Integration and Differentiation
Short Description
Download Integration and Differentiation...
Description
ADDITIONAL MATHEMATICS
DIFFERENTIATION & INTEGRATION
SMK BBSL_2010
PAPER 1(SET 1) JOHOR 2009 1.
Given y
24 4
x
, find the approximate value of y , when x changes from 2 to 2.02. [4 marks]
2.
Find the coordinates of the turning points on the curve y 4 x
1
x
the maximum point. 3.
Given y
2 x 3
[4 marks] dy
and
x 2
and determine
dx
3g x where g x is a function of x . Find the value of
1
g x d x .
[4 marks]
1
KEDAH 2009 4.
Find the gradient of the curve y 4 x 2
3 2 x
5 2
at the point 1,3
1 with respect to x . 2 x 1
[3 marks]
2
4 x
5.
Differentiate
6.
Given that the gradient function of a curve passing through the point 1,2 is 3 2
2 x 1 7.
[2 marks]
2 x , determine the equation of the curve.
Given that y
2 x 3
[4 marks]
5
10
and x is increasing at the rate of 2 units per second, find the
rate of change of y when x
1
2
.
[3 marks]
KELANTAN 2009 4
8.
Given that g x
9.
Two variables r and s are related by the equation r s
, find g 1 . "
3
2 x 1
[4 marks]
3
s2
.Given that r increase at
a constant rate of 5 units per second, find the rate of change of s when s 2 . [3 marks]
1
ADDITIONAL MATHEMATICS
DIFFERENTIATION & INTEGRATION
3
10.
SMK BBSL_2010
3
1
1
Given that g x d x 10 , find the value of m if 2g x mx dx 6m . [3 marks]
MELAKA 2009 6
11.
Differentiate x 2 1 2x with respect to x .
12.
The radius of a sphere increases at the rate of 0.1 cms . When its radius is 5 cm, find
[3 marks] -1
the rate of increase of its surface area. [Given the surface area of a sphere is 2 A 4 r ].
[3 marks] 3
13.
Given that
dx 5 . Find the value of the constant m if f x dx 1
2
3
f x dx f x mxdx 15 1
[3 marks]
2
MRSM 2009 14.
Given that y t 2t and x 4t 1 , find
15.
It is given that y
2
2 x 1 2
x
and
dy dx
dy dx
in terms of x .
[3 marks]
2g x , where g x is a function in terms of x .
2
Find the value of g x d x .
[3 marks]
1
16.
17.
Given
dy dx
3
14 and ydx 9 , find y in terms of x . 0
Diagram 1 shows part of the graph of a curve.
Diagram 1
2
[3 marks]
ADDITIONAL MATHEMATICS
DIFFERENTIATION & INTEGRATION
6
(a)
SMK BBSL_2010
8
0
3
State the value of ydx xdy
8
(b)
Given that xdy 9 , find the area of the shaded region.
[3 marks]
3
PAHANG 2009 x 3x 2
18.
Find the value of lim
19.
Volume, V cm , of a solid is given by V 8 r 2
x 2
[2 marks]
x 4 x 3 2
3
2
3
r , r is the radius. Find the
3
approximate change in V if r increases from 3 cm to 3.005 cm.(Give your answers in terms of ).
[4 marks] 1
20.
Find the value of
6 x 6 x
1
21.
4
x
dx .
[3 marks]
The gradient function of a curve passing through 1,2 is given by
1 2
3 x 4
equation of the curve.
. Find the
[3 marks]
PENANG 2009 22.
The curve y f x is such that
dy dx
2kx 8 where k is a constant. The gradient at
x 3 is 4. Find the value of k .
23.
[2 marks]
Given that y 4 x 3 7 x 2 1 , find the value of
dy dx
at point 2,5 . Hence, find the
small change in x when y increases from 2 to 2.1. 4
24.
It is given that
[3 marks] 3
f x dx m, find the value of m if 2 f x 7 dx 17 . 3
[4 marks]
4
PERAK 2009 25.
The curve y f x is such that
dy dx
2 px 3 , where p is a constant. The gradient of
curve at x 4 is p . Find the value of p . 26.
[2 marks]
2 The curve y 2 x 24 x r has a maximum point at x r , where r is a constant.
Find the value of r .
[3 marks]
3
ADDITIONAL MATHEMATICS
DIFFERENTIATION & INTEGRATION
SMK BBSL_2010
3
27.
Given that
g x d x 5 , find
1 1
(a)
3
g x d x ,
(b)
2g x 3x dx
[4 marks]
1
3
PERLIS 2009 28.
2
2 It is given that y 2x 3x 4 . Find
dy dx
when x 1 .
[3 marks] 2
29.
2
The surface area, A cm , of a solid is given by A 2
3 r 2
6
r
. It is given that the rate
-1
of change of the surface area is 5 cm s . Find (a) (b) 30.
dA dr
, -1
the rate of change of the radius, in cm s , when the radius is 3 cm.[4 marks]
Given that the gradient function of the curve at point (1,10) is 3 x 5. Find the equation of the curve.
