CBSE Class 10 Question Paper 2022 Solution Maths Standard

Strictly Confidential : (For Internal and Restricted use only)
Secondary School Examination
Term–II, 2022

Marking Scheme : MATHEMATICS (Standard) (Subject Code : 041)
[ Paper Code : 30/1/1 ]

General Instructions :
1. You are aware that evaluation is the most important process in the actual and correct assessment of the
candidates. A small mistake in evaluation may lead to serious problems which may affect the future of
the candidates, education system and teaching profession. To avoid mistakes, it is requested that before
starting evaluation, you must read and understand the spot evaluation guidelines carefully.

2. ‘‘Evaluation policy is a confidential policy as it is related to the confidentiality of the examinations
conducted, evaluation done and several other aspects. Its leakage to public in any manner could
lead to derailment of the examination system and affect the life and future of millions of
candidates. Sharing this policy/document to anyone, publishing in any magazine and printing in
Newspaper/ Website, etc., may invite action under IPC.’’

3. Evaluation is to be done as per instruction 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. However, while evaluating, answers which are based on latest
information or knowledge and/or are innovative, they may be assessed for their correctness
otherwise and marks be awarded to them. In Class-X, while evaluating two competency based
questions, please try to understand given answer and even if reply is not from marking scheme
but correct competency is enumerated by the candidate, marks should be awarded.

4. The Head-Examiner must go through the first five answer books evaluated by each evaluator on the first
day, to ensure that evaluation has been carried out as per the instructions given in the Marking Scheme.
The remaining answer books meant for evaluation shall be given only after ensuring that there is no
significant variation in the marking of individual evaluators.

5. Evaluators will mark () wherever answer is correct. For wrong answer ‘’ be marked. Evaluators will
not put right kind of mark while evaluating which gives an impression that answer is correct and no
marks are awarded. This is most common mistake which evaluators are committing.

6. If a question has parts, please award marks on the right-hand side for each part. Marks awarded for
different parts of the question should then be totalled up and written in the left-hand margin and
encircled. This may be followed strictly.

7. If a question does not have any parts, marks must be awarded in the left-hand margin and encircled.
This may also be followed strictly.

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8. If a student has attempted both option given in question, answer of the question deserving more marks
should be retained and the other answer scored out.

9. No marks to be deducted for the cumulative effect of an error. It should be penalized only once.

10. A full scale of marks _____ (example 0–100 marks as given in Question Paper) has to be used. Please
do not hesitate to award full marks if the answer deserves it.

11. Every examiner has to necessarily do evaluation work for full working hours, i.e., 8 hours everyday and
evaluate 20 answer books per day in main subjects and 25 answer books per day in other subjects
(Details are given in Spot Guidelines).

12. Ensure that you do not make the following common types of errors committed by the Examiner in the
past :
• Leaving answer or part thereof unassessed in an answer book
• Giving more marks for an answer than assigned to it
• Wrong totalling of marks awarded on a reply
• Wrong transfer of marks from the inside pages of the answer book to the title page
• Wrong questionwise totalling on the title page
• Wrong totalling of marks of the two columns on the title page
• Wrong grand total
• Marks in words and figures not tallying
• Wrong transfer of marks from the answer book to online award list
• Answers marked as correct, but marks not awarded. (Ensure that the right tick mark is correctly
and clearly indicated. It should merely be a line. Same is with the  for incorrect answer).
• Half or a part of answer marked correct and the rest as wrong, but no marks awarded.

13. While evaluating the answer books if the answer is found to be totally incorrect, it should be marked as
() and awarded zero (0) Mark.

14. Any unassessed portion, non-carrying over of marks to the title page, or totalling error detected by the
candidates shall damage the prestige of all the personnel engaged in the evaluation work as also of the
Board. Hence, in order to uphold the prestige of all concerned, it is again reiterated that the instructions
be followed meticulously and judiciously.

15. The examiners should acquaint themselves with the guidelines given in the guidelines for spot
evaluation before starting the actual evaluation.

16. Every examiner shall also ensure that all the answers are evaluated, marks carried over to the title page,
correctly totalled and written in figures and words.

17. The Board permits candidates to obtain photocopy of the Answer Book on request in an RTI application
and also separately as a part of the re-evaluation process on payment of the processing charges.

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MARKING SCHEME
Secondary School Examination TERM–II, 2022
MATHEMATICS (Standard) (Subject Code–041)
[ Paper Code : 30/1/1 ]
Instructions :
1. The Marking Scheme provides general guidelines to reduce subjectivity in the marking.
The answers given in the Marking Scheme are suggested answers. The content is thus
indicative. If a student has given any other answer which is different from the one given in
the Marking Scheme, but conveys the meaning, such answers should be given full
weightage.
2. Evaluation is to be done as per 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. If a candidate has attempted a question twice, answer of the question deserving more
marks should be retained and the other answer scored out.
5. A full scale of marks - 0 to 40 has to be used. Please do not hesitate to award full marks if
the answer deserves it.
6. Separate Marking Scheme for all the three sets has been given.
7. As per orders of the Hon’ble Supreme Court. The candidates would now be permitted to
obtain photocopy of the Answer book on request on payment of the prescribed fee. All
examiners/Head Examiners are once again reminded that they must ensure that evaluation
is carried out strictly as per value points for each answer as given in the Marking Scheme.
Q. No. EXPECTED ANSWER / VALUE POINTS Marks
SECTION—A
1.a
Sol. Here
a = −30, d = 6, n = 30 1
30
S30 = [−60 + 29  6] ½
2
= 1710 ½
Or
b.

