Marking Scheme

Secondary

October - November, 2000

Subject - Mathematics

Part - A

XXI/IS/0/1

Minimum Marks : 20

Q.No. Answer Q.No. Answer

Set A B C Set A B C

21 8 26 A

22 27 25 B

23 1 19 A

24 2 20 B

25 3 21 B

26 4 22 C

27 5 23 B

28 6 24 D

29 36 8 C

30 35 7 C

31 34 6 A

32 33 5 C

33 40 40 C

34 37 39 B

35 38 38 C

36 39 37 A

37 22 4 C

38 21 3 D

39 20 2 B

40 19 1 B

1 32 9 C

2 31 10 C

3 30 11 D

4 29 12 B

5 28 13 C

6 27 14 D

7 26 15 B

8 25 16 A

9 24 17 D

10 23 18 A

11 18 36 A

12 17 35 A

13 16 34 A

14 15 33 B

15 14 32 B

16 13 31 A

17 12 30 B

18 11 29 C

19 10 28 B

20 9 27 C

(½ mark for each correct response)

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Part - B

Maximum Marks : 80

Q. No Expected Value Points For dISTRIBUTION Total

a b c EAch Step OF MARKS

1. - 4

1

2. 4 -

1

3 - 2 7x = 12+9 = 21

x=3 1

4 3 1 93-31 = 61

(62/93 × 100)% = 66.6 % 1 1

5 5 8 GP = 220×100/110 = Rs.200 1

6 10 9

= 87º

x = 93º, y = 87º 1

7 9 7 yes ; AB = CD;

1

8 6 5 50º 1 1

9 7 6 3/4 1 1

10 8 10 Median = (55+65)/2 = 120/2 = 60 1 1

11 13 - 1

3x + 3 = 48

3x = 45

x = 45/3 = 15

Numbers are 15,16,17 3

OR

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Q. No Expected Value Points For dISTRIBUTION Total

a b c EAch Step OF MARKS

Let numbers be x-1, x, x+1

(x-1)+x+(x+1) = 48 1

3x = 48,

Numbers are 15,16,17 3

12 - 11 Cost of 3 shirts = Rs. (350×3) = Rs. 1050

Sales tax = Rs. (1050×5/100) = Rs. 52.50

Amount to pay = Rs. (1050+52.50) = Rs. 1102.50

Cost of 2 toys = Rs(175 ×2) = Rs. 350 1

Sales tax = Rs. (350×6/100) = Rs. 21

Amount to pay = Rs. 350+21 = Rs. 371 1

Cost of one clock = Rs. 450

Sales tax = Rs. (450×4/100) = Rs. 18

Amount to pay = Rs. (450+18) =Rs. 468 1 3

Total amount to pay =

Rs. (1102.50 +371+468) = Rs. 1941.50

13 12 -

Area of CDE = ×35×40 = 700 m² mark for each

Area of FCB = ×50×25 = 625 m² calculations of

Area of ADF = ×20 ×35= 700 m² area

Area of AFB = ×(20×25)= 250 m² ×4=2 3

Total Area = (700+700+625+250) m²

= 2275 m²

14 15 15 1. Calculate I= PTR/100;2.Write A 1 mark for each 3

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Q. No Expected Value Points For dISTRIBUTION Total

a b c EAch Step OF MARKS

15 - 13 D is mid point of AB; 1

O is mid point of AC

2. In ABC line segment OD joins the mid points

of two sides, hence is parallel and half of third side 1
3. OD =1/2 AC

or 2OD =AC 1 3

16 - 17 1

Exp 2 3

17 - 16 Let the dimensions be 2x m, 3x m and 4x m

Total surface area = 2(2x.3x + 3x.4x + 4x.2x) m²

1

Cost of covering the box with sheet of paper @

Rs. 4 per metre
= Rs. 832

Dimensions are : 4m, 6m,8m 1 3

18. 24 - 1 mark for each box 3

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Q. No Expected Value Points For dISTRIBUTION Total

a b c EAch Step OF MARKS

19 26 - Let the speed of faster train be x km/hr.

speed of slower train will be (x-10) km/hr.

Time taken by faster train = 300/x-10 1

Solving 1

x = 60; Negative value 50 is rejected 4

Speed of the faster train = 60 km/hr.

20 18 - Selling Price of each shirt = Rs. 297

C.P. of Ist shirt = Rs. 297 × = Rs 270 1

C.P of IInd shirt = Rs. 297×10/9 = Rs. 330
Total C.P = Rs. (270+330)

=Rs. 600

Total S.P = Rs. (297×2) 1

= Rs. 594

Loss = Rs. 600 - Rs. 594 = Rs. 6

Loss percent = =1 4

Loss = 1%

21. - 19

But

B D C

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Q. No Expected Value Points For dISTRIBUTION Total

a b c EAch Step OF MARKS

Areas of two traingles are

1

[using (i)] 1 4

22 19 21 Let the radius of the base of cone be r cm. The radius

of hemisphere is also r cm

Volume of cone = 1
Volume of the hemisphere = 1

Volume of cone = Volume of Hemisphere (Given)

1

h = 2r 4

i e h : r = 2 : 1

23 21 20 1 man = 1woman + 1 boy

But 1 woman = 2 boys.

