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高中数学课程图

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Core

Competency

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Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link to

TOK, IM, LP and CAS

boundary condition to determine the constant term.

 Definite integrals using

technology.

 Area of a region enclosed

by a curve y = f(x) and the

x-axis, where f(x) > 0.

HL/SL5.6

 Values of x where the gradient of a curve is zero. Solution of f′(x) = 0.

 Local maximum and minimum points.

HL/SL5.7

 Optimisation problems in

context.

HL/SL5.8

 Approximating areas using

the trapezoidal rule.

such as

increasing

or decreasing, allows

a deeper

appreciation

of the properties of the

function at

any given

point or

instant.

• Calculus is

a concise

form of

communication used

to approximate nature.

• Numerical

integration

4. Is it possible for

an area of knowledge to

describe the world

without transforming it?

5. How can the rise

in tax for plastic containers, for example

plastic bags, plastic

bottles etc be justified

using optimization?

6. Euler was able to

make important advances in mathematical

analysis before calculus

had been put on a solid

theoretical foundation

by Cauchy and others.

However, some work

was not possible until

after Cauchy’s work.

What does this suggest

about the nature of pro-

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ATL Skills

Homework, Link to

TOK, IM, LP and CAS

HL5.9

 The derivatives of sin x, cos

x, tan x, ex , lnx, xn where n

∈ℚ.

 The chain rule, product rule

and quotient rules.

 Related rates of change.

HL5.10

 The second derivative.

 Use of second derivative

test to distinguish between a

maximum and a minimum

point.

HL5.11

 Definite and indefinite integration of xn where n∈ℚ,

including n=−1, sin x, cos x,

1/cos2x and ex .

 Integration by inspection, or

can be used

to approximate areas

in the physical world.

• Optimization of a

function

allows us to

find the

largest or

smallest

value that a

function can

take in

general and

can be applied to a

specific set

of conditions to

solve probgress and development in mathematics? How might this be simi- lar/different to the na- ture of progress and development in other areas of knowledge? 7. Music can be ex- pressed using mathe- matics. Does this mean that music is mathe- matical/that mathemat- ics is musical? 8. What is the role of convention in mathe- matics? Is this similar or different to the role of convention in other areas of knowledge? 9. In what ways do values affect our repre- sentations of the world,

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Homework, Link to

TOK, IM, LP and CAS

substitution of the form:

∫ f(g(x))g′(x)dx.

HL5.12

 Area of the region enclosed

by a curve and the x or

y-axes in a given interval.

 Volumes of revolution

about the x- axis or y- axis.



HL5.13

 Kinematic problems involving displacement s, velocity v and acceleration a.

HL5.14

 Setting up a model/differential equation from

a context.

 Solving by separation of

variables.

lems.

• Maximum

and minimum points

help to

solve optimization

problems.

• The area

under a

function on

a graph has

a meaning

and has

applications

in space and

time.

• Kinematics allows

us to describe the

motion and

for example in statistics,

maps, visual images or

diagrams?

10. To what extent is

certainty attainable in

mathematics? Is certainty attainable, or

desirable, in other areas

of knowledge?

11. How have notable

individuals such as

Euler shaped the development of mathematics

as an area of knowledge?

International-mindedness:

1. Attempts by Indian mathematicians

(500-1000 CE) to explain division by zero.

2. The successful

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Level

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Periods

ATL Skills

Homework, Link to

TOK, IM, LP and CAS

HL5.15

 Slope fields and their diagrams.

HL5.16

 Euler’s method for finding

the approximate solution to

first order differential equations.

 Numerical solution of

dy/dx=f(x,y).

 Numerical solution of the

coupled system dx/dt=

f1(x,y,t) and dy/dt =

f2(x,y,t).

HL5.17

 Phase portrait for the solutions of coupled differential

equations of the form:

dx/dt= ax + by

dy/dt= cx + dy.

direction of

objects in

closed systems in

terms of

displacement, velocity, and

acceleration.

• Many

physical

phenomena

can be

modelled

using differential equations and

analytic and

numeric

methods can

be used to

calculation of the volume of a pyramidal

frustrum by ancient

Egyptians (the Egyptian

Moscow mathematical

papyrus).

3. Accurate calculation of the volume of a

cylinder by Chinese

mathematician Liu Hui;

use of infinitesimals by

Greek geometers; Ibn Al

Haytham, the first

mathematician to calculate the integral of a

function in order to find

the volume of a

paraboloid.

4. Does the inclusion

of kinematics as core

mathematics reflect a

particular cultural heri-

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Level

Teaching

Periods

ATL Skills

Homework, Link to

TOK, IM, LP and CAS

 Qualitative analysis of future paths for distinct, real,

complex and imaginary eigenvalues.

 Sketching trajectories and

using phase portraits to

identify key features such as

equilibrium points, stable

populations and saddle

points.

HL5.18

Solutions of d2x/dt2=f(x, dx/dt, t)

by Euler’s method.

calculate

optimum

quantities.

• Phase

portraits

enable us to

visualize the

behavior of

dynamic

systems.

tage? Who decides what

is mathematics?

Link to other subjects:

1. Marginal cost,

marginal revenue, marginal profit, market

structures (economics);

kinematics, induced emf

and simple harmonic

motion (physics); interpreting the gradient of a

curve (chemistry).

2. Instantaneous

velocity and optics,

equipotential surfaces

(physics); price elasticity (economics).

