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
Quadratic Equations in One Unknown
Exercise()
1. Convert the following recurring decimals into fractions.
(a) 0.72
(b)
0.418
2. Solve the quadratic equation 6x2 + 5x 6 = 0 using the factor method.
6x2 + 5x 6 = 0
3. Solve the following quadratic equatio
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
2. In a right-angled triangle with as one of its interior angles,
More about Probability
Exercises()
1. A bag contains 6 blue balls and 9 yellow balls. One ball is drawn at random from the bag. Find the
probability that
(a)
the ball drawn is blue,
(b) the ball drawn is yellow.
6 9
(a)
(b)
Total number of possible out
More about Probability
Exercises()
1. A bag contains 6 blue balls and 9 yellow balls. One ball is drawn at random from the bag. Find the
probability that
(a)
the ball drawn is blue,
(b) the ball drawn is yellow.
6 9
(a)
(b)
2. A die is thrown. Find the
More about Polynomials
Exercises()
1. Add 5x2 7x + 3 to 2x2 3x 1.
2x2 3x 1 5x2 7x + 3
(2 x 2 3x 1) (5 x 2 7 x 3)
2 x 2 3x 1 5 x 2 7 x 3
2 x 2 5 x 2 3x 7 x 1 3
7 x 2 10x 2
Alternative Solution
2 x 2 3x 1
) 5 x 2 7 x 3
7 x 2 10x 2
2. Multiply 3x2 2x +
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
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
Quadratic Equations in One Unknown
Exercise()
1. Convert the following recurring decimals into fractions.
(a) 0.72
(b)
(a)
0.418
Let
x = 0.72 ,
i.e.
x = 0.727 272
(1)
100x = 72.727 272 (2)
(2) (1), 99x = 72
x=
0.72
(b)
=
72
99
8
11
x = 0.418 ,
x = 0.4
Qualitative Treatment of Locus
Exercise()
1. Sketch and describe the locus of a point P such that it is at a distance of 1 cm from the nearest point in
the following figure.
P 1 cm P
2. In a rectangular room PQRS, a man A moves such that APAQ. Another m
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
2. Find the area of PQR correct to 1 decimal place.
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
Qualitative Treatment of Locus
Exercise()
1. Sketch and describe the locus of a point P such that it is at a distance of 1 cm from the nearest point in
the following figure.
P 1 cm P
The locus of P is the dotted curve as shown:
2. In a rectangular room
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,
Chapter8
SimpleLinearRegression
andCorrelationAnalysis
Introduction
n
SimpleLinearRegression
n
Y = f( X)+ e
= +
n Y =
n X =
n f(X)
SimpleLinearRegression
Y = b 0 + b1Xi + e i, i= 1L ,n
,
i
Y =i
i
Xi =i
ei =i
SimpleLinearRegression
(scatterdiagram)
MATH 1003 Calculus and Linear Algebra (Lecture 4)
Albert Ku
HKUST Mathematics Department
Albert Ku (HKUST)
MATH 1003
1 / 19
Outline
1
Present Value of an Annuity
2
Amortization
Albert Ku (HKUST)
MATH 1003
2 / 19
Present Value of an Annuity
Present Value o
MATH 1003 Calculus and Linear Algebra (Lecture 5)
Albert Ku
HKUST Mathematics Department
Albert Ku (HKUST)
MATH 1003
1 / 16
Outline
1
Systems of Linear Equations in Two Variables
2
Types of Linear Systems
Albert Ku (HKUST)
MATH 1003
2 / 16
Systems of Line
MATH 1003 Calculus and Linear Algebra (Lecture 3)
Albert Ku
HKUST Mathematics Department
Albert Ku (HKUST)
MATH 1003
1 / 16
Outline
1
Future Value of an Annuity
2
Sinking Fund
Albert Ku (HKUST)
MATH 1003
2 / 16
Future Value of an Annuity
Future Value of a
MATH 1003 Calculus and Linear Algebra (Lecture 2)
Albert Ku
HKUST Mathematics Department
Albert Ku (HKUST)
MATH 1003
1 / 17
Outline
1
Compound Interest
2
Annual Percentage Yield
Albert Ku (HKUST)
MATH 1003
2 / 17
Compound Interest
Compound Interest
Exampl