Royal Mile
Teaching Plan of Mathematics
Content and assessment overview for Edexcel qualification ....... ............... 2
G1-G2 Edexcel IAL Mathematics Teaching Plan ........................ ............... 4
A1-A2 Edexcel IAL Further Mathematics Teaching Plan ........... ............... 11
International Mathematics Competition ....................................... ............... 13
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Qualification aims and objectives
The aims and objectives of these qualifications are to enable students to:
•
develop their understanding of mathematics and mathematical processes in a way that promotes
confidence and fosters enjoyment.
•
develop abilities to reason logically and recognise incorrect reasoning, to generalise and to
construct mathematical proofs.
•
extend their range of mathematical skills and techniques and use them in more difficult,
unstructured problems.
•
develop an understanding of coherence and progression in mathematics and of how different
areas of mathematics can be connected.
•
recognise how a situation may be represented mathematically and understand the relationship
between ‘real-world’ problems and standard and other mathematical models and how these can
be refined and improved.
•
use mathematics as an effective means of communication.
•
read and comprehend mathematical arguments and articles concerning applications of
mathematics.
•
acquire the skills needed to use technology such as calculators and computers effectively,
recognise when such use may be inappropriate and be aware of limitations.
•
develop an awareness of the relevance of mathematics to other fields of study, to the world of
work and to society in general.
•
take increasing responsibility for their own learning and the evaluation of their own
mathematical development.
Content and assessment overview
Each unit:
•
is externally assessed
•
has a written examination of 1 hour and 30 minutes
•
has 75 marks.
Unit
P1: Pure
Mathematics 1
WMA11/01
Availability
January,
June and
October
IAL
weighting
16⅔ %
Content overview
Algebra and functions; coordinate geometry in the
(x, y); trigonometry; differentiation; integration.
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P2: Pure
Mathematics 2
WMA12/01
January,
June and
October
16⅔ %
Proof; algebra and functions; coordinate geometry in the (x, y)
plane; sequences and series; exponentials and logarithms;
trigonometry; differentiation; integration.
P3: Pure
Mathematics 3
WMA13/01
January,
June and
October
16⅔ %
Algebra and functions; trigonometry; exponentials and
logarithms; differentiation; integration; numerical methods.
P4: Pure
Mathematics 4
WMA/14/01
January,
June and
October
16⅔ %
Proof; algebra and functions; coordinate geometry in the (x, y)
plane; binomial expansion; differentiation; integration; vectors.
FP1:
Further Pure
Mathematics 1
WFM01/01
January
June
and
16⅔ %
Complex numbers; roots of quadratic equations; numerical
solution of equations; coordinate systems; matrix algebra;
transformations using matrices; series; proof.
FP2:
Further Pure
Mathematics 2
WFM02/01
January
June
and
16⅔ %
Inequalities; series; further complex numbers; first order
differential equations; second order differential equations;
Maclaurin and Taylor series; Polar coordinates.
FP3:
Further Pure
Mathematics 3
WFM03/01
January
June
and
16⅔ %
Hyperbolic
functions;
further
coordinate
systems;
differentiation; integration; vectors; further matrix algebra.
M1:
Mechanics 1
WME01/01
January,
June and
October
16⅔ %
Mathematical models in mechanics; vectors in mechanics;
kinematics of a particle moving in a straight line; dynamics
of a particle moving in a straight line or plane; statics of a
particle; moments.
M2:
Mechanics 2
WME02/01
January,
June and
October
16⅔ %
Kinematics of a particle moving in a straight line or plane; centres
of mass; work and energy; collisions; statics of rigid bodies.
M3:
Mechanics 3
WME03/01
January
June
16⅔ %
Further kinematics; elastic strings and springs; further dynamics;
motion in a circle; statics of rigid bodies.
S1:
Statistics 1
WST01/01
January,
June and
October
16⅔ %
Mathematical models in probability and statistics;
representation and summary of data; probability; correlation
and regression; discrete random variables; discrete
distributions; the Normal distribution.
S2:
Statistics 2
WST02/01
January,
June and
October
16⅔ %
The Binomial and Poisson distributions; continuous random
variables; continuous distributions; samples; hypothesis tests.
S3:
Statistics 3
WST03/01
January
June
and
16⅔ %
Combinations of random variables; sampling; estimation,
confidence intervals and tests; goodness of fit and contingency
tables; regression and correlation.