3. Velocity-time and

acceleration-time graphs

(physics and sports exercise and health science).

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Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link to

TOK, IM, LP and CAS

4. Displacement-time

and velocity-time graphs

and simple harmonic

motion graphs (physics).

5. Kinematics (physics); allocative efficiency (economics).

6. Uniform circular

motion and induced emf

(physics).

7. Simple harmonic

motion (physics).

Homework:

Exercises from the text

books or questions from

the IB exams. Sometimes, may be a summary of what have

learnt.

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Unit/

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Proficiency

Level

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Periods

ATL Skills

Homework, Link to

TOK, IM, LP and CAS

Week

76

~

Week

80

Internal

Assesssessment

(IA)

And

Review

Internal Assessment (IA)

And Review

It enables

students to

demonstrate

the application of their

skills and

knowledge

and to pursue their

personal

interests

without the

time limitations.

Mathematical

modeling，

Data analysis，

Logical reasoning

3 60 Creative

thinking,

Critical

thinking,

Reflection,

Information

literacy

Homework: students

are asked to submit a

mathematical essay

about 12-20 pages.

博实乐“中外融通课程”

150 

4 Assessment

4.1 IB Assessment

(1) Internal Assessment (20%)

Mathematical exploration essay with 12-20 pages.

(2) External Assessment (80%)

Paper 1：Fundamental–30%

Paper 2：Extension–30%

Paper 3：Comprehensive–20%

4.2 In-school Assessment

(1) Formative Assessment

Homework, midterm examination and final term examination

(2) Summative Assessment

No

5 Resources

[1] (HL)Mathematics: Application and Interpretation for the IB Diploma(Pearson)

[2] (SL)Mathematics: Application and Interpretation for the IB Diploma(Pearson)

[3] (HL&SL) Mathematics: Application and Interpretation for the IB Diploma(Oxford)

[4] Mathematics Standard Level for the IB Diploma by Paul Fannon, Vesna Kadelburg,

BenWoolley and Stephen Ward.

[5] Mathematics Higher Level for the IB Diploma by Paul Fannon, Vesna Kadelburg,

BenWoolley and Stephen Ward.

[6] Mathematics Higher Level Core Paperback (IBDP press) by Fabio Cirrito

[7] Mathematics Standard Level Core Paperback (IBDP press) by Fabio Cirrito

[8] Higher lever Mathematics 2012 edition (Pearson) by Wazir, Ibrahim.

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高中数学课程图

[9] Standard lever Mathematics 2012 edition (Pearson) by Wazir, Ibrahim.

[10] Mathematics Higher Level(Core). ISBN:1 876659 11 4

[11] IB past paper and question bank

[12] www.myib.org

[13] http://10.166.1.163/( 广东碧桂园学校教学资源网 )

[14] http://www.turnitin.com/zh_hans/home

[15] http://education.ti.com

[16] https://bgy.managebac.com/login

[17] www.khanacademy.org

[18] www.mathdl.org

[19] www.mathsisfun.com

[20] https://ibmathsresources.com

[21] https://internationalbaccalaureate.force.com/

[22] http://web.b.ebscohost.com/

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill)

Key

concept

Related

Concept

Global

context

Statement

of Inquiry

ATL skills

IB learner

profile&Core

competence

Academic

proficiency

Level

Subject

objectives

Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

MYP Curriculum Mapping

Subject Physics Grade G1&G2 Level SL

Course Code Credit 16 Duration 2 Years

Teaching Periods 320 Contributor

Li Panfang

W a n g j u n c h a o

Yangzhezhen

Jiang Xiaohan

Start from 2023.9

1 Course Introduction

1.1 Introduction

The MYP physics curriculum aims to build on what students learn and do in the PYP

and other student-centred programmes of primary education. There are no prior formal

learning requirements. The main approach to teaching and learning physics is through

structured inquiry in the context of interdisciplinary units. Students are encouraged

to investigate physics by formulating their own questions and finding answers to those

questions, including through research and experimentation. Scientific inquiry enables

students to develop a way of thinking and a set of skills and processes that they can use to

confidently tackle the internal assessment component of DP physics. Moreover, the MYP

physics objectives and assessment criteria A-D are aligned with the DP physics objectives

and internal assessment criteria, supporting the smooth transition from the MYP to the DP.

The aims of all MYP subjects state what a teacher may expect to teach and what a

student may expect to experience and learn. These aims suggest how the student may be

changed by the learning experience.

1.2 Aims

The aims of all MYP subjects state what a teacher may expect to teach and what a

student may expect to experience and learn. These aims suggest how the student may be

changed by the learning experience.

Chinese and International Integrated

Curriculums for Bright Scholar

High School Section

CDP Math AA SL

Curriculum Map

（2022 version）

Complied by Guangdong Country Garden Senior High Section

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高中数学课程图

DP Curriculum Mapping

Subject DP Math AA SL Level G3&G4 Syllabus Code

Course Code Credit 14 Duration 2 years

Teaching Periods 320 Designer Zeng Dehua Completed Date 2022.9

1 Course Introduction

1.1 Introduction

Mathematics has been described as the study of structure, order and relation that has

evolved from the practices of counting, measuring and describing objects. Mathematics

provides a unique language to describe, explore and communicate the nature of the world

we live in as well as being a constantly building body of knowledge and truth in itself that is

distinctive in its certainty. These two aspects of mathematics, a discipline that is studied for

its intrinsic pleasure and a means to explore and understand the world we live in, are both

separate yet closely linked.

