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 Effect of constant

changes on the original data.

 Quartiles of discrete

data.

HL/SL 4.4

 Linear correlation of

bivariate data.

 Pearson’s product-moment correlation

coefficient, r.

 Scatter diagrams;

lines of best fit, by eye,

passing through the mean

point.

happen.

• Statistical literacy

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 outgambling probabilities be considered an ethical ap- plication of mathematics? Should mathematicians be held responsible for un- ethical 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 we know what to include, and what to exclude, in a model?

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 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

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.

comes. 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. Why have some

research journals

“banned” p -values from

their articles because they

deem them too misleading? In practical terms, is

saying that a result is significant the same as saying it is true? How is the

term “significant” used

differently in different

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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).

 Independent events:

P(A∩B)=P(A)P(B).

areas of knowledge?

12. What are the

strengths and limitations

of different methods of

data collection, such as

questionnaires?

13. 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?

14. 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 methods of

mathematics?

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HL/SL 4.7

 Concept of discrete

random variables and their

probability distributions.

 Expected value

(mean), for discrete data.

 Applications.

HL/SL 4.8

 Binomial distribution.

 Mean and variance of

the binomial distribution.

15. 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.

16. To what extent can

mathematical models such

as the Poisson distribution

be trusted? What role do

mathematical models play

in other areas of knowledge?

17. Mathematics and the

world. In practical terms,

is saying that a result is

significant the same as

saying that it is true?

Mathematics and the

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HL/SL 4.9

 The normal distribution and curve.

 Properties of the

normal distribution.

 Diagrammatic representation.

 Normal probability

calculations.

 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:

world. Does the ability to

test only certain parameters in a population affect

the way knowledge claims

in the human sciences are

valued? When is it more

important not to make a

Type I error and when is it

more important not to

make a Type II error?

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

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 P(A|B)=P(A∩B)/P(B)f

or conditional probabilities,

and

 P(A|B)=P(A)=P(A|B′)f

or independent events.

HL/SL 4.12

 Standardization of

normal variables (z- values).

 Inverse normal calculations where mean and

standard deviation are unknown.

HL4.13

 Use of Bayes’ theorem for a maximum of

three events.

from different countries;

discussion of the different

formulae for variance.

4. The St Petersburg

paradox; Chebyshev and

Pavlovsky (Russian).

5. The so-called “Pascal’s triangle” was known

to the Chinese mathematician Yang Hui much earlier than Pascal.

6. De Moivre’s derivation of the normal distribution and Quetelet’s use

of it to describe l’homme

moyen.

Link to other subjects:

1. Descriptive statistics

and random samples (biology, psychology, sports

exercise and health sci-

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HL4.14

 Variance of a discrete random variable.

 Continuous random

variables and their probability density functions.

 Mode and median of

continuous random variables.

 Mean, variance and

standard deviation of both

discrete and continuous

random variables.

 The effect of linear

transformations of X.

ence, environmental systems and societies, geography, 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).

5. Theoretical genetics

and Punnett squares (biology); the position of a

particle (physics).

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6. Normally distributed

real-life measurements

and descriptive statistics

(sciences, psychology,

environmental systems

and societies).

7. Fieldwork (biology,

psychology, environmental systems and societies, sports exercise and

health science).

8. Fieldwork (biology,

psychology, environmental systems and societies, sports exercise and

health science, geography).

9. Data collection in

field work (biology, psychology, environmental

systems and societies,

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sports exercise and health

science, geography, business management and

design technology); data

from social media and

marketing sources (business management)

10. Evaluation of R2 in

graphical analysis (sciences).

11. Data from multiple

samples in field studies

(sciences, and individuals

and societies).

12. Analysis of data

from field studies (sciences and individuals and

societies).

13. Field studies (sciences and individuals and

societies).

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Homework:

Exercises from the text

books or questions from

the IB exams. Sometimes,

may be a summary of

what have learnt.

Week

61

~

Week

75

Calculus HL/SL5.1

 Introduction to the

concept of a limit.

 Derivative interpreted

as gradient function and as

rate of change.

HL/SL 5.2

 Increasing and decreasing functions.

 Graphical interpretation of f′(x)>0,f′(x)=0,f′(x)<0.

• 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

Mathematical

abstraction，

Logical

reasoning，

Mathematical

operations，

Mathe2 110 Critical thinking, Commu- nication, Organiza- tion, Informa- tion liter- acy,Transf er, 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 ab- stract concept of calculus allows us to create mathematical models that permit human feats such

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HL/SL 5.3

 Derivative of f(x)=axnis

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.

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 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

matical

modeling

as getting a man on the

Moon. What does this tell

us about the links between

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 without

transforming it?

5. How can the rise in

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HL/SL 5.5

 Introduction to integration as anti-differentiation of

functions of the form

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

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.

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 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

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 progress and development in

mathematics? How might

this be similar/different to

the nature of progress and

development in other

areas of knowledge?

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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, including the relationship between the graphs

of f,_f′ and f″.

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 optimum

quantities.

