Solutioon to Topic 4 Applicattion of Inte gration
Q1
x = -/2
x = /2
y = tan
t x
x = /3
V =
3
0
=
( tan x )
( sec
3
0
2
2
dx
x 1) dx
= [ tan x x ]0 3
= 3 3 unnits3
Q2
Area =
0
= y dy
1
1
= tann ( 2 )
Solution to Blk A Calculus Topic 1 Application of Differentiation I
1.
(i)
40 = 2 y + 3x
3
y = 20 x
2
1 2
x sin(60 )
2
1 3
= xy + x 2
2 2
Area, A = xy +
3 1 3
= x 20 x + x 2
2 2 2
3
3 2
= 20 x x 2
Pioneer Junior College
2016 J2 H2 Mathematics Revision
Topic 8 Differential Equations
(To be completed by 13 May, Friday)
Tip 1 : (Time Management) 1 mark
1.5 min (Read+ Do) + 0.3 min (check)
Tip 2 :
Pioneer Junior College
H2 Mathematics
Session : Applications of differentiation (Maxima and minima)
At the end of the session, students should be able to understand the underlying concepts in solving
Name: _
Class: _
Cluster 6: Integration and its applications
XIX Integration techniques
Integration is the reverse process of differentiation. So the formulae of integration can be
deduced from formul
Solution to Topic 2
dx
1
dy
1. (i)
= 1+ ,
= 1,
dt
t
dt
dy
1
t
=
=
dx 1 + 1 t + 1
t
dy
t
=
> 0 for all t > 0
dx t + 1
Hence C does not have a stationary point
Since t > 0, t + 1 > 0,
(ii)
(0, 1.567)
y=
Pioneer Junior College
H2 Mathematics
Session: Vectors (Algebra and Lines)
At the end of the session, students should be able to:
(1)
(2)
(3)
(4)
(5)
Find equation of line OR direction vector of line
Name: _
Class: _
Cluster 4: Differentiation and its applications, Maclaurins series
TOPIC XIV Differentiation techniques and its applications (I)
(1) Techniques & implicit differentiation
xn
lnx ex si
Solution to Topic 5 DE
d2 y
1.
= x sin x
dx 2
dy
= x( cos x) cos x dx
dx
= x cos x + sin x + C
= x cos x + sin x + C
y = x sin x (1)(sin x)dx cos x + Cx + D
y = x sin x 2 cos x + Cx + D
y = f ( x ) pa
Pioneer Junior College
H2 Mathematics
Session : Application of Differentiation (Parametric)
At the end of the session, students should be able to
(1) State the coordinates of a general point on curve