Mathematics is driven by abstract concepts and generalization. This mathematics is

drawn out of ideas, and develops through linking these ideas and developing new ones.

These mathematical ideas may have no immediate practical application. Doing such

mathematics is about digging deeper to increase mathematical knowledge and truth. The

new knowledge is presented in the form of theorems that have been built from axioms and

logical mathematical arguments and a theorem is only accepted as true when it has been

proven. The body of knowledge that makes up mathematics is not fixed; it has grown during

human history and is growing at an increasing rate.

The side of mathematics that is based on describing our world and solving practical

problems is often carried out in the context of another area of study. Mathematics is used

in a diverse range of disciplines as both a language and a tool to explore the universe;

alongside this its applications include analyzing trends, making predictions, quantifying

risk, exploring relationships and interdependence.

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154 

1.2 Aims

enjoy mathematics, and develop an appreciation of the elegance and power of

mathematics.

develop an understanding of the principles and nature of mathematics.

communicate clearly and confidently in a variety of contexts.

develop logical, critical and creative thinking, and patience and persistence in

problem-solving.

employ and refine their powers of abstraction and generalization.

apply and transfer skills to alternative situations, to other areas of knowledge and to

future developments.

appreciate how developments in technology and mathematics have influenced each

other.

appreciate the moral, social and ethical implications arising from the work of

mathematicians and the applications of mathematics.

appreciate the international dimension in mathematics through an awareness of the

universality of mathematics and its multicultural and

historical perspectives.

appreciate the contribution of mathematics to other disciplines, and as a particular

“area of knowledge” in the TOK course.

2 Course Structure

Math AA SL

Topic 1

Number and

Algebra

Topic 2

Functions

Topic 3

Geometry and

Trigonometry

Topic 4

Probability

and statistics

Topic 5

Calculs

IA

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高中数学课程图

3 Course outline

G3

3 Course outline

Timeline

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

G3

Week1~

Week 9

Number

and

Algebra

HL/SL1.1

 Operations with numbers in the form a ×10k

where 1 ≤ a < 10 and k is

an integer.

HL/SL1.2

 Arithmetic sequences

and series.

 Use of the formulae for

the nth term and the sum

of the first n terms of the

sequence.

 Use of sigma notation

for sums of arithmetic

sequences.

 Applications.

 Analysis, interpretation

Problem solving is central to learning mathematics and involves the

acquisition of mathematical skills and concepts in a wide range of

situations, including

non-routine, open-ended

and real-world problems. Having followed a

DP mathematics course,

students will be expected to demonstrate

the following: 1.

Knowledge and understanding: Recall, select

and use their knowledge

Logical

reasoning,

Mathematical

operations,

Mathematical

abstraction

2 52 Creative

thinking,

Reflection,

Information

literacy

TOK:

1. Do the names

that we give things

impact how we understand them? For

instance, what is the

impact of the fact

that some large

numbers are named,

such as the googol

and the googolplex,

while others are

represented in this

form?

2. Is all knowledge concerned with

identification and

3 Course outline

Timeline

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

G3

Week1~

Week 9

Number

and

Algebra

HL/SL1.1

 Operations with numbers in the form a ×10k

where 1 ≤ a < 10 and k is

an integer.

HL/SL1.2

 Arithmetic sequences

and series.

 Use of the formulae for

the nth term and the sum

of the first n terms of the

sequence.

 Use of sigma notation

for sums of arithmetic

sequences.

 Applications.

 Analysis, interpretation

Problem solving is central to learning mathematics and involves the

acquisition of mathematical skills and concepts in a wide range of

situations, including

non-routine, open-ended

and real-world problems. Having followed a

DP mathematics course,

students will be expected to demonstrate

the following: 1.

Knowledge and understanding: Recall, select

and use their knowledge

Logical

reasoning,

Mathematical

operations,

Mathematical

abstraction

2 52 Creative

thinking,

Reflection,

Information

literacy

TOK:

1. Do the names

that we give things

impact how we understand them? For

instance, what is the

impact of the fact

that some large

numbers are named,

such as the googol

and the googolplex,

while others are

represented in this

form?

2. Is all knowledge concerned with

identification and

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Timeline

Unit/

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Topic

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Core

Competency

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Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

and prediction where a

model is not perfectly

arithmetic in real life.

HL/SL1.3

 Geometric sequences

and series.

 Use of the formulae for

the nth term and the sum

of the first n terms of the

sequence.

 Use of sigma notation

for the sums of geometric

sequences.

 Applications.

HL/SL 1.4

 Financial applications

of geometric sequences

and series:

 compound interest

 annual depreciation.

of mathematical facts,

concepts and techniques

in a variety of familiar

and unfamiliar contexts.

2. Problem solving:

Recall, select and use

their knowledge of mathematical skills, results

and models in both

abstract and real-world

contexts to solve problems. 3. Communication

and interpretation:

Transform common

realistic contexts into

mathematics; comment

on the context; sketch or

draw mathematical

diagrams, graphs or

constructions both on

use of patterns?

Consider Fibonacci

numbers and connections with the

golden ratio.

3. How do

mathematicians

reconcile the fact

that some conclusions seem to conflict with our intuitions? Consider for

instance that a finite

area can be bounded

by an infinite perimeter.

4. How have

technological advances affected the

nature and practice

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Timeline

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

HL/SL 1.5

 Laws of exponents with

integer exponents.