• Phase portraits

enable us to visualize the behavior of

dynamic systems.

7. Music can be expressed using mathematics. Does this mean that

music is mathematical/that

mathematics is musical?

8. What is the role of

convention in mathematics? Is this similar or different to the role of convention in other areas of

knowledge?

9. In what ways do

values affect our representations of the world,

for example in statistics,

maps, visual images or

diagrams?

10. To what extent is

certainty attainable in

mathematics? Is certainty

attainable, or desirable, in

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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 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 funcother areas of knowledge? 11. How have notable individuals such as Euler shaped the development of mathematics as an area of knowledge? Interna- tional-mindedness: 1. Attempts by Indian mathematicians (500-1000 CE) to explain division by zero. 2. The successful cal- culation of the volume of a pyramidal frustrum by ancient Egyptians (the Egyptian Moscow mathematical papyrus). 3. Accurate calculation of the volume of a cylin- der by Chinese mathema-

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tion ax+b.

Integration by inspection

(reverse chain rule) or by

substitution for expressions of the form:

∫kg′(x)f(g(x))dx.

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.

tician 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 heritage? 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 (phys-

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HL5.12

 Informal understanding

of continuity and differentiability of a function at a point.

 Understanding of limits

(convergence and divergence).

 Definition of derivative

from first principles

f′(x)=limh→0f(x+h)−f(x)/h.

 Higher derivatives.

HL5.13

 The evaluation of limits

of the indeterminate form

using L’Hopital’s rule or

the Maclaurin series

 The repeated use

of L’Hopital’s rule

ics); 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. 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

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HL5.14

 Implicit differentiation.

 Related rates of change.

 Optimisation problems.

HL5.15

 Derivatives of tanx,

secx, cosecx, cotx, ax,

 Logax, arcsinx, arccosx,

arctanx.

 Indefinite integrals of

the derivatives of any of the

above functions.

 The composites of any

of these with a linear function.

 Use of partial fractions

to rearrange the integrand.

(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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HL5.16

 Integration by substitution.

 Integration by parts.

 Repeated integration

by parts.

HL5.17

 Area of the region enclosed by a curve and the

y-axis in a given interval.

 Volumes of revolution

about the x-axis or y-axis.

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HL5.18

 First order differential

equations.

 Numerical solution of

dy/dx=f(x,y)

 Using Euler’s method

 Variable separable

 Homogeneous differential equation dy/dx=f(y/x),

using the solution y=vx

 Solution of

y’+P(x)y=Q(x), using integrating factor

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HL5.18

 Maclaurin series to obtain expansions for ex, sinx,

cosx, ln(1+x), (1+x)p

 Use of simple substitution, products and integration

and differentiation to obtain

other series.

 Maclaurin series developed from differential equations

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 60 Creative

thinking,

Critical

thinking,

Reflection,

Information literacy

Homework: students are

asked to submit a mathematical essay about 12-20

pages.

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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–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: Analysis and Approaches for the IB Diploma(Pearson)

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

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

[4] Mathematics Standard Level for the IB Diploma.

[5] Mathematics Higher Level for the IB Diploma.

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

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

[8] Higher lever Mathematics 2012 edition (Pearson).

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

[10] IB past paper and question bank

[11] www.myib.org

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

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

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

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

[16] www.khanacademy.org

[17] www.mathdl.org

[18] www.mathsisfun.com

[19] https://ibmathsresources.com

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

[21] 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

CIG Mathematics

Curriculum Map

（2022 version）

Complied by Guangdong Country Garden Senior High Section

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高中数学课程图

IGCSE Curriculum Mapping

Subject IGCSE Mathematics Level IG G1&2 Syllabus Code 0580

Course Code Credit 2 Duration 2 Year

Teaching Hours 240 Designer Liu Sa Completed Date 2022.9

1 Course Introduction

1.1 Introduction

Cambridge IGCSE Mathematics is accepted by universities and employers as proof of

Mathematicalknowledge and understanding. Successful Cambridge IGCSE Mathematics

candidates gain lifelong skills,including:

• the development of their mathematical knowledge

• confidence by developing a feel for numbers, patterns and relationships

• an ability to consider and solve problems and present and interpret results

• communication and reason using mathematical concepts

• a solid foundation for further study.

1.2 Aims

The aims are to enable candidates to:

1.1. develop their mathematical knowledge and oral, written and practical skills in a

way which Encouragesconfidence and provides satisfaction and enjoyment.

1.2. read mathematics, and write and talk about the subject in a variety of ways.

1.3. develop a feel for number, carry out calculations and understand the significance

of the results obtained.

1.4. apply mathematics in everyday situations and develop an understanding of the

part which Mathematicsplays in the world around them.

1.5. solve problems, present the solutions clearly, check and interpret the results.

1.6. develop an understanding of mathematical principles.

1.7. recognise when and how a situation may be represented mathematically, identify

and interpret Relevantfactors and, where necessary, select an appropriate mathematical

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method to solve the problem.

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

expression.

1.9. develop an ability to apply mathematics in other subjects, particularly science and

technology.

