? 393

高中數(shù)學(xué)課程圖

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Assignment Teaching Periods

and Data Collection probability;

6. Master the probability of independent events;

7. Can use permutation and combination to find

the probability.

8.Shape, spread, cluster,gap,outlier, mean, mode

median,variance,standard variance

9. Population, sample, survey , observational

study and experiment

14.

Common

logical

language

14.1 Vector concept and

vector arithmetic 14.2

Vector fundamental

theorem and coordinate

representation

14.3 Vector applications

and solution triangles

1. Understand the actual background, concept,

and geometric representation of plane vectors;

understand the meaning of parallel (collinear)

vector, zero vector, equal vector, and unit vector.

2. Master the plane vector addition, subtraction,

number and multiplication operation and

operation rules, understand its geometric

meaning;

3. Understand the basic theorem of the plane

vector and its meaning, and will choose the

appropriate base to represent the plane vector;

4. Understanding the concept of the quantity

product of the plane vector and its physical

Reason

Critical

thinking

Reflective

Problem-solvi

ng

2 Elective

1-1mathemati

cs published

by Beijing

Normal

University

exercise

10

博實(shí)樂(lè)“中外融通課程”

394?

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Assignment Teaching Periods

significance, we will calculate the quantity

product of the plane vector;

5. The vertical relation of the two plane vectors is

judged by the quantity product.

6. Master the orthogonal decomposition and

coordinate representation, can represent the

addition, subtraction and number multiplication

of the plane vector, and can represent the module,

quantity product and angle of the plane vector,

and can represent the collinear and vertical

condition.

7. Use vector method to solve simple problems of

plane geometry and mechanics; master cosine and

sine theorems; and can use cosine theorem to

solve simple practical problems.

15.

Three-dimen

sional

geometry

preliminary

15.1 Basic

three-dimensional

geometry

15.2 Basic location

relationship of

three-dimensional

1. Ability to observe the spatial graphics through

physical objects and geometric software, and

understand the structural characteristics of

columns, cones, tables, balls and simple

combinations; Will use the ball, prism, prism,

platform, ball surface area and volume

Reason

Critical

thinking

Reflective

Problem-solvi

ng

2 Precalculus

Chapter 7

exercise

10

? 395

高中數(shù)學(xué)課程圖

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Assignment Teaching Periods

geometry calculation formula to solve simple practical

problems; Can use the oblique two measurement

method to draw a simple spatial figure of the

intuitive figure.

2. On the basis of intuitive understanding of the

position relationship of space point, straight line

and plane, abstract the position relationship of

space point, straight line and plane), and master

the spatial straight line and straight line, straight

line and plane, plane and plane parallel and

vertical relationship.

16.

Spatial

vector and

stereo

geometry

16.1 Space right-angle

coordinate system

16.2 Spatial vectors and

their operations

16.3 Vector

fundamental theorem

and coordinate

representation

16.4 Application of the

spatial vectors

1. Will use the spatial right-angle coordinate

system to depict the position of the point; The

coordinates of the vertices of special geometry in

space are found; and the distance formula

between two points is derived. 2. Understand the

concept of spatial vector; master the operation

and rules of spatial vector.

3. Understand the basic theorem of space vector

and its significance, master the orthogonal

decomposition of space vector and its coordinate

Reason

Critical

thinking

Reflective

Problem-solvi

ng

2 Precalculus

Chapter

exercise

And Elective

1-1mathemati

cs published

by Beijing

Normal

University

exercise

10

博實(shí)樂(lè)“中外融通課程”

396? Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Assignment Teaching Periods

representation; master the linear operation,

quantity product and its coordinate representation

of space vector.

4. Understand the direction vector of the line and

the normal vector of the plane; Can use vector

language to express the angle between line and

line, line and plane, plane and plane, and vertical

and parallel relationship, and can use vector

method to solve the distance problem of point to

point line, point to point plane, parallel line and

parallel plane.

? 397

高中數(shù)學(xué)課程圖

4 Assessment

4.1 External Assessment Objectives(no)

4.2 Internal Assessment Objectives

Content Percentage Assessment Criteria Description

Exams 50% Mid-term exam： 10% Final Exam：30% (Monthly Exam)5%*2

Assignment 30% 得分 (Score)：26-30，21-25，16-20，11-15，6-10，0-5

Performance

10%

Contents Excellent Good Unsatisfied

Attendance 4 2 0

Presentation 4 2 0

Class notes 4 2 0

Participation 4 2 0

Others 4 2 0

4.3 Details of External Assessment (no)

4.4 Details of Internal Assessment

Homework Assessment Specifics:

AP Score Score Range Credit Recommendation

5

26-30

Each job is completed in time.

Clear thinking, complete process, and accurate calculation.

Writing neatly, knowledge points are firmly mastered, clear

drawing, let a person pleasing to the eye.

The accuracy rate is above 95%, and the last operation is all

corrected in time.

4 21-25

Most of the work was completed in time.

The idea is relatively clear, the process is relatively complete,

and the calculation is basically accurate.

The Writing is relatively neat, the knowledge points are in a

good grasp, and the drawing is also clear.

博實(shí)樂(lè)“中外融通課程”

398?

AP Score Score Range Credit Recommendation

3

16-20

Some jobs are completed in time.

Thinking is not chaotic, the process and principle, you can calculate by themselves.

Writing is not messy, knowledge points in part to master.

The accuracy rate is above 75%, and you can correct the last

job.

2

11-15

There is a phenomenon of overdue work.

Thinking is a little confused, the writing is not very neat, the

knowledge point grasp is not very good.

Above 60% accuracy, occasionally correct the last job.

1

6-10

The default phenomenon is a little serious, can not finish the

homework on time.

Thinking is more chaotic, the writing is not neat, the knowledge

point is obviously not mastered.

Correct rate is above 40%, with no correction situation.

E

0-5

Basically can not finish the homework on time.

The idea is very confused, the homework is blank, obviously did

not listen to the class.

Correct rate of 10% operation, no correction situation.

Remarks: Late submission of homework without special reasons, delayed one day of submission, automatically reduce the score by 10%. One-day deferred submission is automatically reduced by 25%; a three-day deferred submission is automatically reduced by

50%; an extension of more than one week will be deemed invalid.

? 399

高中數(shù)學(xué)課程圖

Performance Assessment Specifics:

Content Assessment Grade and Details

Class Participation)

Excellent

（3-4）

Good

（2）

Unsatisfied

（0-1）

Actively participate in the

class, every question can

actively interact with the

teacher, actively answer

questions.

Students follow the

teacher, but the participation is not too

high, only when they

arrive.

Without any interaction, the class mental

state is very bad, do

something unrelated

to the class.

Attendance

Excellent

（2）

Good

（1）

Unsatisfied

（0）

Never be late or leave early

without any reason, and ask

for leave early for anything.

Occasionally leave

early, the frequency

is not high, from no

reason, things do not

explain in advance.

Often be late and

leave early, and even

be truant phenomenon

is serious.

Class notes

Excellent

（2）

Good

（1）

Unsatisfied

（0）

Class initiative to take notes

carefully, writing clearly,

clear at a glance, and can

keep notes very well.

