Page 24 - (1-1)eng

(1 - 1) The First Derivative of a Function – G(A) A1

Exercise (1 - 1)

Group (A)

Choose the correct answer
3
2
S.B. 1) If y = 2 t + 7 and z = t – 4 , then the rate of change of y with respect to
z equals … … …
(a) 2 t (b) 3 t (c) 6 (d) 12

MOE 2017 2) If x = 2 n + 7 , y = n , n = 1, then dy equals … … …
2
3
dx
3 3
(a) (b) (c) 2 (d) 6
8 4

2
MOE 2017 3) If  ( 2 x ) = x + x , then ' ( 1 ) = … … …
(a) 5 (b) 3 (c) 2 (d) 1

3
MOE 2017 4) If y = t and z = t 2 , then the rate of change of y w.r.t. z at t = 1
equals … … …

(a) 6 (b) 1 (c) 1.5 (d) 2

Answer the following questions

dy
2
S.B. 5) If x = 13 – 2 t and y = 4 t – t , find at t = 4.    127  
dx  8 
S.B. 6) Find the value of the parameter t at which the curve x = 2 t – 5 t + 4 t – 9 ,
2
3
2
y = 2 t + t – 5 has

(a) a vertical tangent  2  3  or 1


(b) a horizontal tangent     1  
4 

z  1 z 1 dy 

S.B. 7) If x = , y = , find at z = 2   1  

z 1 z  1 dx  9 

x 1

S.B. 8) Find the derivative of with respect to 2 x 1 at x = 4    2  

x 1  3 
S.B. 9) Find the rate of change of ( x + 3 ) ( x – 2 ) with respect to x  3 .
x  2
1  2 
 5   2 x  1  x  2 


S.B. 10) Find the rate of change of 9  x with respect to x when x = – 4. [ 20 ]
2

x 1
Calculus 23 Unit (1)