Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > Class 10 Mathematics (Standard) Term II : CBSE (Official) Marking Scheme with Solution (2021-22)
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Page 1
Marking Scheme
Class- X, Session- 2021-22
TERM II
Subject- Mathematics (Standard)
SECTION A
Q.No
.
HINTS/SOLUTION MARKS
1
a = 6, d = 3 ; a
25
= 6 + 24(3) = 78
a
15
= 6 + 14(3) = 48 ; a
25
- a
15
= 78 - 48 = 30
OR
7(?? + 6?? ) = 5(?? + 4?? )
?2?? + 22?? = 0 ? ?? + 11?? = 0 ? ?? 12
= 0
1
1
1
1
2
5mx² - 6mx + 9 = 0
b² - 4ac = 0 ? (-6m)² - 4(5m)(9) = 0
? 36m(m - 5) = 0
? m = 0, 5 ; rejecting m=0, we get m = 5
1
1
3
let ??????? = ??
???????? =
????
????
=
1
2
? ?? = 30
0
? ??????? = 2?? = 60
0
Also ??????? = ??????? = 60
0
(? ???? = ???? )
?? ?????? is equilateral
1/2
1/2
1/2
1/2
4
CSA (cone) = ?????? = 12320
22
7
× 56 × ?? = 12320
?? = 70 ????
h = v70
2
- 56
2
= 42 cm
1/2
1
1/2
O
A
B
P
r
2r
Page 2
Marking Scheme
Class- X, Session- 2021-22
TERM II
Subject- Mathematics (Standard)
SECTION A
Q.No
.
HINTS/SOLUTION MARKS
1
a = 6, d = 3 ; a
25
= 6 + 24(3) = 78
a
15
= 6 + 14(3) = 48 ; a
25
- a
15
= 78 - 48 = 30
OR
7(?? + 6?? ) = 5(?? + 4?? )
?2?? + 22?? = 0 ? ?? + 11?? = 0 ? ?? 12
= 0
1
1
1
1
2
5mx² - 6mx + 9 = 0
b² - 4ac = 0 ? (-6m)² - 4(5m)(9) = 0
? 36m(m - 5) = 0
? m = 0, 5 ; rejecting m=0, we get m = 5
1
1
3
let ??????? = ??
???????? =
????
????
=
1
2
? ?? = 30
0
? ??????? = 2?? = 60
0
Also ??????? = ??????? = 60
0
(? ???? = ???? )
?? ?????? is equilateral
1/2
1/2
1/2
1/2
4
CSA (cone) = ?????? = 12320
22
7
× 56 × ?? = 12320
?? = 70 ????
h = v70
2
- 56
2
= 42 cm
1/2
1
1/2
O
A
B
P
r
2r
5
Modal class is 40 - 60, ?? = 40, h = 20, ?? 1
=? , ?? 0
= 10, ?? 2
= 6
45 = 40 + 20 × [
?? 1
- 10
2?? 1
- 10 - 6
]
?
1
4
=
?? 1
-10
2?? 1
-16
?2?? 1
- 16 = 4?? 1
- 40 ? ?? 1
= 12
1/2
1/2
1
6
Let the present age of Ritu be ?? years
(?? - 5)
2
= 5?? + 11
?? 2
- 15?? + 14 = 0½
(?? - 14)(?? - 1) = 0 ? ?? = 1 ???? 14
x = 14 years (rejecting ?? = 1 as in that case Ritu’s age 5 years ago will be –ve )
OR
9?? 2
- 6???? + (?? 2
- ?? 2
) = 0
?? = 9, ?? = -6?? , ?? = ?? 2
- ?? 2
?? = ?? 2
- 4???? = (-6?? )
2
- 4(9)(?? 2
- ?? 2
) = 36?? 2
?? =
-?? ± v?? 2?? =
6?? ± 6?? 18
=
?? + ?? 3
????
?? - ?? 3
1
1/2
1/2
1/2
1/2
1
SECTION B
7
Distance (in m) 0 - 1 1 – 2 2 - 3 3 - 4 4 - 5
Number of
Students
40 80 62 38 30
???? 40 120 182 220 250
?? 2
=
250
2
= 125 ? ???????????? ?????????? ???? 2 - 3, ?? = 2, h = 1, ???? = 120, ?? = 62
???????????? = ?? +
?? 2
- ????
?? × ??
