Linear Inequalities in Two Unknowns
Exercises()
1. Solve the following compound inequalities graphically.
(a)
x 2 and x < 3
(b)
x < 1 and x < 5
(c)
x 4 and x > 2
(d)
x > 2 and x 1
(a)
(b)
The solution is:
(c)
(d)
Since there is no common region, there ar
PHIL 201
STUDY GUIDE: LESSON 13
Justification, Part 1: Noetic Structure
View and take notes on the presentation, An Overview of Issues in Contemporary Justification,
Part 1.
Two contemporary issues in epistemic justification
o Noetic structure: the struc
Arithmetic and Geometric Sequences
and their Summation
Exercises()
1 (a) Find the general term of the arithmetic sequence 12, 7, 2, 3, .
(b) If the kth term of the sequence is 38, find k.
(a)
12, 7, 2, 3, .
(b) k 38 k
(a)
Let a and d be the first term
Coordinate Treatment of Simple Locus Problems
Exercises()
1. Find the equation of a straight line passing through the origin and the following points.
(a)
A(3, 4)
(b) B(8, 2)
2. Find the equations of the straight lines L1 and L2 as shown in the figure.
L
Exponential and Logarithmic Functions
Exercises()
1. Express each of the following in the form x p , where p is a rational number.
x p p
7
(a)
x4
1
(b)
( x )3
5
1
7
(a)
x4 (x4 ) 7
4
x7
1
(b)
(5 x ) 3
1
1
( x 5 )3
1
3
x5
x
2. Simplify
(6 x 3 ) 2
2 4
3
5
Coordinate Treatment of Simple Locus Problems
Exercises()
1. Find the equation of a straight line passing through the origin and the following points.
(a)
A(3, 4)
(b) B(8, 2)
(a)
The equation of the straight line is
y
(b)
4
x.
3
The equation of the straig
Linear Inequalities in Two Unknowns
Exercises()
1. Solve the following compound inequalities graphically.
(a)
x 2 and x < 3
(b)
x < 1 and x < 5
(c)
x 4 and x > 2
(d)
x > 2 and x 1
2. Solve 5 3x 2
5 3x 2
x 29
, and represent the solutions graphically.
$12 ( We in
HKUST
MATHIODS Calculus and Linear Algebra
Final Exam (Version B) Name:
10th December 2015 Student ID:
12:30-14:30 Lecture Section:
Directions:
0 Do NOT open the exam until instructed to do so.
0 Please turn o all phones and pagers, and remo
Functions and Graphs
Exercise()
1. If f(x) = 4x2 + 3x, find the values of the function when
f(x) = 4x2 + 3x
(a)
x = 1,
(b) x =
1
.
2
2. If f(x) = 2x2 + x, find the values of
f(x) = 2x2 + x
(a)
a
f ,
3
(b) f(b 3).
3. If f(x) = kx x2 and f(5) = 5, find th
Measures of Dispersion
Exercises()
1. Find the inter-quartile range for each of the following data sets.
(a)
2, 4, 5, 6, 6, 7, 8, 10, 13
(b)
4, 2, 0, 6, 8, 9, 14, 15
2. The following data show the weights of 8 men. Find the range of their weights.
53 kg,
Basic Properties of Circles (I)
()
Exercises ()
1. In the figure, ACB is a chord of the circle and OC AB. If AB = 8 cm and OC = 3
cm, find the radius of the circle.
ACB OC AB AB = 8 cm OC = 3 cm
Join OB.
OC AB
AC CB
(given)
(line from centre chord bise
Basic Properties of Circles (II)
()
Exercises()
1. In the figure, AB is a diameter of the circle, DC is the tangent to the circle at D
and BAD = 32. If ABC is a straight line, find x.
AB DC D BAD = 32
ABC x
Join OD.
( at centre twice at ce)
OBQ 2DAB
2
Exponential and Logarithmic Functions
Exercises()
1. Express each of the following in the form x p , where p is a rational number.
x p p
(a)
(b)
7
x4
1
( x )3
5
2. Simplify
(6 x 3 ) 2
and express your answer with positive indices.
(2 x 2 ) 4
(6 x 3 ) 2
Basic Properties of Circles (I)
()
Exercises ()
1. In the figure, ACB is a chord of the circle and OC AB. If AB = 8 cm and OC = 3
cm, find the radius of the circle.
ACB OC AB AB = 8 cm OC = 3 cm
2. In the figure, AV and BV are two equal chords of a circl
Basic Properties of Circles (II)
()
Exercises()
1. In the figure, AB is a diameter of the circle, DC is the tangent to the circle at D
and BAD = 32. If ABC is a straight line, find x.
AB DC D BAD = 32
ABC x
2. In the figure, CB and CA are tangents to th
Arithmetic and Geometric Sequences
and their Summation
Exercises()
1 (a) Find the general term of the arithmetic sequence 12, 7, 2, 3, .
(b) If the kth term of the sequence is 38, find k.
(a)
12, 7, 2, 3, .
