Scheme of Work
Subject: Pure Math 3
Grade: 11
No. of Lessons a week: 4
Course: CIE Grade 11 PM (Paper 3)
Teacher: Joyce Zhou
CIE Period: 2019-20
Context: This course is adapted from the Cambridge International AS/A Level Mathematics 9709 Syllabus for the Pure Mathematics Paper 3. As well as
demonstrating skill in the appropriate techniques, candidates will be expected to apply their knowledge in the solution of problems. Knowledge of the content of
Cambridge O Level/Cambridge IGCSE Mathematics is assumed. The aims are to enable students to 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; acquire a range of mathematical skills, particularly those which will enable them to use applications of mathematics in the context of everyday
situations and of other subjects they may be studying; develop the ability to analyze problems logically, recognize 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.
Lesson
Topic & Essential
Questions
Learning
Objectives
(Learners will know...)
Outcomes
(Learners will
be able to…)
Assessment
Key
Terms
Teaching Methods
Resources
Lesson
19/08/19
–
23/08/19
Topic & Essential
Questions
Polynomials
Inequalities
and Modulus
Learning
Objectives
(Learners will know...)
1. Definition of
modulus function |𝑥|:
𝑥 𝑖𝑓 𝑥 ≥ 0
|𝑥| = {
−𝑥 𝑖𝑓 𝑥 < 0
2. The division
algorithm for
polynomials
Dividend=divisor×quot
ient+reminder
3. the factor theorem
If for a polynomial
𝑃(𝑥), 𝑃(𝐶) = 0 then
𝑥 − 𝑐 is a factor of
𝑃(𝑥).
If fpr a polynomial
𝑏
𝑃(𝑥), 𝑃 ( ) = 0 then
𝑐
𝑎𝑥 − 𝑏 is a factor of
𝑃(𝑥).
4. the reminder
theorem
If a polynomial 𝑃(𝑥) is
divided by 𝑥 − 𝑐, the
reminder is 𝑃(𝑐).
If a polynomial 𝑃(𝑥) is
divided by 𝑎𝑥 − 𝑏, the
𝑏
reminder is 𝑝 ( ).
𝑎
Outcomes
(Learners will
be able to…)
Assessment
• understand the
meaning of |x|, sketch
the graph of y = |ax +
b| and use relations
such as |𝑎| = |𝑏| ⇔
𝑎2 = 𝑏 2 𝑎𝑛𝑑 |𝑥– 𝑎| <
𝑏 ⇔ 𝑎– 𝑏 < 𝑥 < 𝑎 + 𝑏
when solving
equations and
inequalities
• divide a polynomial,
of degree not
exceeding 4, by a
linear or quadratic
polynomial, and
identify the quotient
and remainder (which
may be zero)
• use the factor
theorem and the
remainder theorem.
• Notes and examples
Graphs of y = |f(x)|
and y = f(|x|) for nonlinear functions f are
not included.
e.g. to find factors and
remainders, solve
polynomial equations
or evaluate unknown
coefficients. Including
factors of the form (ax
+ b) in which the
coefficient of x is not
unity, and including
calculation of
remainders.
Formative:
Can students
divide a
polynomial?
Can students
distinguish
different
situations
when the
modulus
function is
involved.
Summative:
Assignment 1
Key
Terms
Teaching Methods
Polynomials
Divisor
Quotient
Remainder
Remainder
Theorem
Factor
Theorem
Inequalities
Modulus
function
Lecture
PowerPoint
lecture/notes
Student
Participation
Resources
Text book P2.1, P2.2
Practice book
Electronic notes:
Supplementary Notes for Paper 1
Learning & teaching resources
Exercises.
https://www.drfrostmaths.com
l&term=S1
http://www.examsolutions.net/mat
maths/sequences-series/binomial
https://www.youtube.com/wa
Lesson
Topic & Essential
Questions
Learning
Objectives
(Learners will know...)
Outcomes
(Learners will
be able to…)
Assessment
Differentiation:
Different students have different algebraic foundation. Some students has no
idea about modulus function. I have to begin with absolute value.
