193

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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

5. Normally

distributed real-life

measurements and

descriptive statistics

(sciences, psychology, environmental

systems and societies).

6. Fieldwork

(biology, psychology, environmental

systems and societies, sports exercise

and health science).

7. Fieldwork

(biology, psychology, environmental

systems and societies, sports exercise

and health science,

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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

geography).

8. Data collection in field work

(biology, psychology, environmental

systems and societies, sports exercise

and health science,

geography, business

management and

design technology);

data from social

media and marketing sources (business management)

9. Data from

multiple samples in

field studies (sciences, and individuals and societies).

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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

10. Analysis of

data from field

studies (sciences

and individuals and

societies).

Homework:

Exercises from the

text books or questions from the IB

exams. Sometimes,

may be a summary

of what

have learnt.

博实乐“中外融通课程”

196 

Timeline

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

Week 61

~

Week75

Calculus

HL/SL 5.2

 Increasing and

decreasing functions.

 Graphical interHL/SL5.1 

pretation of

f′(x)>0,f′(x)=0,f′(x)<0.

Introduction to

the concept of a limit.

 Derivative

interpreted as gradient function and as

rate of change.

• Students will understand the links between

the derivative and the

rate of change and interpret the meaning of

this in context.

• Students will understand the relationship

between the integral and

area and interpret the

meaning of this in context.

• Finding patterns in the

derivatives of polynomials and their behavior, such as increasing

or decreasing, allows a

deeper appreciation of

the properties of the

function at any given

Mathematical

abstraction，

LoMathematical

operations，

Mathematical

modelinggical reasoning，

2 74

Critical

thinking,

Communication,

Organization,

Information

literacy,Transfer

,

Media literacy

TOK:

1. What value

does the knowledge

of limits have? Is

infinitesimal behaviour applicable to

real life? Is intuition

a valid way of

knowing in mathematics?

2. The seemingly

abstract concept of

calculus allows us to

create mathematical

models that permit

human feats such as

getting a man on the

Moon. What does

this tell us about the

links between

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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 5.3

 Derivative of

f(x)=axn is f′(x)=anxn-1,

n∈ℤ

 The derivative of

functions of the form

f(x)=axn+bxn-1....

 where all exponents are integers.

HL/SL 5.4

 Tangents and

normals at a given

point, and their equations.

point or instant.

• Calculus is a concise

form of communication

used to approximate

nature.

• Numerical integration

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

problems.

• Maximum and minimum points help to

mathematical models and reality?

3. In what ways

has technology impacted how knowledge is produced

and shared in

mathematics? Does

technology simply

allow us to arrange

existing knowledge

in new and different

ways, or should this

arrangement itself

be considered

knowledge?

4. Is it possible

for an area of

knowledge to describe the world

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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 5.5

 Introduction to

integration as anti-differentiation of

functions of the form

f(x)=axn+bxn-1+....,wher

e n∈ℤ , n≠−1

 Anti-differentiation with a

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.

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 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 calculate

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. Music can be

expressed using

mathematics. Does

this mean that music

is mathematical/that

mathematics is musical?

7. What is the

role of convention in

mathematics? Is this

similar or different

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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 5.6

 Derivative of

xn(n∈ℚ), sinx, cosx,

ex and lnx.

 Differentiation

of a sum and a multiple of these functions.

 The chain rule

for composite functions.

 The product

rule and quotient

rules

HL/SL 5.7

 The second

derivative.

 Graphical behaviour of functions,

optimum quantities.

• Phase portraits enable

us to visualize the behavior of dynamic systems.

to the role of convention in other

areas of knowledge?

8. In what ways

do values affect our

representations of

the world, for example in statistics,

maps, visual images

or diagrams?

9. To what extent

is certainty attainable in mathematics? Is certainty

attainable, or desirable, in other areas

of knowledge?

International-mindedness:

1. Attempts by

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200 

Timeline

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL Skills

Homework, Link

to TOK, IM, LP

and CAS

including the relationship between the

graphs of f,_f′ and f″.

HL/SL 5.8

 Local maximum and minimum

points.

 Testing for

maximum and minimum.

 Optimization.

 Points of inflexion with zero and

non-zero gradients.

HL/SL 5.9

 Kinematic

problems involving

Indian mathematicians (500-1000 CE)

to explain division

by zero.

2. The successful

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

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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

displacement s, velocity v, acceleration

a and total distance

travelled.

HL/SL 5.10

Indefinite integral of

xn(n∈ℚ),sinx,cosx,1/x

and ex.