 Introduction to logarithms with base 10 and e.

 Numerical evaluation

of logarithms using technology.

HL/SL 1.6

 Simple deductive

proof, numerical and algebraic; how to lay out a

left-hand side to

right-hand side(LHS to

RHS) proof.

 The symbols and notation for equality and identity.

HL/SL 1.7

 Laws of exponents with

paper and using technology; record methods,

solutions and conclusions using standardized

notation; use appropriate notation and terminology. 4. Technology:

Use technology accurately, appropriately and

efficiently both to explore new ideas and to

solve problems. 5. Reasoning: Construct mathematical arguments

through use of precise

statements, logical deduction and inference

and by the manipulation

of mathematical expressions. 6. Inquiry apof mathematics? Consider the use of financial packages for instance. 5. Is mathematics invented or discov- ered? For instance, consider the number e or logarithms–did they already exist before man defined them? (This topic is an opportunity for teachers to generate reflection on “the nature of mathemat- ics”). 6. Is mathemati- cal reasoning dif- ferent from scien-

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Timeline

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

rational exponents.

 Laws of logarithms

log axy = log a x + log a y

log a(x/y)= log a x − log a y

log a x m = mlog a x

for a, x, y > 0

 Change of base of a

logarithm

log a x = log b x/ log b a,

for a, b, x > 0

 Solving exponential

equations, including using

logarithms.

HL/SL 1.8.0

 Sum of infinite convergent geometric sequences.

HL/SL 1.8.1

 The concept and

representation of set.

proaches: Investigate

unfamiliar situations,

both abstract and from

the real world, involving organizing and analyzing information,

making conjectures,

drawing conclusions,

and testing their validity

tific reasoning, or

reasoning in other

areas of knowledge?

7. What role

does language play

in the accumulation

and sharing of

knowledge in

mathematics? Consider for example

that when mathematicians talk about

“imaginary” or

“real” solutions they

are using precise

technical terms that

do not have the

same meaning as the

everyday terms.

8. What is meant

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Timeline

Unit/

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Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

Through examples, understand the meaning of

set, understand the element and set \"belong to\".

For specific problems, can

depict sets with symbolic

language on the basis of

natural language and

graphic language. In specific situations, understand the meaning of the

complete set and the

empty set.

 The basic relationships of the set. Understand the meaning of inclusion and equality between sets and be able to

identify subsets of a given

set.

by the terms “law”

and “theory” in

mathematics. How

does this compare to

how these terms are

used in different

areas of knowledge?

9. Is it possible

to know about

things of which we

can have no experience, such as infinity?

10. Mathematics

can be used successfully to model

real-world processes. Is this because mathematics

was created to mir-

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Timeline

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

 Basic operation of

set. Understand the

meaning of union and

intersection of two sets,

and can solve the union

and of two sets Intersection. Understand the

meaning of the complement of a subset in a given set, can solve the complement of a given subset.

Venn diagrams can be

used to express the basic

relations and operations

of sets. And experience

the role of graphics in

understanding abstract

concepts.

HL/SL 1.8.2

ror the world or

because the world is

intrinsically mathematical?

International-mindedness:

1. The history of

number from

Sumerians and its

development to the

present Arabic system.

2. Aryabhatta is

sometimes considered the “father of

algebra”–compare

with alKhawarizmi;

the use of several

alphabets in mathe-

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Timeline

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

 Necessary conditions, sufficient conditions, sufficient and necessary conditions. ①

Through sorting out typical mathematical propositions, understand the

meaning of necessary

conditions, comprehensibility the relation between

quality theorem and necessary conditions. ②

Understand the meaning

of sufficient conditions

and judgment by combing

typical mathematical

propositions the relation

between definite theorem

and sufficient condition.

③ Through sorting out

matical notation (for

example the use of

capital sigma for the

sum).

3. The chess

legend (Sissa ibn

Dahir)

4. Do all societies view investment

and interest in the

same way?

Links to other

subjects:

1. Chemistry

(Avogadro’s number); physics (order

of magnitude); biology (microscopic

measurements);

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Timeline

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

the typical mathematical

propositions, understand

the meaning of sufficient

and necessary conditions,

understand the number

the relationship between

learning definition and

necessary and sufficient

conditions.

 Universal and existential quantifiers. Understand the meaning of universal quantifiers and

existential quantifiers

through known mathematical examples.

 Negation of universal quantifier proposition

and existential quantifier

proposition. ① Can corsciences (uncer- tainty and precision of measurement) 2. Radioactive decay, nuclear physics, charging and discharging capacitors (physics). 3. Loans and repayments (eco- nomics and business management). 4. Calculation of pH and buffer solu- tions (chemistry). 5. Order of mag- nitudes (physics); uncertainty and precision of meas- urement (sciences).

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Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

rectly use existential

quantifiers to negate universal quantifier propositions. ② Can correctly

use universal quantifiers

to negate existential quantifier propositions.

HL/SL 1.8.3

 The properties of

equality and inequality.

Sort out the properties of

equality, understand the

concept of inequality,

master the properties of

inequality.

 Basic inequality. Understand the basic inequality ƒ„ ≤ ƒ൅„ʹ ǡ ሺƒǡ „ ≥

Ͳሻ.Combined with spe6. Exchange rates (economics), loans (business management). 7. pH, buffer calculations and finding activation energy from ex- perimental data (chemistry). 8. Stochastic processes, stock market values and trends (business management). Homework: Exercises from the text books or ques- tions from the IB exams. Sometimes,

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cific examples, can solve

simple maxima or minima

problems.

may be a summary

of what have learnt.

