result · = 242 0.5 mark (2 ) (b) the annual income of khalid is rs. 2346000. the amount of rebate...

Result

.pk

Grade-8, Mathematics, Part-B of 5

PUNJAB EXAMINATION COMMISSION

EXAMINATION 2015, GRADE 8

MATHEMATICS PART – B (Subjective Type)

Part-A = 48 Marks, Part-B = 52 Marks, Total Marks = 100

Q.No. 33 (a) If A = {2,4,6,8,10} and B={1,2,3,4,5,6,7,8} then find A∩B

B={1,2,3,4,5,6,7,8} وت A∩B ولعمم رکںی ارگ A = {2,4,6,8,10}اور

A = {2,4,6,8,10}

B={1,2,3,4,5,6,7,8}

A∩B = {2,4,6,8,10} ∩{1,2,3,4,5,6,7,8} 2 Marks

A∩B = {2,4,6,8 } 1 Mark

Note: If students directly write A∩B then award 3 marks دںی ربمن 3ےتھکل ںیہ وت A∩B ارگ ہبلط رباہ راتس

(3)

(b): Find the square root of 2 up to 2 decimal places

ااشع رہی کت ذجر ولعمم رکںی۔ رمابت اک دو 2

1 .4 1 4

1 2 . 0 0 0 0 0 0

1 1 mark

2.4 1. 0 0

0 .9 6 1 mark

2 .81 0. 0 4 0 0

0. 0 2 8 1 1 mark

2.824 0. 0 1 1 9 0 0

0. 0 1 1 2 9 6 1 mark

0 . 0 0 0 6 0 4

√𝟐 = 1 . 4 1 1 mark

(5 )

(c) Find the cube root of 125 125عب ولعمم رکںیاک ذجمکل

۔ر ا

3 125 0.5 Mark

= 3 5 5 5 0.5 Mark

= 1

3 3(5 ) 0.5 Mark

= 5 0.5 Mark

(2)

Model Paper 2

RUBRICS

Result

.pk


Q.No. 34 (a) Convert (1432)5 into decimal system.

5(1432)وک ااشعری اظنم ںیم دبتلی رکںی۔

(1432)5 = 1×53 + 4×52 + 3×51 + 2×50 0.5 Mark = (1 125) (4 25) (3 5) (2 1) 0.5 Mark

= 125 + 100 + 15 + 2 0.5 Mark = 242 0.5 Mark

(2 )

(b) The annual income of Khalid is Rs. 2346000. The amount of rebate in tax

is Rs. 400000. Calculate the amount of income tax at the rate of 17.5%.

امکن سکیٹ یک رمق ولعمم رکںی۔ےک اسحب ےس 17.5% روےپ ےہ۔ 000004روےپ ےہ ۔ سکیٹ ںیم رٹیبی 2346000ہن آدمیناسالیک اخدل

Annual income = Rs 2346000

Taxable income = 2346000 – 400000 1 Mark

= Rs 1946000

Amount of Income Tax @17.5%17.5

1946000100

1 Mark

1751,946,000

10 100

= Rs 340,550 2 Marks (1 mark for unit)

Rs 2346000 = اسالہن آدمین

1ربمن 400000 – 2346000 = اقلب سکیٹ آدمین

= Rs 1946000

%17.5رشح ےک اسحب ےس امکن سکیٹ یک رمق 17.5

1946000100

1ربمن

1751,946,000

10 100

= Rs 340,550 2ربمن ( (ااکیئ اک اکی ربمن

(4 )

(c) If the price of 12 metre long and 6 metre wide carpet is Rs.4716, then find

the price of 8 metre long and 3 metre wide such carpet ۔

؟رٹیم وچڑے اقنیل یک تمیق ایک وہ یگ 3رٹیم ےبمل اور 8 اےسی روےپ وہ وت4716رٹیم وچڑے اقنیل یک تمیق 6رٹیم ےبمل اور 12ارگ

Length(in metre) Width(in metre) Price (in Rs.)

تمیق )روےپ ںیم( وچڑایئ )رٹیم ںیم( ابملیئ )رٹیم ںیم(

12 6 4716 1 mark

8 3 x

Identifying correct proportion by arrow sign or by statement 1 Mark

انتبس یک حیحص انشتخ ذبرہعی ریت اک اشنن ای اردو اک ہلمج

(4)

Result

.pk


4716

x =

3

6×

8

12 1 mark

x = 24

72× 4716

x = Rs. 1572 1 mark

Q.No. 35: (a) Solve (2 x2 + 2 x+3) – ( x-2) لح رکںی۔

(2x2 + 2x+3)– (x-2)

= 2x2 + 2x+3–x+2 1 Mark

= 2x2 + x +5 1 Mark

(2 )

(b) Factorize x 2 – 14 x + 49 x2 – 14 x + 49 زجتی رکںی۔

x 2 – 14 x + 49

= x 2 – 7x-7x + 49 1 Mark

= x(x-7) – 7(x-7) 1 Mark

=(x-7) (x-7) 1 Mark Note: If student solve this by any other method of factorization, he / she will be awarded full

marks.

