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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

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.

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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 curve;

2.12 Composite

functions and

inverse functions;

2.13 Linear

programming.

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

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.

Reason

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

Monthly examination

24

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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

algebraic terms and use this form of

expression to find unknown quantities.

2.12 Interpret and use graphs in practical

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Hours

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.

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

f: x →3x – 5, to describe simple functions.

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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.

2.21 Understand the terms function, domain,

range, one-one function, inverse function and

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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

pair of compasses only. Construct other

simple geometrical figures from given data

Critical thinking

Inquiring

Reflective

2 Exercises and

Module test

16

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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

length.

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Hours

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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• at a given distance from a given straight line

• equidistant from two given points

• equidistant from two given intersecting

straight lines.

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

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.

Reason

Critical thinking

Reflective

Problem-solving

1 Exercises and

Module test

6

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Hours

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,

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

Reason

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

10

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Hours

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

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.

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

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

Reason

Critical thinking

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

10

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Level

Homework Teaching

Hours

three dimensions including angle between a

line and a plane.

7. Vectors and

transformations

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 two vectors to express given

vectors in terms of two coplanar vectors. Use

position vectors.

Critical thinking

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

12

8. Probability 8.1 Basic

probability;

8.2 Experimental

and theoretical

8.1 Calculate the probability of a single event

as either a fraction, decimal or percentage.

Reason

Critical thinking

Inquiring

2 Exercises and

Module test

10

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Level

Homework Teaching

Hours

probability;

8.3 Mutually

exclusive and

independent events;

8.4 Probability

diagrams.

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.

Reflective

Problem-solving

9. Statistics 9.1 Collecting and

organizing data;

9.2 Averages;

9.3 Grouped and

continuous data;

9.4 Histograms;

9.5 Dispersion and

cumulative

frequency.

9.1 Collect, classify and tabulate statistical

data. Read, interpret and draw simple

inferences from tables and statistical

diagrams.

9.2 Construct and read bar charts, pie charts,

pictograms, simple frequency distributions,

Reason

Inquiring

Reflective

2 Exercises and

Module test

12

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Level

Homework Teaching

Hours

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

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

博实乐“中外融通课程”

308 

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

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Chinese and International Integrated

Curriculums for Bright Scholar

High School Section

CIG Additional

Mathematics

Curriculum Map

（2022 version）

Complied by Guangdong Country Garden Senior High Section

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310 

IGCSE Curriculum Mapping

Subject

IGCSE Additional

Mathematics

Level IG G1&G2 Syllabus Code 0606

Course Code Credit 4 Duration 2 Year

Teaching Hours 400 Designer Liu Sa Completed Date 2022.9

1 Course Introduction

1.1 Introduction

Cambridge IGCSE Additional Mathematics is accepted by universities and employers

as proof of essential mathematical knowledge and ability.

The Additional Mathematics syllabus is intended for high ability candidates who have

achieved, or are likely to achieve, Grade A*, A or B in the Cambridge IGCSE Mathematics

examination.

Successful Cambridge IGCSE Additional Mathematics candidates gain lifelong skills,

including:

• the further development of mathematical concepts and principles

• the extension of mathematical skills and their use in more advanced techniques

• an ability to solve problems, present solutions logically and interpret results

• a solid foundation for further study.

1.2 Aims

The aims are to enable candidates to:

• consolidate and extend their elementary mathematical skills, and use these in the

context of more advanced techniques.

• further develop their knowledge of mathematical concepts and principles, and use

this knowledge for solving problems.

• appreciate the interrelation of mathematical knowledge.

• acquire a suitable foundation in mathematics for further study in the Math or other

related subjects.

• devise mathematical arguments and use and present them precisely and logically.

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• integrate information technology (IT) to enhance the mathematical experience.

• develop the confidence to apply their mathematical skills and knowledge in

appropriate situations.

• develop creativity and perseverance in the approach to problem solving.

• derive enjoyment and satisfaction from engaging in mathematical pursuits, and gain

an appreciation of the beauty, power and usefulness of mathematics.

2 Course Structure

Functions

Quadraticfunctions

Equations, inequalities and graphs

Factors of polynomials

Indices and surds

Logarithmic and exponential

functions

Circular measure

Trigonometry

Series

Differentiation and integration

Algebra

Straight line graphs

Vectors in two dimensions

Coordinate

geometry

Permutations

and combinations

Probability and

statistics

IGCSE Additional Mathematics

博实乐“中外融通课程”

312 3 Course outline

Grade 1 3 Course outline

Unit/ Theme/

Topic

Contents Objectives Core Competency

Academic

Proficiency

Level

Homework Teaching Hours

Grade 1

1. Functions 1.1 Types of

relations;

1.2 Introduction

to functions;

1.3 Composite

functions;

1.4 Inverse

functions;

1.5 Absolute

valued

functions.

• understand the terms: function,

domain, range (image set), one-one

function, inverse function and

composition of functions.

• use the notation f(x) = sinx, f

–1

(x)

and f2

(x) [= f (f(x))].

• understand the relationship

between y = f(x) and

=itsabsolutevaluefunction, where

f(x) may be linear, quadratic or

trigonometric.

• explain in words why a given

function is a function or why it does

not have an inverse.

• find the inverse of a one-one

function and form composite

functions.

• use sketch graphs to show the

relationship between a function and

its inverse.

Reason

Critical thinking

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

25

2. Simultaneous

equations and

2.1 Two

simultaneous

• solve simultaneous equations in

two unknowns with at least one

Reason

Critical thinking

2 Exercises and 32

3 Course outline

Unit/ Theme/

Topic

Contents Objectives Core Competency

Academic

Proficiency

Level

Homework Teaching Hours

Grade 1

1. Functions 1.1 Types of

relations;

1.2 Introduction

to functions;

1.3 Composite

functions;

1.4 Inverse

functions;

1.5 Absolute

valued

functions.

