Hwa Chong Institution
Subject/Programme : Mathematics
Scheme of Work 2015
Level : Secondary 4
Scheme of Work (incorporating GL-Matrix, Differentiation: italicised for SBGE, italicised & underlined for SSMT)
Learning outcomes are statements of what a student should know, understand and/or be able to demonstrate after completion of a process of
learning.
OVERVIEW
Term 1
Trigonometry IV (6 wk)
Unit 1: Mensuration – Arc Length, Sector Area,
Radian Measure (1 wk)
Unit 2: Further Trigonometric Identities (5 wk)
Binomial Expansion I (1 wk)
Unit 1: Binomial Theorem (1 wk)
Term 2
Calculus I (7 wk)
Unit 1: Differentiation (2 wk)
Unit 2: Tangents, Normals and Rate of
Change (1 wk)
Unit 3: Maxima and Minima (1 wk)
Unit 4: Further Differentiation (2 wk)
Unit 5: Integration (1 wk)
Term 3
Calculus I (4.5 wk)
Unit 5: Integration (1 wk)
Unit 6: Partial Fractions (1 wk)
Unit 7: Applications of Integration – Area of a
Region (1.5 wk)
Unit 8: Applications of Integration – Kinematics (1
wk)
Term 4
Revision (2 wk)
Probability (1 wk)
Unit 1: Probability (1 wk)
Vectors I (1.5 wk)
Unit 1: Vectors in Two Dimensions (1.5 wk)
2 Tests (10%)
Term 1 Test 1: Week 3
(a) Sec 3 Add math topic (Trigonometry –
trigo ratios, simplify, prove and solve]
(b) Mensuration ( Arc Length, Sector Area
and Radian Measure)
Term 1 Test 2: Week 8/9
(a) Further Trigonometric Identities
2 Tests (10%)
Term 2 Test 3: Week 4/5
(a) Binomial Theorem
(b) Differentiation
(c) Tangents, Normals and Rates of
Change
Term 2 Test 4: Week 8
(a) Maxima and Minima
(b) Further Differentiation
2 Tests (10%)
Term 1 Test 5: Week 4
EOY Exam (70%)
All topics
(a) Integration
(b) Partial Fractions
Term 1 Test 6: Week 7
(a) Applications of Integration – Area of a
Region
(b) Applications of Integration – Kinematics
(c) Probability
1
Hwa Chong Institution
Subject/Programme : Mathematics
Scheme of Work 2015
Level : Secondary 4
Time
allocated
In Wks/hrs
1 week
Time frame
Term 1
Week 21
In Wks/hrs
5 weeks
Time frame
Term 1
Week 4 2
to Week 9 6
Content/ Learning Outcomes
Core:
Trigonometry IV (Unit
1/Mensuration – Arc Length,
Sector Area and Radian Measure)
At the end of the topic, students
will be able to
1. define angles in radian
2. determine the arc length and
area of sector/segment
3. apply the various formulae
(including those in
trigonometry) to solve problem
sums involving arc length,
sector, segment, triangles
within a circle.
Core:
Trigonometry IV (Unit 2/Further
Trigonometric Identities)
At the end of the topic, students
will be able to
1. derive
(a) compound angle formulae
(b) double angle formulae
(c) factor formulae
(d) R-formulae
2. use of the above formulae to
(a) simplify trigonometric
expressions.
(b) to solve trigonometrical
equations in a given interval in
degrees or in radians.
Suggested Curriculum of
Parallel/s
Connection:
Apply fractions of the
circumference and the area of
circle respectively to find the arc
length and area of a sector.
Synthesis concepts of area of a
sector and area of triangle to
derive the generalize the formula
for area of segment.
Practice:
Model picatures of art work using
concepts in Circular Measure
using article from Mathematics
teacher | Vol. 104, No. 5 •
December 2010/January 2011
Connection:
Apply the concepts of
trigonometric identities learnt in
Sec 3 to trigonometric identities
learnt in Sec 4
Model periodic waves and signals
in sciences and engineering
(pulse rate or fourier series) using
combinations of trigonometric
functions.
Demonstrate the translation of
trigonometric functions using Rformula
Determine the maximimum or
minimum angle or value of
trigonometric functions
in Physics (e.g. projectile motion)
Using R-formula to illustrate
Learning Activities
Assessment/Feedback
Suggestions:
Suggestions:
Inquiry Learning :
Formative Asssessment :
 Quizlet flash cards on
conversions of angles from
degree to radian and vice
versa.
 Who Wants to be a
Millionaire? Circula Measure
Students establish the
realationship between angles in
degree and radian in a unit
circle.[ Refer to Java Applet and
Activity Worksheet 1]
Blended Learning:
Students explore ivle resource
package to equip them with the
concepts required for mastery of
this unit followed by room
dicussions on any
misconception/s arise from the
assigned assignment.
