Page 1 1 Strictly Confidential: (For Internal and Restricted Use Only) Secondary School Examination March -2015 Marking Scheme--- Mathematics (Outside Delhi) 30/1, 30/2, 30/3 General Instructions 1. The Marking Scheme provides general guidelines to reduce subjectivity and maintain uniformity among large number of examiners involved in the marking. The answers given in the marking scheme are the best suggested answers. 2. Marking is to be done as per the instructions provided in the marking scheme. (It should not be done according to oneâ€™s own interpretation or any other consideration.)Marking Scheme should be strictly adhered to and religiously followed. 3. Alternative methods are accepted. Proportional marks are to be awarded. 4. The Head-Examiners have to go through the first five answer-scripts evaluated by each evaluator to ensure that the evaluation has been done as per instructions given in the marking scheme. The remaining answer scripts meant for evaluation shall be given only after ensuring that there is no significant variation in the marking of individual evaluators. 5. If a question is attempted twice and the candidate has not crossed any answer, only first attempt is to be evaluated. Write â€˜EXTRAâ€™ with second attempt. 6. A full scale of marks 0 to 90 has to be used. Please do not hesitate to award full marks if the answer deserves it. 7. Separate Marking Scheme for all the three sets has been given. 8. The Examiners should acquaint themselves with the guidelines given in the Guidelines for Spot Evaluation before starting the actual evaluation. 9. Every Examiner should stay upto sufficiently reasonable time normally 5-6 hours every day and evaluate 20-25 answer books and should devote minimum 15-20 minutes to evaluate each answer book. 10. Every Examiner should acquaint himself/herself with the marking schemes of all the sets. Page 2 1 Strictly Confidential: (For Internal and Restricted Use Only) Secondary School Examination March -2015 Marking Scheme--- Mathematics (Outside Delhi) 30/1, 30/2, 30/3 General Instructions 1. The Marking Scheme provides general guidelines to reduce subjectivity and maintain uniformity among large number of examiners involved in the marking. The answers given in the marking scheme are the best suggested answers. 2. Marking is to be done as per the instructions provided in the marking scheme. (It should not be done according to oneâ€™s own interpretation or any other consideration.)Marking Scheme should be strictly adhered to and religiously followed. 3. Alternative methods are accepted. Proportional marks are to be awarded. 4. The Head-Examiners have to go through the first five answer-scripts evaluated by each evaluator to ensure that the evaluation has been done as per instructions given in the marking scheme. The remaining answer scripts meant for evaluation shall be given only after ensuring that there is no significant variation in the marking of individual evaluators. 5. If a question is attempted twice and the candidate has not crossed any answer, only first attempt is to be evaluated. Write â€˜EXTRAâ€™ with second attempt. 