Under the teacher’s

reminder, notes can be

taken, but not proactive enough.

Never take notes

Awards

Excellent

（2）

Good

（1）

Unsatisfied

（0）

Actively participate in

various competitions and

win prizes. The class is full

of spirit, never sleep in the

classroom, in and out of the

classroom at will；

Actively participated

in various competitions, but did not win

prizes. Occasionally in

class, but do not sleep.

Not willing to participate in any competition activities, the

class spirit is not good,

sleep on the table, like

to go in and out of the

classroom at will.

博實(shí)樂(lè)“中外融通課程”

400?

5 Resources

Precalculus (ISBN 10:1292079452)

AP Central: http://www.collegeboard.com/html/apcourseaudit/index.html

The Princeton Review: www.PrincetonReview.com

Relevant exam: store.collegeboard.org

http://welkerswikinomics.com/blog/

http://www. tutor2u.com

http://www.bized.ac.uk

Chinese and International Integrated

Curriculums for Bright Scholar

High School Section

CAP Mathematics

Curriculum Map

（2022 version）

Complied by Guangdong Country Garden Senior High Section

博實(shí)樂(lè)“中外融通課程”

402?

AP Curriculum Map

Subject AP Pre-calculus Level G1&G2 Syllabus Code

Course Code Credit 10 Duration 2Year

Teaching Periods 400 Designer NieZiyi Completed Date

1 Course Introduction

1.1 Introduction

In Advanced Precalculus, students will develop a deeper understanding of various

types of functions on the knowledge they have already learned. Topics studied include The

concepts and the property theorems of parallelograms, rectangles, rhombuses, and squares,

Quadratic equations and quadratic functions, Exponential function, logarithmic function

and logistic function. Trigonometric functions,inverse trigonometric functions, laws of sines

and cosines, polar coordinates, parametric functions. Analytical geometry of plane, polar

coordinates, and parametric functions,and an introduction to Calculus.

1.2 Aims

a) Develop logical, critical and creative thinking；

b) Improve the ability of understanding and expression, study the skills of

communication;

c) Apply and transfer skills to alternative situations, and patience and persistence in

problem-solving;

d) Understand mathematics and enjoy the beauty of mathematics;

e) Develop an appreciation of calculus as a coherent body of knowledge and as a

human accomplishment .

2 Course Structure

Numberand

quantity

real

number

complex

number equation inequality special

parallelograms

Quadraticfunctions,

Exponential function,

Logarithmic function and

logistic function.

Trigonometric functions

Polar coordinates,

Parametric functions

circle

CH Pre-calculusG1、2

Algebra Geometry Functions

? 403

高中數(shù)學(xué)課程圖

3 Course Outline

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency Level Assignment Teaching Periods

1. Quadratic

equation in

one variable

1.1 List the formula

1.2Solve quadratic

equations in one variable

1.3 The discriminant of the

roots of a quadratic

equation in one variable

1.4 Relationship between

roots and coefficients

1.5 Application

1.Able to use quantitative relations to list

quadratic equations of one variable;

2.Understand the matching method, and be

able to use the matching method, formula

method, and factorization method to solve

quadratic equations in one variable;

3. The discriminant of roots can be used to

determine how many real roots the equation

has;

4. Understand the relationship between

roots and coefficients;

5. Can check whether the roots of the

equation are valid according to the actual

meaning of the actual problem.

Reason

Critical

thinking

Reflective

Problem-solvi

ng

2 Ninth grade

mathematics

published

by Beijing

Normal

University

Chapter2

exercise

25

2. Quadratic

function

2.1 List quadratic function

expressions

2.2 The graphs and

properties of the quadratic

1. Ability to use tables, relational

expressions, and images to represent the

quadratic function relational expressions

between variables;

Reason

Critical

thinking

Reflective

Problem-solvi

2

Ninth grade

mathematics

published

by Beijing

35

博實(shí)樂(lè)“中外融通課程”

404?Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency Level Assignment Teaching Periods

function

2.3 The relationship

between quadratic function

and straight line

2.4 Find the quadratic

function expression

2.5 Application of quadratic

function

2. According to the specific problem, the

appropriate method can be selected to

express the quadratic function relationship

between the variables;

3. Can make the image of the quadratic

function, and can analyze the nature of the

quadratic function according to the image;

4. According to the expression of the

quadratic function, determine the opening

direction, symmetry axis and vertex

coordinates of the quadratic function;

5. Use the relationship between the

quadratic function and the one-dimensional

quadratic equation to find the approximate

solution of the equation;

6. Use quadratic functions to solve practical

problems.

ng Normal

University

Chapter2

exercise

3.

Figures and

Geometry

3.1 Recognize special

parallelograms;

3.2 The properties and

theorems of special parallel

1. Understand the concepts of

parallelogram, rectangle, rhombus, and

square, and the relationship between them,

and understand the instability of

Reason

Critical

thinking

Reflective

Problem-solvi

2

Ninth grade

mathematics

published

by Beijing

30

? 405

高中數(shù)學(xué)課程圖

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency Level Assignment Teaching Periods

four sides;

3.3 Proof of special

parallelism;

3.4 The basic nature of the

ratio;

3.5 The nature of similar

graphics；

quadrilateral;

2. Explore and prove the property theorems

of rectangles, rhombuses and squares;

3. Understand the basic nature of the ratio,

the ratio of line segments, the golden ratio,

etc.;

4. Prove the similarity of graphics through

specific examples, and learn the definition

and properties of similar graphics;

5. Explore and understand the judgment

theorem of similar triangles, understand the

property theorem of similar triangles,

understand the similarity of graphics, and

solve some practical problems.

ng Normal

University

Chapter1

exercise

4.

Circle

4.1 Definition of circle

4.2 Symmetry of circle,

vertical diameter theorem;

4.3 The relationship

between the circumferential

angle and the central angle;

4.5 Determine the

1. Students improve their mathematical

thinking ability through the process of

exploring circles and related conclusions;

2. Recognize the axis symmetry and center

symmetry of the circle;

3. Understand the relationship between

arcs, chords, central angles, and

Reason

Critical

thinking

Reflective

Problem-solvi

ng

2

Ninth grade

mathematics

published

by Beijing

Normal

University

Chapter3

40

博實(shí)樂(lè)“中外融通課程”

406?Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency Level Assignment Teaching Periods

conditions of the circle;

4.6 The positional

relationship between the

straight line and the circle;

4.7 Tangent Length

Theorem

4.8 Regular polygon

inscribed in circle

4.9 Formulas for arc length

and sector

circumferential angles, and combine other

methods to explore the vertical radius

theorem, the relationship between

circumferential angles and central angles,

and the characteristics of the

circumferential angles facing straight lines;

4. Explore and know the positional

relationship between points and circles,

straight lines and circles, and circles and

circles;

5. Know the concept of tangents, draw

tangents and use the tangent length

theorem.

exercise

5.