• understand the terms: function,

domain, range (image set), one-one

function, inverse function and

composition of functions.

• use the notation f(x) = sinx, f

–1

(x)

and f2

(x) [= f (f(x))].

• understand the relationship

between y = f(x) and

=itsabsolutevaluefunction, where

f(x) may be linear, quadratic or

trigonometric.

• explain in words why a given

function is a function or why it does

not have an inverse.

• find the inverse of a one-one

function and form composite

functions.

• use sketch graphs to show the

relationship between a function and

its inverse.

Reason

Critical thinking

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

25

2. Simultaneous

equations and

2.1 Two

simultaneous

• solve simultaneous equations in

two unknowns with at least one

Reason

Critical thinking

2 Exercises and 32

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Proficiency

Level

Homework Teaching Hours

quadratics linear equations;

2.2 Non-linear

equations.

2.3 Quadratic

equations;

2.4 Quadratic

curve;

2.5 Completing

the square;

2.6 Quadratic

inequality.

linear equation.

• find the maximum or minimum

value of the quadratic function f :x

 ax2 + bx + c by any method.

• use the maximum or minimum

value of f(x) to sketch the graph or

determine the range for a given

domain.

• know the conditions for f(x) = 0 to

have:

(i) two real roots, (ii) two equal

roots, (iii) no real roots

and the related conditions for a

given line to

(i) intersect a given curve, (ii) be a

tangent to a given curve, (iii) not

intersect a given curve.

• solve quadratic equations for real

roots and find the solution set for

quadratic inequalities.

Reflective

Problem-solving

Module test

Monthly

examination

3. Indices and

surds

3.1 Rules of

indices and

surds;

3.2 Exponential

equations;

3.3 Simplifying

surd.

• perform simple operations with

indices and with surds, including

rationalizing the denominator.

Inquiring

Reflective

2 Exercises and

Module test

20

4. Factors of

polynomials

4.1 Polynomial

identities;

4.2 Remainder

• know and use the remainder and

factor theorems.

• find factors of polynomials.

Reason

Criticalthinking

Inquiring

2 Exercises and

Module test

20

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Level

Homework Teaching Hours

theorem;

4.3Factor

theorem;

4.4 Cubic

expressions.

• solve cubic equations. Reflective

5. Equations,

inequalities and

graphs

5.1 Solving

equations of the

type

|ax-b|=|cx-d|

5.2 Solving

modulus

inequalities

5.3 Sketching

graphs of cubic

polynomials and

their moduli

5.4 Solving

cubic

inequalities

graphically

5.5 Solving

more complex

quadratic

equations

• solve graphically or algebraically

equations of the type |ax+b|=c and

|ax+b|=|cx+d|

• solve graphically or algebraically

inequalities of the type |ax+b|>c,

|ax+b|<c and ax+b<cx+d

• use substitution to form and solve

a quadratic equation in order to

solve a related equation

• sketch the graphs of cubic

polynomials and their moduli, when

given in factorized form

y=k(x-a)(x-b)(x-c)

• solve cubic inequalities in the

form k(x-a)(x-b)(x-c)<d graphically

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

22

6. Logarithmic

and

exponential

functions

6.1 Introduction

to logarithms;

6.2 Rules of

logarithms;

6.3 Common

and natural

• know simple properties and

graphs of the logarithmic and

exponential functions including ln x

and ???? (series expansions are not

required).

• know and use the laws of

Reason

Critical thinking

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

25

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Contents Objectives Core Competency

Academic

Proficiency

Level

Homework Teaching Hours

logarithms;

6.4 Logarithmic

equations;

6.5 Graphs of

logarithmic and

exponential

functions.

logarithms (including change of

base of logarithms).

• solve equations of the form ax= b.

7. Straight line

graphs

7.1 Gradient of

a line;

7.2 Equation of

a straight line;

7.3 Equation of

parallel and

perpendicular

lines;

7.4

Perpendicular

bisector;

7.5 Linear law.

• interpret the equation of a straight

line graph in the form y = mx + c.

• transform given relationships,

including y = axnand y = Abx, to

straight line form and hence

determine unknown constants by

calculating the gradient or intercept

of the transformed graph.

• solve questions involving

mid-point and length of a line.

• know and use the condition for

two lines to be parallel or

perpendicular.

Reason

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

25

8. Circular

measure

8.1 Radian

measure;

8.2 Arc length

and area of a

sector and a

segment.

• solve problems involving the arc

length and sector area of a circle,

including knowledge and use of

radian measure.

Inquiring

Reflective

2 Exercises and

Module test

22

9. Trigonometry 9.1 General

angles;

9.2

• know the six trigonometric

functions of angles of any

magnitude (sine, cosine, tangent,

Reason

Critical thinking

Inquiring

2 Exercises and

Module test

22

博实乐“中外融通课程”

316  Unit/ Theme/

Topic

Contents Objectives Core Competency

Academic

Proficiency

Level

Homework Teaching Hours

Trigonometric

ratios of any

angles;

9.3 Solving

trigonometric

equations;

9.4

Trigonometric

graphs;

9.5

Trigonometric

identities.

secant, cosecant, cotangent).

• understand amplitude and

periodicity and the relationship

between graphs of e.g.sinxand

sin2x.

• draw and use the graphs of

y = a sin (bx) + c,

y = a cos (bx) + c,

y = a tan (bx) + c.

where a and b are positive integers

and c is an integer.