6. A full scale of marks 0 to 90 has to be used. Please do not hesitate to award full marks if the answer deserves it. 7. Separate Marking Scheme for all the three sets has been given. 8. The Examiners should acquaint themselves with the guidelines given in the Guidelines for Spot Evaluation before starting the actual evaluation. 9. Every Examiner should stay upto sufficiently reasonable time normally 5-6 hours every day and evaluate 20-25 answer books and should devote minimum 15-20 minutes to evaluate each answer book. 10. Every Examiner should acquaint himself/herself with the marking schemes of all the sets. 2 QUESTION PAPER CODE 30/1 EXPECTED ANSWERS/V ALUE POINTS SECTION - A 1. p = 3 1 m 2. 30 o 1 m 3. 9 1 1 m 4. 120 o 1 m SECTION - B 5. ? ? ? ?POR = 90 â€“ 60 = 30 o ½ m PR 2 OR 2 1 sin30 OR PRO o ? ? ? ? = PR + QR ½ m 6. Let AF = AE = x ? AB = 6 + x, AC = 9 + x, BC = 15 ½ m ? ? 54 3 x 9 x 6 15 2 1 ? ? ? ? ? ? 1 m ? x = 3 ? AB = 9 cm, AC = 12 cm ½ m and BC = 15 cm Q.No. Marks Page 3 1 Strictly Confidential: (For Internal and Restricted Use Only) Secondary School Examination March -2015 Marking Scheme--- Mathematics (Outside Delhi) 30/1, 30/2, 30/3 General Instructions 1. The Marking Scheme provides general guidelines to reduce subjectivity and maintain uniformity among large number of examiners involved in the marking. The answers given in the marking scheme are the best suggested answers. 2. Marking is to be done as per the instructions provided in the marking scheme. (It should not be done according to oneâ€™s own interpretation or any other consideration.)Marking Scheme should be strictly adhered to and religiously followed. 3. Alternative methods are accepted. Proportional marks are to be awarded. 4. The Head-Examiners have to go through the first five answer-scripts evaluated by each evaluator to ensure that the evaluation has been done as per instructions given in the marking scheme. The remaining answer scripts meant for evaluation shall be given only after ensuring that there is no significant variation in the marking of individual evaluators. 5. If a question is attempted twice and the candidate has not crossed any answer, only first attempt is to be evaluated. Write â€˜EXTRAâ€™ with second attempt. 6. A full scale of marks 0 to 90 has to be used. Please do not hesitate to award full marks if the answer deserves it. 7. Separate Marking Scheme for all the three sets has been given. 8. The Examiners should acquaint themselves with the guidelines given in the Guidelines for Spot Evaluation before starting the actual evaluation. 9. Every Examiner should stay upto sufficiently reasonable time normally 5-6 hours every day and evaluate 20-25 answer books and should devote minimum 15-20 minutes to evaluate each answer book. 10. Every Examiner should acquaint himself/herself with the marking schemes of all the sets. 2 QUESTION PAPER CODE 30/1 EXPECTED ANSWERS/V ALUE POINTS SECTION - A 1. p = 3 1 m 2. 30 o 1 m 3. 9 1 1 m 4. 120 o 1 m SECTION - B 5. ? ? ? ?POR = 90 â€“ 60 = 30 o ½ m PR 2 OR 2 1 sin30 OR PRO o ? ? ? ? = PR + QR ½ m 6. Let AF = AE = x ? AB = 6 + x, AC = 9 + x, BC = 15 ½ m ? ? 54 3 x 9 x 6 15 2 1 ? ? ? ? ? ? 