Chinese and International Integrated

Curriculums for Bright Scholar

High School Section

CAP Statistics

Curriculum Map

（2022 version）

Complied by Guangdong Country Garden Senior High Section

博实乐“中外融通课程”

444 

AP Curriculum Map

Subject AP Statistics Level G3/G4 Syllabus Code

Course Code Credit 4 Duration 1 Year

Teaching 240 Designer Liu Jun Completed Date 2022.7.20

1 Course Introduction

1.1 Introduction

The AP Statistics course introduces students to the major concepts and tools for

collecting, analyzing, and drawing conclusions from data. There are four themes evident

in the content, skills, and assessment in the AP Statistics course: exploring data, sampling

and experimentation, probability and simulation, and statistical inference. Students

use technology, investigations, problem solving, and writing as they build conceptual

understanding.

For the single variable contents, AP statistics requires the students to have a very clear

understanding of the categories of the variables, to have full analysis of the statistical tables

and graphs, and to be able to depict the tables and graphs using statistical languages(CUSS)

and complete the comparison and explanation. For the two-variable contents, the students

are required to master the conditions for linear regression and be able to do the regression.

In the data collection and experiments, students are required to conduct reasonable and

scientific experiment to find cause-effect relationship. In sampling distribution, students

are required to understand unbiased estimator and apply the central limit theorem. AP

statistics requires the students to have systematic and full understanding and mastering of

constructing and explaining confidence interval and confidence level, one and two-sample

proportion, one and two-sample mean confidence interval and hypothesis testing, p value,

and type I and II errors,power. In addition to this, student should master t distribution,

confidence interval and hypothesis involved t statistics. Also, students are required to

understand the chi-square distribution and the hypothesis for goodness of fit, independence

and homogeneity. In terms of inference of slope, students should understand why the

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高中数学课程图

slopes vary, explain y-intercept, standard deviation of residual, standard error of slope,

and understand the Minitab output and master the confidence interval for slope and the

hypothesis testing for slopes. All students must possess a TI-Nspire graphing calculator.

1.2 Aims

The aim of AP Statistics is to:

Collect and arrange data;

Data understanding and data processing;

Draw and explain conclusion;

Concept formation and knowledge acquisition;

Students can acquire useful information and develop the capability of quantitative

analysis

To meet the needs of the digital ear, enhance the conscience of expressing the realistic

problems, and thinking qualities

Accumulate the capabilities of exploring the essence of the actual activities, mastering

the rules of the correlated things

2 Course Structure

3

understand the Minitab output and master the confidence interval for slope and the

hypothesis testing for slopes. All students must possess a TI-Nspire graphing calculator.

1.2Aims

The aim of AP Statistics is to:

1. Collect and arrange data;

2. Data understanding and data processing;

3. Draw and explain conclusion;

4. Concept formation and knowledge acquisition;

5. Students can acquire useful information and develop the capability of quantitative

analysis

6. To meet the needs of the digital ear, enhance the conscience of expressing the

realistic problems, and thinking qualities

7. Accumulate the capabilities of exploring the essence of the actual activities,

mastering the rules of the correlated things

2 Course Structure

3 Course Outline

CAP Statistics

Exploring data Sampling and

experimentation

Probability and

simulation Statistical inference

博实乐“中外融通课程”

446 3 Course Outline

Unit Contents Objectives Big Ideas

Core

Competenc

y

Academic

Proficiency Level Assignment Teaching Hours

1.