D1: Decision
Mathematics 1
WDM11/01
January
June
and
16⅔ %
Algorithms; algorithms on graphs; algorithms on graphs II;
critical path analysis; linear programming.
and
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G1-G2 Edexcel IAL Mathematics (YMA01) Teaching Plan
⚫
Teaching materials:
IAL-Maths-Specification-YMA01
Textbook, Notebook, Past Papers, Workbook, PPT
⚫
G1:P1+P2+M1---5 Lessons per week (60min)
2022-2023 Semester 1 （P1+M1）
3 Lessons for P1 and 2 Lessons for M1 each week
Week
Topics / Contents
Date
1
2022/8/15 - 2022/8/21
P1---Ch1 Algebraic expressions
M1---Ch1 Mathematical models in mechanics
2
2022/8/22 - 2022/8/28
P1---Ch2 Quadratics
M1---Ch2 Constant acceleration
3
2022/8/29 - 2022/9/4
4
2022/9/5 - 2022/9/11
5
2022/9/12 - 2022/9/18
6
2022/9/19 - 2022/9/25
7
2022/9/26 - 2022/9/30
8
2022/10/8 - 2022/10/16
9
2022/10/17 - 2022/10/23
P1---Ch3 Equations and Inequalities
M1---Ch2 Constant acceleration
M1 Test1 Kinematics of a particle moving in a straight line
P1---Ch4 Graphs and transformations
P1 Test 1 Algebra and functions
M1---Ch3 Vectors in mechanics
P1---Ch5 Straight line graphs
M1---Ch3 Vectors in mechanics
M1 Test2 Vectors
P1---Ch5 Straight line graphs
P1 Test 2 Coordinate Geometry
M1---Ch4 Dynamics of a particle moving in a straight line or
plane
P1----Ch6 Trigonometric ratios
M1---Ch4 Dynamics of a particle moving in a straight line or
plane
P1---Ch7 Radians
P1 Test 3 Trigonometry
M1-Ch5 Force and Friction
P1---Ch8 Differentiation
M1---Ch5 Force and Friction
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10
2022/10/24 - 2022/10/30
P1---Ch8 Differentiation
M1---Ch7 Statics of a particle
11
2022/10/31 - 2022/11/6
P1---Ch8 Differentiation
P1 Test 4 Differentiation
M1---Ch7 Statics of a particle
M1 Test 3 Dynamics of a particle
12
2022/11/7 - 2022/11/13
P1---Ch9 Integration
M1---Ch6 Momentum and impulse
13
2022/11/14 - 2022/11/20
P1---Ch9 Integration
M1---Ch6 Momentum and impulse
14
2022/11/21 - 2022/11/27
15
2022/11/28 - 2022/12/4
16
2022/12/5 - 2022/12/11
P1---Ch9 Integration
P1 Test 5 Integration
M1---Ch8 Moments
Topic Review for P1
M1---Ch8 Moments
M1 Test 4 Momentum and Moments
Topic Review for M1
Pats papers
17
2022/12/12 - 2022/12/18
Pats papers
18
2022/12/19 - 2022/12/25
Pats papers
19
2022/12/26 - 2022/12/31
Review for difficult questions
20
2023/1/2 - 2023/1/8
Review for P1 and M1 exam in January
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2022-2023 Semester 1 （P2）
Week
Date
Topics / Contents
1
2023/2/13 - 2023/2/19
Ch1 Polynomials and proof
Test 1 Polynomials and proof
2
2023/2/20 - 2023/2/26
Ch2 Coordinate geometry in the (x, y) plan
Test 2 Coordinate geometry in the (x, y) plan
3
2023/2/27 - 2023/3/5
4
2023/3/6 - 2023/3/12
Ch3 Exponentials and logarithms
Test 3 Exponentials and logarithms
5
2023/3/13 - 2023/3/19
Ch4 The Binomial expansion
6
2023/3/20 - 2023/3/26
Ch5 Sequences and Series
Test 4 Expansion and Series
7
2023/3/27 - 2023/4/2
Ch6 Trigonometry
Test 5 Trigonometry
8
2023/4/3 - 2023/4/9
Ch7 Differentiation
9
2023/4/10 - 2023/4/16
Ch8 Integration
10
2023/4/17 - 2023/4/23
Review for Calculus
Test 6 Calculus
11
2023/4/24 - 2023/4/30
Topic Review
12
2023/5/2 - 2023/5/7
Pats papers
13
2023/5/8 - 2023/5/14
Pats papers
14
2023/5/15 - 2023/5/21
Review for difficult questions
15