(3 )

(c) Solve the given simultaneous linear equations by equating coefficient.

ےس لح رکںی۔ دعدی رس وں وک رباربرکےن ےک رطےقی دی یئگ کی دریج اسم واوتں وک

2x + y = 6

x + 2y = 9

2x + y =6 (1)

x + 2y = 9 (2)

4x + 2y =12

±x± 2y = ±9 1 Mark

3x = 3 1 Mark

3

3x

x = 1 1 Mark

By putting value of x in equation (2), we get x ےسردج رکےن ( ںیم2یک تمیق اسموات )

1 + 2y = 9 0.5 Mark

2y = 9-1 0.5 Mark

2y = 8

y= 8

2

(5)

Result

.pk


y =4 1 Mark

so x=1, y=4

Note: Student will be awarded marks for equating the coefficients of any variable.

Q.No.36 (a) By using Hero’s formula, find the area of a triangle when the

lengths of its sides are 6 cm, 8 cm and 10cm.

ےریہو ےک cm , 6 cm 8 اور cm 10ںیہ۔ کلی اعال یک ابملںایں ثلثم اک رہبق ولعمم رکںی ہکبج اس ےکیک دمد ےس

a=6 b= 8 c= 10

2

a b cs

6 8 10

2s

24

2s =12 1 Mark

Area of triangleثلثم اک رہبق= √𝑠(𝑠 − 𝑎)(𝑠 − 𝑏)(𝑠 − 𝑐)

= 12(12 6)(12 8)(12 10)

1 Mark

= 12(6)(4)(2)

= 576

=24cm2 2 Marks (1 mark for correct square root + 1mark for unit)

ربمن( 1ربمن + ااکیئ اک 1)درتس ذجر ےنیل رپ

(4 )

(b) Construct a regular hexagon with each side measuring 4 cm.

مس وہ۔ 4 امیپشئانبےیئ سج ےک رہ علض یک اکی مظنم دسمس

For,

Drawing a circle of radius 4cm 1 Mark

Taking a point A on the circle 1 Mark

Starting from point A , drawing six arcs of radius 4cm at points of the circle at B,

C, D, E, F with centre at A,B,C,D and E respectively. 2 Marks

Joining A to B, B to C, C to D, D to E, E to F and F to A. 2 Marks

ربمن 1 یٹنیس رٹیم رداس اک دارئہ انبےن رپ4

ربمن 1 A ےنیل رپ دارئے رپ اکی ہطقن

ربمن 2 E اور D,C,B,A اقنط ےس رشو رکےت وہےئ F, E, D, C , B )ابرتلبیت رپ A ہطقن

یٹنیس رٹیم رداس یک ھچ وقںیس انبےن رپ 4 (وک رمزک امن رک

ربمن 2 A وک B ، B وک C , C وک D , D وک E , E وک F اور F وک A ےس المےن رپ۔

Note: If students make hexagon by any other correct method, then he will be awarded full

marks.

۔دسمس انبےت ںیہ وت ا ُ رطےقی ےس درتس ارگ ہبلط یسک یھب اور

ں

ئ

ےس وپرے ربمن دےی اجی

( 6 )

A B

C

D E

F O

Result

.pk


Q.No. 37(a) Prove that: If two lines intersect each other, then the opposite

vertical angles are congruent.

ںیہ۔ ارگ دو وطخط اکی دورسے وک عطق رکںی وت رایس اقتمہلب زاوےی امتملث وہےتاثتب رکںی :

Diagram 1 وصتری Mark

Given مولعم 1 Mark

To prove1 ولطمب Mark

Construction1 لمع Mark

Statements2 ایبانت Marks

Reasons1 داللئ Mark

(7 )

(b) Find the value of angle A from the given triangle.

دی یئگ ثلثم ںیم زا و ہیAیک تمیق ولعمم رکںی۔

sin mA= a

b 0.5 mark

sin mA = 2

2 2 1 mark

sin mA = 1

2 0.5 mark

mA = 45o 1 mark

(3 )

(c) Find the mode of data 3, 5, 4, 2, 4, 6, 5, 4, 3, 7

اک ااعدہ ولعمم رکںی۔ 7، 3، 4، 5، 6، 4، 2، 4، 5، 3وماد

Correct answer Mode= 4 2 Marks

(2 )

A B

C

2 2b a=2

c

result · = 242 0.5 mark (2 ) (b) the annual income of khalid is rs. 2346000. the amount of rebate...

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