• use the trigonometric

relationships.

and solve simple trigonometric

equations involving the six

trigonometric functions and the

above relationships (not including

general solution of trigonometric

equations).

• prove simple trigonometric

identities.

Reflective

Problem-solving

  317

高中数学课程图

Grade 2

Unit/ Theme/

Topic

Contents Objectives Core Competency

Academic

Proficiency

Level

Homework Teaching Hours

Grade 2

10.

Permutations

and

combinations

10.1 The basic

counting

principle;

10.2

Permutations;

10.3

Combinations.

• recognize and distinguish

between a permutation case

and a combination case.

• know and use the notation n!

(with 0! = 1), and the

expressions for permutations

and combinations of n items

taken r at a time.

• answer simple problems on

arrangement and selection

(cases with repetition of

objects, or with objects

arranged in a circle or

involving both permutations

and combinations, are

excluded).

Critical thinking

Reflective

Problem-solving

2 Exercises and

Module test

22

11. Series 11.1 Pascal’s

triangle;

11.2 Binomial

theorem and

general term

formulae.

11.3

Arithmetic

progressions

11.4

• use the Binomial Theorem

for expansion of (a + b)

nfor

positive integral n.

• use the general term

nr r

n

a b r

       , 0<r<n.

(knowledge of the greatest

term and properties of the

coefficients is not required).

Reason

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

24

Unit/ Theme/

Topic

Contents Objectives Core Competency

Academic

Proficiency

Level

Homework Teaching Hours

Grade 2

10.

Permutations

and

combinations

10.1 The basic

counting

principle;

10.2

Permutations;

10.3

Combinations.

• recognize and distinguish

between a permutation case

and a combination case.

• know and use the notation n!

(with 0! = 1), and the

expressions for permutations

and combinations of n items

taken r at a time.

• answer simple problems on

arrangement and selection

(cases with repetition of

objects, or with objects

arranged in a circle or

involving both permutations

and combinations, are

excluded).

Critical thinking

Reflective

Problem-solving

2 Exercises and

Module test

22

11. Series 11.1 Pascal’s

triangle;

11.2 Binomial

theorem and

general term

formulae.

11.3

Arithmetic

progressions

11.4

• use the Binomial Theorem

for expansion of (a + b)

nfor

positive integral n.

• use the general term

nr r

n

a b r

       , 0<r<n.

(knowledge of the greatest

term and properties of the

coefficients is not required).

Reason

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

24

博实乐“中外融通课程”

318  Unit/ Theme/

Topic

Contents Objectives Core Competency

Academic

Proficiency

Level

Homework Teaching Hours

Geometric

progressions

11.5 Infinite

geometric

series

11.6 Further

arithmetic and

geometric

series

• recognize arithmetic and

geometric progressions

• use the formulae for the nth

term and for the sum of the

first n terms to solve problems

involving arithmetic and

geometric progression

• use the condition for the

convergence of a geometric

progression, and the formulae

for the sum to infinity of a

convergent geometric

progression

12.

Differentiation

and

integration

12.1

Differentiation

from first

principles;

12.2 Basic

techniques and

rules of

differentiation.

12.3 Tangents

and normals;

12.4 Rates of

change and

small changes;

12.5 Graphical

interpretation

• understand the idea of a

derived function.

• use the notations understand

the notations of

differentiation.

• use the derivatives of the

standard functions xn(for any

rational n), sin x, cosx, tanx,

ex, lnx, together with constant

multiples, sums and composite

functions of these.

• differentiate products and

quotients of functions.

• apply differentiation to

gradients, tangents and

Reason

Critical thinking

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

30

  319

高中数学课程图

Unit/ Theme/

Topic

Contents Objectives Core Competency

Academic

Proficiency

Level

Homework Teaching Hours

of a function;

12.6 Problems

on maximum

and minimum

values;

12.7

Integration

techniques;

12.8 Definite

integral;

12.9

Kinematics.

12.10

Increasing and

decreasing

functions;

12.11 Odevity

of a function

normals, stationary points,

connected rates of change,

small increments and

approximations and practical

maxima and minima

problems.

• discriminate between

maxima and minima by any

method.

• understand integration as the

reverse process of

differentiation.

• integrate sums of terms in

powers of

x.

• integrate functions of the

form (ax + b)

n(excluding n =

–1), ?????? ൅?? , sin (ax + b), cos

(ax + b).

• evaluate definite integrals

and apply integration to the

evaluation of plane areas.

• apply differentiation and

integration to kinematics

problems that involve

displacement, velocity and

acceleration of a particle

moving in a straight line with

variable or constant

acceleration, and the use of x

博实乐“中外融通课程”

320  Unit/ Theme/

Topic

Contents Objectives Core Competency

Academic

Proficiency

Level

Homework Teaching Hours

-t and v -t graphs.

• apply differentiation to

increasing and decreasing

functions.

• know and use odevity of a

function.

13. Vectors in 2

dimensions

and Review

13.1 Basic

concepts of

vectors;

13.2 Laws of

vectors;

13.3 Unit

vectors and

position

vectors;

13.4

Applications

of vectors.

• use vectors in any form, e.g.

a

b

     ,  AB , p

• know and use position

vectors and unit vectors.

• find the magnitude of a

vector; add and subtract

vectors and multiply vectors

by scalars.

• compose and resolve

velocities.

• use relative velocity,

including solving problems on

interception (but not closest

approach).

Critical thinking

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

124

  321

高中数学课程图

4 Assessment

4.1 External assessment

Introduction

to assessment

All candidates will take two written papers.The syllabus content will be

assessed by Paper 1 and Paper 2.