2023/5/22 - 2023/5/28
Review for P2 exam in May
16
2023/5/29 - 2023/6/4
Competition
17
2023/6/5 - 2023/6/11
Competition
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⚫
G2:P3+P4+S1---5 Lessons per week (60min)
2023-2024 Semester 1 （P3+S1）
3 Lessons for P3 and 2 Lessons for S1 each week
Week
Topics / Contents
Date
1
2022/8/15 - 2022/8/21
P3---Ch1 Algebraic Fractions+Ch2
S1---Ch1&2 Measures of location and spread
2
2022/8/22 - 2022/8/28
P3---Ch2 Functions and graphs
S1---Ch3 Representations of data
3
2022/8/29 - 2022/9/4
4
2022/9/5 - 2022/9/11
P3---Ch2 Functions and graphs
P3 Test 1 Algebra and functions
S1 Test 1 Representation and summary of data
P3---Ch3 Trigonometric functions
S1---Ch4 Probability
5
2022/9/12 - 2022/9/18
6
2022/9/19 - 2022/9/25
7
2022/9/26 - 2022/9/30
8
2022/10/8 - 2022/10/16
9
2022/10/17 - 2022/10/23
P3---Ch6 Differentiation
S1 Test 3 Probability and Discrete random variable
10
2022/10/24 - 2022/10/30
11
2022/10/31 - 2022/11/6
P3---Ch6 Differentiation
P3 Test 4 Differentiation
S1---Ch7 Normal distribution
P3---Ch7 Integration
S1---Ch7 Normal distribution
12
2022/11/7 - 2022/11/13
P3---Ch4 Trigonometric additional formula
P3 Test 2 Trigonometry
S1---Ch4 Probability
P3---Ch5 Exponential and logarithms
S1 Test 2 Probability
P3---Ch5 Exponential and logarithms
P3 Test 3 Exponential and logarithms
S1---Ch6 Discrete random variable
P3---Ch6 Differentiation
S1---Ch6 Discrete random variable
P3---Ch7 Integration
S1 Test 4 Normal distribution
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P3---Ch7 Integration
P3 Test 5 Integration
S1---Ch5 Correlation and regression
P3---Ch8 Numerical methos
S1---Ch5 Correlation and regression
13
2022/11/14 - 2022/11/20
14
2022/11/21 - 2022/11/27
15
2022/11/28 - 2022/12/4
16
2022/12/5 - 2022/12/11
17
2022/12/12 - 2022/12/18
Pats papers
18
2022/12/19 - 2022/12/25
Pats papers
19
2022/12/26 - 2022/12/31
Review for difficult questions
20
2023/1/2 - 2023/1/8
Review for P2 and S1 exam in January
P3---Ch8 Numerical methos
P3 Test 6 Numerical methos
S1Test 5 Correlation and regression
Topic Review
Pats papers
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2022-2023 Semester 1 （P4）
Week
Date
Topics / Contents
1
2023/2/13 - 2023/2/19
Ch1 Proof
2
2023/2/20 - 2023/2/26
Ch2 Partial Fractions
3
2023/2/27 - 2023/3/5
4
2023/3/6 - 2023/3/12
5
2023/3/13 - 2023/3/19
6
2023/3/20 - 2023/3/26
Ch3 Coordinate geometry in the (x, y) plane
Test 2 Coordinate geometry in the (x, y) plane
7
2023/3/27 - 2023/4/2
Ch5 Differentiation
8
2023/4/3 - 2023/4/9
Ch6 Integration
9
2023/4/10 - 2023/4/16
Review calculus
Test 3 Calculus
10
2023/4/17 - 2023/4/23
Ch7 Vector
11
2023/4/24 - 2023/4/30
Test 4 Vector
12
2023/5/2 - 2023/5/7
Pats papers
13
2023/5/8 - 2023/5/14
Pats papers
14
2023/5/15 - 2023/5/21
Review for difficult questions
15
2023/5/22 - 2023/5/28
Review for P4 exam in May
16
2023/5/29 - 2023/6/4
Competition
17
2023/6/5 - 2023/6/11
Competition
Ch4 Binomial expansion
Test 1 Proof and Partial and Binomial
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IG 两年完成 Alevel 数学学习。大多数竞赛在下半年举行，完成考试后，学生可根据自己需求选择竞赛进
行准备工作。
澳大利亚 AMC，AMC10,袋鼠数学竞赛较简单。建议学生在 G1 准备参加，累积竞赛经验。进入 G2 后，
学生可在课余时间刷 AMC12 的题，较难。专攻英国方向的学生，UKMT 含金量很高，建议报考 SMC 高
级组的竞赛，获奖率较高，并且分数较高将会获得后续参与 UKMT-BMO 奥林匹克竞赛的资格（难度很
大）。有计算机基础的同学建议参与数学建模竞赛，提高团队协作能力。
