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BELTHANGADY TALUK MATHS TEACHERS WORKSHOP MINIMUM STUDY LEVEL QUESTION PAPER

Time: 2hour SUBJECT: MATHEMATICS TOTAL: 50 I. Choose the best alternative from following options 1 x 7 = 7 1) If Tn = 2n + 1 ,The first sum of first three terms ---

(A) 3 (B) 7 (C) 10 (D)15 2) If n! =24 then the value of i n is ----

(A) 24 (B) 6 (C) 4 (D) 1 3) Probability of sure event is---

(A) 0 (B) (C) (D) 1 4) The formula to find coefficient of variation--- (A) x100 (B x 100 (C)

. (D) .

5) The slope of the equation 3x + 2y +1 is ----- (A) (B) (C) (D)

6) If the standard deviation of a certain data is 4 , its variance is-------- (A) 2 (B) 4 (C) 8 (D) 16

7) The zero of the polynomial f(x) = 3x – 6 is ---- (A) 2 (B) -2 (C) (D)

II. Answer the following 1 x 5 = 5 8) Express 210 in prime factors 9) If A = { 1, 3, 4, 5 }, B = { 1, 4, 9 } ,find A – B 10) State converse of Thales Theorem.

11) The two circles are intersection, what is the maximum number of common tangents to be drawn?

12) Find the curved surface area of a cone, if its radius is 7cm and slant height is 10cm.

III. Answer the following 2x 10 = 20 13) In a circle of radius 3cm draw two radii such that the angle between them is600

Construct tangents at the non-centre ends of the radii. 14) Rationalize the denominator and simplify

√ √

15) Simplify: 4√63 + 5√7 - 8√28 16) There are 50 students in a school. Out o them 30 students are participating in

Dance,17 are in drama, 5 members are participating in both in a school day . Find the number of students who are not participating in any one of these.

17) Classify the following as permutation and combination. a). Five different subject books to be arranged in a shelf. b).There is 8 chairs and 8 people to occupy them. c). A collection of 10 toys are to be divided equally between two children. d).Five keys are to be arranged in a circular key ring.

OR How many committees of five with a given chairperson can be selected from 12 persons?

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18) Solve by using the formula x2 + x = 12 19) Prove that(1 + 푡푎푛 휃).cos휃 = 1. 20) Find the distance between the points (2, 3) and (6, 6). 21) Verify Euler’s formula for the given graph

22) Sketch out the field to the following notes from the field book (1 cm = 25m.)

To D

75To E

225 150 100 50

75 To C

50 To B

From A

IV. Answer the following 3 x 2= 6

23) Calculate the standard deviation of the following data X 0-10 10-20 20-30 30-40 f 1 2 3 4

24) Prove that the tangents drawn from an external point to a circle are equal. V) Answer the following 4 x 3= 12

25) Draw direct common tangents to two circles of radii 5cm and 2.5cm having their Centers 10cm apart and measure their lengths. 26) Draw the graph of y = x2 - 6x - 7 27) State and prove converse of Pythagoras theorem.

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