11497SD Question ICSE 1

8/6/2019 11497SD Question ICSE 1

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Sample Paper – 2010Class – X

Subject – Mathematics

(Two hours and a half)

Answers to this Paper must be written on the paper provided separately.

You will not be allowed to write dur ing 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 from Section A and any four from the questions from Section B.

All working, including rough work, must be clearly shown and must be 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)

Question 1

(a) A sum of Rs.9,600 is invested by Bhuvi for 3 years at 10% per annum at compoundinterest :(i) What is the sum due at the end of the first year?(ii) What is the sum due at the end of the 2nd year?(iii) Find the compound interest earned by Bhuvi in 2 years.

(iv) Find the difference between the answers in (ii) and (i) and find the interest onthis sum for one year.

(v) Hence or otherwise, write down the compound interest for the third year.[4]

(b) A bag contains 4 red , 5 black and 6 white balls. A ball is drawn from the bag bySatovisha Banerjee at random. Find the probability that the ball drawn by her is

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(i) red (ii) black or white , (iii) not black. [3]

(c) Sejal Agarwal buys an article for Rs.2,621.25. If the price includes a discount of 10%on the marked price, sales tax @ 15% on the selling price and a surcharge @ 10%

of the total amount of sales tax payable by her, find the marked price of the article.[3 ]

Question 2

(a) ) Solve x2 +7x =7 and give your answer correct to 2 decimal places. [3](b) Find the value of ‘p’ if the polynomial f(x) = x3 – 3x2 – px + 24 is divisible by

g(x) = x + 3. Hence find all the factors of f(x). [3]

(P.T.O.)

( c) A page from passbook of Mr. Rohan Nagpal is given below:

Date Particulars Amountwithdrawn

(Rs.)

Amountdeposited

(Rs.)

Balance(Rs.)

04-03-04 B/F 4500.00

11-03-04 To Cheque 500 4000.00

28-03-04 To Cash 100 3900.00

18-04-04 By Cash 1000 4900.00

30-04-04 By Cash 8400 13300.00

17-09-04 To Cheque 1280.50 12019.50

10-11-04 To Cheque 5000 7019.5023-11-04 By Cash 6000 13019.50

11.12.04 By Cash 2000 15019.50

(i) Find the sum for which Mr Rohan Nagpal will earn interest for the periodMarch 04 to Dec 04.

(ii) Find the interest he received for the above period at the rate of 5% p.a.(iii) If he closes his account on 31.12.04, find the total amount received by him.

[4] Question 3

(a) ) Chintan Patel has a recurring deposit account in a bank for 5 years at 4% p.a. If hegets Rs.66,100 at the time of maturity find the monthly installment. [3]

(b) The mean of 1, 7, 5, 3, 4 and 4 is m. The numbers 3, 2, 4, 2, 3, 3 and p have meanm – 1 and median q. Find ‘p’ and ‘q’.

[3](c) The centre of a circle is (x + 2, x – 1). Find x if the circle passes through (2, - 2) and

(8, - 2). Hence find the radius. [3]

Question 4






(a) Solve the inequality and plot on the number line : x + 13 > 2x > x + 1. [3]

(b) The triangle ABC where A (1, 2), B (4, 8), C (6, 8) is reflected in the X-axis totriangle A’B’C’. Triangle A’ B’ C’ is then reflected in the origin to triangle A” B” C”.

Write down the co-ordinates of A” B” C”. Write down a single transformation thatmaps ABC on to A” B” C”. [4 ]

(c) Diameters of three concentric circles are in the ratio 1 : 2 : 3. The sum of thecircumferences of these circles is 264 cm. Find the area enclosed between secondand third circle. [3]

Page no. 2

Section B (40 Marks)Attempt any four questions from this section

Question 5

(a) The measure of the angle of elevation of a cloud from a point 60m above a lake is45o and the measure of the angle of depression of its reflection in the lake is 60 o.Find the height of the cloud above the surface of the lake. [3]

(b) In the figure given alongside ∆ ABC ~ ∆ ADE.(i) If AD : DB = 2 : 3 and DE = 5 cm, find BC.

(ii) If ‘x’ be the length of the perpendicular AM from A to DE find the length of theperpendicular AN from A to BC in terms of ‘x’, Hence find A

(a) ∆ ABC : ∆ ADE.(b) ∆ AMD : trapezium DMNB.