Exploring onevariable data

1.1 The

language of

individual

and

variables

Individual and

variables

Variation and

distribution

Critical and

creative

thinking

skills

Level 2

Practice of

Statistics Unit

1 Exercise

26

1.2 Categories

of variables

Categorical variable,

quantitative

variables ,qualitative

variable, numerical

variable,discrete

variable, continuous

variable

Variation and

distribution

Critical and

creative

thinking

skills

Level 2

1.3 Representin

g

categorical

variables

with tabels

Frequency graph,

relative frequency

graph,barchart,pie

chart

Variation and

distribution

Critical and

creative

thinking

skills

Level 2

1.4 Representin

g

quantitative

variables

with graph

Histogram,line

graph, stemplot,

dotplot, boxplot

Variation and

distribution

Critical and

creative

thinking

skills

Level 2

1.5 Shape, spread, Variation and Critical and Level 2

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高中数学课程图

Unit Contents Objectives Big Ideas

Core

Competenc

y

Academic

Proficiency Level Assignment Teaching Hours

Describing

the

Distribution

of a

Quantitativ

e Variable

cluster,gap,outlier,

mean, mode

median,variance,stan

dard variance

distribution creative

thinking

skills

1.6 Summary

Statistics

for a

Quantitativ

e Variable

Quartile, percentile,

standard score, IQR,

range,

Variation and

distribution

Critical and

creative

thinking

skills

Level 2

1.7 Contingenc

y table

Marginal distribution Variation and

distribution

Critical and

creative

thinking

skills

Level 2

1.8 The Normal

Distribution

Empirical rule, table

reading and consult

Variation and

distribution

Critical and

creative

thinking

skills

Level 2

2.

Exploring

Two-Variable

Data

2.1 Representin

g Two

Categorical

Variables

Scatter plot(form,

diraction, outlier,

influential point,

strength),response

variable and

explanatory variable,

lest square line

regression, residual,

linearity. Slope, and

regression line,

Variation and

distribution

Critical and

creative

thinking

skills

Level 2 Practice of

Statistics Unit

2 Exercise

16

博实乐“中外融通课程”

448  Unit Contents Objectives Big Ideas Core Competenc

y

Academic

Proficiency Level Assignment Teaching Hours

exptraoplation,

residual plot ,

r,r2„ ൌ ” •›•š , nonliear

to linear convertion

3.

Collecting

Data

3.1

Introductio

n to

Planning a

Study

population, sample,

survey ,

observational study

and experiment

Variation and

distribution

Critical,

communicat

ion and

cooperation

Level 3 Practice of

Statistics Unit

3 Exercise

28

3.2 Random

Sampling

and Data

Collection

Census, sampling

study, sampling with

replacement,

sampling without

replacement, random

sampling, Simple

random

sampling(SRS),

strata sampling,

cluster sampling,

systematic sampling

Variation and

distribution

Critical,

communicat

ion and

cooperation

Level 3

3.3 Potential

problems of

sampling

Bias, Volunteering

bias, undercoverange

bias, non-response

bias, respinse bias,

wording bias,

convenience

sampling bias

Variation and

distribution

Critical,

communicat

ion and

cooperation

Level 3

3.4 Introductio

n to

Confounding

variables,

Variation and

distribution

Critical,

communicat

Level 3

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高中数学课程图

Unit Contents Objectives Big Ideas

Core

Competenc

y

Academic

Proficiency Level Assignment Teaching Hours

Experiment

al Design

Comparison,

random, control and

replica(CRCR),

double blind,

randomized block

experiment, matchpaired design

ion and

cooperation

4.

Probability,

Random

Variables, and

Probability

Distributions

4.1 Estimating

Probabilitie

s Using

Simulation

Random process,

chance events,

events, outcomes,

trials, simulation

Patterns and

uncertainty

Critical and

creative

thinking

skill

Level 3

Practice of

Statistics Unit

4 Exercise

28

4.2 Introductio

n to

Probability

Sampling space,

probability, the union

of events, exclusive

events, conditional

probability,

independence, the

intersection of events

Patterns and

uncertainty

Critical and

creative

thinking

skill

Level 3

4.3 Introductio

n to

Random

Variables

and

Probability

Distribution

s

Random variable,

probability density

function, discrete

variable distribution,

mean and variance

Patterns and

uncertainty

Critical and

creative

thinking

skill

Level 3

4.4

Combining

Random

The linear

combination of

variables, mean and

Patterns and

uncertainty

Critical and

creative

thinking

Level 3

博实乐“中外融通课程”