The composites of any

of these with the linear

function ax+b.

Integration by inspection (reverse chain rule)

or by substitution for

expressions of the

form:

∫kg′(x)f(g(x))dx.

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 heritage? Who decides

what is mathematics?

Link to other subjects:

1. Marginal cost,

marginal revenue,

marginal profit,

market structures

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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 5.11

 Definite integrals, including analytical approach

 Areas of a region enclosed by a

curve y=f(x) and the

x-axis, where f(x) can

be positive or negative, without the use

of technology.

 Areas between

curves.

(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).

4. Displace-

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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

ment-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 ques-

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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

tions from the IB

exams. Sometimes,

may be a summary

of what have learnt.

Week 76

~

Week 80

Internal Assessment (IA) 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 40 Creative

thinking,

Critical

thinking,

Reflection,

Information

literacy

Homework: students are asked to

submit a mathematical essay about

12-20 pages.

  205

高中数学课程图

4 Assessment

4.1 IB Assessment

(1) Internal Assessment (20%)

Mathematical exploration essay with 12-20 pages.

(2) External Assessment (80%)

Paper 1：Fundamental–40%

Paper 2：Extension–40%

4.2 In-school Assessment

(1) Formative Assessment

Homework, midterm examination and final term examination

(2) Summative Assessment

No

5 Resources

[1] (SL)Mathematics: Analysis and Approaches for the IB Diploma(Pearson)

[2] (HL&SL) Mathematics: Analysis and Approaches for the IB Diploma(Oxford)

[3] Mathematics Standard Level for the IB Diploma.

[4] Mathematics Standard Level Core Paperback (IBDP press)

[5] Standard lever Mathematics 2012 edition (Pearson).

[6] IB past paper and question bank

[7] www.myib.org

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

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

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

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

[12] www.khanacademy.org

[13] www.mathdl.org

[14] www.mathsisfun.com

[15] https://ibmathsresources.com

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

[17] 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 HL

Curriculum Map

（2022 version）

Complied by Guangdong Country Garden Senior High Section

  207

高中数学课程图

DP Curriculum Mapping

Subject DP Math AA HL Level G3&G4 Syllabus Code

Course Code Credit 14 Duration 2 years

Teaching Periods 480 Designer Yan Chaoqun 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.

博实乐“中外融通课程”

208 

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 HL

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 Content

G3 3 Course outline

Time

line

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL

Skills

Homework, Link to

TOK, IM, LP and CAS

G3

Week

1~We

ek 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

and prediction where a model is

not perfectly arithmetic in real

life.

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 demonLogical reasoning, Mathe- matical opera- tions, Mathe- matical abstrac- tion 2 78 Creative thinking, Reflec- tion, Informa- tion liter- acy 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 identifica- tion and use of patterns? Consider Fibonacci num- bers and connections with the golden ratio.

3 Course outline

Time

line

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL

Skills

Homework, Link to

TOK, IM, LP and CAS

G3

Week

1~We

ek 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

and prediction where a model is

not perfectly arithmetic in real

life.

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 demonLogical reasoning, Mathe- matical opera- tions, Mathe- matical abstrac- tion 2 78 Creative thinking, Reflec- tion, Informa- tion liter- acy 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 identifica- tion and use of patterns? Consider Fibonacci num- bers and connections with the golden ratio.

博实乐“中外融通课程”

210  Time

line

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL

Skills

Homework, Link to

TOK, IM, LP and CAS

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.

HL/SL 1.5

 Laws of exponents with

integer exponents.

 Introduction to logarithms

with base 10 and e.

 Numerical evaluation of

strate the following:

1. Knowledge and

understanding: Recall, select and use

their knowledge 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:

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 of

mathematics? Consider

the use of financial packages for instance.

5. Is mathematics invented or discovered? For

instance, consider the

number e or logarithms–did they already

exist before man defined

them? (This topic is an

  211

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line

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL

Skills

Homework, Link to

TOK, IM, LP and CAS

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

rational exponents.

 Laws of logarithms

log a xy = 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

Transform common

realistic contexts

into mathematics;

comment on the

context; sketch or

draw mathematical

diagrams, graphs or

constructions both

on 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

opportunity for teachers to

generate reflection on “the

nature of mathematics”).

