Differentiation(Paper 1)_Set 1@2013

Differentiation(Paper 1)_Set 1@2013 MRSM 2013 1.

A curve has an equation point

(2 , 3).

 =    . Find the equation of the tangent to the curve at [3 m]

[2 [2   = 8 ] Kedah 2013 2.

 Given that rate of change of  at point

 = 2   10  5 and the rate of change of  is 4 units per second. Find the (2,7) [3 m]  2,7)

[-8]

3.

Find the value of



 −9 lim  →− +

[2 m]

[-6]

Melaka 2013 4.

 Given the equation of the curve (a) the coordinate-  of turning point (b) the equation of tangent at point



[4 ;

 = 4  16]

 = 2   16  25. Find,  (  (3 , 4)

[4 m]

N.Sembilan 2013 5.

It is given that

 =   , where  = 6 6  1. Find   in terms of .

[3 m]

9 (6  1)  6.

The gradient of the tangent to the curve of .



 = 2 (  3) at  = 1 is 8. Find the value [3 m]

  Pahang 2013 7.

 It is given  and the rate of change of  is 6 units s-1 at all time. Find the rate of change of  when . [3 m]

 =    4  1   =2



[96]

8.

 (  () =  +  ′(1). − , find the value of ′(

Given that

[3 m]

[14]

P.Pinang 2013 9.

Find the coordinates of the point on the curve the tangent to the curve is 5.

 (  2)( )(  1) where the gradient of  = ( [3 m]

[(1,6)]

10.

The radius of a balloon in the shape of a sphere increases at the rate of 2 cms-1. Find the rate of change of the volume of the balloon when the radius is 3 cm. [3 m]

72 ]

[

Prepared by : Pn Hayati Aini Ahmad

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Differentiation(Paper 1)_Set 1@2013 Perlis 2013 11.

 (  () = (  =  (55  3), find ′′(  ′′(2).

Given

[3 m]

[108]

12.

 = 3    . Given  increases at a constant rate of 4 units per second when  = 2  , find the rate of change in  [3 m] 



Two variables  and  are related by the equation

[10]

13.

Given an equation of a curve maximum.

 = 2   6  1. Find the value of  when  is

[3 m]

 = 0]

[

14.

The area of a circle increases at the rate of radius when the radius is 4 cm.

16 cm s

2 -1.

Find the rate of change of the [3 m]

[2 cms-1]

Putrajaya 2013 15.

Given the gradient of the tangent to the curve



the values of  and of

.

 =    at the point (-1,-5) is 3. Find [4 m]

 = 4  ;  =   16.

 =    2 , express the approximate change in , in terms of ℎ, when  changes [3 m] 5 5  ℎ , where ℎ is a small value.

Given from  to

[55ℎ] SBP 2013 17.

Point A lies on the curve

 

 (52)) . It is given that the gradient of the normal at  = (52

point A is . Find the coordinates of A

[3 m]

[(2 , 1)]

18.

It is given that

 =  , where  = 2  . If    = 1, find the value of .

[3 m]

[ = 3] Terengganu 2013 19.

 = 3   4  5 has a minimum point at  = , where  is a constant. Find  [3 m]

The curve the value of .

 =   20.

Given that

  , find   = − 

[3 m]

 (−) −)

Prepared by : Pn Hayati Aini Ahmad

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