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Page 1
1
Strictly Confidential: (For Internal and Restricted Use Only)
Secondary School Examination
March - 2015
Marking Scheme--- Mathematics (Delhi) 30/1/1, 30/1/2, 30/1/3
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 (Delhi) 30/1/1, 30/1/2, 30/1/3
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 30/1/1
EXPECTED ANSWERS/V ALUE POINTS
SECTION - A
1.
4
9 –
2. 1 : 3 3 .
26
21
4. 25
o
1×4 = 4 m
SECTION - B
5.
o
29 AOQ
2
1
ABQ ? ? ? ?
1 m
? ?
o o o o
61 119 – 180 BAT ABQ – 180 ATQ ? ? ? ? ? ? ? 1 m
6. The given quadratic equation can be written as
? ? 0 b – a x 4a – 4x
4 2 2 2
? ? ½ m
? ? ? ? 0 b – a – 2x or
2
2
2
2
?
1 m
? ? ? ?
?
?
?
?
?
?
? ?
? ? ?
2
b a
,
2
b – a
x
0 b – a – 2x b a – 2x
2 2 2 2
2
2 2 2 2
½ m
7.
?
?
?
?
?
?
?
?
?
? ? ?
?
?
?
OT) to inclined
equally are TQ and (TP 2 1
TC TC
TQ TP
TQC and TPC s ? In
1 m
TQC ? TPC ? ? ?
? ? ? ? ? ? ? 4 3 and QC PC ? ? ? ? ? ½ m
Q.No. Marks
Page 3
1
Strictly Confidential: (For Internal and Restricted Use Only)
Secondary School Examination
March - 2015
Marking Scheme--- Mathematics (Delhi) 30/1/1, 30/1/2, 30/1/3
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 30/1/1
EXPECTED ANSWERS/V ALUE POINTS
SECTION - A
1.
4
9 –
2. 1 : 3 3 .
26
21
4. 25
o
1×4 = 4 m
SECTION - B
5.
o
29 AOQ
2
1
ABQ ? ? ? ?
1 m
? ?
o o o o
61 119 – 180 BAT ABQ – 180 ATQ ? ? ? ? ? ? ? 1 m
6. The given quadratic equation can be written as
? ? 0 b – a x 4a – 4x
4 2 2 2
? ? ½ m
? ? ? ? 0 b – a – 2x or
2
2
2
2
?
1 m
? ? ? ?
?
?
?
?
?
?
? ?
? ? ?
2
b a
,
2
b – a
x
0 b – a – 2x b a – 2x
2 2 2 2
2
2 2 2 2
½ m
7.
?
?
?
?
?
?
?
?
?
? ? ?
?
?
?
OT) to inclined
equally are TQ and (TP 2 1
TC TC
TQ TP
TQC and TPC s ? In
1 m
TQC ? TPC ? ? ?
? ? ? ? ? ? ? 4 3 and QC PC ? ? ? ? ? ½ m
Q.No. Marks
3
?
?
?
?
? ? ? ? ? ? ? ? ?
PQ of bisector right the is OT
90 4 3 180 4 3 But
o o
½ m
8. The given A.P. is 6, 13, 20, ---, 216
Let n be the number of terms, d = 7, a = 6 ½ m
?
216 = 6 + (n – 1) .7
? n = 31 ½ m
?
Middle term is 16th ½ m
?
a
16
= 6 + 15 × 7 = 111 ½ m
9. ABC is right triangle
?
AC
2
= BC
2
+
AB
2
? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
?
?
?
?
?
?
?
? ? ? ? ?
? ? ? ? ? ? ?
? ? ? ? ? ?
2 2 2 2
2 2 2 2
2 2 2
t – 2 49 t – 2 2 5 A
2 t 6 1 2 t 2 2 B
5 AB 25 2 2 2 – 5 AB
C
C
1 m
? ? ? ?
? ? ? ?
?
?
?
?
?
?
?
? ? ? ?
? ?
? ? ? ? ?
1 t 8 2t 4
8 t – 2 – 2 t
2 t 41 t – 2 9 4
2 2
2 2
1 m
10. Let P divide AB in the ratio of k : 1 ½ m
?
?
?
?
?
?
?
? ?