Week10~

week 24

Function HL/SL 2.1  Different forms

of the equation of

straight line.

 Gradient; intercepts.

 Lines with gradients m1and m2.

 Parallel lines

m1=m2.

 Perpendicular

lines m1×m2=−1.

• Different representations of functions,

symbolically and visually as graphs, equations and tables

provide different ways

to communicate mathematical relationships.

• The parameters in a

function or equation

may correspond to notable geometrical features of a graph

and can represent physMathe- matical abstrac- tion, Mathe- matical modeling, Logical reasoning, Mathe- matical operations 2 43 Critical thinking, Transfer, Communi- cation, Re- flection, Information literacy TOK: 1. Descartes showed that geo- metric problems could be solved algebraically and vice versa. What does this tell us about mathematical representation and mathematical knowledge? 2. Do you think mathematics or

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HL/SL 2.2

 Concept of a

function, domain,

range and graph.

 Function notation, for example f(x),

v(t), C(n).

 The concept of a

function as a mathematical model.

 Informal concept

that an inverse function

reverses or undoes the

effect of a function.

 Inverse function

as a reflection in the

line y=x, and the notation f-1(x).

ical quantities in spatial

dimensions.

• Moving between different forms to

represent functions

allows for deeper understanding and provides different approaches to problem

solving.

• Our spatial frame of

reference affects the

visible part of a function

and by changing this

“window” can

show more or less of the

function to best suit our

needs.

• Changing the parameters of a trigonometric

logic should be

classified as a language?

3. Does studying

the graph of a function contain the

same level of

mathematical rigour

as studying the

function algebraically? What are the

advantages and

disadvantages of

having different

forms and symbolic

language in mathematics?

4. What role do

models play in

mathematics? Do

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HL/SL 2.3

 Creating a sketch

from information given

or a context, including

transferring a graph

from screen to paper.

 Using technology

to graph functions including their sums and

differences.

HL/SL 2.4

 Determine key

features of the graphs

 Finding the point

of intersection of two

curves or lines using

technology.

function changes the

position, orientation and

shape of the corresponding graph.

• Different representations facilitate modelling and interpretation

of physical, social,

economic and

mathematical phenomena, which support

solving real-life problems.

• Technology plays a

key role in allowing

humans to represent the

real world as a model

and to quantify the appropriateness of the

model.

they play a different

role in mathematics

compared to their

role in other areas of

knowledge?

5. What is it

about models in

mathematics that

makes them effective? Is simplicity a

desirable characteristic in models?

6. Is mathematics

independent of culture? To what extent

are we aware of the

impact of culture on

what we believe or

know?

7. Does the ap-

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HL/SL 2.5

 Composite function

 Identity function.

Finding the inverse

function f-1(x).

HL/SL 2.6

 The quadratic

function

f(x)=ax2+bx+c: its

graph, y -intercept

(0,c). Axis of symmetry.

 The form

f(x)=a(x−p)(x−q),

x-intercepts (p,0) and

(q,0).

 The form

f(x)=a(x−h)2+k, vertex

• Extending results from

a specific case to a general form and making

connections between

related

functions allows us to

better understand physical phenomena.

• Generalization provides an insight into

variation and allows us

to access ideas such as

half-life and scaling

logarithmically to adapt

theoretical models and

solve complex real-life

problems.

• Considering the reasonableness and validity

of results helps us to

plicability of

knowledge vary

across the different

areas of knowledge?

What would the

implications be if

the value of all

knowledge was

measured solely in

terms of its applicability?

International-mindedness:

1. The development of functions by

Rene Descartes

(France), Gottfried

Wilhelm Leibnitz

(Germany) and

Leonhard Euler

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(h,k).

HL/SL 2.7.1

 Dichotomy and

approximate solution of

equation. ① Understand

the relationship between

the zero of the function

and the solution of the

equation.

 Combined with the

characteristics of specific

continuous function and

its image, understand the

existence theorem of

function zero, explore the

idea of using dichotomy

to find the approximate

make informed, unbiased decisions. (Switzerland); the notation for functions was developed

by a number of different mathematicians in the 17th and

18th centuries–how

did the notation we

use today become

internationally accepted?

2. Bourbaki

group analytical

approach versus the

Mandelbrot visual

approach.

3. The Babylonian method of multiplication:???? ൌ

ሺ??൅??ሻ??−????−????

??

. Sulba

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solution of the equation

and can draw the block

diagram of the program,

can use the calculation

tool to find the approximate solution of the equation with dichotomy,

understand that the approximate solution of the

equation with dichotomy

is general.

Sutras in ancient

India and the Bakhshali Manuscript

contained an algebraic formula for

solving quadratic

equations.

Links to other

subjects:

1. Exchange

rates and price and

income elasticity,

demand and supply

curves (economics);

graphical analysis in

experimental work

(sciences).

2. Sketching and

interpreting graphs

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HL/SL 2.7

 Solution of quadratic equations and

inequalities

 The quadratic

formula.

 The discriminant

Δ=b2−4ac and the nature of the roots, that is,

two distinct real roots,

two equal real roots, no

real roots.

HL/SL 2.8

 The reciprocal

function f(x)=1/x,x≠0:

its graph and

self-inverse nature.

