BHAKTIVEDANTA SWAMI MISSION SCHOOL
1ST TERMINAL EXAM [2012-13]
MATHEMATICS
Std : X
M.Marks : 80
Date: 01.10.2012
Time
: 2 ½ hrs
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Instructions :
This question paper is divided into two sections.
Answer all questions from Section A
Attempt any four questions from Section B.
All working should be clearly shown in a separate rough column on the same page where you have
solved the question.
Mathematical tables will be provided.
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SECTION A (40 marks)
(Answer all questions from this section)
Question 1
a) Mr Balan has an account with the Bank of India. The following entries are
[4]
from his passbook:
Date
Particulars
Withdrawals Deposits
Balance
(in Rs)
(in Rs)
(in Rs)
Jan 15, 2007
B/F
6500
Jan 21, 2007
By cash
1200
7700
Feb 6, 2007
To self
800
6900
April 13, 2007
By cash
1100
8000
May 16, 2007
To cheque
1300
6700
June 5, 2007
To self
600
6100
June 18, 2007
By cash
2600
8700
Calculate the interest for the six months Jan to June, 2007 at 4.5 % p.a.
3
b) Write down the equation of the line whose gradient is 2 and which passes through P,
where P divides the line segment joining A (-2,6) and B(3, -4) in the ratio 2 : 3.
c) Write down the coordinates of the image of A(3, -2)
i)
Reflection in the line x = 0
ii)
Reflection in the line y = 1
( without using the graph paper )
[4]
[2]
Question 2
a) Given that a3 + 3ab2 = 63 find a : b
b3 + 3a2b
62
[3]
C
b) In the given figure, AB is the diameter
of a circle with centre O and OA = 7cm.
Find the area of the unshaded region.
[4]
A
O
B
D
c) Suresh invests ` 12500 partly in shares paying 6% at ` 125 and partly in 8% at ` 150.
his total income is ` 624, find his investment in each.
Question 3.
a) In the adjoining figure, chord ED is parallel
to the diameter AC of the circle. Given
CBE = 55o Calculate  DEC
If
[3]
B
A
[3]
E
C
D
b) Black kings, queens and jacks are removed from a pack of 52 cards and then well shuffled.
A card is drawn from the remaining cards. Find the probability of getting
i) a king ii) a black card iii) a heart
[3]
c) Calculate the mean using the short cut method.
C.I.
10-20
20-30
30-40
40-50
50-60
60-70
70-80
[4]
Frequency
10
15
22
28
16
14
5
Question 4
a) A hollow sphere of internal and external diameters 4cm and 8 cm respectively is
melted into a cone of base diameter 8cm. Find the height of the cone.
[4]
b) Using the data given below draw an ogive.
Marks
No of students
0 - 10
10
10 - 20
18
20 - 30
24
[6]
30- 40
36
40- 50
22
50-060
16
60 -70
10
70 - 80
4
From the ogive determine
i)
The median
ii)
Interquartile range
iii)
If 60 % of students pass the examinations, find the minimum marks to pass
the examination.
SECTION B (40 marks)
(Answer any four questions from this section)
Question 5
a) Find two numbers whose mean proportional is 28 and the third proportional is 224.
[3]
b) Find the length of median AD of a triangle whose vertices are A (4, 4), B (3, -2)
and C (-3, 16)
[3]
c) A path of uniform width surrounds a circular field, whose diameter is 50m.
If the areas of the field and the path are equal, find the width of the path.
[4]
Question 6
a) Lata contributes ` 750 per month to a recurring deposit scheme for 2 years. The interest
is calculated at the end of every month. What is the rate of interest paid by the bank if
the maturity value is ` 19875.
A
[4]
E
b) In the given figure,
B
C
AB = AC = CD, ADC = 40o
Calculate i) ABC
ii) BEC
D
[3]
c) Calculate the mean, median and mode of the following data.
[3]
Age (in yrs)
No. of
students
12
8
13
12
14
18
15
24
16
16
17
13
18
9
Question 7
a) A cylindrical rod of copper whose height is 4 times its radius is melted and recast into
spherical balls of the same radius. Find the number of balls.
[3]
b) Ravi contributes ` 120 per month to a recurring deposit scheme at 7% p.a. interest being
calculated at the end of every month. What should be the minimum number of
installments if the maturity value is ` 1494.60
[3]
c) Construct an isosceles triangle whose base is 6 cm and vertical angle is 90 o
Construct its incircle. Measure the inradius.
[4]
Question 8.
Q
a) In the given figure, PR is a diameter
[3]
of the circle PQ = 7cm, QR = 6 cm and
P
R
RS = 2 cm. Calculate the perimeter of the
cyclic quadrilateral PQRS
S
b) A girl fills a cylindrical bucket 32 cm in height and 18 cm in radius with sand.
She empties the bucket on the ground and makes a conical heap of the sand.
If the height of the conical heap is 24 cm, find
i)
the radius
ii)
the slant height of the heap
(Give your answer correct to one place of decimal)
c) In a single throw of two dice, find the probability of getting
i)
a total of 9
ii)
a total of 5 or 7
Question 9
a) If b is the mean proportional between a and c
prove that a2 – b2 + c2 = b4
a-2 - b-2 + c-2
b) The points P and Q have co-ordinates (-1 , 5) and (7, 3) respectively. Find
[4]
[3]
[4]
[3]
i)
ii)
iii)
the coordinates of R the midpoint of PQ.
the gradient of PQ
equation of RS which is perpendicular to PQ
c) A invests ` 9000 to buy 5% ` 100 shares at ` 10 discount. B invests ` 9000 in
` 100 shares at par. At the end of the year they both receive equal dividend.
Find the rate of dividend received by B.
[3]
Question 10
a) Find the value of k for which the lines kx-5y+3 = 0 and 4x-2y+6 = 0 are perpendicular
to each other.
[3]
b) P and Q have coordinates (-2,3) and (5, 2) respectively.
i)
Reflect P in the x-axis to P’
ii)
Reflect Q in the y-axis to Q’
iii)
Find the mid-point of PP’ and call it L
iv)
Find the mid-point of QQ’ and call it M
v)
Find the length of LM
[4]
c) How many litres of water will a hemispherical tank hold, whose diameter is 4.2m?
[3]
Question 11
a) A bag contains some white and 20 blue balls. If the probability of drawing a white ball
3
is 5 of a blue ball, find the number of white balls in the box.
b) Draw a histogram for the following data. Also find the mode from the graph.
Height (in cm)
No. of pupils
121-130
11
131-140
15
141-150
30
151-160
19
[3]
[4]
161-170 171-180
15
9
c) Nikhil bought 1500 shares each of face value of ` 10 at a premium of 20% per share.
the end of the year, the company declared a dividend of 9%
Calculate the percentage return on his investment.
At
[3]