? ? ? ? ?
?
?
?
5
1
K
3 3K 2 K 8
4
3
1 K
2
1
K 2
1 m
?
Required ratio = 1 : 5 ½ m
Page 4
1
Strictly Confidential: (For Internal and Restricted Use Only)
Secondary School Examination
March - 2015
Marking Scheme--- Mathematics (Delhi) 30/1/1, 30/1/2, 30/1/3
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 30/1/1
EXPECTED ANSWERS/V ALUE POINTS
SECTION - A
1.
4
9 –
2. 1 : 3 3 .
26
21
4. 25
o
1×4 = 4 m
SECTION - B
5.
o
29 AOQ
2
1
ABQ ? ? ? ?
1 m
? ?
o o o o
61 119 – 180 BAT ABQ – 180 ATQ ? ? ? ? ? ? ? 1 m
6. The given quadratic equation can be written as
? ? 0 b – a x 4a – 4x
4 2 2 2
? ? ½ m
? ? ? ? 0 b – a – 2x or
2
2
2
2
?
1 m
? ? ? ?
?
?
?
?
?
?
? ?
? ? ?
2
b a
,
2
b – a
x
0 b – a – 2x b a – 2x
2 2 2 2
2
2 2 2 2
½ m
7.
?
?
?
?
?
?
?
?
?
? ? ?
?
?
?
OT) to inclined
equally are TQ and (TP 2 1
TC TC
TQ TP
TQC and TPC s ? In
1 m
TQC ? TPC ? ? ?
? ? ? ? ? ? ? 4 3 and QC PC ? ? ? ? ? ½ m
Q.No. Marks
3
?
?
?
?
? ? ? ? ? ? ? ? ?
PQ of bisector right the is OT
90 4 3 180 4 3 But
o o
½ m
8. The given A.P. is 6, 13, 20, ---, 216
Let n be the number of terms, d = 7, a = 6 ½ m
?
216 = 6 + (n – 1) .7
? n = 31 ½ m
?
Middle term is 16th ½ m
?
a
16
= 6 + 15 × 7 = 111 ½ m
9. ABC is right triangle
?
AC
2
= BC
2
+
AB
2
? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
?
?
?
?
?
?
?
? ? ? ? ?
? ? ? ? ? ? ?
? ? ? ? ? ?
2 2 2 2
2 2 2 2
2 2 2
t – 2 49 t – 2 2 5 A
2 t 6 1 2 t 2 2 B
5 AB 25 2 2 2 – 5 AB
C
C
1 m
? ? ? ?
? ? ? ?
?
?
?
?
?
?
?
? ? ? ?
? ?
? ? ? ? ?
1 t 8 2t 4
8 t – 2 – 2 t
2 t 41 t – 2 9 4
2 2
2 2
1 m
10. Let P divide AB in the ratio of k : 1 ½ m
?
?
?
?
?
?
?
? ?
? ? ? ? ?
?
?
?
5
1
K
3 3K 2 K 8
4
3
1 K
2
1
K 2
1 m
?
Required ratio = 1 : 5 ½ m
4
SECTION - C
11. P is the mid-point of AB
?
x + 1 = 4 ? x = 3
similarly y = 2 ? B (3, 2) 1 m
similarly finding C (–1, 2) ½ m
? ? ? ? ? ? ? ? sq.u. 12 24
2
1
2 – 4 – 1 – 4 2 3 2 – 2 1
2
1
ABC ? Area ? ? ? ? ? ? ?
1½ m
12. The given quadratic eqn. can be written as
(k + 1)x
2
– 2(k – 1)x + 1 = 0 1 m
?
?
?
? ?
? ? ?
3 0, k
0 3k – k or 0 1) 4(k – 1) – 4(k roots qual For
2 2
1 m
?
Non-zero value of k = 3 : Roots are
2
1
,
2
1
½+½ m
13. Fiqure ½ m
30 y 1 45 tan
y
30
(i)
o
? ? ? ?
1 m
3 10
3
30
3
y
x
3
1
0 3 tan
y
x
(ii)
o
? ? ? ? ? ?
1 m
m 3 10 is building of Height ?