450  Unit Contents Objectives Big Ideas Core Competenc

y

Academic

Proficiency Level Assignment Teaching Hours

Variables variance of

combination

skill

4.5 Introductio

n to the

Binomial

Distribution

Four conditions for

binomial

distribution,

parameters, mean

and variance ,

application of

binomial distribution

Patterns and

uncertainty

Critical and

creative

thinking

skill

Level 3

4.6 The

Geometric

Distribution

Condition for

geometric

distribution, the

difference from

binomial

distribution,

mean ,variance and

the application of the

geometric

distribution

Patterns and

uncertainty

Critical and

creative

thinking

skill

Level 3

5.

Sampling

Distributions

5.1 Statistics

and

sampling

distribution

Statistics,parameters,

and sampling

distribution

Variation and

distribution, Patterns

and uncertainty

Critical and

creative

thinking

skill

Level 3 Practice of

Statistics Unit

5 Exercise

16

5.2 The Normal

Distribution

, Revisited

Calculation and

further understanding

of normal

distribution

Variation and

distribution, Patterns

and uncertainty

Critical and

creative

thinking

skill

Level 3

5.3 The Central Conditions and the Variation and Critical and Level 3

  451

高中数学课程图

Unit Contents Objectives Big Ideas

Core

Competenc

y

Academic

Proficiency Level Assignment Teaching Hours

Limit

Theorem

meaning of the

theorem

distribution, Patterns

and uncertainty

creative

thinking

skill

5.4 Biased and

Unbiased

Point

Estimates

Unbiased estimator,

biased estimator

Variation and

distribution, Patterns

and uncertainty

Critical and

creative

thinking

skill

Level 3

5.5 Four types

of sampling

distribution

Sampling

Distributions for

Sample Proportions

Sampling

Distributions for

Differences in

Sample Proportions

Sampling

Distributions for

Sample Means

Sampling

Distributions for

Differences in

Sample Means

Variation and

distribution, Patterns

and uncertainty

Critical and

creative

thinking

skill

Level 3

6.

Confidence

Interval

6.1 Confidence

Interval of

Z

Confidence level,

confidence level,

critical values,

margin of error

Data-based

predictions,

decisions, and

conclusions

Critical and

creative

thinking

skill

Level 3 Practice of

Statistics Unit

6 Exercise

24

6.2 Confidence

Interval

with t

T-distribution,

degree of freedom,

conditions for t

Data-based

predictions,

decisions, and

conclusions

Critical and

creative

thinking

skill

Level 3

博实乐“中外融通课程”

452  Unit Contents Objectives Big Ideas Core Competenc

y

Academic

Proficiency Level Assignment Teaching Hours

6.3 Confidence

Interval for

proportion

Conditions and

application of 0.5

Data-based

predictions,

decisions, and

conclusions

Critical and

creative

thinking

skill

Level 3

6.4 Confidence

Interval for

two

samples

Formular, and Ti

graphical calculator

usage

Data-based

predictions,

decisions, and

conclusions

Critical and

creative

thinking

skill

Level 3

7. Hypothsis

Testing

7.1 Concepts of

hypothesis

testing

Hypothesis,null

hypothesis,

alternative

hypothesis, p value,

significance level

Data-based

predictions,

decisions, and

conclusions

Critical and

creative

thinking

skill

Level 3 Practice of

Statistics Unit

7 Exercise

26

7.2 Hypothesis

testing for

the

population

mean with z

Data-based

predictions,

decisions, and

conclusions

Critical and

creative

thinking

skill

Level 3

7.3

Test for

Population

Proportion

Pool for two samples Data-based

predictions,

decisions, and

conclusions

Critical and

creative

thinking

skill

Level 3

  453

高中数学课程图

Unit Contents Objectives Big Ideas

Core

Competenc

y

Academic

Proficiency Level Assignment Teaching Hours

7.4 Hypothesis

testing with

t

????−ͳ=??

