Namma Kalvi - The No.1 Educational Website for 9th, 10th, 11th, 12th, TRB TET & TNPSC Materials www.nammakalvi.weebly.com DIRECTORATE OF GOVERNMENT EXAMINATIONS, CHENNAI-6 SSLC EXAMINATIONS, MARCH 2017
KEY ANSWER FOR MATHEMATICS MARKING SCHEME – KEY ANSWERS
GENERAL INSTRUCTIONS 1. If a student has given any answer which is different from one given in this marking scheme, but arrives correct answer should be given full credit with appropriate distribution. 2. In section I award 1 mark for the correct option code and the corresponding answer. If one of them (option or answer) is wrong then award ZERO mark only. 3. In section II, section III& section IV if the solution is correct then
www.kalvikural.com award full mark directly. The stage mark is essential only if the part of the solution is incorrect. 4. If a particular stage is wrong and if the student writes the appropriate formula then suitable mark which is attached with that stage should be awarded for the formula mark should not be deducted for not writing the formula if the student arrives at the correct answer.
1
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Directorate of Government Examinations, Chennai - 6 SSLC Common Examinations – March 2017 Mathematics – Answer Key Total Marks : 100
Section - I (Marks : 15) Choose the correct Answer : 1.
(b)
21
2.
(b)
3
3.
(a)
8
4.
(d)
31
5.
(a)
6.
(c)
7.
(c)
-3
8.
(d)
8
9.
(d)
6 cm
10.
(b)
16 cm
11.
(c)
600
12.
(d)
-9
13.
(c)
5 cm
14.
(c)
15.
(b)
15 x 1 = 15
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2
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Section - II
(Marks : 20)
(i) Answer 10 Questions . (ii) Question No : 30 is compulsory. Select any 9 questions from the first 14 questions. AU(BUC) ={ 1,2,3,4,5,6,7,8} 16. (AUB)UC ={ 1,2,3,4,5,6,7,8} 17.
a=9 b = 15 m -7(m+2)/2 =
10 x 2 = 20 1 2 1 Marks 1 2 1 Marks 1
m 18. (-2/7) m = -1 , m =2
1
x=2 19. y = 4
2 Marks
1
2 1 Marks
1 20.
2 Marks
1 a11 = 1, a12 = 0, a21 = 3, a22 = 2 21.
1 2 Marks
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1 1
2 1 Marks
22.
23.
1
P
P(-2 , 3) 24.
The statement is not true. Reason: All the points are lie on the Y- axis.
1 1 2 1 Marks 1
25. QR = 9cm
2 Marks
2 Marks
CD = 30 m 26. The Height of the Tower BD = 31.5 m
1 1 2 1 Marks
2 r (h+r) = 1540 27. h = 28 cm
1 2 1 Marks 3
www.nammakalvi.weebly.com 28.
Range = L –S L = 71 i) probability of getting two heads P(A)
1 2 1 Marks 1
29. ii) probability of getting exactly one tail P (B) 30.
2 Marks
1 1
4 3 1 r 7241 7 (a) 3 r = 12 cm
1 (OR)
2 Marks
x2 –y2 1 1
(b) 2
2
= a –b
Section – III
(Marks : 45)
(i) Answer 9 Questions . (ii) Question No : 45 is compulsory. Select 8 questions from the first 14 questions . B U C = {1, 2, c, d, e, f, g, y} 1 1 A\(B U C) = {a, b, x, z} 1 A\B = {a, b, f, g, x, y, z} 31. 1 A\C = {a, b, c, x, z} 1 f(6) = 1, f(9) = 2, f(15) = 4, f(18) = 5, f(21) = 6 Arrow Diagram 32. Set of ordered pairs
1 1 1 1 1 1 1 1
9 x 5 = 45
5 Marks
5 Marks
www.kalvikural.com Table Graph 1 – 4 + 9 – 16 + … upto 2n terms = (-3) + (-7) + (-11) + … upto n terms
33.