Suggestions:
Inquiry Learning :
Students explore on applet to
derive the compound angle
formula.
Flipped Learning:
Students will watch two videos on
(a) deriving double angle
formulae .
(b) applying double angle to
simplify trigonometric
expressions, solve trigonometrical
equations and prove
trigonometrical identities. [Pencil
Resources
Online resources:
 ivle package
 Real life Application of
circular Measure
 What is 1 radian?
 Who Wants to be a
Millionaire? Circular
Measure
 Fields
Summative Assessment: Term 1
Test 1:
 Radian measures
 Trigonomtery using compound
angle formulae and double
angle formula
Print Resources:
- New Syllabus Mathematics 3
6th Edition by Shinglee
Chapter 12
Suggestions:
Online resources:
 Proof of compound angle
formula
 Application of
Trigonometry in real life
 Proof of double angle
formula
 R-Formula
Formative Asssessment :
(c) Pop-quiz to access mastery of
concepts
 Concept map or mindmap to
reflect on their mastery of the
skills
 Performance Task: Additional
Mathematics 360 by Marshall
Cavendish Chapter 13 pg 347
Summative Assessment: Term 1
Test 2
 Trigonomtery using factor
formulae and R-formula
 Binomial Theorem
Print Resources:
- Additional Mathematics 360
by Marshall Cavendish
Chapter 13
2
Hwa Chong Institution
Subject/Programme : Mathematics
Scheme of Work 2015
Level : Secondary 4
(c) prove trigonometric identities
(more rigorous, >5 steps – SMTP)
(d) to solve word problems
(e) recognise the structural
difference between factor formulae
and R-formula, and to use them in
correct situations.
(f) identify all complementary
angles  and 90   in
problems especially when applying
R-formula.
(f) recognize and use the reverse
of trigonometric identities, for
example: cos 2 A  1  cos 2 A ,
2
sin 2 A 
Time
allocated
In Wks/hrs
1 week
Time frame
Term 1
Week 1 8
transformation (translation) of
trigonometric functions
College-Unit 13.2 ] [Refer to
Assignment 3]
Blended Learning:
Students will research the
combinations of trigonometric
functions graphs can be used to
model the pluse rate of a person
under different conditions and
share their findings in
1  cos 2 A
2
Content/ Learning Outcomes
Core:
Binomial Expansion I (Unit
1/Binomial Theorem)
At the end of the topic, students
will be able to
1. construct the Pascal’s
triangle (via tossing coins)
n
and use it to expand (a + b) ,
especially for smaller values
of n.
2. use the Binomial Theorem to
n
expand (a + b) for positive
integer n.
3. use of the general term Tr + 1
Suggested Curriculum of
Parallel/s
Connection:
Use tossing coins and algebraic
approach to create the Pascal
Triangle.
Application of Binomial Theorem
in computing, economic
prediction, architecture
Investigate the impact on
expansion of Binomial Theorem
applied to negative or rational
power
Apply binomial theorem to word
problems involving combinatorics
Learning Activities
Assessment/Feedback
Suggestions:
Suggestions:
Inquiry Learning :
Formative Asssessment :
 Pop-quiz to ascertain basic
concepts and skills (using ivle
quiz)
 Comic strip (using Bitstrips
apps via facebook) to
consolidate the concepts and
skills
 Concept map or mindmap to
reflect on their mastery of the
skills
Students establish the
relationship between Pascal
Triangle and Binomial expansion.
Blended Learning:
Students explore the online
resources in ivle to establish the
relationship between
n
 
r
and the Pascal triangle followed
with room dicussion to generalise
Resources
Online resources:
- Tossing coins and algebraic
approach to create Pascal
Triangle
- Real life application of
Binomial Theorem
- Binomial Theorem and
Binomial Coefficients
- ivle lesson package
Working url : online quiz
http://connectatkmtc.wordpress.
com/binomial-theorem/
Print Resources:
- Additional Mathematics 360
by Marshall Cavendish
3
Hwa Chong Institution
Subject/Programme : Mathematics
Scheme of Work 2015
Level : Secondary 4
n  n – r r
= r  a b to find a
 
particular term in the
n
expansion of (a + b) .