−??Ͳ

??Ȁ ??

Data-based

predictions,

decisions, and

conclusions

Critical and

creative

thinking

skill

Level 3

7.5 Hypothesis

testing for

two sample

mean

Two sample t and

paired sample t

Data-based

predictions,

decisions, and

conclusions

Critical and

creative

thinking

skill

Level 3

7.6 Error

analysis

Type One error and

type two error,

power, calculation

Data-based

predictions,

decisions, and

conclusions

Critical and

creative

thinking

skill

Level 3

8. Inference

for Categorical

Data: ChiSquare

8.1 Chi-Square

distribution

Properties of chisquare distribution,

connection and

difference between

normal distribution

Data-based

predictions,

decisions, and

conclusions

Critical and

creative

thinking

skill

Level 3 Practice of

Statistics Unit

8 Exercise

10

8.2 Carrying

Out a ChiSquare Test

for

Goodness

of Fit

The calculation of

chi-square, testing,

degree of freedom

Data-based

predictions,

decisions, and

conclusions

Critical and

creative

thinking

skill

Level 3

博实乐“中外融通课程”

454  Unit Contents Objectives Big Ideas Core Competenc

y

Academic

Proficiency Level Assignment Teaching Hours

8.3 Setting Up

a ChiSquare Test

for

Independen

ce

Degree of freedom,

application

conditions

Data-based

predictions,

decisions, and

conclusions

Critical and

creative

thinking

skill

Level 3

8.4 Setting Up

a ChiSquare Test

for

Homogenei

ty

Degree of freedom,

application

conditions

Data-based

predictions,

decisions, and

conclusions

Critical and

creative

thinking

skill

Level 3

9. Inference

for

Quantitative

Data: Slopes

9.1 Confidence

Intervals for

the Slope of

a

Regression

Model

T calculation, degree

of freedom (two

cases)

Data-based

predictions,

decisions, and

conclusions

Critical and

creative

thinking

skill

Level 3 Practice of

Statistics Unit

9 Exercise

6

9.2 Carrying

Out a Test

for the

Slope of a

Regression

Model

t=

??ͳ−??ͳ

????ͳ

Data-based

predictions,

decisions, and

conclusions

Critical and

creative

thinking

skill

Level 3

Review AP exam review Past papers 60

  455

高中数学课程图

4 Assessment

4.1 External Assessment Objectives

Test Paper Number of questions Weight (%) (Duration)

Part I: Multiple-choice

Questions (MCQ)

40 50% 90 minutes

Part II: Free-response

Questions (FRQ)

6 50% 90 minutes

4.2 Exam Weighting for the Multiple-Choice Section of the AP Exam

Units Exam Weighting

Unit 1: Exploring One-Variable Data 15–23%

Unit 2: Exploring Two-Variable Data 5–7%

Unit 3: Collecting Data 12–15%

Unit 4: Probability, Random Variables, and Probability Distributions

10–20%

Unit 5: Sampling Distributions 7–12%

Unit 6: Inference for Categorical Data: Proportions 12–15%

Unit 7: Inference for Quantitative Data: Means 10–18%

Unit 8: Inference for Categorical Data: Chi-Square 2–5%

Unit 9: Inference for Quantitative Data: Slopes 2–5%

4.3 Internal Assessment Objectives

Content Percentage Assessment Criteria Description

Exams 50% Final Exam：50%

Assignment 40% Mid-term exam： 10% ; test\\quiz 10%; Homework 20%

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

博实乐“中外融通课程”

456 

4.4 Details of External Assessment

AP External Assessment Criteria Description:

AP Score Score Range

Credit Recommendation College Grade Equivalent

5 73-100 Extremely qualified A

4 59-72 Well qualified A-, B+, B

3 44-58 Qualified B-, C+, C

2 32-43 Possibly qualified n/a

1 0-31 No recommendation n/a

4.5 Details of Internal Assessment

Homework Assessment Specifics:

Score

（Total score: 20）

Assessment Criteria

18-20

1) Each homework is done on time

2) Neat and beautiful writing.