1.10. develop the abilities to reason logically, to classify, to generalise and to prove.

1.11. appreciate patterns and relationships in mathematics.

1.12. produce and appreciate imaginative and creative work arising from mathematical

ideas.

1.13. develop their mathematical abilities by considering problems and conducting

individual and co-operativeen quiry and experiment, including extended pieces of work of

a practical and investigative kind.

1.14. appreciate the interdependence of different branches of mathematics.

1.15. acquire a foundation appropriate to their further study of mathematics and of

other disciplines.

2 Course Structure

Number

Number

Algebra and graphs

Coordinate geometry

Algebra

Geometry

Mensuration

Trigonometry

Vectors and

transformations

Shape and space

Probability

Statistics

Probability and

statistics

IGCSE Mathematics

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3 Course outline

Grade 1 3 Course outline

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Homework Teaching

Hours

Grade 1

1. Quadratic

functions with

one unknown

Quadratic equation;

solution by

factorization;

completing the

squares; solution by

differences of two

squares or perfect

squares; determinant;

solve real life

problems by quadratic

equation; sign

function; estimation;

relationship between

solutions and

coefficients

1.1 Quadratic equation;

1.2 Using completing the squares to solving

quadratic equation;

1.3 Solution by differences of two squares or

perfect squares;

1.4 Solving quadratic equation by factorising;

1.5 Solve real life problems by quadratic

equation

1.6 Sign function;

1.7 Estimation;

1.8 Relationship between solutions and

coefficients.

Reason

Critical thinking

Reflective

Problem-solving

1 Exercises and

Module test

8

2. Special

parallelogram

Rhombus; rectangle;

square; parallelogram;

properties theorem

and determinant

theorem of special

parallelogram;

theorems of

right-angled triangle.

2.1 Rhombus;

2.2 rectangle;

2.3 square;

2.4 parallelogram;

2.5 Properties theorem of special parallelogram;

2.6 Determinant theorem of special

parallelogram;

2.7 Theorems of right-angled triangle.

Reason

Critical thinking

Reflective

Problem-solving

1 Exercises and

Module test

6

3 Course outline

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Homework Teaching

Hours

Grade 1

1. Quadratic

functions with

one unknown

Quadratic equation;

solution by

factorization;

completing the

squares; solution by

differences of two

squares or perfect

squares; determinant;

solve real life

problems by quadratic

equation; sign

function; estimation;

relationship between

solutions and

coefficients

1.1 Quadratic equation;

1.2 Using completing the squares to solving

quadratic equation;

1.3 Solution by differences of two squares or

perfect squares;

1.4 Solving quadratic equation by factorising;

1.5 Solve real life problems by quadratic

equation

1.6 Sign function;

1.7 Estimation;

1.8 Relationship between solutions and

coefficients.

Reason

Critical thinking

Reflective

Problem-solving

1 Exercises and

Module test

8

2. Special

parallelogram

Rhombus; rectangle;

square; parallelogram;

properties theorem

and determinant

theorem of special

parallelogram;

theorems of

right-angled triangle.

2.1 Rhombus;

2.2 rectangle;

2.3 square;

2.4 parallelogram;

2.5 Properties theorem of special parallelogram;

2.6 Determinant theorem of special

parallelogram;

2.7 Theorems of right-angled triangle.

Reason

Critical thinking

Reflective

Problem-solving

1 Exercises and

Module test

6

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3. Similarity

of figures

Ratios; proportions

segments; parallel

lines; similar ration;

similar polygons;

similar triangles;

determinant theorem

of similar triangles;

golden section;

homothetic figures;

enlargement and

diminution of figures

3.1 Ratios; proportions segments; parallel lines;

3.2 Similar ration; similar polygons; similar

triangles;

3.3 Determinant theorem of similar triangles;

3.4 Golden section;

3.5 Homothetic figures;

3.6 Enlargement and diminution of figures.

Reason

Critical thinking

Reflective

Problem-solving

1 Exercises and

Module test

8

4. The

relationship

between sides

and angles in

right-angled

triangle

The relationships

between sides and

angled in right-angled

triangle; right-angled

triangle with 30°,

45°or 60°; non-right

angled triangle

trigonometry; solve

problem using

trigonometry. find

angle with special

trigonometric values;

4.1 The relationships between sides and angled

in right-angled triangle;

4.2 Trigonometry functions, sin, cos and tan.

4.3 Use trigonometry functions to solve

problem.

4.4 Right-angled triangle with 30°, 45°or 60°

4.5 Find angle with special trigonometric

values.