½ m
14. Total possible out comes = 36
(i) The possible outcomes are (2, 3), (3, 2), (1, 4), (4, 1) : Number : 4 1 m
9
1
36
4
y Probabilit Required ? ? ?
½ m
Page 5
1
Strictly Confidential: (For Internal and Restricted Use Only)
Secondary School Examination
March - 2015
Marking Scheme--- Mathematics (Delhi) 30/1/1, 30/1/2, 30/1/3
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 30/1/1
EXPECTED ANSWERS/V ALUE POINTS
SECTION - A
1.
4
9 –
2. 1 : 3 3 .
26
21
4. 25
o
1×4 = 4 m
SECTION - B
5.
o
29 AOQ
2
1
ABQ ? ? ? ?
1 m
? ?
o o o o
61 119 – 180 BAT ABQ – 180 ATQ ? ? ? ? ? ? ? 1 m
6. The given quadratic equation can be written as
? ? 0 b – a x 4a – 4x
4 2 2 2
? ? ½ m
? ? ? ? 0 b – a – 2x or
2
2
2
2
?
1 m
? ? ? ?
?
?
?
?
?
?
? ?
? ? ?
2
b a
,
2
b – a
x
0 b – a – 2x b a – 2x
2 2 2 2
2
2 2 2 2
½ m
7.
?
?
?
?
?
?
?
?
?
? ? ?
?
?
?
OT) to inclined
equally are TQ and (TP 2 1
TC TC
TQ TP
TQC and TPC s ? In
1 m
TQC ? TPC ? ? ?
? ? ? ? ? ? ? 4 3 and QC PC ? ? ? ? ? ½ m
Q.No. Marks
3
?
?
?
?
? ? ? ? ? ? ? ? ?
PQ of bisector right the is OT
90 4 3 180 4 3 But
o o
½ m
8. The given A.P. is 6, 13, 20, ---, 216
Let n be the number of terms, d = 7, a = 6 ½ m
?
216 = 6 + (n – 1) .7
? n = 31 ½ m
?
Middle term is 16th ½ m
?
a
16
= 6 + 15 × 7 = 111 ½ m
9. ABC is right triangle
?
AC
2
= BC
2
+
AB
2
? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
?
?
?
?
?
?
?
? ? ? ? ?
? ? ? ? ? ? ?
? ? ? ? ? ?
2 2 2 2
2 2 2 2
2 2 2
t – 2 49 t – 2 2 5 A
2 t 6 1 2 t 2 2 B
5 AB 25 2 2 2 – 5 AB
C
C
1 m
? ? ? ?
? ? ? ?
?
?
?
?
?
?
?
? ? ? ?
? ?
? ? ? ? ?
1 t 8 2t 4
8 t – 2 – 2 t
2 t 41 t – 2 9 4
2 2
2 2
1 m
10. Let P divide AB in the ratio of k : 1 ½ m
?
?
?
?
?
?
?
? ?
? ? ? ? ?
?
?
?
5
1
K
3 3K 2 K 8
4
3
1 K
2
1
K 2
1 m
?
Required ratio = 1 : 5 ½ m
4
SECTION - C
11. P is the mid-point of AB
?
x + 1 = 4 ? x = 3
similarly y = 2 ? B (3, 2) 1 m
similarly finding C (–1, 2) ½ m
? ? ? ? ? ? ? ? sq.u. 12 24
2
1
2 – 4 – 1 – 4 2 3 2 – 2 1
2
1
ABC ? Area ? ? ? ? ? ? ?
1½ m
12. The given quadratic eqn. can be written as
(k + 1)x
2
– 2(k – 1)x + 1 = 0 1 m
?
?
?
? ?
? ? ?
3 0, k
0 3k – k or 0 1) 4(k – 1) – 4(k roots qual For
2 2
1 m
?
Non-zero value of k = 3 : Roots are
2
1
,
2
1
½+½ m
13. Fiqure ½ m
30 y 1 45 tan
y
30
(i)
o
? ? ? ?
1 m
3 10
3
30
3
y
x
3
1
0 3 tan
y
x
(ii)
o
? ? ? ? ? ?
1 m
m 3 10 is building of Height ?
½ m
14. Total possible out comes = 36
(i) The possible outcomes are (2, 3), (3, 2), (1, 4), (4, 1) : Number : 4 1 m
9
1
36
4
y Probabilit Required ? ? ?