3) Including detail process;

4) Accuracy rate is above 90%;

5) Having feedback of homework, especially for the wrong parts.

15-17

1) 85% of homework are done on time

2) Neat and beautiful writing.

3) Including detail process;

4) Accuracy rate is above 80%;

5) Having feedback of homework, especially for the wrong parts.

12-14

1) 70% of homework are done on time

2) Neat and beautiful writing.

3) Including detail process;

4) Accuracy rate is above 70%;

5) Having feedback of homework, especially for the wrong parts.

  457

高中数学课程图

Score

（Total score: 20）

Assessment Criteria

9-11

1) 60% of homework are done on time

2) Including some process;

3) Accuracy rate is above 60%;

4) Having feedback of wrong parts.

6-8

1) 50% of homework are done on time

2) Including some process;

3) Accuracy rate is above 50%;

4) Having feedback of wrong parts.

0-5 1) 50% of homework are done on time

2) Accuracy rate is above 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)

博实乐“中外融通课程”

458 

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

Textbook

1. Starnes Tabor, The Practice of Statistics sixth edition,2018 ISBN-13

9781319113339

2. Roxy Peck, Chris Oslen, Introduction to Statitstics and Data Analysis, 5th edition,

9781305115347

Website

3. https://apstudents.collegeboard.org/

Chinese and International Integrated

Curriculums for Bright Scholar

High School Section

CAP Further Mathematics

Curriculum Map

（2022 version）

Complied by Guangdong Country Garden Senior High Section

博实乐“中外融通课程”

460 

AP Curriculum Map

Subject

AP Further

mathematics

Level Syllabus Code

Course Code Credit 4 Duration 1 Year

Teaching Hours 240 Designer LiuXiaoming Completed Date Jul 9,2022

1 Course Introduction

1.1 Introduction：

This course is a continuation and deeper study of pure mathematics which can enable

the students to better cope with their college study. This course also serves a guidebook for

the Oxbridge interview training. This course basically uses the further pure mathematics of

Edexcel.

1.2 Aims

The aims of Advanced Mathematics are to:

develop their mathematical knowledge and skills in a way which encourages

confidence and provides satisfaction and enjoyment

develop an understanding of mathematical principles and an appreciation of

mathematics as a logical and coherent subject

acquire a range of mathematical skills, particularly those which will enable them to

use applications of mathematics in the context of everyday situations and of other subjects

they may be studying

develop the ability to analyse problems logically, recognise when and how a situation

may be represented mathematically, identify and interpret relevant factors and, where

necessary, select an appropriate mathematical method to solve the problem

use mathematics as a means of communication with emphasis on the use of clear

expression acquire the mathematical background necessary for further study in this or

related subjects

  461

高中数学课程图

2 Course Structure

3

2 Course Structure

3 Course Outline

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Assignment

(homework/a

ctivity/projec

t)

Teaching

periods

Differentiation

and

integration

（4 Weeks）

1. Definition of the

six hyperbolic

functions in terms

of exponentials.

Graphs and

properties of

thehyperbolic

functions.

2. Inverse

hyperbolic

functions,

1. Understand

the definitions.