Reason

Critical thinking

Reflective

Problem-solving

1 Exercises and

Module test

8

5.Quadratic

functions

Quadratic functions;

graphs of quadratic

functions; general

form ; completing

5.1 Quadratic functions;

5.2 graphs of quadratic functions;

5.3 general form ;

5.4 completing quadratic functions to get

Reason

Critical thinking

Reflective

1 Exercises and

Module test

12

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quadratic functions to

get y=a(x-h)2+k;

coordinates of vertex;

parabola; symmetric

line; quadratic

equations; solve real

life problem by using

quadratic functions

y=a(x-h)2+k;

5.5 coordinates of vertex; parabola; symmetric

line;

5.6 The relationships between quadratic

function and quadratic equation;

5.7 solve real life problem by using quadratic

functions

Problem-solving

6.Circle Circle; radius;

segment; chords;

angle at centre;

tangent; angle in a

semi-circle theorem;

chords of a circle

theorem;

radius-tangent

theorem; tangents

from an external point

theorem; minor arc;

major arc; minor

segment; major

segment; angle at the

centre theorem;

angles subtended by

the same arc theorem;

angle between a

tangent and a chord

theorem; cyclic

quadrilaterals; axis

symmetry; central

6.1 Concept: Circle; radius; segment; chords;

angle at centre; tangent;

6.2 angle in a semi-circle theorem;

6.3 chords of a circle theorem;

6.4 radius-tangent theorem;

6.5 tangents from an external point theorem;

6.6 minor arc; major arc; minor segment; major

segment;

6.7 angle at the centre theorem;

6.8 angles subtended by the same arc theorem;

6.9 angle between a tangent and a chord

theorem;

6.10 cyclic quadrilaterals and its theorem;

6.11 axis symmetry; central symmetry;

6.12 vertical theorem;

6.13 regular polygons;

6.14 chord’s length;

6.15 sector’s area;

6.16 circum circle; inscribed circle.

Reason

Critical thinking

Reflective

Problem-solving

1 Exercises and

Module test

12

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symmetry; vertical

theorem; regular

polygons; chord’s

length; sector’s area;

circum circle;

inscribed circle.

7.Inverse

proportional

functions

(optional)

Inverse proportional

function;

graph of inverse

proportional function;

solve problem by

using inverse

proportional function.

7.1 Inverse proportional function;

7.2 graph of inverse proportional function;

7.3 solve problem by using inverse proportional

function.

Reason

Critical thinking

Reflective

Problem-solving

1 Exercises and

Module test

6

1.Number 1.1 Number systems;

1.2 Decimals,

fractions and

percentages.

1.3 Standard form;

1.4 Powers and roots;

1.5 Working with

directed numbers;

1.6 Order of

operations;

1.7 Approximation;

1.8 Set notation and

Venn diagrams;

1.9 Ratio and

proportion;

1.10 Money and

1.1 Identify and use natural numbers, integers

(positive, negative and zero), prime numbers,

square numbers, common factors and common

multiples, rational and irrational numbers (e.g.

π, ), real numbers.

1.2 Use language, notation and Venn diagrams

to describe sets and represent relationships

between sets. Definition of sets.

1.3 Calculate squares, square roots, cubes and

cube roots of numbers.

1.4 Use directed numbers in practical

Reason

Critical thinking

Reflective

Problem-solving

1 Exercises and

Module test

20

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finance;

1.11 Interest;

1.12 Time;

1.13 Using numbers

in everyday life.

situations.

1.5 Use the language and notation of simple

vulgar and decimal fractions and percentages in

appropriate contexts. Recognise equivalence

and convert between these forms.

1.6 Order quantities by magnitude and

demonstrate familiarity with the symbols =, ≠,

<, >, ≤, ≥.

1.7 Understand the meaning and rules of

indices. Use the standard form A × 10n where n

is a positive or negative integer, and 1≤A<10.

1.8 Use the four rules for calculations with

whole numbers, decimals and vulgar (and

mixed) fractions, including correct ordering of

operations and use of brackets.

1.9 Make estimates of numbers, quantities and

lengths, give approximations to specified

numbers of significant figures and decimal

places and round off answers to reasonable

accuracy in the context of a given problem.

1.10 Give appropriate upper and lower bounds

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for data given to a specified accuracy. Obtain

appropriate upper and lower bounds to

solutions of simple problems given data to a

specified accuracy.

1.11 Demonstrate an understanding of ratio and

proportion. Increase and decrease a quantity by

a given ratio. Use common measures of rate.

Calculate average speed.

1.12 Calculate a given percentage of a quantity.

Express one quantity as a percentage of

another. Calculate percentage increase or

decrease. Carry out calculations involving

reverse percentages.

1.13 Use a calculator efficiently. Apply

appropriate checks of accuracy.

1.14 Calculate times in terms of the 24-hour

and 12-hour clock. Read clocks, dials and

timetables.

1.15 Calculate using money and convert from

one currency to another.

1.16 Use given data to solve problems on

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personal and household finance involving

earnings, simple interest and compound

interest. Extract data from tables and charts.

1.17 Use exponential growth and decay in

relation to population and finance.

2. Algebra

and graphs

2.1 Language of

algebra;

2.2 Algebraic

representation and

manipulation;

2.3 Factorising;

2.4 Algebraic

fractions;

2.5 Algebraic indices;

2.6 Equations and

inequalities;

2.7 Sequences,

arithmetic and

geometric

progressions;

2.8 Interpret and use

graphs in practical

situations;

2.9 Functions and

graphs;

2.10 Quadratic

functions;

2.11 The gradient of a

2.1 Use letters to express generalised numbers

and express basic arithmetic processes

algebraically. Substitute numbers for words and

letters in complicated formulae. Construct and

transform complicated formulae and equations.