(sciences, geography, economics).

3. Identification

and interpretation of

key features of

graphs (sciences,

geography, economics); production

possibilities curve

model, market equilibrium (economics).

4. Population

growth, spread of a

virus (biology);

radioactive decay

and half-life, X-ray

attenuation, cooling

of a liquid, kinematics, simple har-

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 Rational functions of the form

f(x)=ax+b/cx+d and

their graphs.

 Equations of

vertical and horizontal

asymptotes.

HL/SL 2.9

 Exponential

functions and their

graphs: f(x)=ax, a>0,

f(x)=ex

 Logarithmic

functions and their

graphs: f(x)=logax,

x>0, f(x)=lnx, x>0.

HL/SL 2.10

 Solving equamonic motion, pro- jectile motion, in- verse square law (physics); com- pound interest, de- preciation (business management); the circular flow of income model (economics); the equilibrium law and rates of reaction (chemistry); oppor- tunities to model as part of experimental work (science). 5. opportunities to model as part of experimental work (science).

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tions, both graphically

and analytically.

 Use of technology to solve a variety

of equations, including those where there

is no appropriate analytic approach.

 Applications of

graphing skills and

solving equations that

relate to real-life situations.

6. Shifting of

supply and demand

curves (economics);

electromagnetic

induction (physics).

7. Half-life

(chemistry and

physics); AC circuits and waves

(physics); the Gini

coefficient and the

Lorenz curve, and

progressive, regressive and proportional taxes, the

J-curve (economics).

8. pH semi-log

curves and finding

activation energy

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HL/SL 2.11

 Transformations

of graphs.

 Translations:

y=f(x)+b;y=f(x−a).

 Reflections (in

both axes):

y=−f(x);y=f(−x).

 Vertical stretch

with scale factor p:

y=pf(x).

Horizontal stretch with

scale factor

1/q:y=f(qx).

 Composite

transformations.

from experimental

data (chemistry);

exponential decay

(physics); experimental work (sciences).

Homework:

Exercises from the

text books or questions from the IB

exams. Sometimes,

may be a summary

of what have learnt.

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Week25~

Week 40

Geometry and

Trigonometry

HL/SL 3.1

 The distance

between two points in

three dimensional

space, and their midpoint.

 Volume and

surface area of

three-dimensional

solids including

right-pyramid, right

cone, sphere, hemisphere and combinations of these solids.

 The size of an

angle between two

intersecting lines or

between a line and a

plane

• The properties of

shapes are highly dependent on the dimension they occupy in

space.

• Volume and surface

area of shapes are determined by formulae,

or general mathematical

relationships

or rules expressed using

symbols or variables.

• The relationships between the length of the

sides and the size of the

angles in a triangle can

be used to solve many

problems involving

position, distance, angles and area.

Intuitive

imagination, Mathematical

abstraction,

Logical

reasoning,

Mathematical

modeling.

2 68 Critical

thinking,

Creative

thinking,

Transfer,

Collaboration,

Information

literacy

TOK:

1. What is an

axiomatic system?

Are axioms self

evident to everybody?

2. Is it ethical

that Pythagoras gave

his name to a theorem that may not

have been his own

creation? What criteria might we use

to make such a

judgment?

3. If the angles of

a triangle can add up

to less than 180°,

180° or more than

180°, what does this

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HL/SL 3.2

 Use of sine, cosine and tangent ratios

to find the sides and

angles of right-angled

triangles

 The sine rule:

a/sinA=b/sinB=c/sinC.

 The cosine rule:

c2=a2+b2−2abcosC;

 cosC=a2+b2−c2/2

ab .

 Area of a triangle

as 1/2absinC.

HL/SL 3.3

 Applications of

right and non-right

angled trigonometry,

including Pythagoras’s

• Different representations of trigonometric

expressions help to

simplify calculations.

• Systems of equations

often, but not always,

lead to intersection

points.

• In two dimensions, the

Voronoi diagram allows

us to navigate, path-find

or establish an optimum

position.

• Different measurement

systems can be used for

angles to facilitate ease

of calculation.

• Vectors allow us to

determine position,

change of position

tell us about the

nature of mathematical knowledge?

4. Does personal

experience play a

role in the formation

of knowledge claims

in mathematics?

Does it play a different role in

mathematics compared to other areas

of knowledge?

5. Is the division

of knowledge into

disciplines or areas

of knowledge artificial?

6. Which is the

better measure of an

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theorem.

 Angles of elevation and depression.

 Construction of

labelled diagrams from

written statements.

HL/SL 3.4

 The circle: radian

measure of angles;

length of an arc; area

of a sector.

HL/SL 3.5

 Definition of

cosθ, sinθ in terms of

the unit circle.

 Definition of

tanθ as sinθcosθ.

(movement) and force

in two and threedimensional space.

• Graph theory algorithms allow us to

represent networks and

to model complex

real-world problems.

• Matrices are a form of

notation which allow us

to show the parameters

or quantities of several

linear equations simultaneously.

angle, degrees or

radians? What criteria can/do/should

mathematicians use

to make such judgments?

7. When mathematicians and historians say that they

have explained

something, are they

using the word “explain” in the same

way?

8. Vectors are

used to solve many

problems in position

location. This can be

used to save a lost

sailor or destroy a

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 Exact values of

trigonometric ratios of

0, π/6, π/4, π/3, π/2and

their multiples.

