C2
Worksheet C
THE BINOMIAL THEOREM
1
Expand (1 + 4x)4 in ascending powers of x, simplifying the coefficients.
(4)
2
Find the first three terms in the expansion of (2 + 5x)6 in ascending powers of x,
simplifying each coefficient.
(4)
a Expand (1 + 3x)4 in
7 - GRAVITATION
Page 1
( Answers at the end of all questions )
1)
The change in the value of g at a height h above the surface of the earth is the same
as at a depth d below the surface of earth. When both d and h are much smaller
than the radius of the e
5 - WORK, ENERGY AND POWER
Page 1
( Answers at the end of all questions )
1)
A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How
much further will it penetrate before coming to rest assuming that it faces constant
res
5 WORK, ENERGY AND POWER
Page 1
5.1 Work
The product of force and displacement ( in the direction of force ), during
which the force is acting, is defined as work.
When 1 N force is applied on a particle and the resulting displacement of the particle, in
27.
(a) A 34.5-m length of copper wire at 20.0 C has a radius of 0.25 mm. If a
potential difference of 9.0 V is applied across the length of the wire, determine the
current in the wire. (b) If the wire is heated to 30.0 C while the 9.0-V potential
differe
Calculate the resistance of a piece of aluminum that is 20cm long and has
a cross-sectional area of 10-4m2. What is the resistance of a piece of glass
with the same dimensions? Al=2.8210-8.m, glass=1010.m.
The resistance of aluminum
The resistance of glas
Chapter 27:
CIRCUITS
1. The sum of the currents into a junction equals the sum of the currents out of the junction is
a consequence of:
A. Newtons third law
B. Ohms law
C. Newtons second law
D. conservation of energy
E. conservation of charge
ans: E
2. Th
1.
C
[1]
2.
(a)
as ideal gases do not have forces between molecules so no potential energy (2)
2
(b)
use of pv = NkT
conversion of T to kelvin and answer = 5.8 1022 molecules
2
[4]
3.
(a)
(b)
(c)
top row : 17 1
(14) 4 (1)
bottom row: 8 1
7
2
(1)
other pro
Measurements
When using a digital voltmeter and digital ammeter to determine the resistance of a wire,
state one possible random error which could occur in the use of the digital meters. How could
this error be kept to a minimum? Explain why the voltmeter
1.
C
[1]
2.
(a)
(b)
use of counter (+GM tube)
determine background count in absence of source
place source close to detector and:
place sheet of paper between source and counter (or increase distance
from source 3-7 cm of air) reduces count to background
1.
A valid set of units for specific heat capacity is
A
kg J1 K1
B
kg J K1
C
kg1 J K1
D
kg J1 K
(Total 1 mark)
2.
An ideal gas is contained in a volume of 2.0 103 m3.
(a)
Explain why the internal energy of an ideal gas is only kinetic.
.
.
.
.
(2)
(b)
The
1.
B
[1]
2.
D
[1]
3.
(a)
(i)
Use of F = kx (1)
F = ma (1)
2
cf with a = 2x ie 2 = k/m (1)
use of T = 2/ to result (1)
2
(i)
resonance (1)
1
(ii)
natural freq = forcing frequency (1)
1
(iii)
use of c = f (1)
answer 9.1 1013 Hz (1)
2
use of T = 1/f eg T = 1
1.
A student is asked: What is meant by background radiation?
She writes: It is the radiation produced by the rocks in the ground.
This answer is
A
correct
B
incorrect rocks do not produce radiation
C
incomplete
D
incorrect this radiation would not be ion
JC1
Raffles Junior College
2008
Physics Tutorial 11
Superposition
SELF-CHECK QUESTIONS:
S1.
What is the principle of superposition?
S2.
How is a stationary wave formed?
S3.
What is the phase difference between particles located between the same two
succes
1.
A child is playing on a swing. The graph shows how the displacement of the child varies with
time.
2
1
Time/ s
0
0
2
4
6
1
2
Displacement / m
The maximum velocity, in m s1, of the child is
A
/2
B
C
2
D
3
(Total 1 mark)
2.
A car driver notices that her
Revision Lecture 3
1. Show that
d
1
x
tan 2 = 1 + cos x .
dx
[2]
x + sin x
Hence, or otherwise, show that 1 + cos x dx = x f ( x) + C , where
f (x) is a single trigonometric function to be determined and C
is an arbitrary constant.
[5]
2.
A curve is
Supplementary Exercise For Test Preparation
1. Given that (1 + ax) n = 1 12x + 63x 2 + , find a and n.
[Ans: a = 1.5, n = 8]
2. Find the coefficient of x22 in the expansion of (1 3x)(1 + x3)10.
[Ans: 360]
3. Write down the expression of (1 + 2x)(1 x) 8 as
Summary on Vector Lines and Planes
1.
Equation of .
LINES
r = a + m,
2.
PLANES
r = a + m1 + m2
r n = D (D = a n )
ax + by + cz = D
x a1 y a2 z a3
=
=
m1
m2
m3
Foot of perpendicular and
perpendicular distance
from a point to .
Q
P
n
A
N
l
Method 1:
By
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certicate of Education
Advanced Subsidiary Level and Advanced Level
9709/12
MATHEMATICS
Paper 1 Pure Mathematics 1 (P1)
October/November 2010
1 hour 45 minutes
*6463108156*
Additional Materials:
A
Binomial Expansion
Pg 1
x 2 5x
A
B
C
. Express f(x) in the form
+
+
,
2
1 x
1 x
(1 x) (1 x)
(1 x) 2
where A, B and C are constants. The expansion of f (x), in ascending powers of x, is
r
2
3
C0 + C1x + C2 x + C3 x + .+ Cr x +.
Let f (x) =
Find C0 , C1 , C
Pure Maths
Vectors
A-level Maths Tutor
www.a-levelmathstutor.com
topic notes
[email protected]
Vectors : Vector Equations
Component rules
Consider two vectors:
a = x1 i +
y1 j + z1 k
and
b = x2 i +
y2 j + z2 k
in three dimensional space.
a = b im
1. AP,GP, series (summation), MOD, MI, partial fractions
n
- be aware of formulas for
r= 1
r,
n
r2
r= 1
n
r 3 and correction measures to be taken
r= 1
when lower limit r is not equals to 1.
- be aware of formulas for nth term and sum to n terms of an AP a
Difference Equations
to
Differential Equations
Section 4.1
The Denite Integral
As we discussed in Section 1.1, and mentioned again at the beginning of Section 3.1, there
are two basic problems in calculus. In Chapter 3 we considered one of these, the prob
Teaching and learning module
Additional mathematics form 5
CHAPTER 3
NAME:.
FORM :
Date received :
Date completed .
Marks of the Topical Test : .
Prepared by :
Addational Mathematics Department
Sek Men Sains Muzaffar Syah Melaka
For Internal Circulations
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MATH 1160 (M15A): Semester I (2010/11)
MATH 1160 (M15A): Semester I (2010/11)
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MATH 1160 (M15A): Semester I (2010/11)
MATH 1160 (M15A): Semester I (2010/11)
MATH 1160 (M15A): Semester I (2010/11)
MATH 1160 (M15A): Semester I (2010/11)
MATH 1160 (M15A): Semester I (2010/11)
MATH 1160 (M15A): Semester I (2010/11)
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