Inverse

proportional

functions

5.1 List inverse proportional

function expressions

5.2 The graphs and

properties of the inverse

proportional function

5.3 Find the inverse

proportional function

expression from graph

1. Draw the graphs of inverse functions.

2. Master the main properties of inverse

functions

3. Model the inverse proportional

functions and solve problems in real life

context

Reason

Critical

thinking

Reflective

Problem-solvi

ng

2

Ninth grade

mathematics

published

by Beijing

Normal

University

Chapter5

exercise

15

? 407

高中數(shù)學(xué)課程圖

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency Level Assignment Teaching Periods

5.4 The transformation of

the inverse proportional

function

5.5 Application of the

inverse proportional

function

6. Sets 6.1 Theconcept and

representation of sets

6.2 Basic relationships of

collections 6.3 Set of basic

operations

1. Understand the meaning of sets,

complete sets and empty sets; understand

the \"belonging\" relationship between

elements and sets; and can describe

collections in natural language, graphic

language and symbolic language.

2. Understand the equivalence of sets;

candetermine a subset of a given set.

3. Understand the meaning of the union,

intersection and complement of two sets;

you can find the union, intersection and

complement of two sets by combining

graphics.

Reason

Critical

thinking

Reflective

Problem-solvi

ng

2 Elective

1-1mathema

tics

published

by Beijing

Normal

University

Chapter1

exercise

15

7. 7.1 Modeling and solving 1. Understand the definition of a function, Reason Precalculus 20

博實(shí)樂(lè)“中外融通課程”

408?Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency Level Assignment Teaching Periods

Functions

and graphs

equations

According to the situation

in real life, establish

numerical, algebraic or

graphical models, list

equations, and solve

equations

7.2 Definition and

properties of functions

7.3 Functions and

operations between

functions

7.4 Composite functions,

Parametric equations and

inverse functions

7.5 Image transformation

the relationship between a set and a

function, understand the elements of a

function, be able to find the domain and

range of the function, and understand the

constituent elements of a function;

2. In actual situations, functions can be

expressed in different ways;

3. Understand the monotonicity and

extrema value of the function;

4. Learn to use the graph of the function to

study and analyze the nature of the

function;

5.Evaluation composite

functions,parametric equations and inverse

functions

Critical

thinking

Reflective

Problem-solvi

ng

2

Chapter 1

exercise

8.

Polynomial

functions,

power

functions

8.1 Linear function,

quadratic function and

modeling

8.2 Power function

properties and graphs

1.Understand the meaning of rational

exponent power, master the operation of

power, and be able to perform simple

analysis using the image of the power

function.

Reason

Critical

thinking

Reflective

Problem-solvi

ng

2

Precalculus

Chapter 2

exercise

25

? 409

高中數(shù)學(xué)課程圖

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency Level Assignment Teaching Periods

and rational

functions

8.3 Properties and graphs of

polynomial functions

8.4 Real roots of

polynomial functions

8.5 Complex Roots of

Polynomial Functions and

Fundamental Theorems of

Algebra

8.6 Image and properties of

rational functions

8.7 Solving equations in

one variable

8.8 Solving inequalities in

one variable

8.9 The binary method

seeks the approximate

solution of the equation

2.Understand the relationship between the

zero point of the function and the solution

of the equation; 3.Understand the function

zero existence theorem, and will be used to

judge the zero existence of the monotone

function.

9.

Exponential

function,

logarithmic

9.1 Exponential function

and logistic function images

and properties

9.2 Exponential function

1. Understand the actual background of the

exponential function model;

2. Understand the meaning of rational

exponent power and the operation of

Reason

Critical

thinking

Reflective

Problem-solvi

2

Precalculus

Chapter 3

exercise

博實(shí)樂(lè)“中外融通課程”

410?Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency Level Assignment Teaching Periods

function and

logistic

function

and logistic function model

9.3 Image and properties of

logarithmic function

9.4 Solving and modeling

equations

9.5 Application of

Mathematics in Finance

power;

3. Understand the concept and meaning of

exponential function, be able to draw

images with the help of a calculator,

explore and understand the monotonicity

and special points of exponential function;

4. Can solve practical problems.

ng 25

10.

Trigonometr

ic function

10.1 Angle and

measurement

10.2 Trigonometric

functions of acute angles

10.3 Trigonometric function

and unit circle of arbitrary

angle

10.4 Graphs of sine and

cosine functions

10.5 Tangent function graph

10.6 Inverse trigonometric

functions

10.7 The application of

1. Understand the expansion of angles,

understand the radian system and angle

values, and be able to convert between

them;

2. Use the unit circle to understand the

theorems of trigonometric functions at any

angle, and be able to judge the signs of

trigonometric functions in each quadrant;

3. Using the transformation of graphics,

master the transformation into, and be able

to find the amplitude, period, phase,

frequency, etc.;

4. Able to determine the value of a, b, c;

Reason

Critical

thinking

Reflective

Problem-solvi

ng

2

Precalculus

Chapter 4

exercise

40

? 411

高中數(shù)學(xué)課程圖

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency Level Assignment Teaching Periods

trigonometric functions in

real life

5. Master images and functions;

6. Can solve practical problems.

11.

Solve the

triangle

11.1 Basic identities

11.2 Proof of Triangular

Identity

11.3 Triangular formulas for

sum and difference of two

angles

11.4 Double angle formula

11.5 The Law of Sines

11.6 The Law of Cosines

1. Discover the relationship between the

angle of a triangle and the length of a side;

2. Master the theorem of sine and cosine

and be able to solve related problems;

3. Master the triangular relationship

formula of two angles and difference, be

able to use and calculate, and master the

formula of product and difference;

4. Master the double angle formula and

application.

Reason

Critical

thinking

Reflective

Problem-solvi

ng

2

Precalculus

Chapter 5

exercise

25

12.

Analytical

Geometry of

Plane and

Space

12.1 Graphs and properties

of parabola

12.2 Circles and ellipses

12.3 Parabola and

hyperbola

12.4 Polar coordinate

equation of conic section

12.5 Polar curves

1. Understand the definition of ellipse,

hyperbola, and parabola;

2. Understand the graphs and properties

of the three, and be able to find the

equations of ellipse, hyperbola and parabola

according to known conditions;

3. Determine whether the given equation is

ellipse, hyperbola or parabola according to

known conditions;

Reason

Critical

thinking

Reflective

Problem-solvi

ng

2

Precalculus

Chapter 8

exercise

25

博實(shí)樂(lè)“中外融通課程”

412?Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency Level Assignment Teaching Periods

4. Ability to use the discriminant of the root

to find the positional relationship between

the conic section and the circle and the

coordinates of the intersection point, etc.;

13.

Discrete

Mathematics

13.1 Permutation and

Combination

13.2 Binomial Theorem

13.3 Sequence

13.4 Number of levels

13.5 Probability

13.6 Describing the

Distribution of a

Quantitative Variable

13.7 Introduction to

Planning a Study

13.8 Random Sampling and

Data Collection

1. Master the difference between

permutation and combination, and choose

the corresponding method to solve the

given problem;

2. Master the formula and related

characteristics of the binomial theorem, and

be able to find out the binomial coefficients

or coefficients with special requirements

such as constant terms;

3. Master the arithmetic sequence and

geometric sequence, and can perform

calculations;

4. Master the sum formula of equal

difference and equal ratio;

5. Learn to master the method of classical

probability;

6. Master the probability of independent

Reason

Critical

thinking

Reflective

Problem-solvi

ng

2 Precalculus

Chapter 10

exercise

20

? 413

高中數(shù)學(xué)課程圖

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency Level Assignment Teaching Periods

events;

7. Can use permutation and combination to

find the probability.