2. Sketch the

graphs

3. Prove

identities

4. Calculate the

differentiation

and integration

Thinking

skills ，

calculating

capabilities

ALevel Homework

1.1 1.2. 1.3,

1.4 1.5 1.6

1.7.1.8

Chapter

revision

24

Further mathematics

Hyperbolic

functions

Complex

number

Ordinary

differential

equation

Vectors

Matrices

1. Functions

2. derivatives

3. integral

1. Demoivre’s

theorem

2. nth root

3. Loci of

argand

diagram

5. First order

6. Second order

7. substitution

8. reduction

1. Plane equation

2. Cross product

3. Distance between

skew lines

2. Inverse of matrix

3. Eigen value and

eigen vectors

4. Diagonalization

Miscellaneous

1.coordinate

system

2.rational functions

3. summing series

4. induction

5.numerical

methods

1. reduction

博实乐“中外融通课程”

462 3 Course Outline

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Assignment

(homework/act

ivity/project)

Teaching

periods

Differentiatio

n and

integration

（4 Weeks）

1. Definition of the six hyperbolic functions in

terms of exponentials.

Graphs and properties of thehyperbolic functions.

2. Inverse hyperbolic functions, theirgraphs,

properties and logarithmicequivalents.

3. Differentiation of hyperbolic functions and

expressions involvingthem.

4. Differentiation of inverse functions,including

trigonometric andhyperbolic functions.

5. Integration of hyperbolic functionsand

expressions involving them.

6. Integration of inverse trigonometricand

hyperbolic functions.

7. Integration using hyperbolic andtrigonometric

substitutions

8. Use of substitution for integralsinvolving

quadratic surds.

1. Understand the

definitions.

2. Sketch the graphs

3. Prove identities

4. Calculate the

differentiation and

integration

Thinking

skills，

calculating

capabilitie

ALevel Homework

1.1 1.2. 1.3, 1.4

1.5 1.6 1.7.1.8

Chapter

revision

24

  463

高中数学课程图

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Assignment

(homework/act

ivity/project)

Teaching

periods

Coordinate

systems(2

weeks）

1. Cartesian equations for the parabolaand

rectangular hyperbola

2. Idea of parametric equation forparabola and

rectangular hyperbola

3. The focus-directrix property of theparabola.

4. Tangents and normals to thesecurves.

5. Cartesian and parametric equationsfor the

ellipse and hyperbola

6. The focus-directrix properties ofthe ellipse and

hyperbola, includingthe eccentricity.

Simple loci problems.

1. Plot and sketch a

curve parametrically

2. Equations

conversions of parabola,

hyberbola, ecllipse

3. Calculate eccentricity

4. Find the tangents and

normals.

Thinking

skills，

calculating

capabilities

ALevel Homework

2.1.2.2

2.3.2.4 2.5

Chapter

revision

12

Complex

numbers

(4 weeks)

1. Definition of complex numbers inthe form a+

ibandrcosθ + irsin θ.

2. Sum, product and quotient ofcomplex numbers.

3. Geometrical representation ofcomplex numbers

in the Arganddiagram.Geometrical representation

ofsums, products and quotients ofcomplex

numbers.

4. Euler’s relation eiθ= cos θ + i sin θ.

5. De Moivre’s theorem and itsapplication to

trigonometricidentities and to roots of a

1. understand the

complex conjugate

2. Understand the

argand diagram

3. Understand the

modulus and argument

4. Express in

exponential form

5. Understand

Demivre’s law

Thinking

skills，

calculating

capabilities

ALevel Homework

3.4.. 3.5.3.6.3.9

Chapter

revision

24

博实乐“中外融通课程”

464 

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Assignment

(homework/act

ivity/project)

Teaching

periods

complexnumber

6. Loci and regions in the Arganddiagram.

6. Derive trigonometric

equations

Polynomials

and rational

functions

(2weeks)

1. Recall and use the relations between the roots

and coefficients of polynomial equations, for

equations of degree 2, 3, 4 only;

2. Use a given simple substitution to obtain an

equation whose roots are related in a simple way

to those of the original equation;

sketch graphs of simple

rational functions,

including the

determination of

oblique asymptotes, in

cases where the degree

of the numerator and

the denominator are at

most 2 (detailed plotting

of curves will not be

required, but sketches

will generally be

expected to show

significant features,

such as turning points,

asymptotes and

intersections with the

axes).

