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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 5 (2015) - Past Year Papers for Class 10
| 1. What is the CBSE Math Past Year Paper SA-2? |  |
Ans. The CBSE Math Past Year Paper SA-2 refers to the mathematics question paper conducted by the Central Board of Secondary Education (CBSE) during the second term or semester of the academic year. It includes questions from the entire syllabus and is used as a tool for assessment and evaluation of students' mathematical knowledge and skills.
| 2. How can I access the CBSE Math Past Year Paper SA-2 of 2015? | |
Ans. To access the CBSE Math Past Year Paper SA-2 of 2015, you can visit the official website of CBSE (cbse.nic.in) or various other educational websites that provide previous year question papers. Look for the class 10 question papers section and search for the 2015 SA-2 Math paper. You can either download it or view it online for practice and reference.
| 3. Are the CBSE Math Past Year Papers SA-2 useful for exam preparation? | |
Ans. Yes, the CBSE Math Past Year Papers SA-2 are extremely useful for exam preparation. These papers provide a clear understanding of the exam pattern, types of questions asked, and the level of difficulty. Solving these papers helps in identifying weak areas, practicing time management, and improving overall performance. It is highly recommended to solve as many past year papers as possible to enhance your preparation and boost confidence.
| 4. Can I rely solely on the CBSE Math Past Year Paper SA-2 for exam preparation? | |
Ans. While solving the CBSE Math Past Year Paper SA-2 is an important part of exam preparation, it is not advisable to rely solely on it. The past year papers should be used as a supplement to your regular studies and practice. It is crucial to thoroughly understand the concepts, practice a wide range of questions, and refer to the textbook and study materials provided by your school. Additionally, seek guidance from teachers or tutors to clarify doubts and ensure comprehensive preparation.
| 5. How can I make the most out of solving the CBSE Math Past Year Paper SA-2? | |
Ans. To make the most out of solving the CBSE Math Past Year Paper SA-2, follow these tips:
1. Set a timer and solve the paper within the specified time limit to practice time management.
2. Attempt the paper in a simulated exam environment to experience real exam conditions.
3. After solving, thoroughly analyze your answers and identify mistakes or areas of improvement.
4. Refer to the solutions provided or seek help from teachers to understand the correct approach for solving each question.
5. Make notes of important formulas, concepts, or techniques that you need to revise or practice more.
6. Repeat the process of solving past year papers multiple times to enhance your speed, accuracy, and confidence.
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The CBSE Math Past Year Paper SA-2: Set 5 (2015) is an invaluable resource that delves deep into the core of the Class 10 exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
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or toppers' notes, this PDF has got you covered. Download the CBSE Math Past Year Paper SA-2: Set 5 (2015) now and kickstart your journey towards success in the Class 10 exam.
Importance of CBSE Math Past Year Paper SA-2: Set 5 (2015)
The importance of CBSE Math Past Year Paper SA-2: Set 5 (2015) cannot be overstated, especially for Class 10 aspirants.
This document holds the key to success in the Class 10 exam.
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CBSE Math Past Year Paper SA-2: Set 5 (2015) Notes
CBSE Math Past Year Paper SA-2: Set 5 (2015) Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to CBSE Math Past Year Paper SA-2: Set 5 (2015).
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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Access to Toppers' notes gives you an edge in understanding complex concepts.
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CBSE Math Past Year Paper SA-2: Set 5 (2015) Class 10 Questions
The "CBSE Math Past Year Paper SA-2: Set 5 (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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The content of CBSE Math Past Year Paper SA-2: Set 5 (2015) is prepared as per the latest Class 10 syllabus.
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