Paper 1

10–12 questions of various lengths. No choice of question.Duration 2

hours. 80 marks. Externally marked. Weighting 50%.

Paper 2

10–12 questions of various lengths. No choice of question.Duration 2

hours. 80 marks.Externally marked. Weighting 50%.

Grades A* to E will be available for candidates who achieve the required standards.

This syllabus is examined in the May/June examination series and the October/

November examination series. Detailed timetables are available from www.cie.org.uk/

examsofficers.

The syllabus assumes that candidates will be in possession of an electronic calculator

with scientific functions for both papers.

Relevant mathematical formulae will be provided on the inside covers of the question

papers.

4.2 In-School Assessment

Grading Components Percentage Description of the assessment criteria

Test 20%+40% Mid-term exam and Final Exam

Monthly test 5%+5% Monthly test

Assignment 20% Mark=(Average score/10)*20

Performance 10%

Content Excellent Good Poor

Attendance 2 1 0

Homework handing in 2 1 0

Note taking 2 1 0

Participation 2 1 0

Others 2 1 0

博实乐“中外融通课程”

322 

5 Resources

[1]Additional Mathematics, by Sue Pemberton, ISBN: 9781108411660, published by

Cambridge Press, etc.

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

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

Chinese and International Integrated

Curriculums for Bright Scholar

High School Section

CIG Additional

Mathematics

Curriculum Map

（2022 version）

Complied by Guangdong Country Garden Senior High Section

博实乐“中外融通课程”

324 

IGCSE Curriculum Mapping

Subject

IGCSE AdditionalMathematics

Level IG G2 Syllabus Code 0606

Course Code Credit 4 Duration 1 Year

Teaching Hours 240 Designer Liu Sa Completed Date 2022.9

1 Course Introduction

1.1 Introduction

Cambridge IGCSE Additional Mathematics is accepted by universities and employers

as proof of essential mathematical knowledge and ability.

The Additional Mathematics syllabus is intended for high ability candidates who have

achieved, or are likely to achieve, Grade A*, A or B in the Cambridge IGCSE Mathematics

examination.

Successful Cambridge IGCSE Additional Mathematics candidates gain lifelong skills,

including:

• the further development of mathematical concepts and principles

• the extension of mathematical skills and their use in more advanced techniques

• an ability to solve problems, present solutions logically and interpret results

• a solid foundation for further study.

1.2 Aims

The aims are to enable candidates to:

• consolidate and extend their elementary mathematical skills, and use these in the

context of more advanced techniques.

• further develop their knowledge of mathematical concepts and principles, and use

this knowledge for problem solving.

• appreciate the interrelation of mathematical knowledge.

• acquire a suitable foundation in mathematics for further study in the Math or other

related subjects.

• devise mathematical arguments and use and present them precisely and logically.

  325

高中数学课程图

• integrate information technology (IT) to enhance the mathematical experience.

• develop the confidence to apply their mathematical skills and knowledge in

appropriate situations.

• develop creativity and perseverance in the approach to problem solving.

• derive enjoyment and satisfaction from engaging in mathematical pursuits, and gain

an appreciation of the beauty, power and usefulness of mathematics.

2 Course Structure

Functions

Quadraticfunctions

Equations, inequalities and graphs

Factors of polynomials

Indices and surds

Logarithmic and exponential

functions

Circular measure

Trigonometry

Series

Differentiation and integration

Algebra

Straight line graphs

Vectors in two dimensions

Coordinate

geometry

Permutations

and combinations

Probability and

statistics

IGCSE Additional Mathematics

博实乐“中外融通课程”

326 3 Course outline 3 Course outline

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Homework Teaching

Hours

1. Functions 1.1 Types of relations;

1.2 Introduction to

functions;

1.3 Composite

functions;

1.4 Inverse functions;

1.5 Absolute valued

functions.

• understand the terms: function, domain,

range (image set), one-one function, inverse

function and composition of functions.

• use the notation f(x) = sinx , f–1(x) and f2(x)

[= f (f(x))].

• understand the relationship between y = f(x)

and itsabsolutevaluefunction, where f(x) may

be linear, quadratic or trigonometric.

• explain in words why a given function is a

function or why it does not have an inverse.

• find the inverse of a one-one function and

form composite functions.

• use sketch graphs to show the relationship

between a function and its inverse.

Reason

Critical thinking

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

15

2. Simultaneous

equations and

quadratics

2.1 Two simultaneous

linear equations;

2.2 Non-linear

equations.

2.3 Quadratic

equations;

2.4 Quadratic curve;

2.5 Completing the

square;

2.6 Quadratic

inequality.

• solve simultaneous equations in two

unknowns with at least one linear equation.

• find the maximum or minimum value of the

quadratic function by any method.

• use the maximum or minimum value of f(x)

to sketch the graph or determine the range for

a given domain.

• know the conditions for f(x) = 0 to have:

(i) two real roots, (ii) two equal roots, (iii) no

real roots

and the related conditions for a given line to

Reason

Critical thinking

Reflective

Problem-solving

2 Exercises and

Module test

Monthly

examination

18

  327

高中数学课程图

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Homework Teaching

Hours

(i) intersect a given curve, (ii) be a tangent to

a given curve, (iii) not intersect a given curve.

• solve quadratic equations for real roots and

find the solution set for quadratic inequalities.

3. Indices and

surds

3.1 Rules of indices

and surds;

3.2 Exponential

equations;

3.3 Simplifying surds.

• perform simple operations with indices and

with surds, including rationalizing the

denominator.