Thinking

skills，

calculating

capabilities

ALevel Homework

4.1.. 4.2

Chapter

revision

12

  465

高中数学课程图

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Assignment

(homework/act

ivity/project)

Teaching

periods

Polar

coordinates

(1weeks)

1. Understand the relations between cartesian and

polar coordinates (using the convention r>=0),

and convert equations of curves from cartesian to

polar form and vice versa;

2. Sketch simple polar curves, for 0 <θ < 2π or −π

< θ<π, or a subset of either of these intervals

(detailed plotting of curves will not be required,

but sketches will generally be expected to show

significant features, such as symmetry, the form

of the curve at the pole and least/greatest values

of r );

3. Recall the formula for the area of a sector, and

use this formula in simple cases.

1. Convert between the

polar and Cartesian

coordinates

2. Sketch curves with r

given as a function of θ

3. Find the enclosed

area

4. Find the tangents and

normals

Thinking

skills，

calculating

capabilities

ALevel Homework

5.1

Chapter

revision

6

Summation of

series

(1weeks)

1. Use the standard results for ∑r,∑r2,∑r3to find

related sums;

2.Use the method of differences to obtain the sum

of a finite series, e.g. by expressing the general

term in partial fractions;recognise, by direct

consideration of a sum to n terms, when a series

is convergent, and find the sum to infinity in such

cases.

1. Use standard results

2. Evaluate and simplify

series of the form when

f(r) is linear, quadratic

or cubic.

Thinking

skills，

calculating

capabilities

ALevel Homework

6.1. 6.2

Chapter

revision

6

博实乐“中外融通课程”

466  Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Assignment

(homework/act

ivity/project)

Teaching

periods

Mathematical

induction

(1weeks)

1.Use the method of mathematical induction to

establish a given result(questions set may involve

divisibility tests and inequalities, for example);

2. Recognise situations where conjecture based

on a limited trial followed by inductive proof is a

useful strategy, and carry this out in simple cases,

e.g. find the nth derivative of

1. Understand the

principle of induction

2. Prove results about

divisibility

3. Prove results in a

recurrence relationship

4. Prove results about

matrices

5. prove other more

difficult cases

Thinking

skills，

calculating

capabilities

ALevel Homework

7.1,7.2

Chapter

revision

6

Differential

equations

(2 weeks)

1. First order linear differentialequations of the

form ????????+Py=Q where Pand Qare functions of x.

2. The linear second order differentialequation

1. Use integrating factor

to solve problems

2. Use auxiliary

equation to solve the

second order

homogeneous

differential equations

3. Understand

complementary function

Thinking

skills，

calculating

capabilities

ALevel Homework

8.1 8.2 8.3 8.4

Chapter

revision

12

  467

高中数学课程图

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Assignment

(homework/act

ivity/project)

Teaching

periods

and particular integral

4. Use substitution to

transform equations.

Vectors

(4weeks)

1. Use the equation of a plane in any of the forms

ax + by + cz = d or r.n = p or r = a + λb + µc, and

convert equations of planes from one form to

another as necessary in solving problems;

2. Recall that the vector product a × b of two

vectors can be expressed either as |a| |b| sin θ nˆ ,

where nˆ is a unit vector, or in component form;

3. Use equations of lines and planes, together

with scalar and vector products where

appropriate, to solve problems concerning

distances, angles and intersections, including:

4. Determining whether a line lies in a plane, is

parallel to a plane or intersects a plane, and

finding the point of intersection of a line and a

plane when it exists, finding the perpendicular

distance from a point to a plane, finding the angle

between a line and a plane, and the angle between

two planes,

1. Understand vector

equation for a line and a

plane

2. Understand cross

product of two vectors

3. Understand the scalar

triple product

4. Use vectors in

problems solving

points, lines and planes

and the equivalent

Cartesian forms for the

equations of line and

planes

Thinking

skills，

calculating

capabilities ,

abstract

deduction

ALevel Homework

9.1 9.2 9.3 9.4

9.5 9.6

Chapter

revision

24

博实乐“中外融通课程”

468 

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Assignment

(homework/act

ivity/project)

Teaching

periods

finding an equation for the line of intersection of

two planes, calculating the shortest distance

between two skew lines, finding an equation for

the common perpendicular to two skew lines.