= 2 +
5
62
=
129
62
= 2
5
62
?? ???? 2.08??
50% of students jumped below2
5
62
m and 50% above it.
1
1/2
1
1/2
8
Draw a circle of radius 4cm
Draw OA and construct ??????? = 120
0
Draw ??????? = ??????? = 90
0
PA and PB are required tangents
1
1
1
9
Runs Scored 0 - 40 40 - 80 80 - 120 120 - 160 160 - 200 TOTAL
Number of
Batsmen (?? ?? )
12 20 35 30 23 120
Page 3
Marking Scheme
Class- X, Session- 2021-22
TERM II
Subject- Mathematics (Standard)
SECTION A
Q.No
.
HINTS/SOLUTION MARKS
1
a = 6, d = 3 ; a
25
= 6 + 24(3) = 78
a
15
= 6 + 14(3) = 48 ; a
25
- a
15
= 78 - 48 = 30
OR
7(?? + 6?? ) = 5(?? + 4?? )
?2?? + 22?? = 0 ? ?? + 11?? = 0 ? ?? 12
= 0
1
1
1
1
2
5mx² - 6mx + 9 = 0
b² - 4ac = 0 ? (-6m)² - 4(5m)(9) = 0
? 36m(m - 5) = 0
? m = 0, 5 ; rejecting m=0, we get m = 5
1
1
3
let ??????? = ??
???????? =
????
????
=
1
2
? ?? = 30
0
? ??????? = 2?? = 60
0
Also ??????? = ??????? = 60
0
(? ???? = ???? )
?? ?????? is equilateral
1/2
1/2
1/2
1/2
4
CSA (cone) = ?????? = 12320
22
7
× 56 × ?? = 12320
?? = 70 ????
h = v70
2
- 56
2
= 42 cm
1/2
1
1/2
O
A
B
P
r
2r
5
Modal class is 40 - 60, ?? = 40, h = 20, ?? 1
=? , ?? 0
= 10, ?? 2
= 6
45 = 40 + 20 × [
?? 1
- 10
2?? 1
- 10 - 6
]
?
1
4
=
?? 1
-10
2?? 1
-16
?2?? 1
- 16 = 4?? 1
- 40 ? ?? 1
= 12
1/2
1/2
1
6
Let the present age of Ritu be ?? years
(?? - 5)
2
= 5?? + 11
?? 2
- 15?? + 14 = 0½
(?? - 14)(?? - 1) = 0 ? ?? = 1 ???? 14
x = 14 years (rejecting ?? = 1 as in that case Ritu’s age 5 years ago will be –ve )
OR
9?? 2
- 6???? + (?? 2
- ?? 2
) = 0
?? = 9, ?? = -6?? , ?? = ?? 2
- ?? 2
?? = ?? 2
- 4???? = (-6?? )
2
- 4(9)(?? 2
- ?? 2
) = 36?? 2
?? =
-?? ± v?? 2?? =
6?? ± 6?? 18
=
?? + ?? 3
????
?? - ?? 3
1
1/2
1/2
1/2
1/2
1
SECTION B
7
Distance (in m) 0 - 1 1 – 2 2 - 3 3 - 4 4 - 5
Number of
Students
40 80 62 38 30
???? 40 120 182 220 250
?? 2
=
250
2
= 125 ? ???????????? ?????????? ???? 2 - 3, ?? = 2, h = 1, ???? = 120, ?? = 62
???????????? = ?? +
?? 2
- ????
?? × ??
= 2 +
5
62
=
129
62
= 2
5
62
?? ???? 2.08??
50% of students jumped below2
5
62
m and 50% above it.
1
1/2
1
1/2
8
Draw a circle of radius 4cm
Draw OA and construct ??????? = 120
0
Draw ??????? = ??????? = 90
0
PA and PB are required tangents
1
1
1
9
Runs Scored 0 - 40 40 - 80 80 - 120 120 - 160 160 - 200 TOTAL
Number of
Batsmen (?? ?? )
12 20 35 30 23 120
?? ?? 20 60 100 140 180
?? ?? ?? ?? 240 1200 3500 4200 4140 13280
???????? ( ?? ¯) =
? ?? ?? ?? ?? ? ?? ?? =
13280
120
= 110.67 ????????
1
?? ??
1
?? ??
10
???? ??????? , ?????? 60
0
=
?? 20
? ?? = 20v3m
???? ??????? , ?????? 30
0
=
?? 20
? ?? =
20
v3
??