2.2 Manipulate directed numbers. Use brackets

and extract common factors. Expand products

of algebraic expressions. Factorise where

possible expressions of the form: 22 22 ax by  ,

2 2 2 a ab b   , 2 ax bx c   .

2.3 Manipulate algebraic fractions. Factorize

and simplify rational expressions.

2.4 Use and interpret positive, negative and

zero indices. Use and interpret fractional

indices. Use the rules of indices.

2.5 Solve simple linear equations in one

Reason

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

Monthly examination

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Hours

curve;

2.12 Composite

functions and inverse

functions;

2.13 Linear

programming.

unknown. Solve simultaneous linear equations

in two unknowns. Solve quadratic equations by

factorisation, completing the square or by use

of the formula. Solve simple linear inequalities.

2.6 Represent inequalities graphically and use

this representation in the solution of simple

linear programming problems.

2.7 Continue a given number sequence.

Recognise patterns in sequences and

relationships between different sequences. Find

the nth term of sequences.

2.8 Recognize arithmetic and geometric

progressions.

2.9 Use the formulae for the nth term and for

the sum of the first n terms to solve problems

involving arithmetic or geometric progressions.

2.10 Use the condition for the convergence of a

geometric progression, and the formula for the

sum to infinity of a convergent geometric

progression

2.11 Express direct and inverse variation in

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algebraic terms and use this form of expression

to find unknown quantities.

2.12 Interpret and use graphs in practical

situations including travel graphs and

conversion graphs. Draw graphs from given

data. Apply the idea of rate of change to easy

kinematics involving distance-time and

speed-time graphs, acceleration and

deceleration. Calculate distance travelled as

area under a linear speed-time graph.

2.13 Construct tables of values and draw graphs

for functions of the form ?????? ,, where a is a

rational constant, and = –2, –1, 0, 1, 2, 3, and

simple sums of not more than three of these and

for functions of the form ax, where a is a

positive integer. Solve associated equations

approximately by graphical methods. Draw and

interpret graphs representing exponential

growth and decay problems.

2.14 Estimate gradients of curves by drawing

tangents.

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2.15 Use function notation, e.g. f(x) = 3x – 5, f:

x→3x – 5, to describe simple functions. Find

inverse functions f–1(x). Form composite

functions as defined by gf(x) = g(f(x)).

2.16 Carry out the process of completing the

square for a quadratic polynomial ax 2+ bx + c,

and use this form, e.g. to locate the vertex of

the graph of y = ax2+ bx + c or to sketch the

graph.

2.17 Find the discriminant of a quadratic

polynomial ax2+ bx + c and use the

discriminant, e.g. to determine the number of

real roots of the equation ax2+ bx + c = 0.

2.18 Solve quadratic equations, and linear and

quadratic inequalities, in one unknown.

2.19 Solve by substitution a pair of

simultaneous equations of which one is linear

and one is quadratic.

2.20 Recognise and solve equations in x which

are quadratic in some function of x, e.g. x4–

5x2+ 4 = 0.

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2.21 Understand the terms function, domain,

range, one-one function, inverse function and

composition of functions.

2.22 Identify the range of a given function in

simple cases, and find the composition of two

given functions.

2.23 Determine whether or not a given function

is one-one, and find the inverse of a one-one

function in simple cases.

2.24 Illustrate in graphical terms the relation

between a one-one function and its inverse.

3. Geometry 3.1 Lines, angles and

shapes;

3.2 Properties of

shapes;

3.3 Constructions;

3.4 Congruent and

similar shapes;

3.5 Circles;

3.6 Symmetry;

3.7 Loci.

3.1 Use and interpret the geometrical terms:

point, line, parallel, bearing, right angle, acute,

obtuse and reflex angles, perpendicular,

similarity and congruence. Use and interpret

vocabulary of triangles, quadrilaterals, circles,

polygons and simple solid figures including

nets.

3.2 Measure lines and angles. Construct a

triangle given the three sides using ruler and

Critical thinking

Inquiring

Reflective

2 Exercises and

Module test

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Hours

pair of compasses only. Construct other simple

geometrical figures from given data using ruler

and protractor as necessary. Construct angle

bisectors and perpendicular bisectors using

straight edge and pair of compasses only.

3.3 Read and make scale drawings.

3.4 Calculate lengths of similar figures. Use the

relationships between areas of similar triangles,

with corresponding results for similar figures

and extension to volumes and surface areas of

similar solids.

3.5 Recognise rotational and line symmetry

(including order of rotational symmetry) in two

dimensions. Recognise symmetry properties of

the prism (including cylinder) and the pyramid

(including cone). Use the following symmetry

properties of circles:

• equal chords are equidistant from the centre.