Key
Terms
Teaching Methods
Resources
Global Citizenship & Intercultural learning
Algebra is one of the key skills in scientific research. The relationship of different variables prove/
scientific knowledge such as quantum theory.
Interdisciplinary
Physics (all topics) – as physics a lot of formulas need to use algebra skills to solve them.
02/09/19
–
06/09/19
Natural
Logarithm
function is an
antiderivativ
e.
Exponential
function as
an inverse
function

The rules of
logarithms
1. log 𝑎 𝑎 𝑥 = 𝑥
2. 𝑎log𝑎 𝑥 = 𝑥
3. log 𝑎 𝑥𝑦 = log 𝑎 𝑥 +
log 𝑎 𝑦
𝑥
4. log 𝑎 (𝑦) =
log 𝑎 𝑥 − log 𝑎 𝑦
5. log 𝑎 (𝑥 𝑘 ) =
𝑘 log 𝑎 𝑥
log 𝑥
6. log 𝑎 𝑥 = 𝑏

log𝑏 𝑎
Natural
logarithms
1. logarithms th the
base of e are called
natural logarithms.
2. 𝑒 = 2.718
• use logarithms to
solve equations and
inequalities in which
the unknown appears
in indices
• use logarithms to
transform a given
relationship to linear
form, and hence
determine unknown
constants by
considering the
gradient and/or
intercept.
e.g. 𝑦 = 𝑘𝑥 𝑛 gives
ln 𝑦 = ln 𝑘 + 𝑛 ln 𝑥
which is linear in ln 𝑥
and ln 𝑦,
Formative
assessment:
Know the key
ideas in ln(x)
and ex. Solving
equations
involving such.
Summative
assessment:
Assignment 2
Antiderivative
Natural Log
function
indices
Change of
base
Exponential
function
Properties of
ex
Lecture with
PowerPoints
lecture/notes
Student
participation in
lecture
Presentation of
proof of laws of
logarithms.
Textbook: P2.3, P2.4
Electronic Notes: Supplementary
pp 71
Learning & teaching resources
https://www.drfrostmaths.com/sow
=S1
http://www.examsolutions.net/mat
maths/sequences-series/binomial
Lesson
Topic & Essential
Questions
Learning
Objectives
(Learners will know...)
3. ln 𝑥 is used to
represent log 𝑒 𝑥.
4. if 𝑦 = 𝑒 𝑥 then 𝑥 =
ln 𝑦
5. all the rules of
logarithms apply for
natural logarithms.
 The diagrams
of logarithms
Outcomes
(Learners will
be able to…)
Assessment
Key
Terms
Teaching Methods
Resources
𝑦 = 𝑘(𝑎 𝑥 ) gives ln 𝑦 =
ln 𝑘 + 𝑥 ln 𝑎 which is
linear in x and ln 𝑦.
Differentiation:
Global Citizenship & Intercultural learning

Interdisciplinary

09/09/19 – Trigonometry
12/09/19
Definition of
all six trig
functions.
Pythagorean
Identities.
Sums and
Double angle
formulas

Cosecant,
secant and
cotangent
• understand the
relationship of the
secant, cosecant and
cotangent functions to
cosine, sine and
tangent, and use
properties and graphs
of all six trigonometric
Formative
Assessment:
Establishing
Identities and
Solving
equations
giving
solutions with
given range.
Sine, cosine,
tangent,
secant,
cosecant,
cotangent,
Pythagorean
Identities,
Formulas for
sums and
differences,
Lecture with
PowerPoints
lecture/notes
Student
participation
Textbook: 5.1-6
Electronic Notes:
Supplementary Notes to Paper 1
Learning & teaching resources
https://www.drfrostmaths.com/sow
=S1
http://www.examsolutions.net/mat
maths/sequences-series/binomial
Lesson
Topic & Essential
Questions
Learning
Objectives
(Learners will know...)