?? - ?? = 20v3 -
20
v3
=
40
v3
=
40v3
3
= 23.06??
OR
Let PR be the building and AB be the boy
???? ??????? , ?????? 60
0
=
????
50
? ???? = 50v3??
Height of the building = ???? = (50v3 + 1.7)?? = 88.2??
1
1/2
1/2
1
1
1
1
SECTION C
11
Volume of shell = Volume of cylinder
?
4?? 3
[ 5³ - 3³] = ?? (7)
2
h
? h =
8
3
= 2
2
3
????
1
?? ??
1
60°
1.7 m
50m
60° 30°
20m
x
y
P
Q
R
S
P
Q
R
A
B
Page 4
Marking Scheme
Class- X, Session- 2021-22
TERM II
Subject- Mathematics (Standard)
SECTION A
Q.No
.
HINTS/SOLUTION MARKS
1
a = 6, d = 3 ; a
25
= 6 + 24(3) = 78
a
15
= 6 + 14(3) = 48 ; a
25
- a
15
= 78 - 48 = 30
OR
7(?? + 6?? ) = 5(?? + 4?? )
?2?? + 22?? = 0 ? ?? + 11?? = 0 ? ?? 12
= 0
1
1
1
1
2
5mx² - 6mx + 9 = 0
b² - 4ac = 0 ? (-6m)² - 4(5m)(9) = 0
? 36m(m - 5) = 0
? m = 0, 5 ; rejecting m=0, we get m = 5
1
1
3
let ??????? = ??
???????? =
????
????
=
1
2
? ?? = 30
0
? ??????? = 2?? = 60
0
Also ??????? = ??????? = 60
0
(? ???? = ???? )
?? ?????? is equilateral
1/2
1/2
1/2
1/2
4
CSA (cone) = ?????? = 12320
22
7
× 56 × ?? = 12320
?? = 70 ????
h = v70
2
- 56
2
= 42 cm
1/2
1
1/2
O
A
B
P
r
2r
5
Modal class is 40 - 60, ?? = 40, h = 20, ?? 1
=? , ?? 0
= 10, ?? 2
= 6
45 = 40 + 20 × [
?? 1
- 10
2?? 1
- 10 - 6
]
?
1
4
=
?? 1
-10
2?? 1
-16
?2?? 1
- 16 = 4?? 1
- 40 ? ?? 1
= 12
1/2
1/2
1
6
Let the present age of Ritu be ?? years
(?? - 5)
2
= 5?? + 11
?? 2
- 15?? + 14 = 0½
(?? - 14)(?? - 1) = 0 ? ?? = 1 ???? 14
x = 14 years (rejecting ?? = 1 as in that case Ritu’s age 5 years ago will be –ve )
OR
9?? 2
- 6???? + (?? 2
- ?? 2
) = 0
?? = 9, ?? = -6?? , ?? = ?? 2
- ?? 2
?? = ?? 2
- 4???? = (-6?? )
2
- 4(9)(?? 2
- ?? 2
) = 36?? 2
?? =
-?? ± v?? 2?? =
6?? ± 6?? 18
=
?? + ?? 3
????
?? - ?? 3
1
1/2
1/2
1/2
1/2
1
SECTION B
7
Distance (in m) 0 - 1 1 – 2 2 - 3 3 - 4 4 - 5
Number of
Students
40 80 62 38 30
???? 40 120 182 220 250
?? 2
=
250
2
= 125 ? ???????????? ?????????? ???? 2 - 3, ?? = 2, h = 1, ???? = 120, ?? = 62
???????????? = ?? +
?? 2
- ????
?? × ??
= 2 +
5
62
=
129
62
= 2
5
62
?? ???? 2.08??
50% of students jumped below2
5
62
m and 50% above it.
1
1/2
1
1/2
8
Draw a circle of radius 4cm
Draw OA and construct ??????? = 120
0
Draw ??????? = ??????? = 90
0
PA and PB are required tangents
1
1
1
9
Runs Scored 0 - 40 40 - 80 80 - 120 120 - 160 160 - 200 TOTAL
Number of
Batsmen (?? ?? )
12 20 35 30 23 120
?? ?? 20 60 100 140 180
?? ?? ?? ?? 240 1200 3500 4200 4140 13280
???????? ( ?? ¯) =
? ?? ?? ?? ?? ? ?? ?? =
13280
120
= 110.67 ????????