1 m ? x = 3 ? AB = 9 cm, AC = 12 cm ½ m and BC = 15 cm Q.No. Marks 3 7. 4x 2 + 4bx + b 2 â€“ a 2 = 0 ? (2 x + b) 2 â€“ (a) 2 = 0 ½ m ? (2x + b + a) (2x + b â€“ a) = 0 ½ m 2 b a x , 2 b a x ? ? ? ? ? ? ½ +½ m 8. ? ? ? ? 167 6d 2a 2 7 4d 2a 2 5 167 S S 7 5 ? ? ? ? ? ? ? 24a + 62d = 334 or 12a + 31d = 167 .............................(i) ½ m ? ? 47 9d 2a or 235 9d 2a 5 235 S 10 ? ? ? ? ? ? ..............(ii) ½ m Solving (i) and (ii) to get a = 1, d = 5. Hence AP is 1, 6, 11, ......... ½ + ½ m 9. Here, AB 2 + BC 2 = AC 2 ½ m ? (4) 2 + (p â€“ 4) 2 + (7 â€“ p) 2 = (3) 2 + (â€“ 4) 2 ? p = 7 or 4 1 m 4 p 7 p since ? ? ? ½ m 10. Using ar ( ? ?ABC) = 0 ½ m ? x (7â€“5) â€“ 5 (5 â€“ y) â€“ 4 (y â€“ 7) = 0 1 m 2x â€“ 25 + 5y â€“ 4y + 28 = 0 2x + y + 3 = 0 ½ m SECTION - C 11. a 14 = 2 a 8 ? a + 13d = 2 (a + 7d) ? a = â€“ d 1 m a 6 = â€“ 8 ? a + 5d = â€“ 8 ½ m solving to get a = 2, d = â€“ 2 ½ m S 20 = 10 (2a + 19d) = 10 (4 â€“ 38) = â€“ 340 1 m Page 4 1 Strictly Confidential: (For Internal and Restricted Use Only) Secondary School Examination March -2015 Marking Scheme--- Mathematics (Outside Delhi) 30/1, 30/2, 30/3 General Instructions 1. The Marking Scheme provides general guidelines to reduce subjectivity and maintain uniformity among large number of examiners involved in the marking. The answers given in the marking scheme are the best suggested answers. 2. Marking is to be done as per the instructions provided in the marking scheme. (It should not be done according to oneâ€™s own interpretation or any other consideration.)Marking Scheme should be strictly adhered to and religiously followed. 3. Alternative methods are accepted. Proportional marks are to be awarded. 4. The Head-Examiners have to go through the first five answer-scripts evaluated by each evaluator to ensure that the evaluation has been done as per instructions given in the marking scheme. The remaining answer scripts meant for evaluation shall be given only after ensuring that there is no significant variation in the marking of individual evaluators. 5. If a question is attempted twice and the candidate has not crossed any answer, only first attempt is to be evaluated. Write â€˜EXTRAâ€™ with second attempt. 6. A full scale of marks 0 to 90 has to be used. Please do not hesitate to award full marks if the answer deserves it. 7. Separate Marking Scheme for all the three sets has been given. 8. The Examiners should acquaint themselves with the guidelines given in the Guidelines for Spot Evaluation before starting the actual evaluation. 9. Every Examiner should stay upto sufficiently reasonable time normally 5-6 hours every day and evaluate 20-25 answer books and should devote minimum 15-20 minutes to evaluate each answer book. 10. Every Examiner should acquaint himself/herself with the marking schemes of all the sets. 2 QUESTION PAPER CODE 30/1 EXPECTED ANSWERS/V ALUE POINTS SECTION - A 1. p = 3 1 m 2. 30 o 1 m 3. 9 1 1 m 4. 120 o 1 m SECTION - B 5. ? ? ? ?POR = 90 â€“ 60 = 30 o ½ m PR 2 OR 2 1 sin30 OR PRO o ? ? ? ? = PR + QR ½ m 6. Let AF = AE = x ? AB = 6 + x, AC = 9 + x, BC = 15 ½ m ? ? 54 3 x 9 x 6 15 2 1 ? ? ? ? ? ? 1 m ? x = 3 ? AB = 9 cm, AC = 12 cm ½ m and BC = 15 cm Q.No. Marks 3 7. 