6. Is mathematical

reasoning different from

scientific 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 by

博实乐“中外融通课程”

212  Time

line

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL

Skills

Homework, Link to

TOK, IM, LP and CAS

 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. 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 beideas and to solve problems. 5. Rea- soning: Construct mathematical argu- ments through use of precise state- ments, logical de- duction and infe- rence and by the manipulation of mathematical ex- pressions. 6. Inquiry approaches: Inves- tigate unfamiliar situations, both abstract and from the real world, in- volving organizing and analyzing in- formation, making conjectures, draw- the terms “law” and “the- ory” in mathematics. How does this compare to how these terms are used in different areas of knowl- edge? 9. Is it possible to know about things of which we can have no experience, such as infin- ity? 10. How does language shape knowledge? For example do the words “imaginary” and “com- plex” make the concepts more difficult than if they had different names? 11. Why might it be said that eiπ +1 = 0 is beauti- ful? What is the place of

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line

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL

Skills

Homework, Link to

TOK, IM, LP and CAS

tween sets and be able to identify subsets of a given set.

 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

 Necessary conditions,

sufficient conditions, sufficient

and necessary conditions. ①

ing conclusions, and

testing their validity

beauty and elegance in

mathematics? What about

the place of creativity?

12. Given the many

applications of matrices in

this course, consider the

fact that mathematicians

marvel at some of the

deep connections between

disparate parts of their

subject. Is this evidence

for a simple underlying

mathematical reality?

Mathematics, sense, perception and reason–if we

can find solutions of

higher dimensions, can we

reason that these spaces

exist beyond our sense

perception?

13. Mathematics can be

博实乐“中外融通课程”

214  Time

line

Unit/

Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Teaching

Periods

ATL

Skills

Homework, Link to

TOK, IM, LP and CAS

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 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

used successfully to

model real-world processes. Is this because

mathematics was created

to mirror 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

mathematical notation (for

example the use of capital

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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 correctly 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.

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);

sciences (uncertainty and

precision of measurement)

2. Radioactive decay,

nuclear physics, charging

and discharging capacitors

(physics).

3. Loans and repayments (economics and

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 Basic inequality. Understand the basic inequality

????≤??൅?? ʹ ǡ ሺ??ǡ??≥

Ͳሻ.Combined with specific

examples, can solve simple

maxima or minima problems.

HL 1.9

 The binomial theorem;

expansion of (a+b)n, n∈??.

 Use of Pascal’s triangle

and nCr.

HL 1.10

 Counting principles, including permutations and combinations.

 Extension of the binomial

theorem of fractional and negative indices, ie (a+b)n, n∈??.

HL1.11

 Partial fractions.

business management).

4. Calculation of pH

and buffer solutions

(chemistry).

5. Order of magnitudes

(physics); uncertainty and

precision of measurement

(sciences).

6. Exchange rates

(economics), loans (business management).

7. Kirchhoff’s laws

(physics).

8. pH, buffer calculations and finding activation energy from experimental data (chemistry).

9. Stochastic processes, stock market values

and trends (business

management).

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HL1.12

 Complex numbers: the

number i such that i 2 = − 1.

 Cartesian form: z = a + bi;

the terms real part, imaginary

part, conjugate, modulus and

argument.

 The complex plane.

AH1.13

 Modulus–argument (polar) form:

z = r cosθ + isinθ = rcisθ.

Exponential form: z = re iθ

 Sums, products and quotients in Cartesian, polar or

Euler forms and their geometric

interpretation.

HL1.14

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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Complex conjugate roots of

quadratic and polynomial equations with real coefficients.

 Calculate sums, differences, products, quotients, by

hand and with technology. Calculating powers of complex

numbers, in Cartesian form,

with technology.

 Complex numbers as

solutions to quadratic equations

of the form ax 2 + bx + c = 0, a

≠ 0, with real coefficients where

b 2 − 4ac < 0.

 Conversion between Cartesian, polar and exponential

forms, by hand and with technology.

 Calculate products, quotients and integer powers in

polar or exponential forms.

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 Adding sinusoidal functions with the same frequencies

but different phase shift angles.

Geometric interpretation of

complex numbers.

HL1.14

 Definition of a matrix: the

terms element, row, column and

order for m × n matrices.

 Algebra of matrices:

equality; addition; subtraction;

multiplication by a scalar for m

× n matrices.

 Multiplication of matrices.

 Properties of matrix multiplication: associativity, distributivity and non-commutativity.

 Identity and zero matrices.

 Determinants and inverses

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of n × n matrices with technology, and by hand for 2 × 2 matrices.

 Awareness that a system

of linear equations can be written in the form Ax = b.

 Solution of the systems of

equations using inverse matrix.

HL1.15

 Eigenvalues and eigenvectors.

