高中数学课程描述(英文)
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Mathematics Course Description
Mathematics
course in
middle
school
has
two
parts:
compulsory
courses
and optional
courses.
Compulsory
courses
content lots
of
modern
mathematical
knowledge and
conceptions,
such
as
calculus,statistics,
analytic
geometry,
algorithm
and
vector.
Optional
courses
are
chosen
by
students which is according their
interests.
Compulsory
Courses:
Set Theory
Course content:
This course
introduces a new vocabulary and set of rules that
is foundational to the mathematical
discussions. Learning the basics of
this all-important branch of mathematics so that
students are
prepared
to
tackle
and
understand
the
concept
of
mathematical
functions.
Students
learn
about
how entities are
grouped into sets and how to conduct various
operations of sets such as unions
and
intersections(i.e.
the
algebra
of
sets).
We
conclude
with
a
brief
introduction
to
the
relationship between
functions and sets to set the stage for the next
step
Key Topics:
The language of
set theory
Set
membership
Subsets, supersets, and equality
Set theory and
functions
Functions
Course content:
This lesson
begins with talking about the role of functions
and look at the concept of mapping
values between domain and range. From
there student spend a good deal of time looking at
how
to
visualize
various
kinds
of
functions
using
graphs.
This
course
will
begin
with
the
absolute
value function and then move on to
discuss both exponential and logarithmic
functions. Students
get an opportunity
to see how these functions can be used to model
various kinds of phenomena.
Key Topics:
Single-variable functions
Two
–
variable functions
Exponential
function
Logarithmic function
Power-
function
Calculus
Course content:
In the first step, the course
introduces the conception of limit, derivative and
differential.
Then
students
can
fully
understand
what
is
limit
of
number
sequence
and
what
is
limit
of
function
through some specific practices.
Moreover, the method to calculate derivative is
also introduced
to students.
Key Topics:
Limit theory
Derivative
Differential
Algorithm
Course
content:
Introduce the conception of
algorithm and the method to design algorithm.
Then the figures of
flow
charts
and
the
conception
of
logical
structure,
like
sequential
structure,
contracture
of
condition
and
cycle
structure
are
introduced
to
students.
Next
step
students
can
use
the
knowledge
of algorithm to make
simple
programming language, during this
procedure,
student
also approach to grammatical rules and
statements which is as similar as BASIC language.
Key Topics:
Algorithm
Logical
structure of flow chart and algorithm
Output
statement
Input
statement
Assignment statement
Statistics
Course content:
The
course
starts
with
basic
knowledge
of
statistics,
such
as
systematic
sampling
and
group
sampling.
During
the
lesson
students
acquire
the
knowledge
like
how
to
estimate
collectivity
distribution
according
frequency
distribution
of
samples,
and
how
to
compute
numerical
characteristics
of
collectivity
by
looking
at
numerical
characteristics
of
samples.
Finally,
the
relationship
and
the
interdependency
of
two
variables
is
introduced
to
make
sure
that
students
mastered
in
how
to
make
scatterplot,
how
to
calculate
regression
line,
and
what
is
Method
of
Square.
Key Topics:
Systematic sampling
Group sampling
Relationship
between two variables
Interdependency of two variables
Basic Trigonometry I
Course content:
This course
talks about the properties of triangles and looks
at the relationship that exists between
their internal angles and lengths
of their sides.
This
leads to discussion of the most
commonly
used trigonometric functions
that relate triangle properties to unit circles.
This includes the sine,
cosine and
tangent functions. Students can use these
properties and functions to solve a number of
issues.
Key
Topics:
Common
Angles
The
polar coordinate system
Triangles properties
Right triangles
The
trigonometric functions
Applications of basic trigonometry
Basic Trigonometry II
Course content:
This course
will look at the very important inverse trig
functions such as arcsin, arcos, and arctan,
and see how they can be used to
determine angle values. Students also learn core
trig identities
such as the reduction
and double angle identities and use them as a
means for deriving proofs.
Key Topics:
Derivative trigonometric functions
Inverse trig
functions
Identities
Pythagorean identities
Reduction
identities
Angle sum/Difference identities
Double-angle
identities
Analytic Geometry I
Course
content:
This
course
introduces analytic
geometry
as
the
means
for
using
functions
and
polynomials
to
mathematically
represent
points,
lines,
planes
and
ellipses.
All
of
these
concepts
are
vital
in
student’s
mathematical
development since they are used in rendering and
optimization, collision
detection,
response and other critical areas.
Students
look at
intersection formulas and distance
formulas with respect to lines, points,
planes and also briefly talk about ellipsoidal
intersections.
Key Topics:
Parametric
representation
Parallel and perpendicular lines
Intersection of
two lines
Distance from a point to a line
Angles between
lines
Analytic Geometry II
Course content:
Students
look at how analytic geometry plays an important
role in a number of different areas of
class
design.
Students
continue
intersection
discussion
by
looking
at
a
way
to
detect
collision
between two convex polygons. Then
students can wrap things up with a look at the
Lambertian
Diffuse Lighting model to
see how vector dot products can be used to
determine the lighting and
shading of
points across a surface.
Key Topics:
Reflections
Polygon/polygon intersection
Lighting
Sequence of Number
Course content:
This
course
begin
with
introducing
several
conceptions
of
sequence
of
number,
such
as,
term,
finite sequence of
number, infinite sequence of number, formula of
general term and recurrence
,
the
conception
of
geometric
sequence
and
arithmetic
sequence
is
introduced
to
students.
Through practices
and
mathematical games,
students
gradually understand
and
utilize