1 1
= -n(2n+1)
…
upto n terms
…
upto n terms … upto n terms]
34.
=
7 9
= [
5 Marks
[(10 + 102+ 103+……… upto n terms) –n ] – n ] (or)
1 1 1 1 1
4
5 Marks
www.nammakalvi.weebly.com T1 =
hr
T2 =
hr
1
1 +
35.
=
1
x2 = 25 X= 5 Speed of Stream = 5 km/hr
1 1
4
-3
+7
4 16 16 8 -3
-24
(a-1)
-24 -24
(a-1) 9
8 -6 +7
36.
5 Marks
(b+1)
a–10 56
49
1 1
b+1 -42
49
1
5 Marks
49
0 a b
= 66 = -43
a = – 46 (Taking -7 instead of +7) b = 41
1 1
( Note : alternative method can be used ) 1
AB =
www.kalvikural.com 37.
ABT =
1
BT =
1
AT =
1
BT AT =
1
5 Marks
Area of the quadrilateral ABCD = 38.
Sq.Units
2 1
=
1 = 28 Sq.Units
1
( Note : alternative method can be used )
5
5 Marks
www.kalvikural.com www.nammakalvi.weebly.com Statement diagram 39. Given, To prove and Construction proof Note : Without diagram give 1 marks only for statement
1 1 1 2
5 Marks
1 5 Marks
40. tan 45o =
41.
1
x=h
h =
1
=
1 1 1 1 1
= 13.66 m R = 7 cm r = 4.2 cm Volume of Frustum = πh (R2 + r2 + Rr) cubic units = x
2
x 14 (7 + 4.2 + 7x 4.2)
1 1 1
= 1408.58 cm3 (or) 1408.6 cm3
Volume of cone =
5 Marks
2
r2h cubic units
www.kalvikural.com Volume of cuboid = l x b x h cubic units 42. Volume of cone = Volume of cuboid Radius r = 21cm Diameter = 42 cm
= 4.428 (approx) c.v. =
1 1 1 1
n(S) = 36 P(A) = P (B) =
1 P(A∪B) =
5 Marks
1
x 100
= 24.6 (approx)
44.
5 Marks
1 1 1 1
X = 18 ∑d = 0, ∑d2 = 98 43.
1 2
1
(m)
6
5 Marks
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(a)
f(x) = 3x(x3+2x2-4x-8) g(x) = 2x (2x3+7x2+4x-4) 3x2 +12x +12 = 3( x2+4x+4) X3+2x2-4x-8 ÷ x2+4x+4, Remainder = 0 G.C.D. = x ( x2+4x+4)
1 1 1 1 1
( Note : alternative method can be used ) (OR)
45.
(b)
5 Marks
Intersecting point on X axis (a,0) Intersecting point on Y axis (0,b) a = 6 and b = 4 + =1
1 1 1 1 1
2x +3y -12 =0 ( Note : alternative method can be used )
Section - IV (Marks : 20) Note : Answer both the questions choosing either of the alternatives. Rough diagram 2 First Circle 2 Line Segment 1 (a) Perpendicular bisector 1 Second Circle 2 Two tangents 1 Length of Tangents = 8 c.m 1 46. (OR)
2 x 10 = 20
10 Marks
www.kalvikural.com (b)
Rough Diagram Line Segment AB Triangle ABC Perpendicular bisector Circumcircle Cyclic Quadrilateral ABCD x y
(a)
(b)
-2 0
-1 -5
0 -6
1 -3
2 4
3 15
Any five points x- axis, y- axis, scale Ploting the Points and drawing the parabola Solution set = { -2, 1.5 } x y
47.
-3 9
2 1 3 1 2 1
1 20
2 10
(OR) 4 5 5 4
10 2
20 1
Any five points x- axis, y- axis, scale Ploting the Points and drawing the Rectangular Hyperbola i) If x =5 then y = 4 ii) If y = 10 then x =2
7
4 2 3 1 10 Marks .3
2 3 1 1