 Characteristic polynomial

of 2 × 2 matrices.

 Diagonalization of 2 × 2

matrices (restricted to the case

where there are distinct real

eigenvalues).

 Applications to powers of

2 × 2 matrices.

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Week

10~w

eek

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.

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.

• 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

physical quantities

in spatial dimensions.

• Moving between

Mathematical

abstraction,

Mathematical

modeling,

Logical

reasoning,

Mathematical

operations

2 64 Critical

thinking,

Transfer,

Communication,

Reflection,

Information literacy

TOK:

1. Descartes showed

that geometric 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 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 dif-

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 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).

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

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 function

changes the position, orientation and

ferent forms and symbolic

language in mathematics?

4. What role do models

play in mathematics? Do

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. Is there a hierarchy

of areas of knowledge in

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using technology.

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 (h,k).

HL/SL 2.7.1

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.

• Extending results

terms of their usefulness

in solving problems?

8. Does the applicability 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 (Switzerland); the

notation for functions was

developed by a number of

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 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 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.

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

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

tion:???? ൌ ሺ??൅??ሻ??−????−????

??

.

Sulba Sutras in ancient

India and the Bakhshali

Manuscript contained an

algebraic formula for

solving quadratic equations.

Links to other subjects:

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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.

 Rational functions of the

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

graphs.

 Equations of vertical and

horizontal asymptotes.

reasonableness and

validity of results

helps us to make

informed, unbiased

decisions.

1. Exchange rates and

price and income elasticity, demand and supply

curves (economics);

graphical analysis in experimental work (sciences).

2. Sketching and interpreting graphs (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 at-

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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 equations, 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.

tenuation, cooling of a

liquid, kinematics, simple

harmonic motion, projectile motion, inverse square

law (physics); compound

interest, depreciation

(business management);

the circular flow of income model (economics);

the equilibrium law and

rates of reaction (chemistry); opportunities to

model as part of experimental work (science).

5. opportunities to

model as part of experimental work (science).

6. Shifting of supply

and demand curves (economics); electromagnetic

induction (physics).

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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.

HL2.12

 Polynomial functions,

their graphs and equations;

zeros, roots and factors.

 The factor and remainder

theorems.

 Sum and product of the

roots of polynomial equation

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 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

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HL2.13

 Rational functions of the

form f(x)=ax+b/cx2+dx+e, and

f(x)=ax2+bx+c/dx+e

HL2.14

 Even and odd function

 Finding the inverse function, f-1(x)

 including domain restriction.

 Self-inverse functions.

HL2.15

 Solutions of g(x)≥f(x), both graphically and analytically.

what have learnt.

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HL2.16

 The graphs of the functions, y=|f(x)| and y=f(|x|),

y=1/f(x), y=f(ax+b), y=[f(x)]2.

 Solution of modulus equations and inequalities.

Week

25~

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.

Intuitive

imagination, Mathematical

abstraction,

Logical

reasoning,

Mathematical

modeling.

2 102 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

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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−c2/2ab .

 Area of a triangle as

1/2absinC.

HL/SL 3.3

 Applications of right and

non-right angled trigonometry,

including Pythagoras’s theorem.

 Angles of elevation and

depression.

 Construction of labelled

diagrams from written state-

• 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.

• 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 navithan 180°, what does this tell us about the nature of mathematical knowledge? 4. Does personal ex- perience play a role in the formation of knowledge claims in mathematics? Does it play a different role in mathematics com- pared 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 angle, de- grees or radians? What criteria can/do/should mathematicians use to make such judgments?

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ments.

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.

 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.

gate, 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

(movement) and

force in two and

threedimensional space.

• Graph theory algorithms allow us to

represent networks

and to model complex real-world

problems.

7. To what extent is

mathematical knowledge

embedded in particular

traditions or bound to

particular cultures? How

have key events in the

history of mathematics

shaped its current form

and methods?

8. When mathematicians and historians say

that they have explained

something, are they using

the word “explain” in the

same way?

9. Vectors are used to

solve many problems in

position location. This can

be used to save a lost

sailor or destroy a building with a laser-guided

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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

 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, pyra-

• Matrices are a

form of notation

which allow us to

show the parameters

or quantities of

several linear equations simultaneously.

bomb. To what extent

does possession of

knowledge carry with it an

ethical obligation?

10. 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?

11. What counts as understanding in mathematics? Is it more than just

getting the right answer?

12. Mathematics and

knowledge claims. Proof

of the four-colour theo-

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mids and prisms, and be able to

use the formulas to solve simple

practical problems.③ Can 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 cuboids and through intuitive

rem. If a theorem is

proved by computer, how

can we claim to know that

it is true?