4. use the Binomial Theorem to
expand trinomials
5. extract relevant powers in
product of two or more
Binomial expansions
6. Know the notation
n
n !,   .
r
7. solve problems involving
Binomial coefficients
8. relate probability and counting
with Binomial Theorem
the result for the Binomial
Theorem
Chapter 5
Complied by Mr ChenZH
(6)(2)
Ex 5.1 (The Binomial Expansion
of (1  b) )
Q1, 2, 10,
n
(3)(5)(7)
Ex 5.2 (The Binomial Expansion
of (a  b) )
Q13, 14, 15, 16, 17,
n
(4)(7)
Revision Ex 5
QA5
(8)
Q:
There are 8 white balls and 12
black balls in a bag. Three balls
are drawn from the bag with
replacement.
(a) Illustrate all the outcomes
with a tree diagram.
(b) Find the probability of
drawing 2 white balls and 1
black ball.
Alan decides to draw 7 balls
from the same bag with
replacement.
(c) Find the number of
outcomes of drawing 3 white
balls and 4 black balls.
(d) Hence find the probability of
drawing 3 white balls and 4
4
Hwa Chong Institution
Subject/Programme : Mathematics
Scheme of Work 2015
Level : Secondary 4
black balls.
*no clear mentioning of (1)
Time
allocated
In Wks/hrs
2 weeks
Time frame
Term 2 Week
1 to 2
Content/ Learning Outcomes
Core:
Calculus I (Unit 1/Differentiation)
At the end of the topic,
students will be able to
1. define and evaluate limits
2. derive the gradient function
of simple polynomials
x 2 , x3
3.
,… from first
principles
differentiate standard
n
4.
5.
functions x , (for any
rational n) together with
constant multiples and sums
and differences of these
functions.
use the notation f ( x ) ,
f ( x) , dy ,
dx
d 2 y d  dy  .
  
dx 2 dx  dx 
address the misconception
d 2 y  dy 
 
dx 2  dx 
differentiate using
(a) chain rule
(b) product rule
(c) quotient rule.
that
6.
2
Suggested Curriculum of
Parallel/s
Connection:
Relate the derivative of a
function to the gradient of the
tangent to a curve at a given
point, including horizontal and
vertical tangents.
Relate the concept of change to
non-linear situations (e.g.
projectile motion, continuous
data)
Practice:
Create meaning through the
application of Calculus in real
life and discuss the reasons,
implications and different
perspectives, thereby showing
social awareness of issues
involved (e.g. manufacturing of
conical paper cups using
optimal amount of material,
roller coaster, football – angle
of coverage vs position of
player).
Comment on the controversy on
invention of calculus between
Newton and Leibniz.
Learning Activities
Assessment/Feedback
Suggestions:
Suggestions:
Inquiry Learning:
Formative Asssessment :
(d) Pop-quiz to access mastery of
concepts
 Concept map or mindmap to
reflect on their mastery of the
skills
 Performance Task: Additional
Mathematics 360 by Marshall
Cavendish Chapter 14 pg 371
Students relate the derivative of a
function to the gradient of the
tangent to a curve at a given point,
including horizontal and vertical
tangents.
Blended Learning :
Students discuss and state their
views on the controversy between
Newton and Leibniz in the room
after viewing this clip.
Summative Assessment: Term 2
Test 1
Resources
Online resources:
 Online calculus Applet
 Slope
 Gradient of tangent
 Online Practice Exercise
 Newton and Leibniz
 What is a derivative?
 Power Rule
Print Resources:
- Additional Mathematics 360
by Marshall Cavendish
Chapter 14
Compiled by Ms OoiTL and Ms
Ang CC
(1)(2)
Activity 14A Pg 350
(3)
Exercise 14.1 (Differentiation of
Polynomials)
Q2, Q3, Q4,Q5,Q6
(3)
Ex 14.1 (Gradient of the
tangent)
Q7, Q8, Q9,Q10b, Q11,
Q12,Q13,Q14,Q15
5
Hwa Chong Institution
Subject/Programme : Mathematics
Scheme of Work 2015
Level : Secondary 4
7.
simplify the algrabraic
fractions (especially with
square roots) after applying
quotient rule.
(6)(7)
Ex 14.2 (Chain Rule)
Q1d, Q1f, Q2b, Q2d,Q3b,
Q3d,Q4b, Q4d, Q5e, 5f,Q6a,
6b, Q7,Q8,Q9, Q11
(6)
Ex 14.3 (Product Rule)
Q1d, Q2d, Q2e, Q2f, Q3a, Q3b,
Q4 (wrong given y: change to
y  x 3  x 2 ) , Q6,
Q7,Q8,Q10
(6)(7)
Ex 14.4 (Quotient Rule)
Q1b, 1d, 1e, Q2, Q4, Q5, Q6
Q7, Q8, Q11 (Higher order
thinking)
In Wks/hrs
1 week
Time frame
Term 2 Week
3
Core:
Calculus I (Unit 2/Tangents,
Normals and Rates of Change)
At the end of the topic,
students will be able to
1. find equations of tangent and
normal using dy .
dx
2. Address the misconception
that equation of tangent is
dy
y  y0 
( x  x0 )
dx
without specifying the value
of dy .
dx
3. apply differentiation to solve
problems involving related
Connection:
Compare the strategies learnt in
Sec 3 to fixed equations of lines
and perpendicular lines to that
of the equations of tangent and
normal using dy
dx
Relate concept of
increasing/decreasing function
to the different types of
standard graphs that they have
learnt in Sec 3
Use increasing/decreasing
function to introduce the
concept of turning point and
point of inflexion
Practice:.