8.Shape, spread, cluster,gap,outlier, mean,

mode median,variance,standard variance

9. Population, sample, survey ,

observational study and experiment

14.

Common

logical

language

14.1 Vector concept and

vector arithmetic

14.2 Vector fundamental

theorem and coordinate

representation

14.3 Vector applications and

solution triangles

1. Understand the actual background,

concept, and geometric representation of

plane vectors; understand the meaning of

parallel (collinear) vector, zero vector,

equal vector, and unit vector.

2. Master the plane vector addition,

subtraction, number and multiplication

operation and operation rules, understand

its geometric meaning;

3. Understand the basic theorem of the

plane vector and its meaning, and will

choose the appropriate base to represent the

plane vector;

4. Understanding the concept of the

Reason

Critical

thinking

Reflective

Problem-solvi

ng

2 Elective

1-1mathema

tics

published

by Beijing

Normal

University

exercise

20

博實(shí)樂(lè)“中外融通課程”

414?Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency Level Assignment Teaching Periods

quantity product of the plane vector and its

physical significance, we will calculate the

quantity product of the plane vector;

5. The vertical relation of the two plane

vectors is judged by the quantity product.

6. Master the orthogonal decomposition and

coordinate representation, can represent the

addition, subtraction and number

multiplication of the plane vector, and can

represent the module, quantity product and

angle of the plane vector, and can represent

the collinear and vertical condition.

7. Use vector method to solve simple

problems of plane geometry and mechanics;

master cosine and sine theorems; and can

use cosine theorem to solve simple practical

problems.

15.

Three-dimen

sional

geometry

15.1 Basic

three-dimensional geometry

15.2 Basic location

relationship of

1. Ability to observe the spatial graphics

through physical objects and geometric

software, and understand the structural

characteristics of columns, cones, tables,

Reason

Critical

thinking

Reflective

Problem-solvi

2 Precalculus

Chapter 7

exercise

20

? 415

高中數(shù)學(xué)課程圖

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency Level Assignment Teaching Periods

preliminary three-dimensional geometry balls and simple combinations; Will use the

ball, prism, prism, platform, ball surface

area and volume calculation formula to

solve simple practical problems; Can use

the oblique two measurement method to

draw a simple spatial figure of the intuitive

figure.

2. On the basis of intuitive understanding of

the position relationship of space point,

straight line and plane, abstract the position

relationship of space point, straight line and

plane), and master the spatial straight line

and straight line, straight line and plane,

plane and plane parallel and vertical

relationship.

ng

16.

Spatial

vector and

stereo

geometry

16.1 Space right-angle

coordinate system

16.2 Spatial vectors and

their operations 16.3 Vector

fundamental theorem and

1. Will use the spatial right-angle

coordinate system to depict the position of

the point; The coordinates of the vertices of

special geometry in space are found; and

the distance formula between two points is

Reason

Critical

thinking

Reflective

Problem-solvi

ng

2 Precalculus

Chapter

exercise

And

Elective

20

博實(shí)樂(lè)“中外融通課程”

416?Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency Level Assignment Teaching Periods

coordinate representation

16.4 Application of the

spatial vectors

derived. 2. Understand the concept of

spatial vector; master the operation and

rules of spatial vector.

3. Understand the basic theorem of space

vector and its significance, master the

orthogonal decomposition of space vector

and its coordinate representation; master the

linear operation, quantity product and its

coordinate representation of space vector.

4. Understand the direction vector of the

line and the normal vector of the plane; Can

use vector language to express the angle

between line and line, line and plane, plane

and plane, and vertical and parallel

relationship, and can use vector method to

solve the distance problem of point to point

line, point to point plane, parallel line and

parallel plane.

1-1mathema

tics

published

by Beijing

Normal

University

exercise

? 417

高中數(shù)學(xué)課程圖

4 Assessment

4.1 External Assessment Objectives(no)

4.2 Internal Assessment Objectives

Content Percentage Assessment Criteria Description

Exams 50% Mid-term exam： 10% Final Exam：30% (Monthly Exam)5%*2

Assignment 30% 得分 (Score)：26-30，21-25，16-20，11-15，6-10，0-5

Performance

10%

Contents Excellent Good Unsatisfied

Attendance 4 2 0

Presentation 4 2 0

Class notes 4 2 0

Participation 4 2 0

Others 4 2 0

4.3 Details of External Assessment (no)

4.4 Details of Internal Assessment

Homework Assessment Specifics:

AP

Score

Score

Range

Credit Recommendation

5 26-30

Each job is completed in time.

Clear thinking, complete process, and accurate calculation.

Writing neatly, knowledge points are firmly mastered, clear drawing, let

a person pleasing to the eye.

The accuracy rate is above 95%, and the last operation is all corrected in

time.

4 21-25

Most of the work was completed in time.

The idea is relatively clear, the process is relatively complete, and the

calculation is basically accurate.

The Writing is relatively neat, the knowledge points are in a good grasp,

and the drawing is also clear.

博實(shí)樂(lè)“中外融通課程”

418?

AP

Score

Score

Range

Credit Recommendation

3

16-20

Some jobs are completed in time.

Thinking is not chaotic, the process and principle, you can calculate by

themselves.

Writing is not messy, knowledge points in part to master.

The accuracy rate is above 75%, and you can correct the last job.

2

11-15

There is a phenomenon of overdue work.

Thinking is a little confused, the writing is not very neat, the knowledge

point grasp is not very good.

Above 60% accuracy, occasionally correct the last job.

1

6-10

The default phenomenon is a little serious, can not finish the homework

on time.

Thinking is more chaotic, the writing is not neat, the knowledge point is

obviously not mastered.

Correct rate is above 40%, with no correction situation.

E

0-5

Basically can not finish the homework on time.

The idea is very confused, the homework is blank, obviously did not listen to the class.

Correct rate of 10% operation, no correction situation.

Remarks: Late submission of homework without special reasons, delayed one day of submission, automatically reduce the score by 10%. One-day deferred submission is automatically reduced by 25%; a three-day deferred submission is automatically reduced by

50%; an extension of more than one week will be deemed invalid.

? 419

高中數(shù)學(xué)課程圖

Performance Assessment Specifics:

Content Assessment Grade and Details

Class Participation)

Excellent

（3-4）

Good

（2）

Unsatisfied

（0-1）

Actively participate in the

class, every question can

actively interact with the

teacher, actively answer

questions.

Students follow the

teacher, but the participation is not too

high, only when they

arrive.

Without any interaction, the class mental

state is very bad, do

something unrelated to

the class.

