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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 one’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 ‘EXTRA’ 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 one’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 ‘EXTRA’ 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 – 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 one’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 ‘EXTRA’ 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 – 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
– a
2
= 0
?
(2 x + b)
2
– (a)
2
= 0 ½ m
?
(2x + b + a) (2x + b – 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 – 4)
2
+ (7 – p)
2
= (3)
2
+ (– 4)
2
?
p = 7 or 4 1 m
4 p 7 p since ? ? ? ½ m
10. Using ar ( ? ?ABC) = 0 ½ m
?
x (7–5) – 5 (5 – y) – 4 (y – 7) = 0 1 m
2x – 25 + 5y – 4y + 28 = 0
2x + y + 3 = 0 ½ m
SECTION - C
11. a
14
= 2 a
8
? a + 13d = 2 (a + 7d) ? a = – d 1 m
a
6
= – 8 ? a + 5d = – 8 ½ m
solving to get a = 2, d = – 2 ½ m
S
20
= 10 (2a + 19d) = 10 (4 – 38) = – 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 one’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 ‘EXTRA’ 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 – 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
– a
2
= 0
?
(2 x + b)
2
– (a)
2
= 0 ½ m
?
(2x + b + a) (2x + b – 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 – 4)
2
+ (7 – p)
2
= (3)
2
+ (– 4)
2
?
p = 7 or 4 1 m
4 p 7 p since ? ? ? ½ m
10. Using ar ( ? ?ABC) = 0 ½ m
?
x (7–5) – 5 (5 – y) – 4 (y – 7) = 0 1 m
2x – 25 + 5y – 4y + 28 = 0
2x + y + 3 = 0 ½ m
SECTION - C
11. a
14
= 2 a
8
? a + 13d = 2 (a + 7d) ? a = – d 1 m
a
6
= – 8 ? a + 5d = – 8 ½ m
solving to get a = 2, d = – 2 ½ m
S
20
= 10 (2a + 19d) = 10 (4 – 38) = – 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 –
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 one’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 ‘EXTRA’ 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 – 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
– a
2
= 0
?
(2 x + b)
2
– (a)
2
= 0 ½ m
?
(2x + b + a) (2x + b – 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 – 4)
2
+ (7 – p)
2
= (3)
2
+ (– 4)
2
?
p = 7 or 4 1 m
4 p 7 p since ? ? ? ½ m
10. Using ar ( ? ?ABC) = 0 ½ m
?
x (7–5) – 5 (5 – y) – 4 (y – 7) = 0 1 m
2x – 25 + 5y – 4y + 28 = 0
2x + y + 3 = 0 ½ m
SECTION - C
11. a
14
= 2 a
8
? a + 13d = 2 (a + 7d) ? a = – d 1 m
a
6
= – 8 ? a + 5d = – 8 ½ m
solving to get a = 2, d = – 2 ½ m
S
20
= 10 (2a + 19d) = 10 (4 – 38) = – 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 –
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 m
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FAQs on CBSE Math Past Year Paper SA-2: Set 3 (2015) - Past Year Papers for Class 10
| 1. What is the weightage of the CBSE Math SA-2 exam for Class 10? |  |
Ans. The CBSE Math SA-2 exam for Class 10 carries a weightage of 80 marks.
| 2. How many questions are there in the CBSE Math SA-2 exam for Class 10? | |
Ans. The CBSE Math SA-2 exam for Class 10 consists of 30 questions.
| 3. Can I use a calculator in the CBSE Math SA-2 exam for Class 10? | |
Ans. No, the use of calculators is not allowed in the CBSE Math SA-2 exam for Class 10. Students are expected to perform calculations without the aid of a calculator.
| 4. Are there any choices available in the CBSE Math SA-2 exam for Class 10? | |
Ans. Yes, the CBSE Math SA-2 exam for Class 10 provides choices in some questions. Students can choose to attempt a certain number of questions out of the given choices.
| 5. Is the CBSE Math SA-2 exam for Class 10 conducted in an offline or online mode? | |
Ans. The CBSE Math SA-2 exam for Class 10 is conducted in an offline mode. Students are required to write their answers on a physical answer sheet provided by the board.
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CBSE Math Past Year Paper SA-2: Set 3 (2015) Notes offer in-depth insights into the specific topic to help you master it with ease.
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It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
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CBSE Math Past Year Paper SA-2: Set 3 (2015) Class 10 Questions
The "CBSE Math Past Year Paper SA-2: Set 3 (2015) Class 10 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 10 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
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Students of Class 10 can study CBSE Math Past Year Paper SA-2: Set 3 (2015) alongwith tests & analysis from the EduRev app,
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The content of CBSE Math Past Year Paper SA-2: Set 3 (2015) is prepared as per the latest Class 10 syllabus.
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