Trigonometric
identities
1 + tan2 𝑥 = sec 2 𝑥
1 + cot 2 𝑥 = 𝑐𝑜𝑠𝑒𝑐 2 𝑥
 Compound
angle formula
sin(𝐴 ± 𝐵) =
sin 𝐴 cos 𝐵 ±
cos 𝐴 sin 𝐵
cos(𝐴 ± 𝐵) =
cos 𝐴 cos 𝐵 ∓ sin 𝐴 𝑠𝑖𝑛𝐵
tan(𝐴 + 𝐵) =

tan 𝐴+tan 𝐵
1−tan 𝐴 tan 𝐵
tan(𝐴 − 𝐵) =
tan 𝐴−tan 𝐵
1+tan 𝐴 tan 𝐵

Double angle
formulae
Outcomes
(Learners will
be able to…)
Assessment
functions for angles of
any magnitude
Notes and examples
• use trigonometrical
identities for the
simplification and
exact evaluation of
expressions, and in the
course of solving
equations, and select
an identity or
identities appropriate
to the context,
showing familiarity in
particular with the use
of
_ sec 2 𝜃 = 1 + tan2 𝜃
and 𝑐𝑜𝑠𝑒𝑐 2 𝜃 = 1 +
cot 2 𝜃
_ the expansions of
sin(𝐴 ± 𝐵) , cos(𝐴 ± 𝐵)
and tan(𝐴 ± 𝐵)
_ the formulae for
sin 2𝐴 , cos 2𝐴 and
tan 2𝐴
Summative
Assessment:
Assignment 3
Class Test 1
Key
Terms
Double and
half angle
formulas and
formulas for
general
solution
Teaching Methods
Resources
Lesson
Topic & Essential
Questions
Learning
Objectives
(Learners will know...)
Outcomes
(Learners will
be able to…)
Assessment
Key
Terms
Teaching Methods
Resources
sin 2𝐴 = 2 sin 𝐴 cos 𝐴
cos 2𝐴
= cos 2 𝐴 − sin2 𝐴
= 1 − 2 sin2 𝐴
= 2 cos 2 𝐴 − 1
2 tan 𝐴
tan 2𝐴 =
1 − tan2 𝐴
Differentiation:
Global Citizenship & Intercultural learning
Week 7:
Week 8:
Oct 8 to
Oct 12
Expressing 𝑎 sin 𝜃 +
𝑏 cos 𝜃 in the form
𝑅 sin(𝜃 ± 𝛼) or
𝑅 cos(𝜃 ± 𝛼)
• use trigonometrical
identities for the
simplification and
exact evaluation of
expressions, and in the
course of solving
equations, and select
an identity or
identities appropriate
to the context,
showing familiarity in
particular with the use
of
_ the expression of
𝑎 sin 𝜃 + 𝑏 cos 𝜃 in the
forms 𝑅 sin(𝜃 ± 𝛼) and
𝑅 cos(𝜃 ± 𝛼)
eg. Simplifying
cos(𝑥 − 30° ) −
3 sin(𝑥 − 60° ).
Formative
assessment:
Student
remembers
the formulas
of
differentiation
and
integration of
functions
involving trig
functions.
Summative
assessment:
Assignment 4
Product Rule
and
Quotient Rule
Derivative of
sin(x), cos(x),
tan(x),
cosec(x),
cot(x), sec(x).
Integration of
sin(x), cos(x)
tan(x), cot(x)
with particular
attention given
to integration
of sec(x) and
cosec(x)
Lecture
PowerPoint
lecture/notes
Student
Participation in
Lectures.
Textbook: 6.1-4
Electronic Notes:
pp. 77
Learning & teaching resources
https://www.drfrostmaths.com/sow
=S1
http://www.examsolutions.net/mat
maths/sequences-series/binomial
Lesson
Topic & Essential
Questions
Learning
Objectives
(Learners will know...)
Outcomes
(Learners will
be able to…)
Assessment
Key
Terms
Teaching Methods
eg. Solving tan 𝜃 +
cot 𝜃 = 4,2 sec 2 𝜃 −
tan 𝜃 = 5,3 cos 𝜃 +
2 sin 𝜃 = 1.
Differentiation:
Global Citizenship & Intercultural learning

Interdisciplinary
Resources
Lesson
Week 8:
Oct 8 to
12
Topic & Essential
Questions
More on
differentiation
,
Derivatives of
products,
quotients and
compositions.
