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Answer key prepared by: Prathap S M( 974 665 3636) HST Maths, GHSS Puthoor, Kollam (Dt)

Qn Sub Qn Description Step

Marks

Score

1 a 45 1

2 b 3√2 1

2 a 4 (Numbers 2,4,6,8) 1

2 b

Probability of a prime number =

1

4

1

3 (b) (0, 5) is a point on the y axis

(c) Distance from (0,5) to the x axis is 5

2

4 Sum of first 25 odd numbers = 625 2

5 a AB = 4cm. Hence BC = 3cm (Using Pythagoras) 2

3 b Cos C = 3/5 1

6 a Draw the rectangle , mark the points left and top right. 1 3

b (7,5) and (3,8) 2

7 3

8 a Base edge( a ) = 10 cm 1

3 b l=√e

2

−(a/2)

2

=√132

−(5)

2

=√144=12 cm

2

9 a Area of the plane surface = 40/4 = 10cm^2 1

3 b Total surface area of hemisphere = 3 x 10 = 30 cm^2 1

c Ratio between the surface area = 30 :40 = 3:4 1

10 a PB = PB +BC = 9 cm 1

3 b PQ x PR = PB x PC = 4 x 9 = 36 1

c PA=√36=6 cm 1

11 a

Volume=1

3

π r

2

h=324 π cm

3 1

3

b

Volume of sphere with radius 1 cm

4

3

π(1)

3

=4

3

π cm

3

Number of spheres =

324 π

3

=243

1

1

12 Rough Figure 1

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SECOND TERM EXAM 2019

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Answer key prepared by: Prathap S M( 974 665 3636) HST Maths, GHSS Puthoor, Kollam (Dt)

h

x

=tan54 h = x tan 54 .......................(1)

h

(x+20)

=tan 27 h = (x+20) tan 27......................(2)

From (1) and (2) x= 20 tan 27

(tan50 – tan 27)

=11.72 m

h = 11.72 ×1.38 = 16.17 m

OR

h = 20 x 0.8 = 16 m

1

1

1

4

13 a 28,24,20.... 1

4

b X8=28+7(−4)=0 1

c S15=15∗x8=15∗0=0 1

d S15=0 1

14 a <POS = 90 1

b

OP =

6

tan 35=60

7

Area of Rhombus =

1

2

d1 x d2 = = 1

2

x12 x

120

7

= 720

7 sq cm =102.85 sq cm

1

1

1

1

4

15 a 100 m 1

4 b 252

−x

2

=525

x= 10

length = 35 m, breadth = 15 m

1

1

1

16 4

17 a Base perimeter = 2π r=60 π 1

4

b l=√h2

+(r)

2

=√402

+302

=√2500=50 cm

1

2

Answer Key_Maths_10th_Second Term Examination_December_2019 2 of 4

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Answer key prepared by: Prathap S M( 974 665 3636) HST Maths, GHSS Puthoor, Kollam (Dt)

Curved surface area = 1/2x 60π x50=1500π cm

2

18 a AC = 3 cm ( Perpendicular bisects the chord) 1

4 b In a triangle with angles 30, 60 90, the sides opposite to them are in the ratio

1: √3 :2 , Radius = 2√3 cm

2

c Radius = 6 cm 1

19 a AB =BC = CD = AD = 5 units 3

4 b Rhombus 1

20 a

[

a

2 ]

2 1

4

b

e=√l

2

+

a

2

2 2

c l=√17cm 1

21 a <BPC = 40 1

4 b <APC =90+40 = 130 1

c < C =10 1

d <A = x, <APC = 90+ x, <C = 180 – (x+ 90+x) = 90-2x 1

22 a Slant height = 36 cm 1

5 b Ratio of central angles = 120 : 240 = 1: 2 1

c

r1=120

360

x 36=12 , r2=240

360

x 36=24

2

d Ratio of radii = 12: 24 = 1: 2 1

23 a <Q = 180 – 110 = 70 1 5

b Central angles 110, 120,130

Construction of circle, and tangents, triangle

4

24 a 1+ 2+ 3+.... +10 = 55 1 5

b 1+ 2+ 3+ ..... + n = 231

n(n+1) = 462

product of two consecutive natural number is 462

n= 21

4

25 a PS = 1/2 x 8 = 4 cm 1

5 b SR = 4 √3 , In triangle PSQ , PS = SQ = 4 cm

QR = 4+ 4 √3 ,PQ = 4 √2

1

1

c Draw the triangle 2

Answer Key_Maths_10th_Second Term Examination_December_2019 3 of 4

Page 4 of 4

Answer key prepared by: Prathap S M( 974 665 3636) HST Maths, GHSS Puthoor, Kollam (Dt)

26 a 2

5

b AC = 4 √2 1

c (6,6) (2,2) 2

27 a AC = 10 cm 1

5 b Area = 1/2 x 6 x 8 = 24 sq cm 1

c Semi perimeter = 24/2 = 12

radius = 24/12 = 2 cm

1

2

28 a Radius = 2 cm 1

5 b PD=√3 x 1=√3 1

c Draw the given figure,

Draw an equilateral triangle with one side CD

3

29 a 0 1

6

b 90 1

c 1 1

d 1 1

e 45 1

f 1 1

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