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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

1

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

(52)) . It is given that the gradient of the normal at = (52

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

2

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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

1

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

(52)) . It is given that the gradient of the normal at = (52

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

2

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