1
?? ??
1
?? ??
10
???? ??????? , ?????? 60
0
=
?? 20
? ?? = 20v3m
???? ??????? , ?????? 30
0
=
?? 20
? ?? =
20
v3
??
?? - ?? = 20v3 -
20
v3
=
40
v3
=
40v3
3
= 23.06??
OR
Let PR be the building and AB be the boy
???? ??????? , ?????? 60
0
=
????
50
? ???? = 50v3??
Height of the building = ???? = (50v3 + 1.7)?? = 88.2??
1
1/2
1/2
1
1
1
1
SECTION C
11
Volume of shell = Volume of cylinder
?
4?? 3
[ 5³ - 3³] = ?? (7)
2
h
? h =
8
3
= 2
2
3
????
1
?? ??
1
60°
1.7 m
50m
60° 30°
20m
x
y
P
Q
R
S
P
Q
R
A
B
TSA of cylinder is
= 2???? (?? + h) = 2 ×
22
7
× 7 × (7 +
8
3
) = 44 ×
29
3
=
1276
3
????
2
???? 425.33????
2
1
?? ??
12
??????? + ??????? + ??????? + ??????? = 360
??
? 90
0
+ 90
0
+ ??????? + ??????? = 360
?? (? ?????????????? ? ???????????? )
? ??????? + ??????? = 180
0
OR
Let ??????? = ??
?????? is an isosceles triangle.
??????? = ??????? =
1
2
(180
?? - ?? ) = 90° -
?? 2
??????? = 90
??
??????? = ??????? - ??????? = 90
?? - (90
?? -
?? 2
) =
?? 2
??????? =
1
2
???????
2??????? = ???????
1
1
?? ??
1
?? ??
1
?? ??
1
?? ??
1
13
Case Study-1
i)
In ??????? , tan 30
?? =
240
?? ? ?? = 240v3 ??
1
1
240m
??
30
°
T
R
P
30°
Page 5
Marking Scheme
Class- X, Session- 2021-22
TERM II
Subject- Mathematics (Standard)
SECTION A
Q.No
.
HINTS/SOLUTION MARKS
1
a = 6, d = 3 ; a
25
= 6 + 24(3) = 78
a
15
= 6 + 14(3) = 48 ; a
25
- a
15
= 78 - 48 = 30
OR
7(?? + 6?? ) = 5(?? + 4?? )
?2?? + 22?? = 0 ? ?? + 11?? = 0 ? ?? 12
= 0
1
1
1
1
2
5mx² - 6mx + 9 = 0
b² - 4ac = 0 ? (-6m)² - 4(5m)(9) = 0
? 36m(m - 5) = 0
? m = 0, 5 ; rejecting m=0, we get m = 5
1
1
3
let ??????? = ??
???????? =
????
????
=
1
2
? ?? = 30
0
? ??????? = 2?? = 60
0
Also ??????? = ??????? = 60
0
(? ???? = ???? )
?? ?????? is equilateral
1/2
1/2
1/2
1/2
4
CSA (cone) = ?????? = 12320
22
7
× 56 × ?? = 12320
?? = 70 ????
h = v70
2
- 56
2
= 42 cm
1/2
1
1/2
O
A
B
P
r
2r
5
Modal class is 40 - 60, ?? = 40, h = 20, ?? 1
=? , ?? 0
= 10, ?? 2
= 6
45 = 40 + 20 × [
?? 1
- 10
2?? 1
- 10 - 6
]
?
1
4
=
?? 1
-10
2?? 1
-16
?2?? 1
- 16 = 4?? 1
- 40 ? ?? 1
= 12
1/2
1/2
1
6
Let the present age of Ritu be ?? years
(?? - 5)
2
= 5?? + 11
?? 2
- 15?? + 14 = 0½
(?? - 14)(?? - 1) = 0 ? ?? = 1 ???? 14
x = 14 years (rejecting ?? = 1 as in that case Ritu’s age 5 years ago will be –ve )
OR
9?? 2
- 6???? + (?? 2
- ?? 2
) = 0
?? = 9, ?? = -6?? , ?? = ?? 2
- ?? 2
?? = ?? 2
- 4???? = (-6?? )
2
- 4(9)(?? 2
- ?? 2
) = 36?? 2
?? =
-?? ± v?? 2?? =
6?? ± 6?? 18
=
?? + ?? 3
????