[3 marks]
SABAH 2009 31.
Differentiate x 2x 1 with respect to x .
32.
A point P lies on the curve y
1 2
2x 5
2
[3 marks]
. Given that the tangent to the curve at P is
parallel to the straight line 2 x y 1 0 . Find the coordinates of P.
[3 marks]
4
33.
Given that g x d x 5, find 1
1
(a)
g x d x , 4
4
(b)
2g x 3x dx.
[4 marks]
1
SARAWAK ZON A 2009 3
34.
2 Find the coordinates of the minimum point of the curve y x x 10. [3 marks]
35.
Two variables, x and y , are related by the equation y 3x
2
16
x
. Given that y
increases at a constant rate of 10 unit per second, find the rate of change of x when x 2.
[3 marks] 4
ADDITIONAL MATHEMATICS
DIFFERENTIATION & INTEGRATION
SMK BBSL_2010
6
36.
Given that g x d x 2 , find 3
3
(a)
6
3g x d x ,
the value of k if g x kx dx 10.
(b)
6
[3 marks]
3
SARAWAK ZON C 2009 4
37.
Given that g x 5 3x , find g " 2 .
38.
A circle has a radius of 5 cm. cm. The radius of the circle circle is decreasing at the rate of 0.1
[3 marks]
cm per second. Find the rate of change of the area of the circle. 39.
Given that
3
3
1
1
[4 marks]
dx 5 , find the value of k if f x kx dx 10, where k is a f x dx
constant.
[3 marks]
SBP 2009 2
40.
Given that f x x 5 3 x , find f ' 2 .
41.
Two variables, P and x are related by the equation P 3x . Given x increases at x
3
[3 marks] 2
a constant rate of 4 units per second when x 2 , find the rate of change of P. [3 marks] 42.
Given y
h
2 x 5
3
and
dy dx
3
g x , find the value of h if g x 1 dx 7. 2
[3 marks] SELANGOR 2009 43.
2
Two variables, x and y , are related by the equation y x 3 x . Given that y increases at a constant rate of 4 units per second, find the rate of change of x when x 2 .
44.
[3 marks]
The gradient function of a curve is px 3 , where p is a constant. The straight line y 5 2x is a tangent to the curve at the point (-2,1). Find (a)
the value of p,
(b)
the equation of the curve.
5
[3 marks]
ADDITIONAL MATHEMATICS
k
45.
Given that
1
4 x
DIFFERENTIATION & INTEGRATION
dx 2
1
4 5
SMK BBSL_2010
, find the value of k .
[3 marks]
KLANG 2009 3
46.
Differentiate
47.
Given that the gradient of a normal to the curve y kx x 2 at the point (1,-6) is
2
4 2 x
with respect to x .
[3 marks]
2
1
6
. Find
(a)
the value of k
(b)
the equation of the tangent to the curve at the point where x 1 . [4 marks] 3
48.
Given that
h x d x , evaluate 0
3
(a)
1
5 h x d x ,
3
3 h x dx.
(b)
0
[3 marks]
0
TERENGGANU 2009 49.
2
Given that the equation of a curve which passes through point P is y 2x 1 . The 1
normal gradient to the curve at point P is
2
. Find the coordinates of P. [3 marks]
4
50.
Given that g x d x 7 , find the value of 1
1
(a)
g x d x ,
4
p if g x pdx 25.
(b)
4
51.
[4 marks]
1
A curve which has gradient function kx 2, where k is a constant, passes through points (0,10) and (2,0). Find (a)
the value of k ,
(b)
the equation of the curve.
[4 marks]
WP 2009 52.
Given an equation of a curve y 2 x 6 x 1 . Find the value of x when y is 3
2
maximum.
[3 marks]
6
ADDITIONAL MATHEMATICS
53.
DIFFERENTIATION & INTEGRATION
2
-1
The area of a circle increases at the rate of 16 cm s . Find the rate of change of the radius when the radius is 4 cm.
[3 marks]
k
4
54.
SMK BBSL_2010
4
1
1
k
29 where 1 k 4 and Given that g x d x 7 and 2g x dx 2 5 g x dx g x 0. Find the value of k.
[3 marks]
TIMES 2009 55.
Given that y
(a) (b)
dy dx
3 2
2 x 3
, find
in terms of x ,
the approximate change in y given that x decreases from 2 to 1.98 [3 marks]
56.
The curve y x kx 4 has a minimum point at x 3 , where k is a constant. Find 2
(a)
the value of k,
(b) the equation of the tangent to the curve at x 0. [4 marks]
57.
Diagram 2 shows the curve y f x . The curve intersects the x-axis at x 2 .
Diagram 2 3
Given that
dx 4 units. Find the area of the shaded region. f x dx
[2 marks]
2
2
58.
Given that
kx 2 dx 5. Find the value of k.
1
7
[3 marks]
View more...
Comments