Sol. a = S1 = 1(4  1 + 1) = 5 ½
a + (a + d ) = S 2 = 2(4  2 + 1) = 18
d = 8
1
Hence, AP is
5, 13, 21, ... ½

2.

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Sol. 1 4
n  .  .(3.5)2 (3) =  (10.5)3 1
3 3
 n = 126 1

3.a.

Sol. For real and equal roots
4(m − 1)2 − 4(m − 1) = 0 ½
 m = 1 or m = 2 1
m  1 m = 2 ½
Or
b.

Sol.
3x2 + 10 x + 7 3 = 0
1
𝑜𝑟 √3𝑥 2 + 3𝑥 + 7𝑥 + 7√3 = 0
or ( 3x + 7) ( x + 3) = 0
7 7 1
⇒ 𝑥=− , −√3 or − 3 √3, −√3
√3

4.

Sol. Modal class is 40–50 ½
17 − 12
Mode = 40 + 10  1
34 − 12 − 4
7
= 42·7 or 429 ½

5.

Sol. Let Rehan’s present age be x years
 ( x − 5) ( x + 7) = 2 x + 1 1
2
 x = 36 ½
x=6 ½

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6.

Sol. For correct figure ½
Here OB = 3 cm, OA = 4 cm
A
OB ⊥ AC
O
B 1
 AB = 42 − 32 = 7 cm

C Hence AC = 2 7 cm ½

SECTION—B

7.

Median class is 30–40 ½
Sol.
Class Frequency c.f.
0–10 3 3
10–20 5 8
20–30 11 19
30–40 10 29
40–50 x 29 + x
50–60 3 32 + x
60–70 2 34 + x
Correct table 1

10  34 + x 
 34·5 = 30 +  − 19  1
10  2 
 x = 13 ½

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8.

Sol. Correct Construction. 3

9.a.

Sol. For correct figure 1

AB 50
tan 30 = and tan 60 =
AX AX

1 50
Y  AB = AX and AX = ½+½
3 3
B
Tower (50 m)
1 50 50 1
Building  AB =  = m
3 3 3
60° 30°
A X

OR
b.

Sol. For correct figure 1

PD 1
Here, = tan 30 =  AD = 3 3 m ½
AD 3
PD
and = tan 45 = 1  BD = 3 m ½
BD

So, AB= AD + BD = (3 3 + 3) m = 3( 3 + 1) m 1

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10.

Sol.
Class x f d f.d

100–120 110 8 –40 –320

120–140 130 3 –20 –60

140–160 150 8 0 0

160–180 170 6 20 120

180–200 190 5 40 200

30 –60

For correct table 2
− 60
Mean = 150 + = 148
30 1
Therefore, mean expenditure = Rs. 148

SECTION—C

11.
a.

1
Sol. 𝑙 = √576 + 49 = 25 𝑐𝑚

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TSA = 2rh + r 2 + rl
7
22 2
=  7 [60 + 7 + 25]
24 7
1
l
30 = 2024 cm2

Or

b.

Sol. Distance covered by water in 1 hr = 12000 m ½
 Volume of water flown in 1 hr
= 8  6 12000 m3 1½

Hence area of field × 0·05 = 8 × 6 × 12000
1½
 Area of field = 1152 104 m2 or 11520000 m2
½

12.

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Sol.

PR=RB (tangents from external point)………………(i) 1
Proving  RPC =  RCP 2
⇒ PR =CR ………………(ii) ½
Using equations (i) and (ii)
BR= RC ½
Hence the tangent drawn at point P bisects BC

13.

Sol. (a) Number of triangles in figures are 4, 6, 8, ... ½
This is an A.P. with a = 4, d = 2 1
 an = 4 + (n − 1)  2 = 2n + 2 ½

(b) Number of matchsticks in figures are 12, 19, 26, ... ½

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This is an A.P. with a = 12, d = 7 1
 61 = 12 + (n − 1)  7
⇒ 𝑛=8 ½
14. Case Study—2

Sol. (a) B

10 – h

45°
A D
60° x
h h

10 m

Correct Figure 2
C

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10 − h
(b) tan 45 = 1 =
x
 x = 10 − h ... (i) ½
10 + h
tan 60 = 3 =
x
10 + h
x= ... (ii) ½
3
Solving (i) and (ii) 10( 3 − 1) = h( 3 + 1)
10 ( 3 − 1)2
h=
2
= 2·67 m or 2.7m 1
***

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