Differentiation(Paper 1)_Set 2@2013 Terengganu 2012 1.
2.
( 5) . It is given that the gradient of the normal at R = ( 4 = 8. Find the coordinates of R. [(3 , 4)] [3 m] , evaluate "( [16] () = − "(0). Given that ( [4 m]
A point R lies on the curve is parallel to the straight line
Kedah 2012 3.
4.
= ( ( 2) has two turning points. Find the values of for those
Given the curve turning points. [ = 2 , = ]
[3 m]
(4 7) and the rate of change of is 3 units per second. Find the rate of = (4 = 2. [24] [3 m]
Given change of when
Melaka 2012 5.
Given the equation of the curve
= 2 16 25 . Find
(a)
the coordinate- of turning point
(b)
the equation of tangent at point
[4]
(3 , 4) [ = 4 16]
[4 m]
MRSM 2012 6.
A piece of wire is bent to form a circle. The wire is heated up and the area of the circle increases at a constant rate of 6 cm 2s-1. Find the rate of change of the radius of the circle [3 m] 9 cm . Give the answer in terms of . Find the equation of the normal to the curve = 2 4 10 at point (0,10) [3 m]
when its area is 7.
2
= 10 N.Sembilan 2012 8. 9.
[40(2 3)] [2 m] = (2 3) . Find in terms of . = ( 7) . It is given that the gradient of the normal at The point Q lies on the curve = ( Q is . Find the coordinates of Q. [(10 , 9)] [2 m] It is given that
Pahang 2012 10.
Given the curve , where and are constants, has a minimum point of [ℎ = 8, = 17 ] . Find the value of and . [4 m]
= 2 ℎ ℎ
(2 , 9)
ℎ
P.Pinang 2012 11.
Given (i)
12.
= 2( 5) , find
(ii) the value of when is minimum
4 4 10; 10;
[3 m]
= 5 . Given that increase at at a constant rate of 0.5 units per second. Find the rate of change of when = 2 [3 m]
Two variables and are related by the equation
Prepared by : Pn Hayati Aini Ahmad
1
Differentiation(Paper 1)_Set 2@2013 Perak 2012 13.
Given the equation of a curve
= 2(3 2), find the coordinates of turning point.
,
[3 m]
Perlis 2013
( () = 4(2 3), find ′(1).
14.
Given that
15.
The area of a circle increases at a rate of 8 cm2s-1. Find the rate of change of the radius of the circle when the area of the circle is
[4 m]
[-20]
16 cm . 2
[3 m]
Sarawak 2012 16.
Given that
= 2 4 3 has a minimum value of 13, find the value of . [4 m]
[k =5]
17.
= 16 18 5, find in terms of , [32 18] 18] If changes from 2.01 to 2, 2 , find the corresponding small change in [3 m]
Given that (a) (b)
[-0.4632]
SBP 2012 18.
Given that (a)
19.
= 16(5). Find
[ 32] 80 32
(b)
the value of when is maximum.
[3 m]
1, lies on a curve with gradient function 3 . Find the
Given that the point M
equation of the tangent at point M.
[2 8 = 5 5]
[3 m]
Selangor 2012 20.
21.
Given that
= 2( 2( 4). Find
(a)
[4 8]
(c)
the minimum value of
(b)
the value of when is minimum
[8]
[2] [3 m]
9.6
The surface area of a sphere is increasing at a constant rate of cm2 s-1. Find the rate of change of the radius radius of the sphere at the instant when the radius is 4 cm. [3 m]
[0.3] 0.3] W.Persekutuan 2012 22. 23.
( () = + − , find the value of f ‘(2)
Given that
[3 m]
= , where and are constants, at the point [ = 5; = 8] (2 ,14) is . Find the value of and of . [4 m] The gradient normal to the curve
Prepared by : Pn Hayati Aini Ahmad
2