4x 2 + 4bx + b 2 â€“ a 2 = 0 ? (2 x + b) 2 â€“ (a) 2 = 0 ½ m ? (2x + b + a) (2x + b â€“ a) = 0 ½ m 2 b a x , 2 b a x ? ? ? ? ? ? ½ +½ m 8. ? ? ? ? 167 6d 2a 2 7 4d 2a 2 5 167 S S 7 5 ? ? ? ? ? ? ? 24a + 62d = 334 or 12a + 31d = 167 .............................(i) ½ m ? ? 47 9d 2a or 235 9d 2a 5 235 S 10 ? ? ? ? ? ? ..............(ii) ½ m Solving (i) and (ii) to get a = 1, d = 5. Hence AP is 1, 6, 11, ......... ½ + ½ m 9. Here, AB 2 + BC 2 = AC 2 ½ m ? (4) 2 + (p â€“ 4) 2 + (7 â€“ p) 2 = (3) 2 + (â€“ 4) 2 ? p = 7 or 4 1 m 4 p 7 p since ? ? ? ½ m 10. Using ar ( ? ?ABC) = 0 ½ m ? x (7â€“5) â€“ 5 (5 â€“ y) â€“ 4 (y â€“ 7) = 0 1 m 2x â€“ 25 + 5y â€“ 4y + 28 = 0 2x + y + 3 = 0 ½ m SECTION - C 11. a 14 = 2 a 8 ? a + 13d = 2 (a + 7d) ? a = â€“ d 1 m a 6 = â€“ 8 ? a + 5d = â€“ 8 ½ m solving to get a = 2, d = â€“ 2 ½ m S 20 = 10 (2a + 19d) = 10 (4 â€“ 38) = â€“ 340 1 m 4 12. 0 3 2 x 2 2 x 3 2 ? ? ? ? ? ? ? 0 2 x 3 6 x 0 3 2 x 2 x 2 3 x 3 2 ? ? ? ? ? ? ? ? ? 1+1 m 3 2 , 6 x ? ? ? ? x ½ + ½ m 13. Let AL = x 0 60 tan x BL ? ? Fig. ½ m m. 1500 x 3 x 3 1500 ? ? ? ? 1 m 3 1 30 tan M L AL CM 0 ? ? ? ? 1500 + LM = 1500 (3) = 4500 1 m ? LM = 3000 m. ? Speed = 15 3000 = 200 m./s. = 720 Km/hr. . ½ m 14. 4 : 3 PB : AP AB 7 3 AP ? ? ? 1 m ? ? ? ? 7 2 7 8 6 x 4 2, 4 : 3 2 2, B y) (x, P A ? ? ? ? ? ? ? ? 1 m 7 20 7 8 2 1 â€“ y ? ? ? ? ½ m ? ? ? ? ? ? ? ? 7 20 , 7 2 P ½ m 15. ? ? ? ? 3 1 blue P , 4 1 Red P ? ? ? ? 12 5 3 1 4 1 1 orange P ? ? ? ? ? 1½ m ? ? 10 balls of no. Total 12 5 ? ? ½ m 24 5 12 10 balls of no. Total ? ? ? ? 1 m Page 5 1 Strictly Confidential: (For Internal and Restricted Use Only) Secondary School Examination March -2015 Marking Scheme--- Mathematics (Outside Delhi) 30/1, 30/2, 30/3 General Instructions 1. The Marking Scheme provides general guidelines to reduce subjectivity and maintain uniformity among large number of examiners involved in the marking. The answers given in the marking scheme are the best suggested answers. 2. Marking is to be done as per the instructions provided in the marking scheme. (It should not be done according to oneâ€™s own interpretation or any other consideration.)Marking Scheme should be strictly adhered to and religiously followed. 3. Alternative methods are accepted. Proportional marks are to be awarded. 4. The Head-Examiners have to go through the first five answer-scripts evaluated by each evaluator to ensure that the evaluation has been done as per instructions given in the marking scheme. The remaining answer scripts meant for evaluation shall be given only after ensuring that there is no significant variation in the marking of individual evaluators. 5. If a question is attempted twice and the candidate has not crossed any answer, only first attempt is to be evaluated. Write â€˜EXTRAâ€™ with second attempt. 6. A full scale of marks 0 to 90 has to be used. Please do not hesitate to award full marks if the answer deserves it. 7. Separate Marking Scheme for all the three sets has been given. 8. The Examiners should acquaint themselves with the guidelines given in the Guidelines for Spot Evaluation before starting the actual evaluation. 