THE HONG KONG POLYTEOHNIO UNIVERSITY
Department of Applied Mathematics
Subject Code: AMA203 Subject Title: Mathematics la
Session: Semester 1, 2010/2011
Date: December 14, 2010 Time: 09:30 12:30
Time Allowed: 3 hours
This question paper has 7 pages (a
THE HONG KONG POLYTECHNIC UNIVERSITY
Department of Applied Mathematics
Subject Code: AMA203 Subject Title: Mathematics Ia
Session: Semester 1, 2008/09
Date: 16 December 2008 Time: 2:00 5:00 pm
Time Allowed: 3 Hours
This question paper has 6 pages (attac
THE HONG KONG POLYTECHNIC UNIVERSITY
Department of Applied Mathematics
Subject Code: AMA203 Subject Title: Mathematics IA
Session: Semester 1, 2009/2010
Date: 10 December 2009 Time: 14:00 - 17:00 pm
Time Allowed: 3 Hours
This question paper has 6 page
AMA203: Mathematics IA
AMA203: Mathematics IA
AMA203: Mathematics IA
Ordinary Differential Equations
Second Order Linear Differential Equations
A second order linear differential equation may be written as
y 00 + P(x)y 0 + Q(x)y = R(x).
In general such eq
AMA203: Mathematics IA
AMA203: Mathematics IA
AMA203: Mathematics IA
Linear Algebra
Matrices and Determinants
A matrix is a rectangular array of scalars, and each array in the
array is called an entry of the matrix. If a matrix has m rows and
n columns, t
AMA203: Mathematics IA
AMA203: Mathematics IA
AMA203: Mathematics IA
Linear Algebra
Inner Product
Let v = [v1 v2 . . . vn ]T and w = [w1 w2 . . . wn ]T be two vectors
in Rn , the inner product of them is defined as
hv, wi = vT w = v1 w1 + v2 w2 + . . . vn
AMA203: Mathematics IA
AMA203: Mathematics IA
AMA203: Mathematics IA
Laplace Transform, Convolution, and Fourier Transform
Laplace Transform
For a real valued function f : [0, ) 7 R, the Laplace transform of
f is defined as
Z
F(s) =
est f(t) dt.
0
Note th
AMA203: Mathematics IA
AMA203: Mathematics IA
AMA203: Mathematics IA
Algebra of Complex Number
Complex Numbers
A complex number is an expression of the form
z = x + iy,
where x and y are real numbers. x is called the real part of z
denoted by x = Re(z), y
AMA203
1. The set of all complex numbers z satisfying
25i
|z 4 + 5i| = 2 z +
3 + 4i
is a circle on the complex plane. Find the center c and the radius of the circle R
such that the circle can be written as
|z c| = R.
(15 marks)
2. (a) Express z = 1 i and
2000 2001 F.3 Mathematics Test 2
Laws of Indices
MARYMOUNT SECONDARY SCHOOL
Time allowed: 35 minutes
Name: _
Class: _
Number: _
1. a. If an = 5 find the value of a2n.
b. Find the value of x in the equation 2 23x = 4x+2.
(3 marks)
(4 marks)
2. Simplify ONE
2000 2001 F.3 Mathematics Test 3
Common Logarithms
MARYMOUNT SECONDARY SCHOOL
Time allowed: 35 minutes
Name: _
Class: _
Number: _
1. Use a calculator to find the following:
1
4
a. 3 log 5.4 2 log 8
b.
1
1
3
4
log
10
10
(Correct your answers to 4 decima
2000 2001 F.3 Mathematics Test 10A
Co-ordinate Geometry
MARYMOUNT SECONDARY SCHOOL
Time allowed: 35 minutes
Name: _
Class: _
Number: _
1. In the figure below, ABC is an isosceles triangle with BA = BC. The coordinates of B and C
are (0, 3) and (6, 0) resp
2000 2001 F.3 Mathematics Test 7
Mensuration
MARYMOUNT SECONDARY SCHOOL
Time allowed: 35 minutes
Name: _
Class: _
Number: _
Unless otherwise specified, all answers must be corrected to 3 decimal places.