 Extension of the

sine rule to the ambiguous case.

HL/SL3.6

 The Pythagorean

identity cos2θ+sin2θ=1.

 Double angle

identities for sine and

cosine.

 The relationship

between trigonometric

ratios.

HL/SL 3.6.1

building with a laser-guided bomb. To

what extent does

possession of

knowledge carry

with it an ethical

obligation?

9. Mathematics

and the knower:

Why are symbolic

representations of

three-dimensional

objects easier to deal

with than visual

representations?

What does this tell

us about our

knowledge of

mathematics in

other dimensions?

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 Basic

three-dimensional graph.

① Observe spatial graphics by physical objects

and computer software,

and understand the structural characteristics of

column, cone, table, ball

and simple combination,

and can use these characteristics to describe the

structure of simple objects

in real life. ② Know the

formulas for calculating

the surface area and volume of spheres, prisms,

pyramids and prisms, and

be able to use the formulas to solve simple practical problems.③ Can

10. What counts

as understanding in

mathematics? Is it

more than just getting the right answer?

International-mindedness:

1. Diagrams of

Pythagoras’ theorem

occur in early Chinese and Indian

manuscripts. The

earliest references to

trigonometry are in

Indian mathematics;

the use of triangulation to find the curvature of the Earth

in order to settle a

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draw simple space graphics (cuboid, ball, cylinder,

cone, prism and its simple

combination) with oblique

two measurement method.

 Position relation of

basic graph. ① With the

help of cuboids, on the

basis of an intuitive understanding of the position relations of space

points, lines and planes,

the definition of the position relations of space

points, lines and planes is

abstracted, and several

facts and theorems are

understood. ② Starting

from the definition and

basic facts, with the aid of

dispute between

England and France

over Newton’s gravity.

2. The use of

triangulation to find

the curvature of the

Earth in order to

settle a dispute between England and

France over Newton’s gravity.

3. Seki Takakazu

calculating π to ten

decimal places;

Hipparchus, Menelaus and Ptolemy;

why are there 360

degrees in a complete turn? Why do

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cuboids and through intuitive perception, we can

understand the relations

between straight lines,

straight lines and planes,

and the parallel and vertical relations between

planes in space, and conclude the following property theorems and prove

them.③ Starting from the

definition and basic facts,

with the aid of cuboids

and through intuitive

perception, we can understand the relationship

between straight lines,

straight lines and planes,

and the parallel and vertical relations between

we use minutes and

seconds for time?;

Links to Babylonian

mathematics.

4. The origin of

the word “sine”;

trigonometry was

developed by successive civilizations

and cultures; how is

mathematical

knowledge considered from a sociocultural perspective?

Link to other subjects:

1. Design technology; volumes of

stars and inverse

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planes in space, and conclude the judgment theorem.④Using the obtained

results to prove the simple

propositions of the position relation of basic spatial figures

HL/SL 3.7

 The circular

functions sinx, cosx,

and tanx; amplitude,

their periodic nature,

and their graphs

 Composite functions of the form

f(x)=asin(b(x+c))+d.

 Transformations.

 Real-life contexts.

square law (physics).

2. Vectors

(physics).

3. Vectors, scalars, forces and dynamics (physics);

field studies (sciences).

4. Diffraction

patterns and circular

motion (physics).

5. Vector sums,

differences and

resultants (physics).

Homework:

Exercises from the

text books or questions from the IB

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HL/SL 3.8

 Solving trigonometric equations in a

finite interval, both

graphically and analytically.

 Equations leading to quadratic equations in sinx,cosx or

tanx.

exams. Sometimes,

may be a summary

of what have learnt.

G4

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Week41~

week 60

Probability

and

Statistics

HL/SL 4.1

 Concepts of

population, sample,

random sample, discrete and continuous

data.

 Reliability of

data sources and bias

in sampling

 Interpretation

of outliers

 Sampling techniques and their effectiveness

HL/SL 4.2

 Presentation

of data (discrete

and continuous):

• Organizing,

representing, analysing

and interpreting data,

and utilizing different

statistical tools

facilitates prediction

and drawing of conclusions.

• Different statistical

techniques require justification and the identification of their limitations and

validity.

• Approximation in data

can approach the truth

but may not always

achieve it.

• Correlation and regression are powerful

Logical

reasoning，

Data

analysis，

Mathematical

operations.

2 44 Reflection,

Information

literacy,

Critical

thinking

Transfer

Collaboration,

Reflection

TOK:

1. Why have

mathematics and

statistics sometimes

been treated as

separate subjects?

How easy is it to be

misled by statistics?

Is it ever justifiable

to purposely use

statistics to mislead

others?

2. What is the

difference between

information and

data? Does “data”

mean the same thing

in different areas of

knowledge?

3. Could matheG4

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frequency distributions (tables).

 Histograms.

 Cumulative

frequency; cumulative frequency

graphs; use to find

median, quartiles,

percentiles, range

and interquartile

range (IQR).

 Production

and understanding

of box and

whisker diagrams.

HL/SL 4.3

 Measures of central tendency (mean,

tools for identifying

patterns and equivalence of systems.

Syllabus content

50 Mathematics: applications and interpretation guide

• Modelling and finding

structure in seemingly

random events facilitates prediction.

• Different probability

distributions provide a

representation of the

relationship between the

theory and

reality, allowing us to

make predictions about

what might happen.