若申请大学或专业（如图中所列大学）需 Step 或 MAT 成绩，建议 Alevel 年级后继续学习高数，并开始
准备这两个入学考试。Step 相对更难，需要花更多时间准备。针对需要的同学，会在 G2 完成大考后开
始进行基础训练，争取能在 A1 年级 6 月参加考试。
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A1-A2 IAL Further Mathematics (YFM01) Teaching Plan
Teaching materials:
IAL-Maths-Specification-YFM01
Textbook, Notebook, Past Papers, Workbook, PPT
⚫
A1:FP1+S2+M2---5 Lessons per week (60min)
FP1 (Aug-Nov) Take exam in next January
1. Complex numbers; (2 weeks)---Test 1
2. Roots of quadratic equations; (2 weeks)
3. Numerical solution of equations; (1 week)---Test 2
4. Coordinate systems; (2 weeks)---Test 3
5. Matrix algebra; (2 week)
6. Transformations using matrices; (1 week)---Test 4
7. Series; (2 week)
8. Proof.(2 week)---Test 5
S2 (Dec-Feb) Take exam in next May/June
1. The Binomial and Poisson distributions; (2 weeks)
2. Continuous random variables; (2 weeks)
3. Continuous distributions; (2 weeks)
4. Samples; (2 weeks)
5. Hypothesis tests.(3 weeks)
M2 (Mar-May) Take exam in next May/June
1. Kinematics of a particle moving in a straight line or plane; (2 weeks)
2. Centres of mass; (3 weeks)
3. Work and energy; (3 weeks)
4. Collisions; (2 weeks)
5. Statics of rigid bodies.(2 weeks)
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⚫
A2:FP2+FP3+M3/S3/D1---5 Lessons per week (60min)
（高数最后一本书取决于学生更擅长力学还是统计学，选择 D1 相对容易，但是
由于 D1 属于 AS 范畴，可能对总分结算不利。若是在学第三门课之前学生已经
获得三门总分 270 以上的成绩，选择 D1 更容易）
FP2 (Aug-Nov) Take exam in next January
1. Inequalities; (1 Week)
2. Series; (1 week)
3. Further complex numbers; (3 weeks)
4. First order differential equations;(2 weeks)
5. Second order differential equations; (2 weeks)
6. Maclaurin and Taylor series; (3weeks)
7. Polar coordinates.(2 weeks)
FP3 (Dec-Feb) Take exam in next May/June
1. Hyperbolic functions; (3 weeks)
2. Further coordinate systems; (2 weeks)
3. Differentiation; (2 weeks)
4. Integration; (3 weeks)
5. Vectors; (2 weeks)
6. Further matrix algebra.(2 weeks)
M3/S3/D1 (Mar-May) Take exam in next May/June
M3: Further kinematics; elastic strings and springs; further dynamics; motion in a circle; statics of
rigid bodies.
S3: Combinations of random variables; sampling; estimation, confidence intervals and tests;
goodness of fit and contingency tables; regression and correlation.
D1: Algorithms; algorithms on graphs; algorithms on graphs II; critical path analysis; linear
programming.
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International Mathematics competition
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UKMT-BMO
全称为 British Mathematical Olympia，英国数学奥林匹克竞赛，作为一个高水平的
竞赛，只有首先参加 SMC(Senior Mathematical Challenge) 高年级数学个人挑战赛
并取得优胜的学生才有机会参加 BMO。BMO 分为两轮，通过 SMC， 每年会邀请
大约 1000 名学生会参加 BMO Round 1, Round 1 题型为 6 道简答题，重视英语写作
能力。而在 BMO Round 1 中取得了排名前 100 的高分选手会被免费邀请参加
BMO Round2，其他 100 名以后的学生就要交钱作为 discretionary candidates 参加
第二轮。Round 2 题型为 4 道简题。
总的来说，STEP 和 MAT 是牛剑、帝国理工、华威等大学部分专业的必需考试，
MAT 的备考周期通常为 3-4 个月，而 STEP 的备考周期则为半年至一年左右。
BMO 则是学生为提升自身竞争力可自行选择的数学竞赛，含金量很高，如果
SMC 是基础款，那 BMO 一定是申请大学时的豪华加分项。非常建议对数学感兴
趣或是想申请数学、计算机等相应专业的学生，提前开始准备此类考试。
Step & MAT 介绍
剑桥 STEP 数学考试成绩通常作为英国几所顶尖高等院校，包括剑桥大学、帝国理
工学院、伦敦大学学院、华威大学等院校的数学、计算机等相关专业录取条件之
一。而牛津 MAT 数学考试则是申请牛津大学、帝国理工学院数学相关专业时必须
参加的笔试，大学在录取时会参考 MAT 成绩。有需求的同学，将在 A1 年级学习
Further maths 同时开始练习。
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