Parametricall
y defined
functions.
Differentiation:
Learning
Objectives
(Learners will know...)
Use of combinations
of product, quotient
and chain rules to find
derivatives of
functions involving ex,
ln(x), sin(x), cos(x) etc.
Find the derivative of
parametrically defined
functions.
Outcomes
(Learners will
be able to…)
Assessment
Student can find the
derivative of most any
function
Formative
Assessment:
Can student
find derivative
of any
function?
Summative
Assessment:
Assignment 5
Key
Terms
Teaching Methods
Product rule,
quotient rule,
chain rule.
Parametrically
defined
functions
Lecture
PowerPoint
lecture/notes
Student
Participation in
lectures.
Global Citizenship & Intercultural learning
Interdisciplinary
Resources
Textbook
Electronic
Supplementary note
pp.71-
Lesson
Week 9
(part 1)
Oct 15-17
Topic & Essential
Questions
Solving
equations
numerically
Differentiation:
Learning
Objectives
(Learners will know...)
Review of geometric
and/or trigonometric
relations.
Exercise on how an
equation can be set
up.
Locate a root of an
equation and use a
recursive formula to
determine the value of
a root to a prescribed
degree of accuracy
Outcomes
(Learners will
be able to…)
Student can solve an
equation numerically
which cannot be
solved using other
methods.
Assessment
Formative
Assessment:
Can student
set up an
equation
under given
conditions.
Can student
solve the
equation?
Key
Terms
Teaching Methods
Arcs and
sectors.
Sequences
Iterations or
Recursive
relations
Limits of
sequence
Convergence
and
divergence
Sign change
rule
Lecture
PowerPoint
Student
participation in
lectures.
Global Citizenship & Intercultural learning
Interdisciplinary
Resources
Textbo
8.1, 8.3 ,8
Electronic
p.9
Lesson
Week 9
(part 2)
Oct 17-19
Topic & Essential
Questions
Binomial
series
Differentiation:
Learning
Objectives
(Learners will know...)
Expanding (a+b)n
where n is not an
integer. The condition
under which such
expansion is possible.
Expanding related
expressions.
Outcomes
(Learners will
be able to…)
Assessment
The student should
know how to expand
the binomial series
using (a) a formula (b)
using recursion
Key
Terms
Formative
assessment:
Student can
expand (a+b)n
when asked.
Summative
Assessment:
Assignment: 6
Binomial
series
Binomial
coefficient
Algorithm
Recursive
formula
Teaching Methods
Lecture
PowerPoint
lecture/notes
Student
participation
Global Citizenship & Intercultural learning
Interdisciplinary
Resources
Textbook:
Electronic
pp. 1
Lesson
Topic & Essential
Questions
Week 10
Oct 22-26
Techniques of
Integration
(part 1)
Learning
Objectives
(Learners will know...)
Substitution
Integration by parts
Outcomes
(Learners will
be able to…)
Use of differential
Integration by parts
formula
Assessment
Key
Terms
Formative
Assessment:
Can student
perform a
change of
variable? Can
student
recognize when
to use
integration by
parts? Can
students choose
u and dv?
Substitution
u=g(x) then
du=g’(x)dx
Teaching Methods
Lecture
PowerPoint
lecture/notes
Student participation
in class.
∫udv=uv-∫vdu
Differentiation:
Weeks 16-17
Differentiation:
Global Citizenship & Intercultural learning
Resources
Textbook: 18.1-4
Electronic Notes:
pp 99
Lesson
Topic & Essential
Questions
Weeks
16-17
Learning
Objectives
(Learners will know...)
Outcomes
(Learners will
be able to…)
Assessment
Key
Terms
Teaching Methods
Any explicit
language &
learning taking
place
Learning
experiences and
strategies- Please
delete what is not
being used. Aim
for a variety to
facilitate learning
Lecture
Socratic seminar
Small group/pair
work PowerPoint
lecture/notes
Individual
presentations
Group
presentations
Student
lecture/leading
Interdisciplinary
learning Details:
Other/s:
Weeks 18-19
Differentiation:
Global Citizenship & Intercultural learning
Resources
Lesson
Topic & Essential
Questions
Weeks 1819
Weeks 20-22
Week 23
Interdiscipli
nary
Learning
Objectives
(Learners will know...)