• the perpendicular bisector of a chord passes

through the centre.

• tangents from an external point are equal in

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length.

3.6 Calculate unknown angles using the

following geometrical properties:

• angles at a point

• angles at a point on a straight line and

intersecting straight lines

• angles formed within parallel lines

• angle properties of triangles and quadrilaterals

• angle properties of regular polygons

• angle in a semi-circle

• angle between tangent and radius of a circle.

• angle properties of irregular polygons

• angle at the centre of a circle is twice the

angle at the circumference

• angles in the same segment are equal

• angles in opposite segments are

supplementary; cyclic quadrilaterals.

3.7 Use the following loci and the method of

intersecting loci for sets of points in two

dimensions which are:

• at a given distance from a given point

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Hours

• at a given distance from a given straight line

• equidistant from two given points

• equidistant from two given intersecting

straight lines.

Unit/ Theme/

Topic

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Competency

Academic

Proficiency

Level

Homework Teaching

Hours

Grade 2

4.

Measureation

4.1 Measures;

4.2 Perimeter and area

in two dimensions;

arc length and sector

areas;

4.3 Surface area and

volumes of solids.

4.1 Use current units of mass, length, area,

volume and capacity in practical situations and

express quantities in terms of larger or smaller

units.

4.2 Carry out calculations involving the

perimeter and area of a rectangle, triangle,

parallelogram and trapezium and compound

shapes derived from these.

4.3 Carry out calculations involving the

Reason

Critical thinking

Reflective

Problem-solving

1 Exercises and

Module test

6

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Homework Teaching

Hours

• at a given distance from a given straight line

• equidistant from two given points

• equidistant from two given intersecting

straight lines.

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Homework Teaching

Hours

Grade 2

4.

Measureation

4.1 Measures;

4.2 Perimeter and area

in two dimensions;

arc length and sector

areas;

4.3 Surface area and

volumes of solids.

4.1 Use current units of mass, length, area,

volume and capacity in practical situations and

express quantities in terms of larger or smaller

units.

4.2 Carry out calculations involving the

perimeter and area of a rectangle, triangle,

parallelogram and trapezium and compound

shapes derived from these.

4.3 Carry out calculations involving the

Reason

Critical thinking

Reflective

Problem-solving

1 Exercises and

Module test

6

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Homework Teaching

Hours

• at a given distance from a given straight line

• equidistant from two given points

• equidistant from two given intersecting

straight lines.

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Homework Teaching

Hours

Grade 2

4.

Measureation

4.1 Measures;

4.2 Perimeter and area

in two dimensions;

arc length and sector

areas;

4.3 Surface area and

volumes of solids.

4.1 Use current units of mass, length, area,

volume and capacity in practical situations and

express quantities in terms of larger or smaller

units.

4.2 Carry out calculations involving the

perimeter and area of a rectangle, triangle,

parallelogram and trapezium and compound

shapes derived from these.

4.3 Carry out calculations involving the

Reason

Critical thinking

Reflective

Problem-solving

1 Exercises and

Module test

6

Grade 2

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circumference and area of a circle. Solve

problems involving the arc length and sector

area as fractions of the circumference and area

of a circle.

4.4 Carry out calculations involving the volume

of a cuboid, prism and cylinder and the surface

area of a cuboid and a cylinder. Carry out

calculations involving the surface area and

volume of a sphere, pyramid and cone.

4.5 Carry out calculations involving the areas

and volumes of compound shapes.

5.Co-ordinate

geometry

5.1 Straight line

graphs;

5.2 the length and the

midpoint of a line

segment;

5.3 Parallel and

perpendicular lines;

5.4 The relationship

between a graph and

its associated

algebraic equation.

5.1 Demonstrate familiarity with Cartesian

co-ordinates in two dimensions.

5.2 Find the gradient of a straight line.

Calculate the gradient of a straight line from the

co-ordinates of two points on it.

5.3 Calculate the length and the co-ordinates of

the midpoint of a straight line from the

co-ordinates of its end points.

5.4 Interpret and use linear equations,

Reason

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

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particularly the forms y = mx + c and y – y1 =

m(x – x1).

5.5 Understand and use the relationships

between the gradients of parallel and

perpendicular lines.

5.6 Find the equation of a straight line given

sufficient information (e.g. the coordinates of

two points on it, or one point on it and its

gradient).

5.7 Understand the relationship between a

graph and its associated algebraic equation, and

use the relationship between points of

intersection of graphs and solutions of

equations (including, in simple cases, the

correspondence between a line being tangent to

a curve and a repeated root of an equation).

6.

Trigonometry

6.1 Bearings;

6.2 Pythagoras’

theorem; the sine,

cosine and tangent

ratios;

6.3 Solve problems

6.1 Interpret and use three-figure bearings.

6.2 Apply Pythagoras’ theorem and the sine,

cosine and tangent ratios for acute angles to the

calculation of a side or of an angle of a

right-angled triangle. Solve trigonometrical

problems in two dimensions involving angles

Reason

Critical thinking

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

10

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using trigonometry;

6.4 Trigonometry for

any triangle;

6.5 Area of a triangle;

6.6 the sine rule and

cosine rule;

6.7 Applied

trigonometry.

of elevation and depression. Extend sine and

cosine values to angles between 90° and 180°.