Attendance

Excellent

（2）

Good

（1）

Unsatisfied

（0）

Never be late or leave early

without any reason, and ask

for leave early for anything.

Occasionally leave

early, the frequency

is not high, from no

reason, things do not

explain in advance.

Often be late and

leave early, and even

be truant phenomenon

is serious.

Class notes

Excellent

（2）

Good

（1）

Unsatisfied

（0）

Class initiative to take notes

carefully, writing clearly,

clear at a glance, and can

keep notes very well.

Under the teacher’s

reminder, notes can be

taken, but not proactive enough.

Never take notes

Awards

Excellent

（2）

Good

（1）

Unsatisfied

（0）

Actively participate in various competitions and win

prizes. The class is full of

spirit, never sleep in the

classroom, in and out of the

classroom at will；

Actively participated

in various competitions, but did not win

prizes. Occasionally in

class, but do not sleep.

Not willing to participate in any competition activities, the

class spirit is not good,

sleep on the table, like

to go in and out of the

classroom at will.

博實(shí)樂(lè)“中外融通課程”

420?

5 Resources

Precalculus (ISBN 10:1292079452)

AP Central: http://www.collegeboard.com/html/apcourseaudit/index.html

The Princeton Review: www.PrincetonReview.com

Relevant exam: store.collegeboard.org

http://welkerswikinomics.com/blog/

http://www. tutor2u.com

http://www.bized.ac.uk

Chinese and International Integrated

Curriculums for Bright Scholar

High School Section

CAP Calculus AB

Curriculum Map

（2022 version）

Complied by Guangdong Country Garden Senior High Section

博實(shí)樂(lè)“中外融通課程”

422?

AP Curriculum Map

Subject AP Calculus AB Level G2/G3 Syllabus Code

Course Code Credit 4 Duration 1 Year

Teaching Hours 240 Designer Zhuang xinrui Completed Date 2022.7.5

1 Course Introduction

1.1 Introduction

The AP Calculus AB course is a standard course in the calculus of a single variable.

The goal is to teach conceptual reasoning, enabling students to present a solution

algebraically, geometrically, numerically or verbally. Emphasis is placed not only on a

clear understanding of the concepts, but also on their applicability in real world situations.

All of the topics in the AP Calculus AB syllabi are covered, as well as additional topics

as time permits. Major topics include limits, continuity, derivatives and applications,

integrals and applications, first order linear differential equations, inverse trigonometric

functions, transcendental functions. This student-centered course features discussions,

reflections, and projects that help students to master the course material in an engaging

way. Technology and graphing calculators are used extensively in this course to reinforce

the concepts covered. All students must possess a TI-Nspire graphing calculator.

1.2 Aims

The aim of AP Calculus AB is to:

1. Develop logical, critical and creative thinking；

2. Improve the ability of understanding and expression, study the skills of

communication;

3. Apply and transfer skills to alternative situations, and patience and persistence in

problem-solving;

4. Understand mathematics and enjoy the beauty of mathematics;

5. Develop an appreciation of calculus as a coherent body of knowledge and as a

human accomplishment.

2 Course Structure

3

2Course Structure

3 Course Outline

Unit Contents Objectives Big Ideas Core

Competency

Acade

mic

Profici

ency

Level

Assignm

ent

Teac

hing

hour

Unit1:

Functions,

Graphs, ,Li

mits and

continuity

a. Analysis

of graphs

b. Limits

of

functions

c.

Asymptoti

c and

unbounded

behavior

d.

Continuity

as a

property of

functions

1.Interpret the rate of

change

2.Represent limits

analytically

3.Estimate and

determine the limits

4.Justify conclusions

about continuity

5.Determine

continuity intervals

6.Interpret the

behavior of functions

using limits

Change

Limits

analysis

of

Functions

Mathematical

abstract

logic

reasoning

Intuitive

imagination

Mathematical

operation

Level

2

Barron

Unit 1

exercise

AP QB

unit 1

exercise

30

Unit 2:

Differentia

tion:

Definition

and

Properties

a. Conce

pt of

the

derivat

ive

b. b.

Deriva

1. Determine

average rates

2. Represent the

derivative of a

function as a

limit .

3. Estimate

Change

Limits

analysis

of

Functions

Mathematical

abstract

logic

reasoning

Mathematical

operation

Level

3

Barron

Unit 2

exercise

AP QB

unit 2

exercise

20

CAP Calculus AB

Limit and continuity differentiation and

application integration and application

? 423

高中數(shù)學(xué)課程圖

3 Course Outline

Unit Contents Objectives Big Ideas Core Competency Academic Proficiency Level Assignment Teaching hour

Unit1:

Functions,Graphs

,Limits and

continuity

a. Analysis of graphs

b. Limits of functions

c. Asymptotic and

unbounded behavior

d. Continuity as a property of

functions

1.Interpret the rate of

change

2.Represent limits

analytically

3.Estimate and

determine the limits

4.Justify conclusions

about continuity

5.Determine continuity

intervals

6.Interpret the behavior

of functions using limits

Change

Limits

analysis of

Functions

Mathematical

abstract

logic

reasoning

Intuitive

imagination

Mathematical

operation

Level2 Barron Unit 1

exercise

AP QB unit 1

exercise

30

Unit 2:

Differentiation:

Definition and

Properties

a. Concept of the derivative

b. Derivative at a point

c. Derivative as a function

d. rule of differentiation

1. Determine average

rates

2. Represent the

derivative of a function

as a limit .

3. Estimate derivatives.

4. Explain the

relationship

5. between

differentiability

Change

Limits

analysis of

Functions

Mathematical

abstract

logic

reasoning

Mathematical

operation

Level3 Barron Unit 2

exercise

AP QB unit 2

exercise

20

博實(shí)樂(lè)“中外融通課程”

424?

Unit Contents Objectives Big Ideas Core Competency Academic Proficiency Level Assignment Teaching hour

andcontinuity.

6. Calculate derivatives

Unit 3:

Differentiation:

Composite,

Implicit, and

Inverse Functions

a. The Chain Rule

b. Implicit Differentiation

c. Differentiating Inverse

Functions

d. Calculating Higher-Order

Derivatives

1.Calculate derivatives

of composite functions.

2. implicit

differentiation

3.Calculate derivatives

of inverse function

4.Determine higher

order derivatives

Analysis

of

Functions

Mathematical

abstract

logic

reasoning

Mathematical

operation

Level3 Barron Unit 3

exercise

AP QB unit 3

exercise

15

Unit 4:

Contextual

Applications of

Differentiation

a. Straight-Line Motion

b. Rates of Change in Applied

Contexts

c. Related Rates

d. Linear approximation

1. Calculate and

Interpret rates of change

in applied contexts

2. Linear approximation

3. Determine limits of

functions that result in

indeterminate forms.