Matrices and

linear spaces

(4weeks)

1. Recall and use the axioms of a linear (vector)

space (restricted to spaces of finite dimension

over the field of real numbers only);

2. Understand the idea of linear independence,

and determine whether a given set of vectors is

dependent or independent;

3. Understand the idea of the subspace spanned

by a given set of vectors;

4. Recall that a basis for a space is a linearly

independent set of vectors that spans the space,

and determine a basis in simple cases;

5. Recall that the dimension of a space is the

number of vectors in a basis;

6. Understand the use of matrices to represent

linear transformations from Rn→Rm.

7. Understand the terms ‘column space’, ‘row

space’,‘range space’ and ‘null space’, and

1. Understand the

concept of a matrix

2. Define the zero and

identity matrices

3. Add and subtract

matrices

4. Multiply matrices

5. Calculate the

determinant of a matrix

6. Find the inverse of a

matrix

7. Find transpose,

determinants and

inverses of 3x3 matrices

8. Represent linear

transformations by 2x2

or 3x3 matrices

Thinking

skills，

calculating

capabilities ,

abstract

deduction

ALevel Homework

10.1. 10.2 10.3

10.4 10.5 10.6

Chapter

revision

24

  469

高中数学课程图

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Assignment

(homework/act

ivity/project)

Teaching

periods

determine the dimensions of, and bases for, these

spaces in simple cases;

8. Determine the rank of a square matrix, and use

(without proof) the relation between the rank, the

dimension of the null space and the order of the

matrix;

9. Use methods associated with matrices and

linear spaces in the context of the solution of a set

of linear equations;

10. Evaluate the determinant of a square matrix

and find the inverse of a non-singular matrix (2×2

and 3×3 matrices only), and recall that the

columns (or rows) of a square matrix are

independent if and only if the determinant is

non-zero;

11. Understand the terms ‘eigenvalue’ and

‘eigenvector’, as applied to square matrices;

12. Find eigenvalues and eigenvectors of 2×2 and

3×3 matrices (restricted to cases where the

eigenvalues are real and distinct);

13. Express a matrix in the form QDQ−1, where

9. Find the eigenvalues

and eigenvector of 2x2

and 3x3 matrices

10. Reduce symmetric

matrices to diagonal

form

博实乐“中外融通课程”

470  Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Assignment

(homework/act

ivity/project)

Teaching

periods

D is a diagonal matrix of eigenvalues and Q is a

matrix whose columns are eigenvectors, and use

this expression, e.g. in calculating powers of

matrices.

Numerical

Methods

(1 week)

1. Approximate location of roots

2. Iterative methods

3. Method

4. Numerical integration

problems in context

1. Understand the

method of change of

sign

2. Understand and apply

interval bisection.

3. Understand and apply

linear interpolation.

4. Understand and apply

Newton-Raphson

Thinking

skills，

calculating

capabilities

ALevel Homework

11.1 11.2

Chapter

revision

6

Revision FP1 FP2 FP3 All contents Thinking

skills，

calculating

capabilities

ALevel Past papers

form

2000-2022

84

  471

高中数学课程图

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% (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.

博实乐“中外融通课程”

472 

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.

  473

高中数学课程图

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.

5 Resources

Further mathematics: Further pure 1 2 3

‎978-1292244648，978-1292244655，978-1292244662

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