So 1man = 2 boys + 1 boy = 3 boys

2 men : 3 women : 4 boys. 2

= 6 boys : 6 boys : 4 boys

Dividing Rs. 192 in the ratio 6 : 6 : 4

one man's share = Rs. = Rs. 36

one woman's share = Rs. = Rs. 24 2

one boy's share == Rs. 12 4

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Q. No Expected Value Points For dISTRIBUTION Total

a b c EAch Step OF MARKS

24 25 26

1 mark for axes

mark for each bar 4

25 22 24 Let AB be the tower figure
C and D be the observer

In 1

tan 45º = AB/AD

AC = 1
AC = 30

= 51.90 m 4

CD = (90+51.90)m = 141.90 m

26 23 25 Class Class Frequency Frequency x

interval mark Class mark

0-10 5 8 5×8 = 40

10-20 15 10 15×10 = 150

20-30 25 16 25×16 = 400

30-40 35 10 15×10 = 350

40-50 45 6 45×6 = 270

========= =========

Total = 125 Total = 1210 3

========= =========

Mean = 1210/125 = 9.68 1 4

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Q. No Expected Value Points For dISTRIBUTION Total

a b c EAch Step OF MARKS

27 28 - Suppose the sum = Rs. 100

Simple Interest on Rs. 100

= Rs. 10×3 = Rs. 30 1

Compund interest on Rs. 100

= Rs. 100

= Rs. 100

= Rs.100×331/1000 2

= Rs. 331/10

C.I- S.I = Rs. 331/10 - Rs. 30 = Rs. 31/10 1

Rs. 31/10 is the diff. then sum = Rs. 100 1

Re 1 is the diff. then sum = Rs. (100×10/31) 2 7

if Rs 62 is he difference, then sum =

Hence sum = Rs. 2000
28 - 27

Figure : 5

Step 1: Draw AC = 7cm

Step 2: With A as Centre and Steps : 2

radius 4 cm, draw an are

extending on both sides of AC.

Step 3 : With C as centre and a radius 4 cm, draw an

are extending on both sides of AC, which cuts the

previous are at B and D.
Step 4 : Draw AB, BC CD, and DA then ABCD is
the required rhombus. 7

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Note : New questions for Set - B

XXI/IS/0/1 b

Q. No Expected Value Points For dISTRIBUTION Total

seT b EAch Step OF MARKS

1. Exp.=x²-

2

2. Let the number be x

4x = 48

2

11. Market Value of machine = Rs.12000

5% Discount = Rs 1

= Rs.600

S.P of machine = Rs. (12000-600)

= Rs. 912 1

Coustomer will pay : Rs. [11400 + 912] 3

= Rs. 12312 1

14.

Now 1

2 3

= 50º

16. Let the diemension of box be 2x,3x and 4x metres

Volume of the box = (1+b+h) m³

= (2x)×(3x)×(4x)m³ 1

Now

1

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Q. No Expected Value Points For dISTRIBUTION Total

seT b EAch Step OF MARKS

x = 4 m

Dimension are 8m, 12 m and 16m 3

17. 1

Exp. = (1+1/3)×3/2 = 4/3×3/2 = 2 2 3

20. Let AD bisect A Figure : 1

Draw CE parallet to AD 1

Showing that AC=AE 1

Then, BA/AE = BD/DC

BA/AC=BD/DC 1 4

27

Step 1: Draw AB= 3.8 cm fig. 4

Step 2:With A and B as centers and radi i4.5 cm and

3cm respectively draw two ares intersting at

(Step : 2 of Construction)
Step 3:Join BC
Step 4:With B and A as centres and radi 3.8 cm and

2.3 cm respectively draws arecs intersecting at D

Step 5: Join AD and DC steps : 2 7
Then ABCD is the required quadrilateral

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XXI/IS/0/1 C

Note : New questions for Set - C

Q. No Expected Value Points For dISTRIBUTION Total

seT C EAch Step OF MARKS

3. Exp.

1

12. Multiply both sides by 6 we get 1

3x-2x-24=x 1

5x-x=24

4x=24 1 3

x=6

14. Areas of tringle CDL

(1/2×30×28) m²

=420 m² mark for fig.

Area of mark for

= (1/2×45×32)m² calculating of

=720 m² area of each

Area of AEN region

(1/2×15×20)m² (×5)

=150m²

Area of trapezium DLNE

= 1/2 ×(20+28)×40

=960m² 3

Total Area =(420+640+720+150+960)m²

=2890 m²

18. L.H.S : cos (60º-30º)= cos 30º= 1

R.H.S : cos 60º cos30º +sin 60º sin 30º

1 3

R.H.S = L.H.S 1

22. Let the Cost price of A be = Rs. x

C.P of B =x+x/10=11×/10 1

C.P of C = 11x/10×1/5+11x/10

= 11×/10(1+1/5)=66/10x 1

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Q. No Expected Value Points For dISTRIBUTION Total

seT C EAch Step OF MARKS

C.P of D = [ (66/50)x × 1/4] +(66/50)x

1

C.P of D is Rs. 132

33/20x=132 1 4

Hence, x =132×20/33= Rs. 80

23. Let my rate of walking be = x km/hr

Time taken to walk 2km=2/x 1

If my speed is (x + 1) km/hr

Time taken will be 2/(x + 1)

1

i.e

or

1

x = 3 or x = _ 4 1 4

Rate of walking = 3km/hr

28. A 's investment = Rs. 8000×36 1

B 's investment = Rs. 10000×36 1

C 's investment = Rs. 6000×30 1

A:B:C =24:30:15

A's share Rs. (9660/69)×24=Rs. 3360 1

B's share = Rs. (9660/69)×30=Rs.4200 1

C's share = Rs. (9660/69)×15= Rs. 2100 1 7

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