Change

Limits

Mathematical

abstract

logic

reasoning

mathematical

modeling

Intuitive

imagination

Mathematical

operation

Level3 Barron Unit 4

exercise

AP QB unit 4

exercise

15

? 425

高中數(shù)學(xué)課程圖

Unit Contents Objectives Big Ideas Core Competency Academic Proficiency Level Assignment Teaching hour

Unit 5:

Analytical

Applications of

Differentiation

a. Mean Value Theorem

b. Extreme Value Theorem

c. Monotonicity

d. Extrema value

e. Concavity of

Functions

f. Graphs of Functions and

Their Derivatives

g. Optimization Problems

h. Implicit

Relations

1.Justify conclusions

about functions by

applying the MVT,EVT.

2.Justify conclusions

about the behavior of a

function based on the

behavior of its

derivatives.

3.Calculate minimum

and maximum values in

applied contexts or

analysis of functions.

4.Interpret minimum

and maximum values

calculated in applied

contexts.

5. Determine critical

points of implicit

relations.

6. Justify conclusions

about the behavior of an

implicitlydefined

function based on

evidence from its

derivatives

Analysis

of

Functions

logic

reasoning

Intuitive

imagination

Mathematical

operation

Level3 Barron Unit 5

exercise

AP QB unit 5

exercise

20

博實(shí)樂(lè)“中外融通課程”

426?

Unit Contents Objectives Big Ideas Core Competency Academic Proficiency Level Assignment Teaching hour

Unit 6:

Integration and

Accumulation

of Change

a. Riemann Sums

b. Fundamental

Theorem of Calculus and

Accumulation Functions

c.Properties of

Definite integrals

d.Antiderivatives

and Indefinite Integrals

e.Integration Using

Substitution and by Parts

1.Approximate a

definite Integral

2.Interpret and

Represent the limiting

case of the Riemann

sum as a definite

integral.

3.Represent

accumulation

functions using definite

integrals.

4.Calculate a definite

integral

5.Determine

antiderivatives

of functions and

indefinite integrals

6.integration by parts

Change

Limits

analysis of

Functions

Mathematical

abstract

logic

reasoning

Intuitive

imagination

Mathematical

operation

Level3 Barron Unit 6

exercise

AP QB unit 6

exercise

30

Unit 7:

Differential

Equations

a.Modeling with

Differential equation

b.Verifying Solutions

c.Slope Fields

d.Finding Solution

Using Separation of Variables

e. Exponential Models

1. Verify solutions to

differential equations.

2. Estimate solutions

3. Determine solutions

4. Interpret the meaning

of a differential

equation and its

variables in context.

Analysis

of

Functions

logic

reasoning

Intuitive

imagination

Mathematical

operation

Level3 Barron Unit 7

exercise

AP QB unit 7

exercise

15

? 427

高中數(shù)學(xué)課程圖

Unit Contents Objectives Big Ideas Core Competency Academic Proficiency Level Assignment Teaching hour

Unit 8:

Application

of Integration

a. Finding the Average Value

b. Linear motion

c. Area Between Curves

d. Determine Volumes using

integration

1.Determine the average

value of a function

2. Determine values for

positions and rates of

change

using definite integrals

3. Interpret the meaning

of a definite integral in

accumulation problems.

4. Calculate areas in the

plane using the definite

integral.

5.Calculate volumes of

solids with known cross

sections

6.Calculate volumes of

solids of revolution

Change Mathematical

abstract

logic

reasoning

mathematical

modeling

Intuitive

imagination

Mathematical

operation

Level3 Barron Unit 8

exercise

AP QB unit 8

exercise

25

Review AP exam review Past papers

One calculus

project

55

博實(shí)樂(lè)“中外融通課程”

428?

4 Assessment

4.1 External Assessment Objectives

Test Paper Test Paper Description Weight

(%) (Duration)

Part I: Multiple-choice Questions

(MCQ)

Part A: Graphing calculator not permitted

Part B: Graphing calculator required

50% 105

Part II: Free-response Questions

(FRQ)

Part A: Graphing calculator required

Part B: Graphing calculator not permitted

50& 90

4.2 Internal Assessment Objectives

Content Percentage Assessment Criteria Description

Exams 70% Mid-term exam： 10% Final Exam：50% test\\quiz 10%

Assignment 20% Each semi-semester 10%

Performance

10%

Contents Excellent Good Unsatisfied

Attendance 2 1 0

Presentation 2 1 0

Class notes 2 1 0

Participation 2 1 0

Others 2 1 0

4.3 Details of External Assessment

AP External Assessment Criteria Description:

AP Score Score Range Credit Recommendation College Grade Equivalent

5 68-108 Extremely qualified A

4 54-67 Well qualified A-， B+， B

3 41-53 Qualified B-， C+， C

2 26-40 Possibly qualified n/a

1 0-25 No recommendation n/a

? 429

高中數(shù)學(xué)課程圖

4.4 Details of Internal Assessment

Homework Assessment Specifics:

Score（Total score: 20） Assessment Criteria

18-20

1) Submit on time

2) Neat and beautiful writing.

3) content is accurate;

4) Meet the specific requirements of the teacher;

5) The accuracy rate is more than 90%.

15-17 Meet at least 3 of 1) 2)3)4)

5) The accuracy rate is more than 80%.

12-14 Meet at least 3 of 1) 2)3)4)

5) The accuracy rate is more than 70%.

9-11 Meet at least 2 of 1) 2)3)4)

5) The accuracy rate is more than 60%.

6-8 Meet at least 2 of 1) 2)3)4)

5) The accuracy rate is more than 50%.

0-5 Meet at least 2 of 1) 2)3)4)

5) The accuracy rate is less than 50%.

Performance Assessment Specifics:

Content Assessment Grade and Details

Class Participation)

Excellent

（3-4）

Good

（2）

Unsatisfied

（0-1）

1）Listen attentively

2）active participation;

3）no illegal use of digital products

Two of 1)2)3) At most one of

1)2)3)

Attendance

Excellent

（2）

Good

（1）

Unsatisfied

（0）

1）be punctual

2）come to classroom 3 minutes in advance and

well-prepared for class;

3）no excuses of leaving the classroom during the

class (like asking for leave to go to washrooms or

drink water,etc. )

Two of 1)2)3) At most one of

1)2)3)

博實(shí)樂(lè)“中外融通課程”

430?

Content Assessment Grade and Details

Class notes

Excellent

（2）

Good

（1）

Unsatisfied

（0）

1）take careful notes of every class;

2）notes are well-organized and efficient; One of 1) 2) None of 1)2)

Awards

Excellent

（2）

Good

（1）

Unsatisfied

（0）

1）active participation of cl ass discussion;

2）well-prepared presentation；

One of 1) 2) None of 1)2)

5 Resources

[1] Calculus: Graphical, Numerical, Algebraic: AP Edition

[2] Barron’s AP Calculus: With 8 Practice Tests

Chinese and International Integrated

Curriculums for Bright Scholar

High School Section

CAP Calculus BC

Curriculum Map

（2022 version）

Complied by Guangdong Country Garden Senior High Section

博實(shí)樂(lè)“中外融通課程”

432?

AP Curriculum Map

Subject AP Calculus BC Level G2/G3/G4 Syllabus Code

Course Code Credit 4 Duration 1 Year

Teaching

Hours

240 Designer Zhuang xinrui Completed Date 2022.7.5

1 Course Introduction

1.1 Introduction

The AP Calculus BC course is a standard course in the calculus of a single variable.