Suggestions:
Suggestions:
Inquiry Learning:
Formative Asssessment :
(e) Pop-quiz to access mastery of
concepts
 Concept map or mindmap to
reflect on their mastery of the
skills
 Performance Task: Additional
Mathematics 360 by Marshall
Cavendish Chapter 15 pg 398
Students relate the sign of the first
derivative of a function to the
behaviour of the function
(increasing or decreasing), locate
points on the graph where the
derivative is zero, and describe the
behaviour of the function before, at
and after these points.
Summative Assessment: Term 2
Test 3
*no clear mentioning of (4)(5)
Online resources:
 Increasing Function,
Increasing or Decreasing
Function
 Point of Inflection
 Ladder Problem
 Oil Problem
 Conical Flask
 Rate of Change
Print Resources:
- Additional Mathematics 360
by Marshall Cavendish
Chapter 15
Compiled by Ms OoiTL and Ms
Ang CC
6
Hwa Chong Institution
Subject/Programme : Mathematics
Scheme of Work 2015
Level : Secondary 4
4.
5.
rates of change
explain
increasing/decreasing
functions using dy .
dx
Distinguish between
Increasing and decreasing
and strictly increasing or
decreasing
Use rate of change and product
rule to derive Newton’s second
law of motion and apply to the
launch of rocket where mass is
changing
(1)
Ex 15.1 (Equation of tangent
and normal)
Q6, Q7, Q8, Q9, Q14, Q15,
Q16, Q17
(4)
Ex 15.2 (Increasing /Decreasing
fns)
Q4, Q5, Q9, Q10, Q12, Q13
(3)
Ex 15.3 (Rate of Change &
Connected Rate of change)
Q4,Q5,Q6
Ex 15.4
Q1a, Q1b, 1d, Q2c, Q2d,Q3,
Q4, Q6, Q7, Q9, Q10,Q12,
Q13, Q14, Q15
In Wks/hrs
1 week
Time frame
Term 2 Week
5
Core:
Calculus I (Unit 3/Maxima and
Minima)
At the end of the topic,
students will be able to
1. apply differentiation to find
stationary points .
2. apply differentiation to solve
maxima and minima
problems. Must prove
maximum or minimum using
d 2 y or d y sign test.
dx
dx 2
3. Discuss cases where the
second derivative test to
discriminate between
maxima and minima fails
Connection:
Solve using examples
discussed in Unit 1 (e.g.
manufacturing of conical paper
cups using optimal amount of
material, roller coaster, football
– angle of coverage vs position
of player).
Discuss and relate the
alternative methods (e.g. vertex
form, differentiation)to
maximise/ minimise quadratic
functions
Relate point of inflexion to point
symmetry of cubic graphs
Relate concepts of stationary
point, intercept and asymptote
to curve sketching
Suggestions:
Suggestions:
Blended Learning:
Formative Asssessment :
(f) Pop-quiz to access mastery of
concepts
 Concept map or mindmap to
reflect on their mastery of the
skills
 Performance Task: Additional
Mathematics 360 by Marshall
Cavendish Chapter 16 pg 421
Students discuss on how to apply
differentiation to solve real-life
problems
(a) Dirt Farm
(b) Particle Motion
(c) Diving into related rate of
change
Summative Assessment: Term 2
Test 4
*no clear mentioning of (2)
Online resources:
 Increasing Function,
Increasing or Decreasing
Function
 Point of Inflection
 Ladder Problem
 Oil Problem
 Conical Flask
 Rate of Change
Print Resources:
- Additional Mathematics 360
by Marshall Cavendish
Chapter 16
Compiled by Ms OoiTL and Ms
Ang CC
7
Hwa Chong Institution
Subject/Programme : Mathematics
Scheme of Work 2015
Level : Secondary 4
(e.g. y  x , y  x )
and instead, use the first
derivative test and introduce
the concept of point of
inflexion.