• Statistical literacy

matics make alternative, equally true,

formulae? What

does this tell us

about mathematical

truths? Does the use

of statistics lead to

an over-emphasis on

attributes that can be

easily measured

over those that cannot?

4. Correlation

and causation–can

we have knowledge

of cause and effect

relationships given

that we can only

observe correlation?

What factors affect

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median and mode).

 Estimation of

mean from grouped

data.

 Modal class.

 Measures of dispersion (interquartile range, standard

deviation and variance).

 Effect of constant

changes on the

original data.

 Quartiles of discrete data.

HL/SL 4.4

 Linear correlation of bivariate

data.

involves identifying

reliability and validity

of samples and whole

populations in a

closed system.

• A systematic approach

to hypothesis testing

allows statistical inferences to be tested for

validity.

• Representation of

probabilities using transition matrices enables

us to efficiently predict

long-term

behaviour and outcomes.

the reliability and

validity of mathematical models in

describing real-life

phenomena?

5. To what extent

are theoretical and

experimental probabilities linked?

What is the role of

emotion in our perception of risk, for

example in business,

medicine and travel

safety?

6. Can calculation of gambling

probabilities be

considered an ethical application of

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 Pearson’s product-moment correlation coefficient, r.

 Scatter diagrams; lines of best

fit, by eye, passing

through the mean

point.

 Equation of the

regression line of y

on x.

 Use of the equation of the regression line for prediction purposes.

 Interpret the

meaning of the

parameters, a and

b, in a linear regression y=ax+b

mathematics?

Should mathematicians be held responsible for unethical applications

of their work?

7. What do we

mean by a “fair”

game? Is it fair that

casinos should make

a profit?

8. What criteria

can we use to decide

between different

models?

9. To what extent

can we trust mathematical models such

as the normal distribution? How can

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Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

HL/SL4.5

 Concepts of trial,

outcome, equally

likely outcomes,

relative frequency,

sample space (U)

and event.

 The probability of

an event A is

P(A)=n(A)/n(U).

 The complementary events A and

A′(not A).

 Expected number

of occurrences.

we know what to

include, and what to

exclude, in a model?

10. Does correlation imply causation? Mathematics

and the world.

Given that a set of

data may be approximately fitted

by a range of curves,

where would a

mathematician seek

for knowledge of

which equation is

the “true” model?

11. What are the

strengths and limitations of different

methods of data

博实乐“中外融通课程”

188 

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Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

HL/SL 4.6

 Use of Venn

diagrams, tree

diagrams, sample

space diagrams

and tables of outcomes to calculate

probabilities.

 Combined

events:

P(A∪B)=P(A)+P(

B)−P(A∩B).

Mutually exclusive events:

P(A∩B)=0.

 Conditional

probability:

P(A|B)=P(A∩B)P

(B)

collection, such as

questionnaires?

12. Mathematics

and the world: In the

absence of knowing

the value of a parameter, will an

unbiased estimator

always be better

than a biased one?

13. The central

limit theorem can be

proved mathematically (formalism),

but its truth can be

confirmed by its

applications (empiricism). What does

this suggest about

the nature and

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高中数学课程图

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Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

 Independent

events:

P(A∩B)=P(A)P(B

).

HL/SL 4.7

 Concept of

discrete random

variables and their

probability distributions.

 Expected

value (mean), for

discrete data.

 Applications.

methods of mathematics?

14. Mathematics

and the world.

Claiming brand A is

“better” on average

than brand B can

mean very little if

there is a large

overlap between the

confidence intervals

of the two means.

15. To what extent

can mathematical

models such as the

Poisson distribution

be trusted? What

role do mathematical models play in

other areas of

博实乐“中外融通课程”

190 

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Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

HL/SL 4.8

 Binomial

distribution.

 Mean and

variance of the

binomial distribution.

HL/SL 4.9

 The normal

distribution and

curve.

 Properties of

the normal distribution.

 Diagrammatic representation.

 Normal

probability calculations.

knowledge?

International-Mindedness:

1. The Kinsey

report–famous sampling techniques.

2. Discussion of

the different formulae for the same

statistical measure

(for example, variance).

3. The benefits

of sharing and analysing data from

different countries;

discussion of the

different formulae

for variance.

4. The St Pe-

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高中数学课程图

Timeline

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

 Inverse normal calculations

HL/SL 4.10

 Equation of

the regression line

of x on y.

 Use of the

equation for prediction purposes.

SL4.11

 Formal definition and use of

the formulae:

 P(A|B)=P(A

∩B)/P(B)for conditional probabilities, and

 P(A|B)=P(A)

tersburg paradox;

Chebyshev and

Pavlovsky (Russian).

5. The so-called

“Pascal’s triangle”

was known to the

Chinese mathematician Yang Hui much

earlier than Pascal.

Link to other subjects:

1. Descriptive

statistics and random samples (biology, psychology,

sports exercise and

health science, environmental systems

and societies, geog-

博实乐“中外融通课程”

192 

Timeline

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

=P(A|B′)for independent events.

HL/SL 4.12

 Standardization of normal

variables (z- values).

 Inverse normal calculations

where mean and

standard deviation

are unknown

raphy, economics;

business management); research

methodologies

(psychology).

2. Presentation of

data (sciences, individuals and societies).

3. Descriptive

statistics (sciences

and individuals and

societies); consumer

price index (economics).

4. Curves of best

fit, correlation and

causation (sciences);

scatter graphs (geography).