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MATHEMATICS PAPER – 2ND YEAR Roll No.

Class & Session._______________

Sig. of Candidate: _______________

Sig. of Teacher. _______________

Test Syllabus: Test # 2 Chapter # 2 Time: 40 Minutes

Marks: 25

FEDERAL BOARD

PAPER OBJECTIVE Q#1. Encircle the correct answer: ax dy (i) If y  then =? ax dx 2a a A. B. 2 2 a  x a  x dy (ii) If y 2  x 2  4 x  5  0 then  dx 2 x A. 2  x B. y x (iii) If f  x   e then by Maclaurin Series f  x   A. 1  x 

x2 x3   ... 2! 3!

B. 1+2x+

(i)

If y  sin 1 x  cos1 x then

(ii)

A. 0 d x 10   dx A. x10 x 1

(5×1=5)

C.

C.

4 x2 8 x3   ... 2! 3!

a

a  x

2

x2 y

C. 1–x+

D.

D.

x2 x3   ... 2! 3!

2a

a  x

2

x2 y

D. 1  x 

x 2 x3   ... 2! 3!

dy  dx

B. x

C. 2x

D. 4x

B. 10x9

C. 10 x.ln100

D. 10 x n10

SECTION-B (Marks 12) Q#2. Write short answer. x y dy y  if  tan 1   (i) Show that dx x x  y

(4 × 3 =12)

(ii)

Find the derivative of f  x   x2 by definition.

(iii)

Discus the function defined as f  x   sin x 

   Q#3. Show that 2 xh  2 x 1   n2  h   

1 2 2

cos 2 x for extreme values in the interval  0,2  .

SECTION-C (Marks 8) 2 3  n 2  h 2  n 2  h3    ... using Taylor’s theorem 2 3  

(8)