3
In Wks/hrs
2 weeks
Time frame
Term 2 Week
6 to Week 7
(1)
Ex 16.1 (Stationary points)
Q4, Q5, Q7b, Q7c,Q7d, Q9,
Q10, Q11,Q12,
Q13,Q14,Q15,Q16, Q18
5
Core:
Calculus I (Unit 4/Further
Differentiation)
At the end of the topic,
students will be able to
1. extend differentiation from
first principle to derive first
derivative of sine, cosine and
tangent functions.
2. extend differentiation from
first principle to derive first
derivative logarithmic
(general base) and
exponential functions.
3. find the derivatives of
trigonometric functions using
the concept of chain rule.
4. find the derivatives of
exponential and logarithmic
functions (base e). using the
concept of chain rule
5. apply the above to solve
problems involving
(a) trigonometric functions,
Identity:
Consider the various
viewpoints, thus improving
decision-making by maximising
or minimising desired objectives
such as profits,quality and time,
cost-benefit.
Connection:
Discuss and relate the
alternative methods (e.g. Rformula, diffferentiation)to
maximise/ minimise
trigonometric functions
Practice:
Discuss examples of problems
in real-world contexts (e.g.
radioactivity, cable signal and
landing of an object), involving
the use of differentiation of
trigonometric functions,
exponential functions and
logarithmic functions.
(2)
Ex 16.2 (Maxima and Minima)
Q3, Q6, Q8,Q9,Q10,Q15, Q15,
Q16
Suggestions:
Suggestions:
Inquiry Learning:
Formative Asssessment:
(g) Pop-quiz to access mastery of
concepts
 Journal writing on the
common mistake of
Students observe the shape of the
derivative function of
y  sin x and y  cos x and
establish the following results.
d
 sin x   cos x
dx
d
 cos x    sin x
dx
Blended Learning:
Students research on Cardiac
Output and discuss the use of
differentiation of trigonometric
functions, exponential functions and
logarithmic functions to improve
decision-making.
d x
 e   xe x1 .
dx


Student designed Jeopardy
game on Differentiation.
[Sample]
Performance Task: Additional
Mathematics 360 by Marshall
Cavendish Chapter 17 pg 447
Summative Assessment: Term 2
Test 4
*check whether any questions
cover (3)
Online resources:
 Ladder Problem
 Oil Problem
 Conical Flask
 Rate of Change
Print Resources:
- Additional Mathematics 360
by Marshall Cavendish
Chapter 17
Compiled by Ms OoiTL and Ms
Ang CC
(3)
Ex 17.1 (Derivatives of Trigo
Fns - Skill Check)
Q1, Q2, Q3, Q4, Q5, Q8
(3)(5)
Ex 17.1 (Derivatives of Trigo
Fns - Application)
Q6, q7, Q9, Q10, Q11, Q13,
Q14,Q15, Q16, Q17, Q22
(4 - exponential)(5)
8
Hwa Chong Institution
Subject/Programme : Mathematics
Scheme of Work 2015
Level : Secondary 4
(b) exponential functions
and
(c) logarithmic functions.
Ex 17.2 (Derivatives of
Exponential Fns - Skill Check)
Q1, Q2, Q3, Q4, Q5, Q6,Q11
Ex 17.2 (Derivatives of
Exponential Fns - Application)
Q12, Q13, Q14, Q15, Q16,
(4 – log)(5)
Ex 17.3 (Derivatives of Log Fns
- Skill Check)
Q1, Q2, Q7c, 7d, 7e
Ex 17.3 (Derivatives of Log Fns
- Application)
Q8, Q9, Q11, Q13, Q18(Higher
order)
, Q20(Higher order), , Q21
(Higher order)
In Wks/hrs
2 weeks
Core:
Calculus I (Unit 5/Integration)
Time frame
Term 2 Week
10 & Term 3
Week 1
At the end of the topic,
students will be able to
1. understand integration as a
reverse process of
differentiation.
2. determine indefinite integrals
of sums of terms with powers
of x including
k (ax  b) , ke
k sin(ax  b) ,
k cos(ax  b) ,
ax  b
Suggestions:
Suggestions:
Inquiry Learning:
Formative Asssessment :
(h) Pop-quiz to access
mastery of concepts
(i) Concept map or mindmap
to reflect on their mastery
of the skills
(j) Student create Jeopardy
game on Integration.
(k) Performance Task:
Additional Mathematics
360 by Marshall
Cavendish Chapter 18 Pg
479
Students observe and establish the
relationship that integration as a
reverse process of differentiation.
