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.

OVERVIEWTerm 1 Term 2 Term 3 Term 4

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)

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)

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)

Probability (1 wk)Unit 1: Probability (1 wk)

Vectors I (1.5 wk)Unit 1: Vectors in Two Dimensions (1.5 wk)

Revision (2 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

(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

EOY Exam (70%)All topics

1

Hwa Chong Institution Subject/Programme : Mathematics

Scheme of Work 2015 Level : Secondary 4

Time allocated Content/ Learning Outcomes

Suggested Curriculum of Parallel/s

Learning Activities Assessment/Feedback Resources

In Wks/hrs1 week

Time frameTerm 1 Week 21

Core:Trigonometry IV (Unit 1/Mensuration – Arc Length, Sector Area and Radian Measure)

At the end of the topic, students will be able to1. define angles in radian2. determine the arc length and

area of sector/segment3. apply the various formulae

(including those in trigonometry) to solve problem sums involving arc length, sector, segment, triangles within a circle.

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

Suggestions:

Inquiry Learning :

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:

Formative Asssessment : Quizlet flash cards on

conversions of angles from degree to radian and vice versa.

Who Wants to be a Millionaire? Circula Measure

Summative Assessment: Term 1 Test 1: Radian measures Trigonomtery using compound

angle formulae and double angle formula

Online resources: ivle package Real life Application of

circular Measure What is 1 radian? Who Wants to be a

Millionaire? Circular Measure

Fields

Print Resources:- New Syllabus Mathematics 3

6th Edition by Shinglee Chapter 12

In Wks/hrs5 weeks

Time frameTerm 1 Week 4 2 to Week 9 6

Core:Trigonometry IV (Unit 2/Further Trigonometric Identities)

At the end of the topic, students will be able to1. 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.(c) prove trigonometric identities(more rigorous, >5 steps – SMTP)(d) to solve word problems(e) recognise the structural

Connection:Apply the concepts of trigonometric identities learnt in Sec 3 to trigonometric identities learnt in Sec 4Model 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 R-formulaDetermine the maximimum or minimum angle or value of trigonometric functionsin Physics (e.g. projectile motion)Using R-formula to illustrate transformation (translation) of trigonometric functions

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 College-Unit 13.2 ] [Refer to Assignment 3]

Blended Learning:

Suggestions:

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

Online resources: Proof of compound angle

formula Application of

Trigonometry in real life Proof of double angle

formula R-Formula

Print Resources:- Additional Mathematics 360

by Marshall Cavendish Chapter 13

2

Hwa Chong Institution Subject/Programme : Mathematics

Scheme of Work 2015 Level : Secondary 4

difference between factor formulae and R-formula, and to use them in correct situations.(f) identify all complementary

angles and in problems especially when applying R-formula.(f) recognize and use the reverse of trigonometric identities, for

example:

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

Time allocated Content/ Learning Outcomes

Suggested Curriculum of Parallel/s

Learning Activities Assessment/Feedback Resources

In Wks/hrs1 week

Time frameTerm 1 Week 1 8

Core:Binomial Expansion I (Unit 1/Binomial Theorem)

At the end of the topic, students will be able to1. construct the Pascal’s

triangle (via tossing coins) and use it to expand (a + b)n, especially for smaller values of n.

2. use the Binomial Theorem to expand (a + b)n for positive integer n.

3. use of the general term Tr + 1

= an – rbr to find a particular term in the expansion of (a + b)n.

Connection:Use tossing coins and algebraic approach to create the Pascal Triangle.Application of Binomial Theorem in computing, economic prediction, architectureInvestigate the impact on expansion of Binomial Theorem applied to negative or rational powerApply binomial theorem to word problems involving combinatorics

Suggestions:

Inquiry Learning :

Students establish the relationship between Pascal Triangle and Binomial expansion.