Inquiring

Reflective

2 Exercises and

Module test

12

4. Factors of

polynomials

4.1 Polynomial

identities;

4.2 Remainder

theorem;

4.3 Factor theorem;

4.4 Cubic

expressions.

• know and use the remainder and factor

theorems.

• find factors of polynomials.

• solve cubic equations.

Reason

Critical thinking

Inquiring

Reflective

2 Exercises and

Module test

12

5. Equations,

inequalities and

graphs

5.1 Solving equations

of the type

|ax-b|=|cx-d|

5.2 Solving modulus

inequalities

5.3 Sketching graphs

of cubic polynomials

and their moduli

5.4 Solving cubic

inequalities

graphically

5.5 Solving more

complex quadratic

• solve graphically or algebraically equations

of the type |ax+b|=c and |ax+b|=|cx+d|

• solve graphically or algebraically

inequalities of the type |ax+b|>c, |ax+b|<c and

ax+b<cx+d

• use substitution to form and solve a

quadratic equation in order to solve a related

equation

• sketch the graphs of cubic polynomialsand

their moduli, when given in factorized form

y=k(x-a)(x-b)(x-c)

• solve cubic inequalities in the form

k(x-a)(x-b)(x-c)<d graphically

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

12

博实乐“中外融通课程”

328  Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Homework Teaching

Hours

equations

6. Logarithmic

and

exponential

functions

6.1 Introduction to

logarithms;

6.2 Rules of

logarithms;

6.3 Common and

natural logarithms;

6.4 Logarithmic

equations;

6.5 Graphs of

logarithmic and

exponential functions.

• know simple properties and graphs of the

logarithmic and exponential functions

including lnxand ???? (series expansions are

not required).

• know and use the laws of logarithms

(including change of base of logarithms).

• solve equations of the form ax= b.

Reason

Critical thinking

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

15

7. Straight line

graphs

7.1 Gradient of a line;

7.2 Equation of a

straight line;

7.3 Equation of

parallel and

perpendicular lines;

7.4 Perpendicular

bisector;

7.5 Linear law.

• interpret the equation of a straight line graph

in the form y = mx + c.

• transform given relationships, including y =

axnand y = Abx, to straight line form and

hence determine unknown constants by

calculating the gradient or intercept of the

transformed graph.

• solve questions involving mid-point and

length of a line.

• know and use the condition for two lines to

be parallel or perpendicular.

Reason

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

15

8. Circular

measure

8.1 Radian measure;

8.2 Arc length and

area of a sector and a

segment.

• solve problems involving the arc length and

sector area of a circle, including knowledge

and use of radian measure.

Inquiring

Reflective

2 Exercises and

Module test

12

  329

高中数学课程图

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Homework Teaching

Hours

9.

Trigonometry

9.1 General angles;

9.2 Trigonometric

ratios of any angles;

9.3 Solving

trigonometric

equations;

9.4 Trigonometric

graphs;

9.5 Trigonometric

identities.

• know the six trigonometric functions of

angles of any magnitude (sine, cosine,

tangent, secant, cosecant, cotangent).

• understand amplitude and periodicity and

the relationship between graphs of

e.g.sinxand sin2x.

• draw and use the graphs of

y = a sin (bx) + c,

y = a cos (bx) + c,

y = a tan (bx) + c.

where a and b are positive integers and c is an

integer.

• use the trigonometric relationships.

and solve simple trigonometric equations

involving the six trigonometric functions and

the above relationships (not including general

solution of trigonometric equations).

• prove simple trigonometric identities.

Reason

Critical thinking

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

12

10.

Permutations

and

combinations

10.1 The basic

counting principle;

10.2 Permutations;

10.3 Combinations.

• recognize and distinguish between a

permutation case and a combination case.

• know and use the notation n! (with 0! = 1),

and the expressions for permutations and

combinations of n items taken r at a time.

• answer simple problems on arrangement

and selection (cases with repetition of objects,

or with objects arranged in a circle or

involving both permutations and

combinations, are excluded).

Critical thinking

Reflective

Problem-solving

2 Exercises and

Module test

24

11. Series 11.1 Pascal’s triangle;

11.2 Binomial

• use the Binomial Theorem for expansion of

(a + b)nfor positive integral n.

Reason

Inquiring

2 Exercises and 24

博实乐“中外融通课程”

330  Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Homework Teaching

Hours

theorem and general

term formulae.

11.3 Arithmetic

progressions

11.4 Geometric

progressions

11.5 Infinite

geometric series

11.6 Further

arithmetic and

geometric series

• use the general term nr r

n

a b

r

       , 0<r<n.

(knowledge of the greatest term and

properties of the coefficients is not required).

• recognize arithmetic and geometric

progressions

• use the formulae for the nth term and for the

sum of the first n terms to solve problems

involving arithmetic and geometric

progression

• use the condition for the convergence of a

geometric progression, and the formula for

the sum to infinity of a convergent geometric

progression

Reflective

Problem-solving

Module test

12.

Differentiation

and

integration

12.1 Differentiation

from first principles;

12.2 Basic techniques

and rules of

differentiation.

12.3 Tangents and

normals;

12.4 Rates of change

and small changes;

12.5 Graphical

interpretation of a

function;

12.6 Problems on

maximum and

minimum values;

12.7 Integration

• understand the idea of a derived function.

• use the notations understand the notations of

differentiation.

• use the derivatives of the standard functions

x

n(for any rational n), sin x, cosx, tanx, ex, lnx,

together with constant multiples, sums and

composite functions of these.

• differentiate products and quotients of

functions.

• apply differentiation to gradients, tangents

and normals, stationary points, connected

rates of change, small increments and

approximations and practical maxima and

minima problems.

• discriminate between maxima and minima

by any method.

