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Mathematics Design of the Question Paper for SSLC Examination DIMENSION 1 WEIGHTAGE TO CONTENT Sl. No. Units Marks 1. Sets 03 2.* Progressions 08 3. Real Numbers 03 4.* Permutations and Combinatiions 05 5. Probability 03 6. Statistics 04 7. Surds 04 8.* Polynomials 04 9.* Quadratic Equations 09 10.* Circle 10 11.* Similar Triangles 06 12.* Pythagoras Theorem 04 13.* Trigonometry 06 14. Coordinate Geometry 04 15.* Mensuration 07 Total 80 K.S.E.E.B., Malleshwaram, Bangalore, Mathematics 81 1 DIMENSION 2 WEIGHTAGE TO OBJECTIVES Sl. No. Objectives % Marks 1. Remembering 10% 2. Understanding 55% 3. Applying (Including Analysis) 20% 4. Skill 15% Total 100% DIMENSION 3 WEIGHTAGE TO OBJECTIVES Objectives MCQs 1 Marks 1 Mark Question S.A. 2 Marks L.A. 3 Marks L.A. 4 Marks Total Marks Percent age Remembering 1x2=2 1x4=4 2x1=2 - - 08 10% Understanding 1x6=6 1x2=2 2 x 10 = 20 3 x 4 = 12 4x1=4 44 55% - 2x3=6 3x2=6 4x1=4 16 20% Applying (Including Analysis) - Skill - - 2x2=4 - 4x2=8 12 15% Total 1x8=8 1x6=6 2 x 16 = 32 3 x 6 = 18 4 x 4 = 16 80 100% K.S.E.E.B., Malleshwaram, Bangalore, Mathematics 81 2 DIMENSION 4 WEIGHTAGE TO FORM OF QUESTIONS Sl. No. Type of Questions No. of Questions Marks 1. M.C. Questions 08 08 2. Short Answer Type (1 Marks) 06 06 3. Short Answer Type (2 Marks) 16 32 4. Long Answer Type (3 Marks) 06 18 5. Long Answer Type (4 Marks) 04 16 40 80 Total DIMENSION 5 ESTIMATED DIFFICULTY LEVEL Easy 30% Average 50% Difficult 20% K.S.E.E.B., Malleshwaram, Bangalore, Mathematics 81 3 SSLC MODEL QUESTION PAPER SUBJECT : MATHEMATICS Time : 2 Hours 45 Min. Max. Marks : 80 I. Four alternatives are given to each of the following question / incomplete statements. Only one of them is correct or most appropriate. Choose the correct alternative and write the complete answer along with its letter in the space provided against each question. 1x8=8 1. In a G.P. If T2 = 2 2 and T9 = 32 then common ratio is A) B) 2 C) 2 2 D) 4 2 2. The value of nP0 + nC n is 3. 4. 5. 6. 7. 8. II. 9. A) 2n B) n C) 2 D) 0 Probability of a certain event A) 0 B) 1 C) less than 0 D) more than 1 X = 1, 2, 3, 4, 5 its standard deviation is 2 then the value of variance is A) B) 3 C) 2 D) 3 2 3 2 If p(x) = x 4x 2x + 20 the factor for this polynomial is A) x+2 B) x-2 C) x-1 D) x+1 The slope of an equation 3x+2y+1 = 0 is A) - B) C) 3/2 D) - 3/2 The distance between origion and a point (0, 4) is A) 2 B) 4 C) 8 D) 16 If 2cos =1 and is an Acute angle then the value of is A) 00 B) 300 C) 450 D) 600 Answer the following 1x6=6 In Venn diagram the value n(A1 B1) ? 10. In prime factorization of 1309 write the highest prime factor. 11. If p(x) = 2-x3 find the value of p(-1) ? 12. In the adjoining figure the perimeter of PQR is 20cm then calculate the measure of (AB+AC) ? 