Blended Learning:

Students explore the online resources in ivle to establish the

relationship between and the Pascal triangle followed with room dicussion to generalise the result for the Binomial Theorem

Suggestions:

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

Online resources:- Tossing coins and algebraic

approach to create Pascal Triangle

- Real life application of Binomial Theorem

- Binomial Theorem and Binomial Coefficients

- ivle lesson packageWorking url : online quiz http://connectatkmtc.wordpress.com/binomial-theorem/

Print Resources:- Additional Mathematics 360

by Marshall Cavendish Chapter 5

Complied by Mr ChenZH

(6)(2)Ex 5.1 (The Binomial Expansion

3

Hwa Chong Institution Subject/Programme : Mathematics

Scheme of Work 2015 Level : Secondary 4

4. use the Binomial Theorem to expand trinomials

5. extract relevant powers in product of two or more Binomial expansions

6. Know the notation .

7. solve problems involving Binomial coefficients

8. relate probability and counting with Binomial Theorem

of )Q1, 2, 10,

(3)(5)(7)Ex 5.2 (The Binomial Expansion

of )Q13, 14, 15, 16, 17,

(4)(7)Revision Ex 5QA5

(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 black balls.

*no clear mentioning of (1)

Time allocated Content/ Learning Outcomes

Suggested Curriculum of Parallel/s

Learning Activities Assessment/Feedback Resources

In Wks/hrs Core: Connection: Suggestions: Suggestions: Online resources:

4

Hwa Chong Institution Subject/Programme : Mathematics

Scheme of Work 2015 Level : Secondary 4

2 weeks

Time frameTerm 2 Week 1 to 2

Calculus I (Unit 1/Differentiation)

At the end of the topic, students will be able to1. define and evaluate limits2. derive the gradient function

of simple polynomials

,… from first principles

3. differentiate standard

functions (for any rational n) together with constant multiples and sums and differences of these functions.

4. use the notation ,

, ,

.5. address the misconception

that 6. differentiate using

(a) chain rule(b) product rule(c) quotient rule.

7. simplify the algrabraic fractions (especially with square roots) after applying quotient rule.

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.

Inquiry Learning:

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.

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

Summative Assessment: Term 2 Test 1

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

(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

) , Q6,

5

Hwa Chong Institution Subject/Programme : Mathematics

Scheme of Work 2015 Level : Secondary 4

Q7,Q8,Q10

(6)(7)Ex 14.4 (Quotient Rule)Q1b, 1d, 1e, Q2, Q4, Q5, Q6Q7, Q8, Q11 (Higher order thinking)

*no clear mentioning of (4)(5)In Wks/hrs1 week

Time frameTerm 2 Week 3

Core:Calculus I (Unit 2/Tangents, Normals and Rates of Change)

At the end of the topic, students will be able to1. find equations of tangent and

normal using .2. Address the misconception

that equation of tangent is

without specifying the value

of .3. apply differentiation to solve

problems involving related rates of change

4. explain increasing/decreasing

functions using .5. Distinguish between

Increasing and decreasing and strictly increasing or decreasing

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 usingRelate concept of increasing/decreasing function to the different types of standard graphs that they have learnt in Sec 3Use increasing/decreasing function to introduce the concept of turning point and point of inflexion

Practice:.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

Suggestions:

Inquiry Learning: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.

Suggestions:

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

Summative Assessment: Term 2 Test 3

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

(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

6

Hwa Chong Institution Subject/Programme : Mathematics

Scheme of Work 2015 Level : Secondary 4

Ex 15.4Q1a, Q1b, 1d, Q2c, Q2d,Q3, Q4, Q6, Q7, Q9, Q10,Q12, Q13, Q14, Q15

*no clear mentioning of (2)In Wks/hrs1 week

Time frameTerm 2 Week 5

Core:Calculus I (Unit 3/Maxima and Minima)

At the end of the topic, students will be able to1. apply differentiation to find

stationary points .2. apply differentiation to solve

maxima and minima problems. Must prove maximum or minimum using

or sign test.3. Discuss cases where the

second derivative test to discriminate between maxima and minima fails

(e.g. ) and instead, use the first derivative test and introduce the concept of point of inflexion.

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 functionsRelate point of inflexion to point symmetry of cubic graphsRelate concepts of stationary point, intercept and asymptote to curve sketching

Identity:Consider the various viewpoints, thus improving decision-making by maximising or minimising desired objectives such as profits,quality and time, cost-benefit.