The goal is to teach conceptual reasoning, enabling students to present a solution

algebraically, geometrically, numerically or verbally. Emphasis is placed not only on a

clear understanding of the concepts, but also on their applicability in real world situations.

All of the topics in the AP Calculus BC syllabi are covered, as well as additional topics as

time permits. Major topics include limits, continuity, derivatives and applications, integrals

and applications, first order linear differential equations, inverse trigonometric functions,

transcendental functions, infinite series, Taylor polynomials, vectors,parametrically defined

functions, and polar coordinates. This student-centered course features discussions,

reflections, and projects that help students to master the course material in an engaging

way. Technology and graphing calculators are used extensively in this course to reinforce

the concepts covered. All students must possess a TI-Nspire graphing calculator.

1.2 Aims

The aim of AP Calculus BC is to:

1. Develop logical, critical and creative thinking；

2. Improve the ability of understanding and expression, study the skills of

communication;

3. Apply and transfer skills to alternative situations, and patience and persistence in

problem-solving;

? 433

高中數(shù)學(xué)課程圖

4. Understand mathematics and enjoy the beauty of mathematics;

5. Develop an appreciation of calculus as a coherent body of knowledge and as a

human accomplishment .

2 Course Structure

3

accomplishment .

2 Course Structure

3 Course Outline

Unit Contents Objectives Big Ideas

Core

Competenc

y

Academic

Proficienc

y Level

Assignm

ent

Teachi

ng

hour

Unit1:

Functi

ons,Gr

aphs, ,

Limits

and

continu

ity

a. Analysis of

graphs

b. Limits of

functions

c. Asymptotic

and

unbounded

behavior

d. Continuity

as a property

of functions

e. Parametric,

1.Interpret the rate

of change

2.Represent limits

analytically

3.Estimate and

determine the limits

4.Justify

conclusions about

continuity

5.Determine

continuity intervals

6.Interpret the

behavior of

functions using

limits

Change

Limits

analysis

of

Functions

Mathematica

l abstract

logic

reasoning

Intuitive

imagination

Mathematica

l operation

Level 2 Barron

Unit 1

exercise

AP QB

unit 1

exercise

20

CAP Calculus BC

Limit and continuity Differentiation and

application

Integration and

application Sequence and series

博實(shí)樂(lè)“中外融通課程”

434?3 Course Outline

Unit Contents Objectives Big Ideas Core Competency Academic Proficiency Level Assignment Teachin g hour

Unit1:

Functions,Grap

hs, Limits and

continuity

a. Analysis of graphs

b. Limits of functions

c. Asymptotic and

unbounded behavior

d. Continuity as a

property of functions

e. Parametric, polar,

and vector functions

1.Interpret the rate of change

2.Represent limits analytically

3.Estimate and determine the

limits

4.Justify conclusions about

continuity

5.Determine continuity

intervals

6.Interpret the behavior of

functions using limits

Change

Limits

analysis of

Functions

Mathematical

abstract

logic

reasoning

Intuitive

imagination

Mathematical

operation

Level 2 Barron Unit

1 exercise

AP QB unit

1 exercise

20

Unit 2:

Differentiation:

Definition and

Properties

a. Concept of the

derivative

b. Derivative at a point

c. Derivative as a

function

d. rule of

differentiation

1. Determine average rates

2. Represent the derivative of

a function as a limit .

3. Estimate derivatives.

4. Explain the relationship

5. between differentiability

and

continuity.

6. Calculate derivatives

Change

Limits

analysis of

Functions

Mathematical

abstract

logic

reasoning

Mathematical

operation

Level 3 Barron Unit

2 exercise

AP QB unit

2 exercise

15

? 435

高中數(shù)學(xué)課程圖

Unit Contents Objectives Big Ideas Core Competency Academic Proficiency Level Assignment Teachin g hour

Unit 3:

Differentiation:

Composite,

Implicit, and

Inverse

Functions

a. The Chain Rule

b. Implicit

Differentiation

c. Differentiating

Inverse Functions

d. Calculating HigherOrder Derivatives

1.Calculate derivatives

of composite functions.

2. implicit differentiation

3.Calculate derivatives

of inverse function

4.Determine higher order

derivatives

Analysis of

Functions

Mathematical

abstract

logic

reasoning

Mathematical

operation

Level 3 Barron Unit

3 exercise

AP QB unit

3 exercise

15

Unit 4:

Contextual

Applications of

Differentiation

a. Straight-Line

Motion

b. Rates of Change in

Applied Contexts

c. Related Rates

d. Linear

approximation

e. L’Hospital’s Rule

1. Calculate and Interpret rates

of change in applied contexts

2. Linear approximation

3. Determine limits of

functions that result in

indeterminate forms.

Change

Limits

Mathematical

abstract

logic

reasoning

mathematical

modeling

Intuitive

imagination

Mathematical

operation

Level 3 Barron Unit

4

exercise

AP QB unit

4 exercise

15

Unit 5:

Analytical

Applications of

Differentiation

a. Mean Value

Theorem

b. Extreme Value

Theorem

c. Monotonicity

d. Extrema value

e. Concavity of

Functions

1.Justify conclusions about

functions by applying the

MVT,EVT.

2.Justify conclusions about

the behavior of a function

based on the behavior of its

derivatives.

3.Calculate minimum and

Analysis of

Functions

logic

reasoning

Intuitive

imagination

Mathematical

operation

Level 3 Barron Unit

5

exercise

AP QB unit

5 exercise

20

博實(shí)樂(lè)“中外融通課程”

436?

Unit Contents Objectives Big Ideas Core Competency Academic Proficiency Level Assignment Teachin g hour

f. Graphs of Functions

and Their Derivatives

g. Optimization Proble

ms

h. Implicit Relations

maximum values in applied

contexts or analysis of

functions.

4.Interpret minimum and

maximum values calculated

in applied contexts.

5. Determine critical points of

implicit relations.

6. Justify conclusions about

the behavior of an implicitly

defined function based on

evidence from its derivatives

Unit 6:

Integration and

Accumulation

of Change

a. Riemann Sums

b. Fundamental

Theorem of Calculus

and

Accumulation

Functions

c.Properties of

Definite integrals

d.Antiderivatives

and Indefinite

Integrals

e.Integration Using

Substitution and

by Parts

f.Evaluating Improper

Integrals

1.Approximate a definite

Integral

2.Interpret and Represent the

limiting case of the Riemann

sum as a definite integral.

3.Represent accumulation

functions using definite

integrals.

4.Calculate a definite integral

5.Determine antiderivatives

of functions and indefinite

integrals

6.integration by parts

7. integration by linear partial

fractions

8. Evaluate an improper

integral

9.

Change

Limits

analysis of

Functions

Mathematical

abstract

logic

reasoning

Intuitive

imagination

Mathematical

operation

Level 3 Barron Unit

6

exercise

AP QB unit

6 exercise

25

? 437

高中數(shù)學(xué)課程圖

Unit Contents Objectives Big Ideas Core Competency Academic Proficiency Level Assignment Teachin g hour

Unit 7:

Differential

Equations

a.Modeling with

Differential equation

b.Verifying Solutions

c.Slope Fields

d.Euler’s Method

e.Finding Solution

Using Separation of

Variables

f. Exponential Models

g. Logistic Models

1. Verify solutions to

differential equations.

