ICSE_Math_2

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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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(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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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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(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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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

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