Students will view through the video
on integration of
k sin(ax  b) ,
k cos(ax  b) , k sec (ax  b)
2
1.
x
3. integrate functions of the form
n
Connection:
Verify the solutions from
integrand and illustrate its nonuniqueness through
differentiation of the
integrand.(i.e..Emphasise +c for
indefinite integrals)
,
Blended Learning:
Students apply integration to
determine the indefinite integrals of
sums of terms with powers of x
*no clear mentioning of (1) and
(2) – first derivative
Online resources:
 Derivative and Indefinite
integral
 Definite and Indefinite
Integral
 Definite integral applet
 Integration trigonometrical
functions

Integration of
e( ax b )
Print Resources:
- Additional Mathematics 360
by Marshall Cavendish
Chapter 18
Compiled by Dr ANGLC
Summative Assessment: Term 3
9
Hwa Chong Institution
Subject/Programme : Mathematics
Scheme of Work 2015
Level : Secondary 4
k sec2 (ax  b) , e
( ax  b )
including
where a, b and n are real.
4. integrate Integral involving the
use of double angle formulae
sin x cos x dx, cos 2 x dx .

Test 5
1.
x
Students deduce that when they
integrate intergral such as

(1)
Ex. 18.1 (Indefinite Integral)
Q15, 16, 18, 22, 23
 sin x cos x dx,  cos x dx it
2
5. Recognise the conditions for
direct integrals and for the
case of non-direct integrals,
use trigo identities to
transform into direct integrals
(e.g. direct integral = sec2x,
indirect integral = cos2x, sin2x)
6. Use Integration by substitution
and by parts - SMTP
(1)
Activity 18A (pg 449)
involves the use of double angle
formulae.
(1)(2)
Activity 18B (pg 460)
(1)(2)
Ex. 18.2 (Definite Integral)
Q7, 11, 12, 13
(3 – Trigo only)
Ex. 18.3 (Integration of Trigo
Functions)
Q8, 9, 11, 12
For SMTP:
Integration by Substitution and
by Parts
In Wks/hrs
1 week
Time frame
Term 3 Week
2
Core:
Calculus I (Unit 6/Partial
Fractions) (covered in Sec 3 SIP)
At the end of the topic,
students will be able to
1.
2.
3.
identify whether an algebraic
fraction is a proper or an
improper fractions.
decompose a rational
expression into partial
fractions,
perform long division on
improper rational
Connection:
Suggestions:
Suggestions:
Perform long division [Sec 3] on
an improper fraction and
express it as the sum of a
polynomial and a proper
fraction before expressing it as
partial fractions.
Comment on the use of “coverup” method developed by Oliver
Heaviside to determine the
unknown constants and discuss
its limitations
Flipped Learning:
Formative Asssessment :
(l) Pop-quiz to access mastery of
concepts
(m) Research on Oliver Heaviside
(n) Performance Task: Additional
Mathematics 360 by Marshall
Cavendish Chapter 3 pg 89
Students view this video on
teachertube [Long division of
Polynomial] on improper fraction on
express it as the sum of a
polynomial and a proper fraction
before expressing it as partial
fractions.
Blended Learning:
Students discuss on applications of
partial fractions in real life
Summative Assessment:
 Class test:
Topics for Term 3 Test 5
(a) Integration
*no clear mentioning of (4) & (5)
Online resources:
 Partial Fractions
 Online quiz on Partial
fraction
Print Resources:
- Additional Mathematics 360
by Marshall Cavendish
Chapter 3
Compiled by Dr ANGLC
(1)(2)(3)(4 – not all cases, but
complete the rest of the cases
in Ex 18.4)
10
Hwa Chong Institution
Subject/Programme : Mathematics
Scheme of Work 2015
Level : Secondary 4
4.
expressions before
expressing the proper
rational expressions as
partial fractions,
include cases where
denominator is of the form
(ax  b)(cx  d ) ,
application eg. electrical or
mechanical engineering where
partial fractions is used not only for
finding integrals, but also for
analyzing linear differential systems
like resonant circuits and feedbackcontrol systems.
(b) Partial Fractions
Ex. 3.6 (Partial Fraction)
Q7, 8, 9, 11, 12
(3)
Ex. 18.4 (Integration of
Exponential Functions)
Q9, 12, 13,
Q22 & Q23 (Higher order)?? –
up to Q19 only
(ax  b)(cx  d )2 and
(ax  b)( x 2  c 2 )
In Wks/hrs
1.5 weeks
Time frame
Term 3 Week
3 to Week 4
Core:
Calculus I (Unit 7/Applications of
Integration – Area of a Region)
At the end of the topic,
students will be able to
1
2
understand and define
definite integrals,
understand the mathematical
and graphical interpretation
d
of
 f ( x)  ,
dx
 f ( x) dx and

b
a
3
4
f ( x) dx
evaluate definite integrals
define and relate definite
integrals to the area
bounded by a curve and
axes
5 find area under curve by
(a) estimation by drawing
rectangles / trapeziums,
(b) definite integral.