13. What practical

problems can or does

mathematics try to solve?

Why are problems such as

the travelling salesman

problem so enduring?

What does it mean to say

the travelling salesman

problem is “NP hard”?

International-mindedness:

1. Diagrams of Pythagoras’ theorem occur

in early Chinese and Indian manuscripts. The

earliest references to

trigonometry are in Indian

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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 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

mathematics; 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.

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

we use minutes and seconds for time?; Links to

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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.

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.

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?

5. The “Bridges of

Konigsberg” problem.

6. The “Bridges of

Konigsberg” problem; the

Chinese postman problem

was first posed by the

Chinese mathematician

Kwan Mei-Ko in 1962.

Link to other subjects:

1. Design technology;

volumes of stars and inverse square law (phys-

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HL3.9

 Definition of the reciprocal trigonometric ratios

secθ, cosecθ and cotθ.

 Pythagorean identities:

1+tan2θ=sec2θ1+cot2θ=cosec2θ

 The inverse functions

f(x)=arcsinx,f(x)=arccosx,f(x)=

arctanx; their domains and

ranges; their graphs.

HL3.10

 Compound angle identities.

 Double angle identity for

tan.

HL3.11

 Relationships between

trigonometric functions and

the symmetry properties of

ics).

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).

6. Magnetic forces and

fields, and dynamics

(physics).

Homework:

Exercises from the text

books or questions from

the IB exams. Sometimes,

may be a summary of

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their graphs.

HL3.12

 Concept of a vector; position vectors; displacement vectors.

 Representation of vectors

using directed line segments.

 Base vectors i, j, k.

 Components of a vector:

 v=(v1,v2,v3)=v1i+v2j+v3k.

 Algebraic and geometric

approaches to the following:

the sum and difference of two

vectors

the zero vector 0, the vector −v

multiplication by a scalar, kv,

parallel vectors

magnitude of a vector and unit

vector

position vector and displacement

what have learnt.

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vector

 Proofs of geometrical properties using vectors

HL3.13

 The definition of the scalar product of two vectors.

 The angle between two

vectors.

 Perpendicular vectors;

parallel vectors.

HL3.14

 Vector equation of a line

in two and three dimensions:

r=a+λb.

 The angle between two

lines.

 Simple applications to

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kinematics

HL3.15

 Coincident, parallel, intersecting and skew lines, distinguishing between these cases.

 Points of intersection.

HL3.16

 The definition of the

vector product of two vectors.

 Properties of the vector

product.

 Geometric interpretation

of |v×w|

HL3.17

 Vector equations of a

plane:

 r=a+λb+μc, where b and c

G4

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are non-parallel vectors within

the plane.

 r·n=a·n, where n is a

normal to the plane and a is the

position vector of a point on the

plane.

 Cartesian equation of a

plane ax+by+cz=d.

HL3.18

 Intersections of: a line

with a plane; two planes; three

planes.

 Angle between: a line and

a plane; two planes.

G4

Week

41~

week

Probability

and

HL/SL 4.1

 Concepts of popula-

• Organizing,

representing, analysing and interLogical reason- ing， 2 66 Reflec- tion, Informa- TOK: 1. Why have mathe- matics and statistics

Time

line

Unit/

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Competency

Academic

Proficiency

Level

Teaching

Periods

ATL

Skills

Homework, Link to

TOK, IM, LP and CAS

are non-parallel vectors within

the plane.

 r·n=a·n, where n is a

normal to the plane and a is the

position vector of a point on the

plane.

 Cartesian equation of a

plane ax+by+cz=d.

HL3.18

 Intersections of: a line

with a plane; two planes; three

planes.

 Angle between: a line and

a plane; two planes.

G4

Week

41~

week

Probability

and

HL/SL 4.1

 Concepts of popula-

• Organizing,

representing, analysing and interLogical reason- ing， 2 66 Reflec- tion, Informa- TOK: 1. Why have mathe- matics and statistics

G4

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60 Statistics tion, 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):

frequency distributions

(tables).

preting 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 tools for

Data

analysis，

Mathematical

operations.

tion literacy,

Critical

thinking

Transfer

Collaboration,

Reflection

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 mathematics

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

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Homework, Link to

TOK, IM, LP and CAS

 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, median and

mode).

 Estimation of mean

from grouped data.

 Modal class.

 Measures of dispersion (interquartile range,

standard deviation and variance).

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

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 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