icse_math_2
TRANSCRIPT
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Math Class-X 1 Model Test Paper-
Model Test Paper 2
Maximum Marks : 80 Time Allowed:1
22
hour
Section A
(Answer all questions from this section)
1.(a) Mamta has a cumulative Time Deposit Account in a bank. She deposits Rs
800 per month and gets Rs 15198 as maturity value. If the rate of interest be
7% p.a., find the total time for which the account was held. [4
(b) A solid metallic sphere of diameter 21 cm is melted and recasted into a
number of smaller cones each of diameter 7 cm and height 3 cm. Find the
number of cones so formed. [4
(c) The diameter of an iron sphere is 18 cm. The sphere is melted and is drawn
into a long wire of uniform cross section. If the length of the wire is 108 m,
find its diameter. [4
2. (a)In figure, A, D, B, C are four points on the circumference
of a circle with centre O. Arc AB = 2 arc BC and AOB =
108. Calculate :
(i) ACB (ii) ADB
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Math Class-X 2 Model Test Paper-
(b) The marks scored by 40 pupils of a class in a test were as follows :
Calculate the mean mark. [3
(c) Name the figure and draw a neat diagram showing the lines of symmetry.
(i) A triangle with one line of symmetry.
(ii) A triangle with three lines of symmetry.
(iii) A triangle with no line of symmetry. [3
3.(a) Solve 2 2x 3 < 5,x R and mark it on the number line. [3
(b) Find the value of mif (x m) is a factor of 3x3+ 2x2 19x+ 3m. [3
(c) Findxandyif3 2 5
0 5 2
x
y
=
. [3
4.(a) What must be added to each of the numbers 7, 15, 19 and 35 so that the
resulting numbers are in proportion? [2
(b) Show that the angle in a semicircle is a right angle. [2
(c) Without using trigonometrical tables, calculate :2tan 40 cosec 61
cot 50 sec 29
[2
(d) Using the remainder theorem, find the remainder when 7x3+ 5x2 4x 1 is
divided by (x+ 1).
(e) The price of an almirah including sales tax is Rs 7884. If its marked price is
Rs 7300, find the rate of sales tax. [2
Marks 0 1 2 3 4 5
No. of pupils 2 4 5 14 11 4
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Math Class-X 3 Model Test Paper-
P
X
RY
Q
Section B
(40 Marks)
(Answer any four questions from this section)
5.(a) In the figure, XY || PQ, and PQ = 7.7 cm.
Find (i)YR
XR (ii) XY. [4
(b) A bag contains 6 red, 5 black and 4 white balls. A ball is drawn from the bag
at random. Find the probability that the ball drawn is :
(i) white (ii) red (iii) not black (iv) red or white. [6
6.(a) The point A (3, 0) on reflection in a line is mapped as A(3, 0) and the poin
B (2, 3) on reflection in the same line is mapped as B(2, 3).
(i) Name the mirror line.
(ii) Write the coordinates of the image of (3, 4) in the mirror line. [3
(b) Using quadratic formula, solve :
4x2 4ax+ (a
2 b
2) = 0 [5
(c) Prove that the equation 3x2+ 7x+ 8 = 0 is not true for any real value ofx. [2
7.(a) A man invests Rs 1716 in buying shares of nominal value Rs 24 and sellingat 10% premium. The dividend on the shares is 15% per annum. Calculate :
(i) The number of shares he buys.
(ii) The dividend he receive annually. [4
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Math Class-X 4 Model Test Paper-
(b) Construct a circle of radius 2.5 cm. Mark the centre as O. Mark a point P on
the circle. Draw OA such that AOP = 30. Construct a circle to touch OA
and the circle at P. Measure the radius of this cirlce. [6
8.(a) The horizontal distance between two towers is 140 m. The angle of elevation
of the top of the first tower when seen from the top of the second tower is
30. If the height of the second tower is 60 m, find the height of the first
tower. [5
(b) State the locus of centres of all circles passing through two fixed points. [2
(c) A man invests Rs 46875 at 4% per annum compound interest for 3 years.
Calculate :
(i) the amount outstanding to his credit at the end of the second year.
(ii) the interest for the third year. [3
9.(a) The circumference of a circle is 44 cm.
(i) By how much should the radius be increased to make the circumference
22 cm longer?
(ii) Calculate the area of the larger circle. [3
(b) Find the equation of a straight line parallel toy-axis and passing through the
point (3, 5). [3
(c) In the figure, O is the centre of the circle. If BAD = 30, find the values of
x,yandz. [3
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Math Class-X 6 Model Test Paper-
Answers
1. (a) 18 months (b) 126 (c) 6 mm
2. (a) (i) 54 (ii) 126 (b) 3
3. (a)1
2 42
x < (b) 2 (c)x= 3,y= 10
4. (a) 5 (c) 1 (d) 1 (e) 8%
5. (a) (i)2
7 (ii) 2.2 cm (b) (i)
4
15(ii)
2
5(iii)
2
3(iv)
2
3
6. (a) (i) y-axis (ii) (3, 4) (b)
,2 2
a b a b+
7. (a) (i) 65 (ii) Rs 234 (b) 2.3 cm
8. (a) 148.83 m (b) A straight line perpendicular to the line joining the
given points.
(c) (i) Rs 50700 (ii) Rs 2028
9. (a) (i) 3.5 cm (ii) 346.5 cm2
(b)x+ 3 = 0
(c)x= 150,y= 60,z= 30
10. (a) (i) (1, 6) (b) 85.8
11. (c) 23