Reason

Critical thinking

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

33

  331

高中数学课程图

Unit/ Theme/

Topic

Contents Objectives

Core

Competency

Academic

Proficiency

Level

Homework Teaching

Hours

techniques;

12.8 Definite integral;

12.9 Kinematics;

12.10 Increasing and

decreasing functions;

12.11 Odevity of a

function

• understand integration as the reverse

process of differentiation.

• integrate sums of terms in powers of x.

• integrate functions of the form (ax +

b)n(excluding n = –1), ?????? ൅?? , sin (ax + b),

cos (ax + b).

• evaluate definite integrals and apply

integration to the evaluation of plane areas.

• apply differentiation and integration to

kinematics problems that involve

displacement, velocity and acceleration of a

particle moving in a straight line with

variable or constant acceleration, and the use

of x -t and v -t graphs.

• apply differentiation to increasing and

decreasing functions.

• know and use odevity of a function.

13. Vectors in 2

dimensions

13.1 Basic concepts

of vectors;

13.2 Laws of vectors;

13.3 Unit vectors and

position vectors;

13.4 Applications of

vectors.

• use vectors in any form, e.g.

a

b

     ,  AB , p

• know and use position vectors and unit

vectors.

• find the magnitude of a vector; add and

subtract vectors and multiply vectors by

scalars.

• compose and resolve velocities.

• use relative velocity, including solving

problems on interception (but not closest

approach).

Critical thinking

Inquiring

Reflective

Problem-solving

2 Exercises and

Module test

24

博实乐“中外融通课程”

332 

4 Assessment

4.1 External assessment

Introduction to

assessment

All candidates will take two written papers.The syllabus content will be

assessed by Paper 1 and Paper 2.

Paper 1

10–12 questions of various lengths. No choice of question.Duration 2

hours. 80 marks. Externally marked. Weighting 50%.

Paper 2

10–12 questions of various lengths. No choice of question.Duration 2

hours. 80 marks.Externally marked. Weighting 50%.

Grades A* to E will be available for candidates who achieve the required standards.

This syllabus is examined in the May/June examination series and the October/

November examination series. Detailed timetables are available from www.cie.org.uk/

examsofficers.

The syllabus assumes that candidates will be in possession of an electronic calculator

with scientific functions for both papers.

Relevant mathematical formulae will be provided on the inside covers of the question

papers.

4.2 In-School Assessment

Grading Components

Percentage Description of the assessment criteria

Test 20%+40% Mid-term exam and Final Exam

Monthly test 5%+5% Monthly test

Assignment 20% Mark=(Average score/10)*20

Performance 10%

Content Excellent Good Poor

Attendance 2 1 0

Homework handing in 2 1 0

Note taking 2 1 0

Participation 2 1 0

Others 2 1 0

  333

高中数学课程图

5 Resources

[1]Additional Mathematics, by Sue Pemberton, ISBN: 9781108411660, published by

Cambridge Press, etc.

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

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

博实乐“中外融通课程”

334 

Chinese and International Integrated

Curriculums for Bright Scholar

High School Section

CALMathematics

Curriculum Map

（2022 version）

Complied by Guangdong Country Garden Senior High Section

  335

高中数学课程图

CAL Curriculum Mapping

Subject AL Mathematics Grade G2，G3，G4 Subject Code 9709

Course Code Credit 8 Duration 2 Years

Teaching Hours 560 Contributor Yan Zheng Completed Date 2022.9

1 Course Introduction

1.1 Introduction

Cambridge International AS and A Level Mathematics is accepted by universities and

employers as proof ofmathematical knowledge and understanding. Successfulcandidates

gain lifelong skills, including:

A deeper understanding of mathematical principles;

The further development of mathematical skills including the use of applications of

mathematics in the context of everyday situations and in other subjects that they may be

studying;

The ability to analyse problems logically, recognising when and how a situation may be

represented mathematically;

The use of mathematics as a means of communication;

A solid foundation for further study.

The syllabus allows centres flexibility to choose from three different routes to as

level mathematics – puremathematics only or pure mathematics and mechanics or pure

mathematics and probability and statistics. Centres can choose from three different routes

to cambridge international a level mathematics dependingon the choice of mechanics, or

probability and statistics, or both, in the broad area of ‘applications’.

1.2 Aims

Develop their mathematical knowledge and skills in a way which encourages

confidence and provides satisfaction and enjoyment;

Develop an understanding of mathematical principles and an appreciation of

mathematics as a logical and coherent subject;

博实乐“中外融通课程”

336 

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

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

they may be studying;

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

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

necessary, select an appropriate mathematical method to solve the problem;

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

expression;

Acquire the mathematical background necessary for further study in this or related

subjects.

1.3 Objectives

Understand relevant mathematical concepts, terminology and notation;

recall accurately and use successfully appropriate manipulative techniques;

recognise the appropriate mathematical procedure for a given situation;

apply combinations of mathematical skills and techniques in solving problems;

present mathematical work, and communicate conclusions, in a clear and logical way.

2 Course Structure

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

use applications ofmathematics in the context of everyday situations and of other

subjects they may be studying;

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

situation may be represented mathematically, identify and interpret relevant factors

and, where necessary, select an appropriate mathematical method to solve the

problem;

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

expression;

 acquire the mathematical background necessary for further study in this or related

subjects.

1.3 Objectives

 understand relevant mathematical concepts, terminology and notation;

 recall accurately and use successfully appropriate manipulative techniques;

 recognise the appropriate mathematical procedure for a given situation;

 apply combinations of mathematical skills and techniques in solving problems;

 present mathematical work, and communicate conclusions, in a clear and logical

way.