13. In the adjoining figure ABC=900 and BD AC, express (ADxDC) in terms of BD? K.S.E.E.B., Malleshwaram, Bangalore, Mathematics 81 4 14. Write the formula to find Volume of a sphere II. Answer the following. 2 x 16 = 32 15. In a Group of 58 people, 28 people drink tea only, 18 people drink coffee only and 10 people drink both coffee and tea then find the number of people who drink neither of these? 16. Prove that 3 2 is an irrational number 17. Write the value of a) nPn nPn 1 b) nC n r nC r 18. Find the value of n if 2nC3 : nc3 = 11 : 1 19. In a Randam experiment there is a chance of win or loss. But the probability of winning is four times the loss then find the probability of win ? 20. Simplify 23 16 3 54 3 128 3x 4 3x 2 2 then find the value of x. 2 3x 2 When Polynomials (2x3+ax2+3x-5) and (x3+x2-4x-a) are divisible by (x-1) leaves the same reminder find the value of a Or Find the quotient and remainder when (x6-2x5-x+2) is divided by (x-2) Solve by using formula method x2-2ax+(a+1) (a-1)=0 Construct a pair of tangents to a circle of radius 3cm. Such that angle between the tangents is 400. In ABC, DE||BC and CD||EF. Prove that AD2=AF.AB 21. If 22. 23. 24. 25. =150 then prove that 4sin2B. cos4B. sin6B = 1 26. If B 27. The Vertices of a triangle are (8, -4), (9, 5) and (0, 4). Prove that triangle is an isosceles triangle. 28. The diameter of the base of Cylinder is 2m and height is 1.8m is method to recast a cone of diameter 3m, find the height of a cone. Or Diameter of garden roller is 1.4m and length 2m takes 5 revolutions to complete the garden find the area of the garden? 29. Dust bin in the form of frustum having radii 15cm and 8cm respectively and its depth is 63 cm. Find its volume? 30. Draw a scale drawing for the following information. Scale : 20 m = 1 cm Towards D In meters 200 140 To C 60 To E 60 120 40 To B 50 From A K.S.E.E.B., Malleshwaram, Bangalore, Mathematics 81 5 III. Answer the following. 3 x 6 = 18 31. Find the sum of all natural numbers between 200 and 300 which are divisible by 6. Or Find GP for which sum of the first 2 terms is 4 and fifth term is 4 times the third term. 32. Find the standard deviation for the following Distribution by step deviation method. Marks (x) 10 20 30 40 50 Number of 4 3 6 5 2 students (f) 33. In ABC, AB=BC, BD is the altitude for the base AC of a triangle. DC = x units, BD = 2x-1 units, BC =(2x+1) units. Find the measure of the sides of a triangle. Or Shweta takes 6 days less than the Ankitha to complete the work. The same work is completed together in 4 days. How many days required to complete the work by Ankitha alone? 34. If two circles touch each other externally then the point of contact and the centres are collinear Prove this. 35. In ABD, BC:CD=1:4. C is a point on BD, and ABC is an equiangular triangle. Prove that AD2=21AC2 Or In ABC BD:CD=3:1 and AD BC. Prove that 2(AB2-AC2)=BC2. 