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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