is 16 and the term is 128. Find the first term and the common ratio of the series. [3]
(b) A man invests Rs. 22500 in Rs. 50 shares available at 10% discount. If the dividend paid by the company is 12%, calculate:
(i) The number of shares purchased
(ii) The annual dividend received
(iii) The rate of return he gets on his investment. Give your answer correct to the nearest whole number. [3]
(c) Use graph paper for this question (Take 2 cm = 1 unit along both ). is a quadrilateral whose vertices are .
(i) Reflect quadrilateral on the yaxis and name it as
(ii) Write down the coordinate of
(iii) Name two points which are invariant under the above reflection
(iv) Name the polygon [4]
Answers:
(a)
(b) Face Value
Total Investment
(c)
(i) Refer to the graph
(ii)
(iii) are irrelevant to the reflection
(iv) is a trapezium
Question 6:
(a) Using the properties of proportion, solve for . Given that is positive
Answers:
Applying Componendo and Dividendo
(b)
(c)
Hence Proved
Question 7:
(a) Find the value of for which the following equation has equal roots.
[3]
(b) On a map drawn to a scale of , a rectangular plot of land has the following dimensions. ; and all angles are right angles. Find :
(i) the actual length of the diagonal of the plot in km
(ii) the actual area of the plot in sq. km [3]
(c) are the vertices of the triangle , is a point on such that . Find the coordinates of . Hence find the equation of the line passing through the point . [4]
Answers:
(a) Given
Therefore
For equal roots,
(b) Scale is
(i)
Let the length of be on the ground
(ii) on the ground
on the ground
Therefore Area of
(c)
Let
Hence
Therefore equation of
Question 8:
(a) Rs. 7500 was divided equally among a certain number of children. Had there been 20 less children each would have received Rs.100 more. Find the original number of students. [3]
(b) If the mean of the following distribution is 24, find the value of . [3]
Marks  010  1020  2030  3040  4050 
No. of Students  7  8  10  5 
(c) Using ruler and compass only, construct a such that
(i) Construct a semicircle of
(ii) Construct a cyclic quadrilateral , such that is equidistant from . [4]
Answers:
(a) Let the number of children be
Therefore if children received
Let the number of children be
Therefore if children received
Given
Therefore the number of children be
(b)
Marks  Mid Term  No. of Students  
010  5  7  35 
1020  15  
2030  25  8  200 
3040  35  10  350 
4050  45  5  225 
(c)
Question 9:
(a) Priyanka has a recurring deposit account of Rs. 1000 per month at 10% per annum. If she gets Rs. 5550 as interest at the time of maturity, find the total time for which the account was held. [3]
(ii) Prove that are similar
[3]
(c) The following figure represents a solid consisting of a right circular cylinder with a hemisphere at one end and a cone at the other. Their common radius is 7 cm. The height of the cylinder and cone is each 4 cm. Find the volume of the solid. [4]
Answers:
(a) Monthly Income
(negative number is not possible)
Therefore
(b)
(i) In
is common
SInce
(alternate angles)
Therefore (by AAA Postulate)
(ii) Consider &
Since
Therefore (AAA Postulate)
(c) Radius , Height of Cylinder Height of Cone
Volume of total solid = Volume of Cone + Volume of Cylinder + Volume of Hemisphere
Question 10:
(a) Use remainder theorem to factorize the following polynomial.
[3]
(b) In the figure given below is the center of the circle. If . Find the value of giving reasons. [3]
(c) The angle of elevation from a point of the top of the tower , high is and that the tower from the point is . Find the height of the tower , correct to the nearest meter. [4]
Answers:
(a)
Let be a factor
Therefore is a factor
(b) Radius
(given)
Therefore
In since (Isosceles triangle)
Since is Isosceles triangle,
Therefore
Therefore (straight line)
(c) From
From
Question 11:
(a) The term of an A.P. is 22 and term is 66. Find the first term and the common difference. Hence find the sum of the series to 8 terms. [4]
(b) Use graph paper for this question
A survey regarding height (in cm) of 60 boys belonging to Class 10 of a school was conducted. The following data was recorded:
Taking 2 cm = height of 10 cm along one axis and 2 cm = 10 boys along the other axis draw an ogive of the above distribution. Use the graph to estimate the following:
Height in cm  135140  140145  145150  150155  155160  160165  165170 
No of boys  4  8  20  14  7  6  1 
(i) the median
(ii) the lower quartile
(iii) if above 158 cm is considered as a tall boy in a class, find the number of boys who are tall in the class. [6]
Answers:
(a)
… … … … … (i)
… … … … … (ii)
Solving (i) and (ii)
Substituting in (i)
(b)
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 boys students