36. From the top of a building 16m high the angular elevation of the top of a hill is 600 and the angular depression of the foot of the hill is 300 find the height of the hill. Or Two windmills of height 50m and 40m are on either side of the field. A person observes the top of the windmills from a point in between the towers the angle of elevation was found to be 450 in both the cases. Find the distance between the windmills. IV. Answer the following : 4 x 4 = 16 37. Five positive integers are in AP. The sum of 3 middle terms is 24 and product of First and Fifth term is 48. Find the terms of A.P. Or Find four terms of G.P. whose product of first three terms is 8 and sum of last three terms is 14. 38. Solve graphically x2-5x+6=0 39. Construct a transverage common tangent to two congruent circles of radii 2.5 cm, whose centres are 9cm apart measure its length and verify by calculation. 40. The areas of two-similar triangles are proportional to the squares on the corresponding sides prove this. *** K.S.E.E.B., Malleshwaram, Bangalore, Mathematics 81 6 J J J j P Ai w P Ai i z j U t v DAi i 1 Ai P rg R v P . AS . Ai CAP U 1. U tU 03 2.* r U 08 3. AS U 03 4.* P Ai d v P U 05 5. A s Ai v 03 6. AS 04 7. P g t U 04 8.* z Q U 04 9.* U P g tU 09 10.* v U 10 11.* g w s dU 06 12.* x U g Ai 04 13.* w P w 06 14. z AP g S U t v 04 15.* P v U t v 07 Ml 80 K.S.E.E.B., Malleshwaram, Bangalore, Mathematics 81 7 DAi i 2 G U U R v P . AS . P q CAP U G U 1. g u 10% 2. w P 55% 3. C P ( u v ) 20% 4. P 15% Ml 100% DAi i 3 Gz U U rg R v DAi U G U . W W Gv g Gv g U 2 U 1 CAP U CAP W Gv g U 3 CAP U W Gv g U 4 Ml CAP U P q CAP U g u 1x2=2 1x4=4 2x1=2 - - 08 10% w P 1x6=6 1x2=2 2 x 10 = 20 3 x 4 = 12 4x1=4 44 55% - 2x3=6 3x2=6 4x1=4 16 20% C P ( u v ) - P - - 2x2=4 - 4x2=8 12 15% Ml 1x8=8 1x6=6 2 x 16 = 32 3 x 6 = 18 4 x 4 = 16 80 100% K.S.E.E.B., Malleshwaram, Bangalore, Mathematics 81 8 DAi i 4 Ai g U U rg R v P . AS . Ai g U AS U CAP U 1. DAi U 08 08 2. W Gv g U (1 CAP ) 06 06 3. W Gv g U (2 CAP U ) 16 32 4. W Gv g U (3 CAP U ) 06 18 5. W Gv g U (4 CAP U ) 04 16 40 80 Ml DAi i 5 P ptv Ai l s 30% i 50% P pt 20% K.S.E.E.B., Malleshwaram, Bangalore, Mathematics 81 9 J J J i z j w P Ai : U t v Ai : 2 U Am 45 U U j CAP U : 80 I. P V U U Cx C t P U U Ai i Gv g U P n z . C U jAi i z v Z P z Gv g Dj , Gv g P P n g e U z Ai P i P g z q t Gv g g j. 1x8=8 1. U u v g r Ai T2 = 2 2 v T9 = 32 Dz g i C v B) 2 C) 2 2 D) 4 2. A) 2 nP0 + nC n A) B) n C) 2 D) 0 3. 2n Rav W l Ai A s Ai v Ai A) 0 B) 1 C) 0 VAv P r D) 1 Q Av P r 4. X = 1, 2, 3, 4, 5 F AP U i P Z Ai D) 3 5. A) B) 3 C) 2 2 3 2 p(x) = x 4x 2x + 20 z Q Ai MAz C v A) x+2 B) x-2 3x+2y+1 = 0 P g tz E e g C) x-1 D) x+1 6. A) C) 3/2 D) - 3/2 D) 16 D) 600 1x6=6 - B) 7. Az v (0, 4) Az q z g 8. A) 2 B) 4 C) 8 2cos =1 v W P z g , Ai 2 Dz g g t Z A) II. 00 B) 300 C) 450 F P V U Gv j . 9. F P n g av z n(A1 B1) J ? 10. 1309 AS Ai C s d C v U g U j C s d AS Ai g j. 11. If p(x) = 2-x3 z Q Ai p(-1) g J ? 