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S N Kansagra SchoolTime Allotted: 2hr 30min Math Prelim2 Std 10 Max Marks: 80

You will NOTbe 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.................................................................................................................................................

Answer all questions from Section A and any fourquestions from Section B.

Al l worki ng, including rough work, must be clearly shown and must be done on the same sheet as

the rest of the answer. Omission of essenti al working wi ll resul t in loss of marks.

The intended marks for questions or parts of questions are given in [ ].

Mathematical tables and graph papers are provided.

Section A (40 marks)(Answer allquestions from this Section)

Q1. (a) Solve the following equation forx. Give your answer to 3 significant figures.

2x23x4 = 0 [3]

(b) Without using trigonometrical tables evaluate the following: [3]

(c) Neil borrows Rs.15,000 at 10% pa, interest considered annually. He repays Rs.7,500 at the

end of first year and Rs.5000 at the end of second year. Calculate the amount he must repay at the

end of third year to settle the loan completely. Also, calculate the total interest he pays for his loan.

[4]

Q2. (a) If using properties of proportions, evaluate the following:

(i) x:y and hence (ii)

[3]

(b) The line 2y = 3x + cpasses through the point P(3, 4). Find the numerical value of c. Also,

find the equation of a line which intersects the given line perpendicularly at P. [3]

(c) Use only a pair of compasses and a ruler to answer this question.

Draw a circle with centre O and radius 2.8cm. P is any point outside the circle such that OP = 7cm.Construct a tangent from P on to the circle. Measure and record its length. [4]

Q3.(a) Solve the following inequation for x. Represent your solution on a number line.

. [3]

(b) The figure shows the flooring plan of a temple. ABCD is a squarewith side 14 m. Its diagonals intersect at O. Arcs AB and CD are arcs of a

circle with centre O. The shaded area is to be tiled with marble. Calculate the

cost of the marble required at Rs.900 per m2. [Take = 22/7]

Also find the perimeter of the shaded region in terms of . [3]

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(c) In the figure alongside,

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Q6.(a) In the figure, PT is a tangent to the circle at T.

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(c) Mr. Khan opens a savings bank account with Dena Bank on 14th

April, 2008. Dena Bank pays

interest every six months. All the transactions till 30th

Sept. 2008 are shown in the table below.

DATE

2008

PARTICULARS WITHDRAWALS

(Rs)

DEPOSITS

(Rs)

BALANCE

(Rs)

14t

Apr

21stApr23

rd

4th

May

10th

May

11th

June13

thAug

21st

By Cash New account

By cashTo check

By check

By cash

To checkBy draft

To cash

---------

---------3,400

--------

--------

9,500--------

3,800

10,000

6,800--------

7,800

3,500

--------7,100

--------

10,000

16,80013,400

21,200

24,700

15,20022,300

18,500

The interest that Mr. Khan gets on 1stOct., 2008 is Rs.370. Calculate the rate of interest that the

Bank offers. [4]

Q9.(a) The triplicate ratio of 3:4 is equal to (5x + 3y) : (12x + 7y). Find y : x. [3]

(b) The model of a ship is made to scale 1:200.

(i) If the actual length of the ship is 600m, calculate the length of the model.(ii) The area of the deck in the model is 4.5m

2. Calculate the actual deck area on the ship.

(iii)The volume of the model is 150 litres. Calculate the actual volume of the ship in m3. [3]

(c) The mean of 50 observations for the following data is 59.5. Calculate the numerical values of

the two missing frequencies, p and q. [4]

Variate 4550 5055 5560 6065 6570

Frequency 4 p 12 q 4

Q10(a) Refer to the incomplete figure given alongside. Complete it in

your answer script in such a way that the x-axis and the y-axis become the

lines of symmetry of the completed figure. (A correct free-hand sketch inyour answer script will be awarded full marks.) [2]

(b) Given 3sin22xcos

22x = 0, evaluate the following:

cot23x . sin 6x [3]

(c) The following table shows the weight analysis of 1000 apples as conducted by The TGES

Orchards & Exports Ltd.Wt. (gm) 100120 120140 140160 160180 180200 200220

No of apples 120 170 228 270 168 44

Using an appropriate scale, draw an ogive.(i)From the curve, estimate and record the median weight.

(ii) If apples weighing less than 150 gm are rejects for exports, find the percentage of apples that

may be exported. [5]

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Q11(a)

= tanx+ cotx+ 1 [3]

(b) Find the ratio in which the point A(2, 2) divides the join of P(a, 4) and Q(b,2). [3]

(c) When f(x) = x3

2px2

+ 11x11 is divided by (x3), it leaves the same remainder as theone obtained when g(x) = px

3+ 9x

2+ x 15 is divided by (x + 2). Find the numerical value of p.

Hence, find the integer that must be added to the expression f(x) so that (x 3) becomes a factor of

the resulting expression. Factorise the resulting expression. [4]

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