Connection:
Suggestions:
Suggestions:
Relate area under curve to
Fundamental Theorem of
Calculus
Inquiry learning :
Formative Asssessment :
(o) Pop-quiz to access mastery of
concepts.
(p) Student create Jeopardy
game on Integration.
 Performance Task: Additional
Mathematics 360 by Marshall
Cavendish Chapter 19 pg 499
Discuss various methods learnt
to find area of triangle (e.g.
1
1
bh, ab sin C ,
2
2
Shoelace method, Integration)
and area of trapezium
Discuss the different methods
(e.g.limiting process of
rectangles or trapeziums) used
to find area under the curve
Students use VTi or graphing tool to
deduce that area under curve can
be estimated by drawing
rectangles. [ Area Under curve ]
Online resources:
 Area under the curve
 Area under curve
(rectangles)
 Area between two curves
Print Resources:
- Additional Mathematics 360
by Marshall Cavendish
Chapter 19
Compiled by Dr ANGLC
Summative Assessment:
 Class test:
Topics for Term 3 Test 5
(a) Integration
(b) Partial Fractions
(1)
Activity 19A (pg 484)
(6)
Activity 19B (pg 486)
(3)(4)(5b)
Ex. 19.1 (Area between a Curve
and an Axis)
Q11, 12, 13, 16, 20, 21
(5b)(7)
Ex. 19.2 (Area between a Curve
and a Line)
Q8, 9, 11, 12
11
Hwa Chong Institution
Subject/Programme : Mathematics
Scheme of Work 2015
Level : Secondary 4
6. find area bounded by curve
and y-axis
7. find area bounded by curve
and line/another curve
8. find the volume of revolution
- SMTP
In Wks/hrs
1 week
Time frame
Term 3 Week
5
Core:
Calculus I (Unit 7/Applications of
Integration – Kinematics)
At the end of the topic,
students will be able to
1. distinguish between constant,
average and instantaneous
rate of change with reference
to graphs. Not to confuse with
and apply the kinematics
equations taught in Physics
which involves only constant
acceleration.
2. apply differentiation and
integration to kinematics
problems involving
 displacement / total
distance travelled
 velocity
 acceleration of a particle
For SMTP:
Volume of Revolution
*no clear mentioning of (5a) and
(2 – “f(x)” notation)
Connection:
Derive the kinematics equations
(e.g. v=u+at, s=ut+1/2at2) using
v-t and s-t graphs by integration
and differentiation.
Practice:
Model the motion of a particle in
a straight line, using
displacement, velocity and
acceleration as vectors (e.g.
velocity in the positive direction
of x-axis is positive)
Extend the kinematics
equations to the horizontal and
vertical components of
projectile motion
Translate the motion of
pendulum using v-t graphs
Consider real world factors
influencing motion (for e.g. air
resistance) and link to terminal
Suggestions:
Suggestions:
Inquiring Learning:
Formative Asssessment :
(q) Pop-quiz to access mastery of
concepts
(r) Student create Jeopardy
game on Integration.
 Performance Task: Additional
Mathematics 360 by Marshall
Cavendish Chapter 20 pg 516
Students summaries the differences
between the three types (constant,
average and instaneous) rate of
change by using the gradient of the
graphs. [Refer to Textbook Activity
15C]
Summative Assessment: Term 3
Test 6
Online resources:
 Using calculus in
kinematics
 Kinematics
Print Resources:
- Additional Mathematics 360
by Marshall Cavendish
Chapter 20
Compiled by Dr ANGLC
(-)
Activity 20B (pg 502)
(1)
Activity 20C (pg 505)
(2)
Ex. 20.1 (Kinematics)
Q9, 12,16, 19, 20
*no clear mentioning on
“distance travelled on 3rd sec”
12
Hwa Chong Institution
Subject/Programme : Mathematics
Scheme of Work 2015
Level : Secondary 4

Time
allocated
In Wks/hrs
1 Week
Time frame
Term 3 Week
6
moving in a straight line
with variable.
distance travelled on 3rd
sec (for example)
Content/ Learning Outcomes
Core:
Probability I (Unit 1/Probability)
At the end of the topic,
students will be able to
1. Understand probability as a
measure of chance. the
properties of probability
2. calculate the probability of a
single event
3. calculate combined events
probabilities with the help of
possibility diagrams and
probability trees
4. distinguish between
mutually exclusive and nonmutually exclusive events,
and between independent
and dependent events.
5. understand probability trees
and use them to illustrate
probability problems.
6. problems involving set
symbols.
7. relate probability to binomial
theorem.