(c) ∆ AME : ∆ ANC.(d) ∆ ANC : trapezium MECN.

[4]B

(c) In a flight of 2800 km an aircraft slowed down due to bad weather. Its average speedfor the trip was reduced by 100 km/per hour and time increased by 30 minutes. Findthe original duration of the flight. [3]

Question 6

(a) Evaluate without using tables:

2 cos 60o - 2 sin 60o

- tan 45o cos 0o xcot 45o cosec 60o

sec 60o sin 90o

[3]

ED

C






(b) An exhibition tent is in the form of cylinder surmounted by a cone. The height of thetent above the ground is 85m and the height of the cylindrical part is 50m. If thediameter of the base is 168m, find the quantity of canvas required to make the tent.Allow 20% extra for folds and for stitching. Give your answer to the nearest m2.

[4](c) A line intersects X-axis at ( -2, 0) and cuts off an intercept of 3 from the positive side of

Y-axis. Write the equation of the line. [3]

Question 7

(a) If sec θ + tan θ = m, show that: [3]

m2 – 1= sin θ.

m2 + 1

Page no. 3

(b) If a, b, c are in continued proportion, prove that – [3]

a=

a2 + ab + b2

c b2 + bc + c2

(c) In the given figure, O is the centre of the circle. TQ and TR are two tangents drawnfrom T to the circle and ⁄ QTR = 50○ .

Calculate ⁄ QPR and ⁄ QSR. [4]

Question 8

(a) In a public collection towards the erection of a memorial 1000 people of Kolkatacontributed money varying from Re.1 to Rs.100 (in units of Re.1). The following tablegives the frequency distribution of contribution.






Contributionin Rs.

1-10

11-20

21-30

31-40

41-50

51-60

61-70

71-80

81-90

91-100

No. of People

30 60 80 170 200 180 140 70 40 30

Using suitable scale, draw an ogive on graph paper and use it to answer thefollowings:

(i) Estimate the median.(ii) If it is agreed to allow only those who contributed Rs.45 or more to attend the

unveiling ceremony what percent would attend?(iii) If it is decided to invite the top 25% of the contributors to attend the official

dinner, what would be the lowest contribution which would qualify acontributor to attend the dinner? [6]

(b) Udisha Patodia invested her savings as follows : 20% of her savings in buying 10%Rs.100 shares of a Company A quoted at Rs.160. 60% of her savings in buying 6%

Rs.50 shares of Company B quoted at Rs.60. 20% of her savings in buying 5%Rs.100 shares of a Company C quoted at Rs.80. Given that he obtained 40 sharesof Company A. Calculate –(i) No. of shares of Company B and C bought by her.(ii) Total dividend earned by him at the end of the year.(iii) Overall percentage return on her entire investment. [4]

Page no. 4

Question 9

(a) The centre of a circle is at (5, 3) and its radius is 5. Find the length of the chord whichis bisected at (3, 2). [3]

(b) Draw a Δ ABC in which AB = 5.2 cm, BC = 4.8 cm and CA = 6.9 cm. Construct thecircum-circle of the Δ ABC. Hence draw tangents to the circle from the point ‘P’ 7 cmfrom the centre. [4]

(c) Prove that:[3]

sin θ cos (90o – θ) cos θ+

cos θ sin (90o – θ) sin θ

sin (90o – θ) cos (90o – θ)

Question 10

(a) Find the mean of the marks obtained by students of La Martiniere for boys, Kolkatausing step deviation method.

Marksobtained

Less than10

Less than20

Less than30

Less than40

Less than50

No. of students

7 19 32 42 50






[4](b) Using properties of proportion solve for ‘x’.

1 + x + x2

=

62 (1 + x)1 – x + x2 63 (1 – x)

[3](c) Lines 2x – by + 5 = 0 and ax + 3y = 2 are parallel. Find the relation connecting a and b. [3]

Question 11Prove that : 2 (sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0 [3](b) Find the coordinates of ortocentre of the triangle whose vertices are (2, -5), (3, 9)

and ( -8, 11). [3](c) Two tangents TP and TQ are drawn to a circle with centre O from an external point T.

Prove that OPQ PTQ ∠=∠ 2 [4]



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11497SD Question ICSE 1