9. Every Examiner should stay upto sufficiently reasonable time normally 5-6 hours every day and evaluate 20-25 answer books and should devote minimum 15-20 minutes to evaluate each answer book. 10. Every Examiner should acquaint himself/herself with the marking schemes of all the sets. 2 QUESTION PAPER CODE 30/1 EXPECTED ANSWERS/V ALUE POINTS SECTION - A 1. p = 3 1 m 2. 30 o 1 m 3. 9 1 1 m 4. 120 o 1 m SECTION - B 5. ? ? ? ?POR = 90 â€“ 60 = 30 o ½ m PR 2 OR 2 1 sin30 OR PRO o ? ? ? ? = PR + QR ½ m 6. Let AF = AE = x ? AB = 6 + x, AC = 9 + x, BC = 15 ½ m ? ? 54 3 x 9 x 6 15 2 1 ? ? ? ? ? ? 1 m ? x = 3 ? AB = 9 cm, AC = 12 cm ½ m and BC = 15 cm Q.No. Marks 3 7. 4x 2 + 4bx + b 2 â€“ a 2 = 0 ? (2 x + b) 2 â€“ (a) 2 = 0 ½ m ? (2x + b + a) (2x + b â€“ a) = 0 ½ m 2 b a x , 2 b a x ? ? ? ? ? ? ½ +½ m 8. ? ? ? ? 167 6d 2a 2 7 4d 2a 2 5 167 S S 7 5 ? ? ? ? ? ? ? 24a + 62d = 334 or 12a + 31d = 167 .............................(i) ½ m ? ? 47 9d 2a or 235 9d 2a 5 235 S 10 ? ? ? ? ? ? ..............(ii) ½ m Solving (i) and (ii) to get a = 1, d = 5. Hence AP is 1, 6, 11, ......... ½ + ½ m 9. Here, AB 2 + BC 2 = AC 2 ½ m ? (4) 2 + (p â€“ 4) 2 + (7 â€“ p) 2 = (3) 2 + (â€“ 4) 2 ? p = 7 or 4 1 m 4 p 7 p since ? ? ? ½ m 10. Using ar ( ? ?ABC) = 0 ½ m ? x (7â€“5) â€“ 5 (5 â€“ y) â€“ 4 (y â€“ 7) = 0 1 m 2x â€“ 25 + 5y â€“ 4y + 28 = 0 2x + y + 3 = 0 ½ m SECTION - C 11. a 14 = 2 a 8 ? a + 13d = 2 (a + 7d) ? a = â€“ d 1 m a 6 = â€“ 8 ? a + 5d = â€“ 8 ½ m solving to get a = 2, d = â€“ 2 ½ m S 20 = 10 (2a + 19d) = 10 (4 â€“ 38) = â€“ 340 1 m 4 12. 0 3 2 x 2 2 x 3 2 ? ? ? ? ? ? ? 0 2 x 3 6 x 0 3 2 x 2 x 2 3 x 3 2 ? ? ? ? ? ? ? ? ? 1+1 m 3 2 , 6 x ? ? ? ? x ½ + ½ m 13. Let AL = x 0 60 tan x BL ? ? Fig. ½ m m. 1500 x 3 x 3 1500 ? ? ? ? 1 m 3 1 30 tan M L AL CM 0 ? ? ? ? 1500 + LM = 1500 (3) = 4500 1 m ? LM = 3000 m. ? Speed = 15 3000 = 200 m./s. = 720 Km/hr. . ½ m 14. 4 : 3 PB : AP AB 7 3 AP ? ? ? 1 m ? ? ? ? 7 2 7 8 6 x 4 2, 4 : 3 2 2, B y) (x, P A ? ? ? ? ? ? ? ? 1 m 7 20 7 8 2 1 â€“ y ? ? ? ? ½ m ? ? ? ? ? ? ? ? 7 20 , 7 2 P ½ m 15. ? ? ? ? 3 1 blue P , 4 1 Red P ? ? ? ? 12 5 3 1 4 1 1 orange P ? ? ? ? ? 1½ m ? ? 10 balls of no. Total 12 5 ? ? ½ m 24 5 12 10 balls of no. Total ? ? ? ? 1 m 5 16. r = 14 cm. ? = 60 0 Area of minor segment ? sin r 2 1 360 ? r p 2 2 ? ? ½ m 2 3 14 14 2 1 360 60 14 14 7 22 ? ? ? ? ? ? ? ? ½ m Approx. cm 17.9 or cm 17.89 or cm 3 49 3 308 2 2 2 ? ? ? ? ? ? ? ? 1 m Area of Major segment ? ? ? ? ? ? ? ? ? 3 49 3 308 r p 2 ½ m 2 2 cm 598.10 or cm 3 49 3 1540 ? ? ? ? ? ? ? ? ½ m Approx. cm 598 or 2 17. Slant height ? ? ? ? cm. 3.5 2.1 2.8 ) ( 2 2 ? ? ? ? ½ m ? ? tent one for 3.5 2.1 7 22 4 2.1 7 22 2 canvas of Area ? ? ? ? ? ? ? ? = 6.6 (8 + 3.5) = 6.6 ? 11.5 m 2 ½ m ? Area for 100 tents = 66 ?115 m 2 Cost of 100 tents = Rs. 66 ?115 ?100 ½ m 50% Cost = 33 ? 11500 = Rs. 379500 ½ m V alues : Helping the flood victims 1 m 18. Volume of liquid in the bowl = ? ? 3 3 cm 18 p 3 2 ? ? ½ m Volume, after wastage = ? ? 3 3 cm 100 90 18 3 p 2 ? ? ½ m Volume of liquid in 72 bottles = ? ? 3 2 cm 72 3 p ? ? h ½ m ? ? ? ? cm. 5.4 72 3 p 10 9 18 p 3 2 h 2 3 ? ? ? ? ? ½ + 1 mRead More

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!