2. Course Structure

Structure of AS Level and A Level Mathematics

AS Level Mathematics A Level Mathematics

Paper 1 and Paper 2

Pure mathematics only

Paper 1 and Paper 4

Pure mathematics and Mechanics

Paper 1 and Paper 5

Pure Mathematics and Probability

& Statistics

Paper 1, 3, 4 and 5

Pure Mathematics, Mechanics and

Probability & Statistics

Paper 1, 3, 5 and 6

Pure Mathematics and Probability

& Statistics

(No progression to A Level)

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高中数学课程图

3 Course outline

AS P1 (Pure Mathematics 1)

3. Course outline

AS P1 (Pure Mathematics 1)

Unit/ Theme/

Topic Contents Objectives Core Competency Home- work Teaching Hours

1. Quadratics 1.1 Solving quadratic equations

by factorisation

1.2 Completing the square

1.3 The quadratic formula

1.4 Solving simultaneous equations (one linear and one

quadratic)

1.5 Solving more complex quadratic equations maximum

and minimum values of a

quadratic function

1.6 Solving quadratic inequalities

1.7 The number of roots of a

quadratic equation

1.8 Intersection of a line and a

quadratic curve

1. Carry out the process of completing the

square for a quadratic polynomial ax2+ 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. 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.

3. Solve quadratic equations, and linear and

quadratic inequalities, in one unknown.

4. Solve by substitution a pair of simultaneous

equations of which one is linear and one is

quadratic.

5. Recognise and solve equations in x which are

quadratic in some function of x, e.g. x4 – 5x2

+ 4 = 0.

1. Mathematical abstraction

2. Logical reasoning

Related

exercises

12

2.Equality

and inequality

2.1 The properties of equality

and inequality

2.2 Basic inequality

1. Understand the concept of inequality and

grasp the properties of inequality.

2. Understand basic inequalities

( , 0) 2 a b ab a b    ；Be able to solve simple

maximum value problems with basic inequalities.

1. Logical reasoning

2. Mathematics operation

Related

exercises

3

博实乐“中外融通课程”

338 Unit/ Theme/

Topic Contents Objectives Core Competency Home- work Teaching Hours

3.Set 3.1 The concept and representation of set

3.2 Basic relations of sets

3.3 Basic operations of sets

1. Understand the meaning of set, complete set

and empty set; Understand the \"belonging\"

relationship between elements and sets; Be

able to use natural language and graphic language; Symbolic language description set.

2. Understand the meaning of inclusion and

equality between sets; Can determine a subset

of a given set.

3. Understand the meaning of union, intersection and complement of two sets; Can combine graphics to find the union, intersection

and complement of two sets.

1. Mathematical abstraction

2. Logical reasoning

3. Mathematics operation

Related

exercises

4

4.Common

logic

4.1 Necessary conditions, sufficient conditions and necessary sufficient conditions

4.2 universal quantifier and

existential quantifier

4.3 The negation of the proposition of universal quantifier

and the proposition of existential quantifier

1. Understand the significance of necessary

conditions and their relationship with property theorems; Understand the meaning of sufficient condition and its relationship with decision theorem; Understand the meaning of

sufficient and necessary conditions and their

relationship with mathematical definitions.

2. Understand the meaning of full quantifiers

and existential quantifiers.Be able to correctly

use existential quantifiers and full quantifiers

to deny the full quantifier proposition and existential quantifier proposition respectively.

1. Mathematical abstraction

2. Logical reasoning

3. Data analysis

Related

exercises

5

5. Functions 5.1 Definition of a function

5.2 Composite functions

5.3 Inverse functions

5.4 The graph of a function and

its inverse

5.5 Transformations of functions

5.6 Reflections

1. Understand the terms function, domain,

range, one-one function,inverse function and

composition of functions.

2. Identify the range of a given function in simple cases, and find the composition of two

given functions.

3. Determine whether or not a given function is

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

1. Mathematical abstraction

2. Logical reasoning

3. Mathematical

modeling

4. Intuitive imagination

5. Mathematics opRelated exercises 12

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高中数学课程图

Unit/ Theme/

Topic Contents Objectives Core Competency Home- work Teaching Hours

5.7 Stretches

5.8 Combined transformations

function in simple cases.

4. Illustrate in graphical terms the relation between a one-one function and its inverse.

5. Understand and use the transformations of the

graph of y = f(x) given by y = f(x) + a, y = f(x

+ a), y = af(x), y = f(ax) and simple combinations of these.

eration

6.Coordinate

geometry

6.1 Length of a line segment

and midpoint

6.2 Parallel and perpendicular

lines

6.3 Equations of straight lines

6.4 The equation of a circle

6.5 Problems involving intersections of lines and circles

1. 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 itsgradient);

2. Interpret and use any of the forms y = mx + c,

y –y1 = m(x – x1), ax + by + c = 0 in solving

problems.

3. Understand that the equation (x – a)2 + (y –

b)2 = r2 represents the circle with centre (a, b)

and radius r.

4. Use algebraic methods to solve problems

involving lines andcircles.

5. 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.

1. Mathematical abstraction

2. Logical reasoning

3. Intuitive imagination

4. Mathematics operation

Related

exercises

12

7.Circular

measure

7.1 Radians

7.2 Length of an arc

7.3 Area of a sector

1. Understand the definition of a radian, and use

the relationship between radians and degrees;

2. Use the formulae s = rθ and A = 0.5 r r2θin

solving problems concerning the arc length

and sector area of a circle.