1. The figure shows a right pyramid with a rectangul
2000 2001 F.3 Mathematics Test 10B
Co-ordinate Geometry
MARYMOUNT SECONDARY SCHOOL
Time allowed: 35 minutes
Name: _
Class: _
Number: _
1. In the figure below, the coordinates of A and B are (3a, 4a + 1), where a > 0, and (0, 1)
respectively. The length of
2000 2001 F.3 Mathematics Test 11A
Practical Problems in Trigonometry
MARYMOUNT SECONDARY SCHOOL
Time allowed: 30 minutes
Name: _
Class: _
Number: _
Correct your answers in 3 significant figures if necessary. All figures are NOT drawn to
scale.
Convention
2000 2001 F.3 Mathematics Test 9B
Co-ordinate Geometry
MARYMOUNT SECONDARY SCHOOL
Time allowed: 25 minutes
Name: _
Class: _
Number: _
In the figure below, the coordinates of A, B, C and D are (1, 11), (7, 3), (-5, -6), and (-11, 2)
respectively.
a. Show t
2000 2001 F.3 Mathematics Test 1
Percentages
MARYMOUNT SECONDARY SCHOOL
Time allowed: 35 minutes
Use the following table for all tax calculations in this test.
Type of tax
Tax rate
*
Rate
8%
12%
Property tax*
18% of annual rent
Property tax allowance*
Pro
2000 2001 F.3 Mathematics Test 10C
Co-ordinate Geometry
MARYMOUNT SECONDARY SCHOOL
Time allowed: 35 minutes
Name: _
Class: _
Number: _
1. a. Given that ABC with vertices A (-13, k), B (-10, 2) and C (k, 11) is right-angled at B.
Find k.
(5 marks)
b. Hence
2000 2001 F.3 Mathematics Test 11B
Practical Problems in Trigonometry
MARYMOUNT SECONDARY SCHOOL
Time allowed: 30 minutes
Name: _
Class: _
Number: _
Correct your answers in 3 significant figures if necessary. All figures are NOT drawn to
scale.
Convention
2000 2001 F.3 Mathematics Test 8
Some Important Geometrical Theorems
MARYMOUNT SECONDARY SCHOOL
Time allowed: 35 minutes
Name: _
Class: _
Number: _
1. In figure 1, D is the mid-point of AB and E is the
mid-point of BC. If AC = 6 cm, BED = 40
and BAC = 80.
MA1200 Exercise for Chapter 7 Techniques of Differentiation
First Principle
1. Use the First Principle to find the derivative of the following functions:
2x 3
2x 1
(a) f ( x)
(b) f ( x)
3x 4
Product/Quotient/Chain Rules
2. Differentiate the following func
MA1200
Chapter 6
1
Calculus and Basic Linear Algebra I
Limits, Continuity and Differentiability
The concept of limits (p.217 p.229, p.242 p.249, p.255 p.256)
1.1 Limits
Consider the function determined by the formula
x3 1
x 1
Note that it is not defined a
MA1200
Chapter 1
1
Calculus and Basic Linear Algebra I
Coordinate Geometry and Conic Sections
Review
In the rectangular/Cartesian coordinates system, we describe the location of points using coordinates.
y
P2(x2, y2)
P(x, y)
O
P1(x1, y1)
x
The distance d
MA1200
Chapter 7
Calculus and Basic Linear Algebra I
Techniques of Differentiation
1 Differentiability and Differentiation
We say that a function y f x is differentiable at x
lim
a if the limit
f a h
f a
h
exists. If it exists, we denote it by f ' a . Now
MA1200
Chapter 8
1
Calculus and Basic Linear Algebra I
Applications of Derivatives
Dynamical applications (p.306 p.312, p.348 p.352)
The concept of derivatives can be applied to solve some physical problems. Consider an object which is
moving along a stra
MA1200
Practice Exercise for Ch. 4 Trigonometric Functions and Inverse Trigonometric Functions
1.
2.
(a) Convert the following angles to radians.
(i) 48
(ii)
120
(b) Convert the following angles to degree.
123
(i) rad
(ii)
rad
6
180
(iii)
315
2
rad
5
(iii
MA1200
Applications of Derivatives
Rate of change
1. An airplane, flying horizontally at an altitude of 1 km, passes directly over an observer. If the constant
speed of the plane is 240 km/hr, how fast is its distance from the observer increasing 30 secon