Outcomes
(Learners will
be able to…)
Assessment
Key
Terms
Teaching Methods
Any explicit
language &
learning taking
place
Learning
experiences and
strategies- Please
delete what is not
being used. Aim
for a variety to
facilitate learning
Lecture
Socratic seminar
Small group/pair
work PowerPoint
lecture/notes
Individual
presentations
Group
presentations
Student
lecture/leading
Interdisciplinary
learning Details:
Other/s:
Christmas and New Year Holidays
Revision for the End of Semester Exam
Resources
Lesson
Topic & Essential
Questions
Learning
Objectives
(Learners will know...)
Outcomes
(Learners will
be able to…)
Assessment
Key
Terms
Teaching Methods
Week 24
End of Semester Exams for Semester I
Week 25
EOS Feedback & Quarter III Topics Overview
Week 26
Differenti
ation:
Global Citizenship & Intercultural learning
Resources
Lesson
Week 26
Topic & Essential
Questions
Learning
Objectives
(Learners will know...)
Interdiscipli
nary
Outcomes
(Learners will
be able to…)
Assessment
Key
Terms
Teaching Methods
Any explicit
language &
learning taking
place
Learning
experiences and
strategies- Please
delete what is not
being used. Aim
for a variety to
facilitate learning
Lecture
Socratic seminar
Small group/pair
work PowerPoint
lecture/notes
Individual
presentations
Group
presentations
Student
lecture/leading
Interdisciplinary
learning Details:
Other/s:
Weeks 27-29
Week 30
Ching Spring festival Holiday
Resources
Lesson
Topic & Essential
Questions
Differenti
ation:
Week 30
Learning
Objectives
(Learners will know...)
Outcomes
(Learners will
be able to…)
Assessment
Key
Terms
Teaching Methods
Global Citizenship & Intercultural learning
Interdiscipli
nary
Any explicit
language &
learning taking
place
Learning
experiences and
strategies- Please
delete what is not
being used. Aim
for a variety to
facilitate learning
Lecture
Socratic seminar
Small group/pair
work PowerPoint
lecture/notes
Individual
presentations
Group
presentations
Student
lecture/leading
Interdisciplinary
learning Details:
Other/s:
Weeks 31-33
Differentiation:
Resources
Lesson
Topic & Essential
Questions
Learning
Objectives
(Learners will know...)
Outcomes
(Learners will
be able to…)
Assessment
Key
Terms
Teaching Methods
Global Citizenship & Intercultural learning
Weeks 3133
Interdiscipli
nary
Any explicit
language &
learning taking
place
Learning
experiences and
strategies- Please
delete what is not
being used. Aim
for a variety to
facilitate learning
Lecture
Socratic seminar
Small group/pair
work PowerPoint
lecture/notes
Individual
presentations
Group
presentations
Student
lecture/leading
Interdisciplinary
learning Details:
Other/s:
Weeks
34-35
Differentiation:
Resources
Lesson
Topic & Essential
Questions
Learning
Objectives
(Learners will know...)
Outcomes
(Learners will
be able to…)
Assessment
Key
Terms
Teaching Methods
Global Citizenship & Intercultural learning
Weeks
34-35
Interdiscipli
nary
Any explicit
language &
learning taking
place
Learning
experiences and
strategies- Please
delete what is not
being used. Aim
for a variety to
facilitate learning
Lecture
Socratic seminar
Small group/pair
work PowerPoint
lecture/notes
Individual
presentations
Group
presentations
Student
lecture/leading
Interdisciplinary
learning Details:
Other/s:
Week 36
Week 37
Mock Exams Week
Mock Exam Feedback and Quarter IV Activities Overview
Resources
Lesson
Topic & Essential
Questions
Weeks 3845
CIE Period
Learning
Objectives
(Learners will know...)
Outcomes
(Learners will
be able to…)
Assessment
Key
Terms
Teaching Methods
Resources