1. Mathematical abstraction

2. Intuitive imagination

3. Mathematics operation

Related

exercises

12

8.Trigonometry 8.1 Angles between 0° and 90° 8.2 The general definition of an 1. Sketch and use graphs of the sine, cosine and tangent functions (for angles of any size, and 1. Mathematical ab- straction Related exercises 30

博实乐“中外融通课程”

340 Unit/ Theme/

Topic Contents Objectives Core Competency Home- work Teaching Hours

angle

8.3 Trigonometric ratios of

general angles

8.4 Graphs of trigonometric

functions

8.5 Inverse trigonometric functions

8.6 Trigonometric equations

8.7 Trigonometric identities

8.8 Further trigonometric equations

using either degrees or radians).

2. Use the exact values of the sine, cosine and

tangent of 30°, 45°, 60°, and related angles,

e.g. cos 150°=

2

3  .

3. Use the notations

x 1 sin  , x 1 cos  ,

x 1 tan to denote the principal values of the

inverse trigonometric relations.

4. Use theidentities x

x x

sin

cos

tan

 ,

1 cos sin 2 2 



x

x .

5. Find all the solutions of simple trigonometrical equations lying in a specified interval

(general forms of solution are not included).

2. Logical reasoning

3. Mathematical

modeling

4. Intuitive imagination

5. Mathematics operation

9.Series 9.1 Binomial expansion of

(a+b)n

9.2 Binomial coefficients

9.3 Arithmetic progressions

9.4 Geometric progressions

9.5 Infinite geometric series

9.6 Further arithmetic and geometric series

1. Use the expansion of n b

a ) (  , where n is a

positive integer (knowledge of the greatest

term and properties of the coefficients are not

required, but the notations 















n

r

,and n! should

be known).

2. Recognise arithmetic and geometricprogressions.

3. Use the formulae for the nth term and for the

sum of the first n terms to solve problems involving arithmetic or geometric progressions.

4. Use the condition for the convergence of a

geometric progression, and the formula for

the sum to infinity of a convergent geometric

progression.

1. Mathematical abstraction

2. Logical reasoning

3. Mathematical

modeling

4. Mathematics operation

Related

exercises

24

  341

高中数学课程图

Unit/ Theme/

Topic Contents Objectives Core Competency Home- work Teaching Hours

10. Differentiation 10.1 Derivatives and gradient functions

10.2 The chain rule

10.3 Tangents and normals

10.4 Second derivatives

10.5 Increasing and decreasing

functions

10.6 Stationary points

10.7 Practical maximum and

minimum problems

10.8 Rates of change

10.9 Practical applications of

connected rates of change

1. Understand the idea of the gradient of a

curve, and use the notations

2

2

'' ' , ), ( ), ( dx

y

d dy

dx x f x f for first and second

derivative (the technique of differentiation

from first principles is not required).

2. Use the derivative of n x (for any rational n),

together with constant multiples, sums, differences of functions, and of composite functions using the chain rule.

3. Apply differentiation to gradients, tangents

and normals, increasing and decreasing functions and rates of change (including connected rates of change).

4. Locate stationary points, and use information

about stationary points in sketching graphs

(the ability to distinguish between maximum

points and minimum points is required, but

identification of points of inflexion is not included).

1. Mathematical abstraction

2. Logical reasoning

3. Mathematical

modeling

4. Mathematics operation

Related

exercises

25

11. Integration 11.1 Integration as the reverse of differentiation

11.2 Finding the constant of

integration

11.3 Integration of expressions

of the form (ax+b)n

11.4 Further indefinite integration

11.5 Definite integration

11.6 Area under a curve

11.7 Area bounded by a curve

and a line or by two curves

1. Understand integration as the reverse process

of differentiation, and integrate n b ax ) (  .

(for any rational n except

–1), together with

constant multiples, sums and differences.

2. Solve problems involving the evaluation of a

constant of integration, e.g. to find the equation of the curve through (1,

–2) for which

1 2 

 x dy

dx

.

3. Evaluate definite integrals (including simple

cases of ‘improper’ integrals, such as

1. Logical reasoning

2. Mathematical

modeling

3. Mathematics operation

Related

exercises

30

博实乐“中外融通课程”

342 Unit/ Theme/

Topic Contents Objectives Core Competency Home- work Teaching Hours

11.8 Improper integrals

11.9 Volumes of revolution dx x

1

2 1

0



 and dx x

2

1



 .

4. Use definite integration to find the area of a

region bounded by a curve and lines parallel

to the axes, or between two curves, a volume

of revolution about one of the axes.

12.Basic

Content of

Solid geometry

12.1 Basic 3-dimension figure.

12.2 Basic graphic position relationship.

1. Basic three-dimensional figure

(1) Be able to observe spatial graphics through

real objects, geometric software, etc., and understand the structural characteristics of columns, cones, platforms, balls and simple

combinations.

(2) Be able to solve simple practical problems

with the calculation formulas of the surface

and volume, such as balls, prisms, pyramids,

pyramids, and spheres.

(3) Be able to draw an intuitive diagram of simple spatial graphics by oblique dichotomy.

2. Position relations of basic figure

(1) Be able to abstract the positional relationship

and related properties of spatial points, lines

and planes on the basis of intuitive understanding of the positional relationship of spatial points, lines and planes.

(2) Understand the decision theorem and property theorem of parallel and perpendicular between straight line and plane， two straight

lines and two planes.

1. Mathematical abstraction

2. Logical reasoning

3. Intuitive imagination

4. Mathematics operation

Related

exercises

10

13.Plane analytic geometry 13.1 Conic section andequations 1. Understand the definitions, standard equa- tions and simple geometric properties of el- lipse, parabola and hyperbola. 1. Mathematical ab- straction 2. Logical reasoning Related exercises 10