12. F P U P n g av z PQR v v =20cm Dz g (AB+AC) C v w . K.S.E.E.B., Malleshwaram, Bangalore, Mathematics 81 10 13. P n g av z ABC=900 v BD AC, Dz g (ADxDC) Ai Ai BD Ai g z g j? 14. U z W s P Aq rAi v g j. F P V U Gv j . 2 x 16 = 32 15. 58 d g U A 28 d g n Ai i v , 18 d g P Ai i v v 10 d g n v P Jg q E q v g . U z g n Cx P Jg q E q z g AS Ai P Aq r j. III. 3 2 MAz C s U AS JA z . 16. 17. P V U Ai g j. a) nPn nPn 1 b) nC n r nC r 18. 2n C3 : nc3 = 11 : 1 Dz g n P Aq r j. 19. MAz Ai i z a P Ai U z s v A U Cx DVz . U A s Ai v Ai A s Ai v Ai A s Ai v Ai P Aq r j. g z . U z g U 20. s g P v 23 16 3 54 3 128 3x 4 3x 2 2 Dz g x Ai P Aq r j. 2 3x 2 22. z Q U z (2x3+ax2+3x-5) v (x3+x2-4x-a) E U (x-1) jAz 21. s V z U G Ai MAz DVz g , a P Aq r j. Cx (x6-2x5-x+2) (x-2) Az s V z U g s U v P Aq r j. 23. U P g tz v z Ai Az r . x2-2ax+(a+1) (a-1)=0 24. 3cm w d v P P U q P 400 Eg Av MAz e v P U g a . 25. ABC Ai DE||BC v CD||EF DVz . AD2=AF.AB JAz . K.S.E.E.B., Malleshwaram, Bangalore, Mathematics 81 11 26. =150 Dz g , 4 sin2B. cos4B. sin6B = 1 JAz . B 27. MAz w s dz AU U (8, -4), (9, 5) v (0, 4) DVz U , Cz w s d Vg v z JAz . 28. 2m z z g v 1.8m Jv g z W z v P g z Aq g P g V , v Cz 3m v P g z AP P wU j w Vz . U j w z U AP Jv g P Aq r j. Cx v lz g g 1.4m v Gz 2m Cz v 5 t v U J t v z ? 29. P g z P z n Ai v P g z Jg q Ai w d U P V 15cm v 8cm DVz . Ez g D 63cm z g , P z n Ai W s P Aq r j. 30. P P v P Az P n g z v A U P Aq MAz d P J j. P i t : 20m = 1cm D U lg U 200 140 E U 60 C U 60 120 B U 50 40 A Az F P V U Gv j . 3 x 6 = 18 31. 6 jAz V s U U 200 v 300g q J s P AS U v P Aq r j. Cx U u v g r Ai z Jg q z U v -4 v 5 z 3 Ai z z g z g , r Ai g j. 32. P n g v g u U i P Z Ai Av Z zs P Aq r j. IV. CAP U (x) z y U AS (f) 10 20 30 40 50 4 3 6 5 2 K.S.E.E.B., Malleshwaram, Bangalore, Mathematics 81 12 33. ABC w s dz , AB=BC v BD Ai z AC U Jv g Vz . DC =x, BD = 2x-1 v BC =(2x+1) Dz g w s dz g U Gz P Aq r j. 34. 35. 36. V. 37. 38. 39. 40. Cx MAz P w i q v , CAQv VAv 6 U P r v U z P v . Cz P v v CAQv Mn U j 4 U V g . Vz g CAQv M D P V v U z P U AS Ai P Aq r j. Jg q v U V z U , v P Az U v Az KP g S U v Vg v z JAz . ABD Ai BC:CD=1:4 DU Av BD Ai C Ai MAz Az v ABC Ai w s d Vz g , AD2=21AC2 JAz . Cx ABC Ai BD:CD=3:1 v AD BC DVz g , 2(AB2-AC2)=BC2 JAz . 16 Jv g z P l q z Az , MAz l z v Ai rz U GAm z G v P 600 DVz . U Ai l z z rz U GAm z C v P 300 DVz . U z g l z Jv g P Aq r j. Cx MAz d Jg q P q 50m v 40m Jv g g Jg q U Ai Av U . D Jg q U Ai Av U q Awg M Q Ai C U v Ai Q v . Jg q Az s U G v P 450 U Vz U Ai Av U q z g P Aq r j. F P V U Gv j . 4 x 4 = 16 i Av g r Ai z Lz zs u AP U , zs z g z U v 24. z v Lz z U U t 48 Dz g i Av g r Ai g j. Cx U u v g r Ai g z U z g z U U t 8 v P Ai g z U v 14 Dz g D z U P Aq r j. P Ai P r . x2-5x+6=0 P Az U q CAv g 9cm Eg 2.5cm w d g Jg q v U U MAz v i P g a , Gz C z P Z g Az v r. g w s dU t U C U C g U U U U i v z g v JAz . *** K.S.E.E.B., Malleshwaram, Bangalore, Mathematics 81 13
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