6.3 Solve problems using the sine and cosine

rules for any triangle and the formula area of

triangle = 1 sin

2

ab C .

6.4 Solve simple trigonometrical problems in

three dimensions including angle between a line

and a plane.

7. Vectors

and

transformatio

ns

7.1 Simple plane

transformations;

7.2 Vectors;

7.3 Further

transformations;

7.1 Describe a translation by using a vector

represented by e.g.

x

y

     ,  AB or a. Add and

subtract vectors. Multiply a vector by a scalar.

7.2 Reflect simple plane figures in horizontal or

vertical lines. Rotate simple plane figures about

the origin, vertices or midpoints of edges of the

figures, through multiples of 90°. Construct

given translations and enlargements of simple

plane figures. Recognise and describe

reflections, rotations, translations and

enlargements.

7.3 Calculate the magnitude of a vector

x

y

     

as

2 2

x y  . Represent vectors by directed

line segments. Use the sum and difference of

Critical thinking

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

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two vectors to express given vectors in terms of

two coplanar vectors. Use position vectors.

8. Probability 8.1 Basic probability;

8.2 Experimental and

theoretical

probability;

8.3 Mutually

exclusive and

independent events;

8.4 Probability

diagrams.

8.1 Calculate the probability of a single event

as either a fraction, decimal or percentage.

8.2 Understand and use the probability scale

from 0 to 1.

8.3 Understand that the probability of an event

occurring = 1 – the probability of the event not

occurring.

8.4 Understand relative frequency as an

estimate of probability.

8.5 Calculate the probability of simple

combined events. Understand the meaning of

exclusive and independent events, and calculate

and use conditional probabilities in simple

cases, e.g. situations that can be represented by

means of a tree diagram.

Reason

Critical thinking

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

10

9. Statistics

and Review

9.1 Collecting and

organizing data;

9.2 Averages;

9.3 Grouped and

9.1 Collect, classify and tabulate statistical data.

Read, interpret and draw simple inferences

from tables and statistical diagrams.

Reason

Inquiring

Reflective

2 Exercises and

Module test

82

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Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Homework Teaching

Hours

continuous data;

9.4 Histograms;

9.5 Dispersion and

cumulative frequency.

9.2 Construct and read bar charts, pie charts,

pictograms, simple frequency distributions,

histograms with equal and unequal intervals

and scatter diagrams.

9.3 Calculate the mean, median, mode and

range for individual and discrete data and

distinguish between the purposes for which

they are used.

9.4 Calculate an estimate of the mean for

grouped and continuous data. Identify the

modal class from a grouped frequency

distribution.

9.5 Construct and use cumulative frequency

diagrams. Estimate and interpret the median,

percentiles, quartiles and inter-quartile range.

9.6 Understand what is meant by positive,

negative and zero correlation with reference to

a scatter diagram.

9.7 Draw a straight line of best fit by eye.

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4 Assessment

4.1 External assessment

Introduction

to assessment

Cambridge IGCSE Mathematics is assessed via two components. All

candidates take two written papers. Candidates who follow the Extended

curriculum take Papers 2 and 4 and are eligible for grades A* to E.

Paper 2 1 hour 30 minutes, Short-answer questions based on the Extended curriculum. 70 marks. Externally marked. Weighting 35%.

Paper 4 2 hours 30 minutes, Structured questions based on the Extended curriculum. 130 marks. Externally marked.Weighting 65%.

Relationship between assessment objectives and components

The relationship between the assessment objectives and the scheme of assessment is

shown in the tables below.

Assessment objective Paper 2 (marks) Paper 4 (marks)

Extended

assessment

AO1: Mathematical techniques 28–35 52–65 40–50%

AO2: Applying mathematical

techniques to solve problems

35–42 65–78 50–60%

The weightings of the main topic areas of Mathematics are shown in the table below.

Components Number Algebra Space and shape

Statistics and

probability

Extended (Papers 2 and 4) 15–20% 35–40% 30–35% 10–15%

• Candidates should have an electronic calculator for all papers. Algebraic or graphical

calculators are not permitted. Three significant figures will be required in answers except

where otherwise stated.

• Candidates should use the value of π from their calculators if their calculator

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provides this. Otherwise,they should use the value of 3.142 given on the front page of the

question paper only.

• Tracing paper may be used as an additional material for all of the written papers.

4.2 In-School Assessment

Grading Components Percentage Description of the assessment criteria

Test 60% Mid-term exam and Final Exam

Assignment 10% Six grades: A, B, C, D, E, F

Marks were 10,8,6,4,2,0

Monthly test 10% Monthly test

Performance 20%

Content Excellent Good Poor

Attendance 2 1 0

Presentation 2 1 0

Note taking 2 1 0

Participation 2 1 0

Others 2 1 0

5 Resources

[1] Cambridge IGCSE Mathematics Core and Extended Third Edition with CD, by

Pimentel, R and Wall, T, ISBN: 9781444191707. Published by Hodder Education, UK.

