Semester A, 2015-16
MA1200
Calculus and Basic Linear Algebra I
Chapter 4
Dr. Emily Chan
Page 1
Semester A, 2015-16
MA1200
Calculus and Basic Linear Algebra I
Chapter 4
Trigonometric Functions
In elementary trigonometry, the 3 basic trigonometric functions
MA1200, om, Mock Test 1 (2015/16, SemA)
Name:
Total: 100 points. rI‘ime: 60 min.
1. (25 points) Given that the equation of a conic section is
3:24-43? «~24y+20=0.
a) Using completing square, identify the type of the conic section;
b) Hence, sketch the gra
City University of Hong Kong
Department of Mathematics
MATHEMATICS PLACEMENT TEST FOR MA1200
Sample Questions & Solutions
1
1.
The general solution of the equation tan x = 1 is
A.
B.
x = n
C.
x = n + ( 1)
D.
2.
x = n +
x = 2n +
The graph of
4
4
, nZ .
,
City University of Hong Kong
Department of Mathematics
MATHEMATICS COMBINED PLACEMENT TEST FOR MA1200 & MA1201
Sample Questions & Solutions
1
Section A
1.
The general solution of the equation tan x = 1 is
A.
B.
x = n
C.
x = n + ( 1)
D.
2.
x = n +
x = 2n
MA1200
Practice Exercise for Ch. 4 Trigonometric Functions and Inverse Trigonometric Functions
1.
(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
(iii)
2
rad
5
t
MA1200
1.
Practice Exercise 5
Exponential and Logarithmic Functions
Determine whether each of the following is true or false. If it is false, give a counterexample.
i. If N is positive, then as N increases, log5 N increases. (T / F)
ii. If a, b are positi
MA1200
Chapter 4
Calculus and Basic Linear Algebra I
Trigonometric Functions and Inverse Trigonometric Functions
1
Trigonometric Functions
1.
In elementary trigonometry, the trigonometric functions are defined as the ratios of sides of a
right-angled tria
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 3
Calculus and Basic Linear Algebra I
Polynomials and Rational Functions
Review
A function f x an x n an 1 x n 1 a0 (where the a' i s are real numbers and n is a non-negative
integer) is called a polynomial function. If a n 0 , n is the deg
MA1200
Chapter 5
1
Calculus and Basic Linear Algebra I
Exponential and Logarithmic Functions
Exponential Functions
Definition:
The exponential function f with base b is defined by
f x b x
or
y bx ,
where b is a positive constant other than 1 ( b 0 and b 1
jQuery Selectors
A jQuery Selector is a function which makes
use of expressions to find out matching
elements from a DOM based on the given
criteria.
1
The $() factory function
jQuery
Tag Name:
Tag ID:
Tag Class:
Description
Represents a tag name availab
MA1200 Calculus and Basic Linear Algebra I
Semester A 2016/2017
Course Information
1. OBTL and course webpage of MA1200
(a) MA1200 adopts OBTL practice.
(b) Please visit the MA1200 Canvas regularly for any update (announcements, course materials,
etc.)
2.
TFA 33 (1971-1973) 187-189
187
REVIEW
THE ANALYSIS
OF MORTALITY
AND
OTHER ACTUARIAL
STATISTICS
by
B. Benjamin, Ph.D., F.I.A. and the late H. W. Haycocks
Pp. viii+ 392. Cambridge University Press. 3.00
Dr. Benjamin pays tribute in the Preface to his co-aut
MA1200, CEl, Quiz 1 (2015/16, SemA)
Name:
Total: 40 points. Time: 30 min.
1. (15 points) Given that the equation of a conic section is
wmz + 4y2 — 24y + 20 = 0.
3.) Using completing square, identify the type of the conic section;
b) Hence, sketch the grap
Semester A, 2015-16
MA1200
Calculus and Basic Linear Algebra I
Chapter 7
Dr. Emily Chan
Page 1
Semester A, 2015-16
MA1200
Calculus and Basic Linear Algebra I
Chapter 7
Brief table of derivatives of some elementary functions with respect to
Function
= ()
Sem est er A, 2 0 1 5 - 1 6
M A1 2 0 0
Ca l cu l u s a n d Ba si c Li n ea r Al g eb r a I
D r . Em i l y Ch a n
Sem est er A, 2 0 1 5 - 1 6
Ch a pt er 2
Pa g e 1
M A1 2 0 0
Ca l cu l u s a n d Ba si c Li n ea r Al g eb r a I
Ch a pt er 2
Set Notation
A s
MA1200 Exercise for Chapter 6 Limits, Continuity and Differentiability
Limits
1. Evaluate the following limits:
2.