½ m
5
(ii) The possible outcomes are
(2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), (6, 6)
their number is 9
1 m
4
1
36
9
y Probabilit Required ? ? ?
½ m
15. Let a be the first term and d the common difference
S
12
= 6 [2a + 11d] = 12a + 66d 1 m
S
8
= 4 [2a + 7d] = 8a + 28d ½ m
S
4
= 2 [2a + 3d] = 4a + 6d ½ m
3 (S
8
– 3
4
) = 3 (4a + 22d) = 12a + 66d = S
12
1 m
16. Let OA = OB = r
?
?
?
?
?
?
? ? ? ? ? ? ? ?
7 r
40r 280 r r
7
22
2
r
7
22
40
1 m
2
cm 7 7
7
22
2
1
2
7
2
7
7
22
2
1
area shaded ?
?
?
?
?
?
? ? ? ? ? ? ? ? ?
1 m
2 2
cm
4
1
96 cm
4
385
4
5
7 7 ? ?
?
?
?
?
?
? ? or
1 m
17. ? ?ARQ ~ ? ?ADC ½ m
2 x
12
4
6
x
? ? ? ?
½ m
5 4 4 8 QC
2 2
? ? ?
½ m
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FAQs on CBSE Math Past Year Paper with Solutions SA-2: Set 4 (2015) - Past Year Papers for Class 10
| 1. What is the format of the CBSE Math Past Year Paper SA-2 for Class 10? |  |
Ans. The CBSE Math Past Year Paper SA-2 for Class 10 follows a specific format. It includes multiple choice questions, short answer questions, and long answer questions. The paper is divided into different sections, each focusing on various topics of the syllabus.
| 2. How can I access the CBSE Math Past Year Paper SA-2 with solutions for Class 10? | |
Ans. You can access the CBSE Math Past Year Paper SA-2 with solutions for Class 10 through various sources. You can either purchase a book or find the papers online on educational websites or forums. Additionally, some coaching centers also provide these papers with solutions.
| 3. What is the significance of solving CBSE Math Past Year Papers SA-2 for Class 10? | |
Ans. Solving CBSE Math Past Year Papers SA-2 for Class 10 is important as it helps students understand the exam pattern, boosts their confidence, and enhances their time management skills. It also gives them an idea about the types of questions asked in the board exams and allows them to practice and evaluate their preparation level.
| 4. Are the solutions provided for the CBSE Math Past Year Paper SA-2 for Class 10 accurate? | |
Ans. The solutions provided for the CBSE Math Past Year Paper SA-2 for Class 10 are usually accurate. However, it is advisable to cross-check the solutions with your teacher or a subject expert to ensure their correctness. Sometimes, there may be alternate methods or approaches to solve a particular question, and it is essential to understand and learn those as well.
| 5. How can solving CBSE Math Past Year Papers SA-2 for Class 10 help in scoring better marks? | |
Ans. Solving CBSE Math Past Year Papers SA-2 for Class 10 can help in scoring better marks by familiarizing students with the exam pattern, improving their problem-solving skills, and enhancing their speed and accuracy. It also helps in identifying weak areas and focusing on them for improvement. Regular practice of past year papers can significantly increase the chances of achieving higher marks in the board exams.
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Additional Information about CBSE Math Past Year Paper with Solutions SA-2: Set 4 (2015) for Class 10 Preparation
CBSE Math Past Year Paper with Solutions SA-2: Set 4 (2015) Free PDF Download
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CBSE Math Past Year Paper with Solutions SA-2: Set 4 (2015) Notes
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CBSE Math Past Year Paper with Solutions SA-2: Set 4 (2015) Class 10 Questions
The "CBSE Math Past Year Paper with Solutions SA-2: Set 4 (2015) Class 10 Questions" guide is a valuable resource for all aspiring students preparing for the
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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.
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Students of Class 10 can study CBSE Math Past Year Paper with Solutions SA-2: Set 4 (2015) alongwith tests & analysis from the EduRev app,
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The content of CBSE Math Past Year Paper with Solutions SA-2: Set 4 (2015) is prepared as per the latest Class 10 syllabus.
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