8. calculate advanced
probability problems
combining combinatorics
methods of counting
9. understand and apply
conditional probability
velocity for skydiving
Suggested Curriculum of
Parallel/s
Connection:
Establish connection between
probability of tossing a coin and
binomial theorem.
Extend the concept of probability
using Galton machine as a
example to illustrate binomial
distribution
Practice:
Discuss the concept of probability
(or chance) using everyday
events, including simple
experiments such as tossing a
coin.
Compare and discuss the
experimental and theoretical
values of probability using
computer simulations.
Link probability to mathematics
games such as Pachinko –
Japanese arcade games
Connect probability to expected
value of variable and concept of
calculation of average with
frequency of data
Use probability tree and
conditional probability to analyse
the chances of winning in the
Game of Crap
Interpret Gross Domestic Product
(GDP) using confidence interval
Learning Activities
Assessment/Feedback
Suggestions:
Suggestions:
Inquiry Learning :
Formative Asssessment :
 Student video record their
experiment of tossing a coin
and establish the connection
between probability, binomial
theorem and probability tree.
Students discuss the concept of
probability (or chance) using
everyday events, including simple
experiments such as tossing a
coin and relate probability to
binomial theorem and tree
diagram.
Blended Learning :
Students distinguish between
mutually exclusive and nonmutually exclusive events, and
between independent and
dependent events and use
probability tree to illustrate
probability problems.

Student write a mathematical
reflective jounrnal after
reading this article Parking
Lot
Summative Assessment: Term 3
Test 6
Resources
Online resources:
 Independent and Dependent
events
 Mutually Exclusive events
 Birthday paradox
 Exploration with chance
 Forest Fire Simulation
 Monty Hall Game
 Random Drawing Tool
 Adjustable Spinner
 What happen if you gusess?
(TED EDUCATION)
Print Resources:
- New Syllabus Mathematics 2 7th
Edition by Shinglee Chapter 11
- New Syllabus Mathematics 4 6th
Edition by Shinglee Chapter 6
13
Hwa Chong Institution
Subject/Programme : Mathematics
Scheme of Work 2015
Level : Secondary 4
10. illustrate law of total
probability using Venn
diagram
Identity:
Discuss the ills of gambling and
the impact on family especially
loansharks
Using the story of MIT university
undergrads, discuss how they
have devised the winning
strategies using probability and
use this story to let students be
aware of legal implications for
beating the game
14
Hwa Chong Institution
Subject/Programme : Mathematics
Scheme of Work 2015
Level : Secondary 4
Time
allocated
In Wks/hrs
1.5 weeks
Time frame
Term 3 Week
8 to Week 9
Content/ Learning Outcomes
Core:
Vectors I (Unit 1/Vectors in Two
Dimensions)
At the end of the topic,
students will be able to
1. use notations such as
 x
.
  , AB, a, AB , a , a
 y
2. understand vector as a
directed line segments.
3. understand concept of
translation by a vector.
4. understand concept of
position vector. And link it to
coordinates geometry.
5. define the magnitude of a
 x
2
2
 as x  y .
y
 
vector 
8. understand and represent
graphically the sum and
difference of two vectors
and a multiple of a vector.
9. express given vectors in
terms of coplanar vectors
using sum and difference of
vectors.
7. multiply a vector by a scalar.
8. Ratio Theorem and mid-point
theorem for vectors
9. solve geometric problems
using vector, e.g. computing
area ratios, proving
parallelogram, trapezium
and other special types of
Suggested Curriculum of
Parallel/s
Connection:
Relate to Physics problems
involving resolution of vectors
Relate to Arithmetic concept of
negative numbers as numbers
with direction
Relate to unit vector as a basic
unit
Compare and contrast method
in Coordinate Geometry to
Vector method in proving
geometrical problems
Learning Activities
Assessment/Feedback
Suggestions:
Suggestions:
Inquiring Learning:
Formative Asssessment :
(s) Pop-quiz to access mastery of
concepts
Students use the Vector Applets
and Resultant Vector represent
graphically the sum and
difference of two vectors and a
multiple of a vector.
Summative Assessment: EOY
Exam
Resources
Online resources:
 Vector Applets
 Resultant Vector
 relative velocity problems,
 mechanics problems
 Vectors in movie making
 Vectors (TED Education
difference between scalar and
vector)
Print Resources:
- New Syllabus Mathematics 4 6th
Edition by Shinglee Chapter 3
- ivle online package
Compare the different notations
used in Coordinate Geometry,
Matrices, and Vectors
Extend the concept of vectors
to find dot product and scalar
product
15
Hwa Chong Institution
Subject/Programme : Mathematics
Scheme of Work 2015
Level : Secondary 4
quadrilaterals, collinearity
etc.
10. Calculate dot product and
explain the significance –
SMTP
16