x2 1
x 2 x 3 x
(a)
lim
(c)
lim
(b) lim
x
m sin mx n sin nx
x 0
tan mx tan nx
x + x4 x2 1
2x 2 1 x 4 1
( m n)
Evaluate the following limit
Sem est er A, 2 0 1 5 - 1 6
M A1 2 0 0
Ca l cu l u s a n d Ba si c Li n ea r Al g eb r a I
D r . Em i l y Ch a n
Ch a pt er 6
Pa g e 1
Sem est er A, 2 0 1 5 - 1 6
M A1 2 0 0
Ca l cu l u s a n d Ba si c Li n ea r Al g eb r a I
Ch a pt er 6
Limit of a funct
Semester A, 2015-16
MA1200
Calculus and Basic Linear Algebra I
Dr. Emily Chan
Semester A, 2015-16
Chapter 8
Page 1
MA1200
Calculus and Basic Linear Algebra I
Chapter 8
Applications of Differentiation
In this chapter, we will study the following applicatio
Semester A, 2015-16
MA1200
Calculus and Basic Linear Algebra I
Dr. Emily Chan
Chapter 3
Page 1
Semester A, 2015-16
MA1200
Calculus and Basic Linear Algebra I
Chapter 3
Polynomials
A polynomial function of degree
( )=
where the
is a function of the form
MA1200 (CB1)
1.
Let F (x) and G (x) be two functions defined by F ( x)
(a)
(b)
2.
Semester A, 2015-16
x2 1
x2 9
and G ( x ) x 1 .
Find their largest possible domains.
F
Find (x ) and state its largest possible domain.
G
Let F (x) and G (x) be two functio
MA1200 (CB1)
Additional Exercises on Chapter 3
5 x 3 27 x 2 51x 24
Semester A, 2015-16
1.
Express
2.
Express
3.
(a)
Find the quotient and the remainder when 2 x 5 x 4 2 x 3 8 x 2 5 x 1 is
divided by x 4 x 3 x 1 .
(b)
Factorize x 4 x 3 x 1 .
2 x5 x4 2 x3 8
MA1200 (CB1)
Additional Exercises on Chapter 6
sin( 2 x)
.
x 0
x
sin
2
1.
Evaluate the limit lim
2.
Evaluate the limit lim
3 sin 2 x tan x
( x 3 5) x 2
x 0
3.
Evaluate the limit lim
1 cos3 x
x0
4.
Evaluate the limit lim
x
5.
6.
7.
8.
9.
Semester A, 20
MA1200 (CB1)
1.
2.
3.
Additional Exercises on Chapter 7
(a)
dy
for each of the following.
dx
y e 2 x cos 3x
(b)
y sin 2 x 5 sec3 x
(c)
y x2 x2 1
(d)
y loge
(e)
y2
(f)
y x 3x
Find
Semester A, 2015-16
1 x
1 x
x
For each of the following, find
dy
in terms of
MA1200 (CB1)
Additional Exercises on Chapter 1
Semester A, 2015-16
1.
A straight line passes through the point (5, 2) and has equal x -intercept and y intercept. Find the equation of the straight line.
2.
The straight line
3.
The equation of a conic is y
MA1200 (CB1)
Additional Exercises on Chapter 5
1.
Evaluate log 5 100 log 5 4 log 6 12 log 6 18 7 log 7 8
2.
The functions F (x ) and G (x) are defined by
(ii)
(iii)
G 1 ( x) ,
( F G )( x) .
The functions F and G are defined as follows:
1
F ( x) (e x e x
slé/g
Conic Sections
A conic may be dened as follows:
If F is a xed point (focus) and l is a xed line (directrix) which does not pass
through F , then the locus of a moving point P(x ,3!) which moves in the plane of
F and 1 so that its distance from F i
MA1200
Chapter 2
1
Calculus and Basic Linear Algebra I
Sets and Functions
Set Notation
A set is a collection of distinct objects called elements or members of that set. For example,
A 1, 2,3, 4,5 is a set and a list of all its elements is given. In genera
MA1200 Calculus and Basic Linear Algebra I
Semester A 2014/2015
Course Information
1. OBTL and course webpage of MA1200
(a) MA1200 adopts OBTL practice.
(b) Please visit the MA1200 Blackboard regularly for any update (announcements, course
materials, etc.