?? - ?? 3
1
1/2
1/2
1/2
1/2
1
SECTION B
7
Distance (in m) 0 - 1 1 – 2 2 - 3 3 - 4 4 - 5
Number of
Students
40 80 62 38 30
???? 40 120 182 220 250
?? 2
=
250
2
= 125 ? ???????????? ?????????? ???? 2 - 3, ?? = 2, h = 1, ???? = 120, ?? = 62
???????????? = ?? +
?? 2
- ????
?? × ??
= 2 +
5
62
=
129
62
= 2
5
62
?? ???? 2.08??
50% of students jumped below2
5
62
m and 50% above it.
1
1/2
1
1/2
8
Draw a circle of radius 4cm
Draw OA and construct ??????? = 120
0
Draw ??????? = ??????? = 90
0
PA and PB are required tangents
1
1
1
9
Runs Scored 0 - 40 40 - 80 80 - 120 120 - 160 160 - 200 TOTAL
Number of
Batsmen (?? ?? )
12 20 35 30 23 120
?? ?? 20 60 100 140 180
?? ?? ?? ?? 240 1200 3500 4200 4140 13280
???????? ( ?? ¯) =
? ?? ?? ?? ?? ? ?? ?? =
13280
120
= 110.67 ????????
1
?? ??
1
?? ??
10
???? ??????? , ?????? 60
0
=
?? 20
? ?? = 20v3m
???? ??????? , ?????? 30
0
=
?? 20
? ?? =
20
v3
??
?? - ?? = 20v3 -
20
v3
=
40
v3
=
40v3
3
= 23.06??
OR
Let PR be the building and AB be the boy
???? ??????? , ?????? 60
0
=
????
50
? ???? = 50v3??
Height of the building = ???? = (50v3 + 1.7)?? = 88.2??
1
1/2
1/2
1
1
1
1
SECTION C
11
Volume of shell = Volume of cylinder
?
4?? 3
[ 5³ - 3³] = ?? (7)
2
h
? h =
8
3
= 2
2
3
????
1
?? ??
1
60°
1.7 m
50m
60° 30°
20m
x
y
P
Q
R
S
P
Q
R
A
B
TSA of cylinder is
= 2???? (?? + h) = 2 ×
22
7
× 7 × (7 +
8
3
) = 44 ×
29
3
=
1276
3
????
2
???? 425.33????
2
1
?? ??
12
??????? + ??????? + ??????? + ??????? = 360
??
? 90
0
+ 90
0
+ ??????? + ??????? = 360
?? (? ?????????????? ? ???????????? )
? ??????? + ??????? = 180
0
OR
Let ??????? = ??
?????? is an isosceles triangle.
??????? = ??????? =
1
2
(180
?? - ?? ) = 90° -
?? 2
??????? = 90
??
??????? = ??????? - ??????? = 90
?? - (90
?? -
?? 2
) =
?? 2
??????? =
1
2
???????
2??????? = ???????
1
1
?? ??
1
?? ??
1
?? ??
1
?? ??
1
13
Case Study-1
i)
In ??????? , tan 30
?? =
240
?? ? ?? = 240v3 ??
1
1
240m
??
30
°
T
R
P
30°
ii) Distance of boat from tower= 240v3 - 240(
v3 - 1) = 240??
Let the angle of depression = ??
???????? =
240
240
= 1 ? ?? = 45
??
1
1
14
i) 3000, 3005, 3010, ...,3900.
?? ?? = ?? + (?? - 1)??
3900 = 3000 + (n - 1)5
? 900 = 5?? - 5 ? 5?? = 905 ? ?? = 181
Minimum number of days of practice = ?? - 1 = 180 ????????
ii) ?? ?? =
?? 2
(?? + ?? )
=
181
2
× (3000 + 3900) = 624450 pushups
1
1
1
1
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Additional Information about Class 10 Mathematics (Standard) Term II : CBSE (Official) Marking Scheme with Solution (2021-22) for Class 10 Preparation
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Class 10 Mathematics (Standard) Term II : CBSE (Official) Marking Scheme with Solution (2021-22) Notes
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The content of Class 10 Mathematics (Standard) Term II : CBSE (Official) Marking Scheme with Solution (2021-22) is prepared as per the latest Class 10 syllabus.
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