(b) k 38 k
2. Consider the following sequence
(MATH1003)[2013](s)midterm~=upvv40^_99002.pdf downloaded by ylinbg from http:/petergao.net/ustpastpaper/down.php?course=MATH1003&id=3 at 2016-12-13 14:00:35. Academic use within HKUST only.
HKUST
MATH1003 Calculus and Linear Algebra
Make-up Exam (Version
HKUST
MATH1003 Calculus and Linear Algebra
2nd Midterm Exam (Version A) Name:
14 November 2015 Student ID:
10:30am-12pm Lecture Section:
Directions:
0 Do NOT open the exam until instructed to do so.
0 Please turn off all phones and pagers, and remove he
HKUST
MATH1003 Calculus and Linear Algebra
2nd Midterm Exam (Version A) Name:
14 November 2015 Student ID:
10:30am-12pm Lecture Section:
Directions:
Do NOT open the exam until instructed to do so. -
Please turn off all phones and pagers, and remove head
Functions and Graphs
Exercise()
1. If f(x) = 4x2 + 3x, find the values of the function when
f(x) = 4x2 + 3x
(a)
x = 1,
(b) x =
(a)
1
.
2
f (1) 4(1) 2 3(1)
4 3
7
The value of the function is 7 when x = 1.
2
(b)
1
1
1
f 4 3
2
2
2
3
1
2
1
2
The value
More about Polynomials
Exercises()
1. Add 5x2 7x + 3 to 2x2 3x 1.
2x2 3x 1 5x2 7x + 3
2. Multiply 3x2 2x + 2 by 2 x, and arrange the answer in descending powers of x.
3x2 2x + 2 2 x x
3. Subtract 5x3 + x 3 from 3x3 + x2 x + 1.
3x3 + x2 x + 1 5x3 + x
Weighting:
20% Online Homework
5% in class Quizzes
50% 2 Midterm Exam
- 3 October 2015 (Saturday)
- 14 November 2015 (Saturday)
35% One 2-hour Final Exam (35%)
Lecture 1:
A=P(1+rt)
From its lecture Question:
P= RMB10000
For 3 months:
R=2.4% (3Months rate)
Variations
Exercises()
1. Given that y varies directly as x, the following table shows some corresponding values of x and y.
y x x y
x
8
12
16
20
y
(a)
4
2
4
6
8
10
Find the variation constant.
(b) Plot the graph of y against x.
(c)
When y 7, find the v
More about Trigonometry (II)
()
Exercises()
1. The area of PQR is 120 cm2. If PQ = 20 cm and QR = 17 cm, find the
possible values of Q correct to 1 decimal place.
PQR 120 cm2 PQ = 20 cm QR = 17 cm Q
Area of PQR 1 QP QR sin Q
2
1
120 20 17 sin Q
2
sin Q
Variations
Exercises()
1. Given that y varies directly as x, the following table shows some corresponding values of x and y.
y x x y
x
8
12
16
20
y
(a)
4
2
4
6
8
10
Find the variation constant.
(b) Plot the graph of y against x.
(c)
When y 7, find the v
Uses and Abuses of Statistics
Exercises()
1. A staff member of a museum wants to conduct a survey on the visitors opinions on the museum. She
interviews a visitor every 15 minutes, choosing whoever happens to leave the museum at that time.
(a)
Name the sa
Uses and Abuses of Statistics
Exercises()
1. A staff member of a museum wants to conduct a survey on the visitors opinions on the museum. She
interviews a visitor every 15 minutes, choosing whoever happens to leave the museum at that time.
(a)
Name the sa
More about Trigonometry (I)
Exercises()
1. In the figure, B = 74, A = 90 and AC = 15 cm. Find the lengths of AB and BC correct to 3
significant figures.
ABC B = 74
A = 90 AC = 15 cm AB BC
tan B
AC
AB
tan 74
15 cm
AB
AB
15
cm
tan 74
4.30 cm
sin B
AC
Soil/117i UVL
HKUST
MATHIOOB Calculus and Linear Algebra
Midterm 2 (Version A) Name:
12th November 2016 Student ID:
10:30-12:00 Lecture Section:
Directions:
0 Do NOT open the exam until instructed to do so.
0 Please turn off all phones and pagers, and rem
Asymptotes of Fraction of Linear Functions
MATH 1003 Calculus and Linear Algebra
(Lecture 22)
a0 x+a1
b0 x+b1 , b0
6= 0
lim f (x) =
a0
;
b0
Given f (x) =
x
Maosheng Xiong
Department of Mathematics, HKUST
lim
x(b1 /b0 )
where a is either or + to be decided
Fundamental Theorem of Calculus
MATH 1003 Calculus and Linear Algebra
(Lecture 28)
TheoremZ(Fundamental Theorem of Calculus)
Suppose
f (x)dx = F (x) + C . Then
Z
b
a
Maosheng Xiong
Department of Mathematics, HKUST
Maosheng Xiong Department of Mathematics,