2. Estimate solutions

3. Determine solutions

4. Interpret the meaning of a

differential equation and its

variables in context.

5. Interpret the meaning of the

logistic growth model in

context.

Analysis of

Functions

logic

reasoning

Intuitive

imagination

Mathematical

operation

Level 3 Barron Unit

7

exercise

AP QB unit

7exercise

15

Unit 8:

Application

of Integration

a. Finding the Average

Value

b. Linear motion

c. Area Between

Curves

d. Determine Volumes

using integration

e.The Arc Length of a

Smooth, Planar Curve

and Distance Traveled

1.Determine the average

value of a function

2. Determine values for

positions and rates of change

using definite integrals

3. Interpret the meaning

of a definite integral in

accumulation problems.

4. Calculate areas in the plane

using the definite integral.

5.Calculate volumes of solids

with known cross sections

6.Calculate volumes of solids

of revolution

7.Determine the length of a

curve in the plane.

Change Mathematical

abstract

logic

reasoning

mathematical

modeling

Intuitive

imagination

Mathematical

operation

Level 3 Barron Unit

8

exercise

AP QB unit

8 exercise

20

Unit 9:

Parametric

Equations,

Polar

Coordinates,

a.Differentiating

Parametric

Equations

b. Finding Arc

Lengths of Curves

1.Calculate derivatives of

parametric functions.

2.Determine the length of a

curve defined by parametric

functions

Change

analysis of

Functions

Mathematical

abstract

logic

reasoning

Level 3 Barron Unit

9

exercise

AP QB unit

9 exercise

15

博實(shí)樂(lè)“中外融通課程”

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Unit Contents Objectives Big Ideas Core Competency Academic Proficiency Level Assignment Teachin g hour

and

Vector-Valued

Functions

c. Differentiating

Vector-Valued

Functions

d.Integrating Vector

Valued Functions

e.Solving Motion

Problems

f. Differentiating in

Polar Form

g. Find the Area

bounded by polar

curve

3.Calculate derivatives of

vector-valued functions

4.Determine a particular

solution given a rate vector

and initial conditions.

5.Determine values for

positions and rates of change

in problems involving planar

motion

6.Calculate derivatives of

functions written in polar

coordinates.

7.Calculate areas of regions

defined by polar curves.

Mathematical

operation

Unit 10:

Infinite

Sequences

and Series

a.Defining Convergent

and

Divergent Infinite

Series

b.Geometric

Series

c. The n th Term Test

for Divergence

d. Integral Test

e. Harmonic Series

and p -Series

f.Comparison Tests

g.Alternating Series

Test

h. Ratio Test

i.Determining

Absolute or

Conditional

1.Determine whether a series

converges or diverges.

2.Approximate the sum of a

series

3.Represent a function at a

point as a Taylor polynomial.

4. Determine the error bound

associated with a Taylor

polynomial approximation.

5.Determine the radius of

convergence and interval of

convergence for a power

series.

6.Represent a function as a

Taylor series or a Maclaurin

Series.

7.Interpret Taylor series and

Maclaurin series

Limits Mathematical

abstract

logic

reasoning

Intuitive

imagination

Mathematical

operation

Level 3 Barron Unit

10

exercise

AP QB unit

10 exercise

25

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高中數(shù)學(xué)課程圖

Unit Contents Objectives Big Ideas Core Competency Academic Proficiency Level Assignment Teachin g hour

Convergence

j.Alternating Series

Error Bound

k. Taylor

Polynomial

Approximations

l. Radius and Interval

of

Convergence

8.Represent a given function

as a power series

Review AP exam review AP past

papers.

one calculus

project

55

博實(shí)樂(lè)“中外融通課程”

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4 Assessment

4.1 External Assessment Objectives

Test Paper Test Paper Description Weight (%) (Duration)

Part I: Multiple-choice Questions (MCQ)

Part A: Graphing calculator not permitted

Part B: Graphing calculator required

50% 105

Part II: Free-response Questions

(FRQ)

Part A: Graphing calculator required

Part B: Graphing calculator not permitted

50& 90

4.2 Internal Assessment Objectives

Content Percentage Assessment Criteria Description

Exams 70% Mid-term exam： 10% Final Exam：50% test\\quiz 10%

Assignment 20% Each semi-semester 10%

Performance

10%

Contents Excellent Good Unsatisfied

Attendance 2 1 0

Presentation 2 1 0

Class notes 2 1 0

Participation 2 1 0

Others 2 1 0

4.3 Details of External Assessment

AP External Assessment Criteria Description:

AP Score Score Range Credit Recommendation College Grade Equivalent

5 73-105 Extremely qualified A

4 58-72 Well qualified A-， B+， B

3 43-57 Qualified B-， C+， C

2 30-42 Possibly qualified n/a

1 0-29 No recommendation n/a

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高中數(shù)學(xué)課程圖

4.4 Details of Internal Assessment

Homework Assessment Specifics:

Score（Total score: 20） Assessment Criteria

18-20

1) Submit on time

2) Neat and beautiful writing.

3) content is accurate;

4) Meet the specific requirements of the teacher;

5) The accuracy rate is more than 90%.

15-17 Meet at least 3 of 1) 2)3)4)

5) The accuracy rate is more than 80%.

12-14 Meet at least 3 of 1) 2)3)4)

5) The accuracy rate is more than 70%.

9-11 Meet at least 2 of 1) 2)3)4)

5) The accuracy rate is more than 60%.

6-8 Meet at least 2 of 1) 2)3)4)

5) The accuracy rate is more than 50%.

0-5 Meet at least 2 of 1) 2)3)4)

5) The accuracy rate is less than 50%.

Performance Assessment Specifics:

Content Assessment Grade and Details

Class Participation)

Excellent

（3-4）

Good

（2）

Unsatisfied

（0-1）

1）Listen attentively

2）active participation;

3）no illegal use of digital products

Two of

1)2)3) At most one of 1)2)3)

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Content Assessment Grade and Details

Attendance

Excellent

（2）

Good

（1）

Unsatisfied

（0）

1）be punctual

2）come to classroom 3 minutes

in advance and well-prepared for

class;

3）no excuses of leaving the classroom during the class (like asking

for leave to go to washrooms or drink

water,etc. )

Two of

1)2)3) At most one of 1)2)3)

Class notes

Excellent

（2）

Good

（1）

Unsatisfied

（0）

1）take careful notes of every class;

2）notes are well-organized and

efficient;

One of 1) 2) None of 1)2)

Awards

Excellent

（2）

Good

（1）

Unsatisfied

（0）

1）active participation of cl ass

discussion;

2）well-prepared presentation；

One of 1) 2) None of 1)2)

5 Resources

[1] Calculus: Graphical, Numerical, Algebraic: AP Edition

[2] Barron’s AP Calculus: With 8 Practice Tests