[2] Cambridge IGCSE Mathematics Core and Extended Coursebook (with CD), by

Morrison, K and Hamshaw, N, ISBN: 9781107606272. Published by Cambridge University

Press, UK. etc.

[3] www.cie.org.uk/igcse/

[4] http://teachers.cie.org.uk

博实乐“中外融通课程”

288 

Chinese and International Integrated

Curriculums for Bright Scholar

High School Section

CIG Mathematics

Curriculum Map

（2022 version）

Complied by Guangdong Country Garden Senior High Section

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IGCSE Curriculum Mapping

Subject IGCSE Mathematics Level IG G2 Syllabus Code 0580

Course Code Credit 2 Duration 1 Year

Teaching Hours 120 Designer Completed Date 2022.9

1 Course Introduction

1.1 Introduction

Cambridge IGCSE Mathematics is accepted by universities and employers as proof of

Mathematicalknowledge and understanding. Successful Cambridge IGCSE Mathematics

candidates gain lifelong skills,including:

• the development of their mathematical knowledge

• confidence by developing a feel for numbers, patterns and relationships

• an ability to consider and solve problems and present and interpret results

• communication and reason using mathematical concepts

• a solid foundation for further study.

1.2 Aims

The aims are to enable candidates to:

1.1. develop their mathematical knowledge and oral, written and practical skills in a

way which Encouragesconfidence and provides satisfaction and enjoyment.

1.2. read mathematics, and write and talk about the subject in a variety of ways.

1.3. develop a feel for number, carry out calculations and understand the significance

of the results obtained.

1.4. apply mathematics in everyday situations and develop an understanding of the

part which Mathematicsplays in the world around them.

1.5. solve problems, present the solutions clearly, check and interpret the results.

1.6. develop an understanding of mathematical principles.

1.7. recognise when and how a situation may be represented mathematically, identify

and interpret Relevantfactors and, where necessary, select an appropriate mathematical

method to solve the problem.

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

expression.

1.9. develop an ability to apply mathematics in other subjects, particularly science and

technology.

1.10. develop the abilities to reason logically, to classify, to generalise and to prove.

1.11. appreciate patterns and relationships in mathematics.

1.12. produce and appreciate imaginative and creative work arising from mathematical

ideas.

1.13. develop their mathematical abilities by considering problems and conducting

individual and co-operativeen quiry and experiment, including extended pieces of work of

a practical and investigative kind.

1.14. appreciate the interdependence of different branches of mathematics.

1.15. acquire a foundation appropriate to their further study of mathematics and of

other disciplines.

2 Course Structure

Number

Number

Algebra and graphs

Coordinate geometry

Algebra

Geometry

Mensuration

Trigonometry

Vectors and

transformations

Shape and space

Probability

Statistics

Probability and

statistics

IGCSE Mathematics

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3 Course outline

3 Course outline

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Homework Teaching

Hours

1.Number 1.1 Number

systems;

1.2 Decimals,

fractions and

percentages.

1.3 Standard form;

1.4 Powers and

roots;

1.5 Working with

directed numbers;

1.6 Order of

operations;

1.7 Approximation;

1.8 Set notation and

Venn diagrams;

1.9 Ratio and

proportion;

1.10 Money and

finance;

1.11 Interest;

1.12 Time;

1.13 Using numbers

in everyday life.

1.1 Identify and use natural numbers, integers

(positive, negative and zero), prime numbers,

square numbers, common factors and

common multiples, rational and irrational

numbers (e.g. π, e ), real numbers.

1.2 Use language, notation and Venn

diagrams to describe sets and represent

relationships between sets. Definition of sets.

1.3 Calculate squares, square roots, cubes

and cube roots of numbers.

1.4 Use directed numbers in practical

situations.

1.5 Use the language and notation of simple

vulgar and decimal fractions and percentages

in appropriate contexts. Recognise

equivalence and convert between these forms.

1.6 Order quantities by magnitude and

Reason

Criticalthinking

Reflective

Problem-solving

1 Exercises and

Module test

20

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292  Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Homework Teaching

Hours

demonstrate familiarity with the symbols =,

≠, <, >, ≤, ≥.

1.7 Understand the meaning and rules of

indices. Use the standard form A × 10n where

n is a positive or negative integer, and

1≤A<10.

1.8 Use the four rules for calculations with

whole numbers, decimals and vulgar (and

mixed) fractions, including correct ordering

of operations and use of brackets.

1.9 Make estimates of numbers, quantities

and lengths, give approximations to specified

numbers of significant figures and decimal

places and round off answers to reasonable

accuracy in the context of a given problem.

1.10 Give appropriate upper and lower

bounds for data given to a specified accuracy.

Obtain appropriate upper and lower bounds to

solutions of simple problems given data to a

specified accuracy.

1.11 Demonstrate an understanding of ratio