Suggestions:

Blended Learning: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

Suggestions:

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

Summative Assessment: Term 2 Test 4

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

(1)Ex 16.1 (Stationary points)Q4, Q5, Q7b, Q7c,Q7d, Q9, Q10, Q11,Q12, Q13,Q14,Q15,Q16, Q18

(2)Ex 16.2 (Maxima and Minima)Q3, Q6, Q8,Q9,Q10,Q15, Q15, Q16

*check whether any questions cover (3)

In Wks/hrs2 weeks

Time frameTerm 2 Week

Core:Calculus I (Unit 4/Further Differentiation)

Connection:Discuss and relate the alternative methods (e.g. R-formula, diffferentiation)to maximise/ minimise

Suggestions:

Inquiry Learning:

Students observe the shape of the

Suggestions:

Formative Asssessment:(g) Pop-quiz to access mastery of

concepts

Online resources: Ladder Problem Oil Problem Conical Flask Rate of Change

7

Hwa Chong Institution Subject/Programme : Mathematics

Scheme of Work 2015 Level : Secondary 4

6 to Week 7 At the end of the topic, students will be able to1. 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,(b) exponential functions

and(c) logarithmic functions.

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.

derivative function of

and establish the following results.

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.

Journal writing on the common mistake of

. 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

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)Ex 17.2 (Derivatives of Exponential Fns - Skill Check)Q1, Q2, Q3, Q4, Q5, Q6,Q11Ex 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)

*no clear mentioning of (1) and (2) – first derivative

8

Hwa Chong Institution Subject/Programme : Mathematics

Scheme of Work 2015 Level : Secondary 4

In Wks/hrs2 weeks

Time frameTerm 2 Week 10 & Term 3 Week 1

Core:Calculus I (Unit 5/Integration)

At the end of the topic, students will be able to1. understand integration as a

reverse process of differentiation.

2. determine indefinite integrals of sums of terms with powers

of x including .3. integrate functions of the form

, ,

,

,

, where a, b and n are real.

4. integrate Integral involving the use of double angle formulae

.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

Connection:Verify the solutions from integrand and illustrate its non-uniqueness through differentiation of the integrand.(i.e..Emphasise +c for indefinite integrals)

Suggestions:

Inquiry Learning:

Students observe and establish the relationship that integration as a reverse process of differentiation.

Students will view through the video

on integration of ,

,

Blended Learning:

Students apply integration to determine the indefinite integrals of sums of terms with powers of x

including .

Students deduce that when they integrate intergral such as

it

involves the use of double angle

formulae.

Suggestions:

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

Summative Assessment: Term 3 Test 5

Online resources: Derivative and Indefinite

integral Definite and Indefinite

Integral Definite integral applet Integration trigonometrical

functions

Integration of

Print Resources:- Additional Mathematics 360

by Marshall Cavendish Chapter 18

Compiled by Dr ANGLC

(1)Activity 18A (pg 449)

(1)Ex. 18.1 (Indefinite Integral)Q15, 16, 18, 22, 23

(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

*no clear mentioning of (4) & (5)

9

Hwa Chong Institution Subject/Programme : Mathematics

Scheme of Work 2015 Level : Secondary 4

In Wks/hrs1 week

Time frameTerm 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. identify whether an algebraic fraction is a proper or an improper fractions.

2. decompose a rational expression into partial fractions,

3. perform long division on improper rational expressions before expressing the proper rational expressions as partial fractions,

4. include cases where denominator is of the form

,

and

Connection:

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 “cover-up” method developed by Oliver Heaviside to determine the unknown constants and discuss its limitations

Suggestions:

Flipped Learning:

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 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 feedback-control systems.

Suggestions:

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

Summative Assessment: Class test:

Topics for Term 3 Test 5(a) Integration(b) Partial Fractions

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)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

In Wks/hrs1.5 weeks

Time frameTerm 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 understand and define definite integrals,

2 understand the mathematical and graphical interpretation

of ,

Connection:

Relate area under curve to Fundamental Theorem of Calculus

Discuss various methods learnt to find area of triangle (e.g.

, Shoelace method, Integration) and area of trapezium

Discuss the different methods

Suggestions:

Inquiry learning :

Students use VTi or graphing tool to deduce that area under curve can be estimated by drawing rectangles. [ Area Under curve ]

Suggestions:

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

Summative Assessment: Class test:

Online resources: Area under the curve Area under curve

(rectangles) Area between two curvesPrint Resources:- Additional Mathematics 360

by Marshall Cavendish Chapter 19

Compiled by Dr ANGLC

(1)Activity 19A (pg 484)

10

Hwa Chong Institution Subject/Programme : Mathematics

Scheme of Work 2015 Level : Secondary 4

and

3 evaluate definite integrals4 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.

6. find area bounded by curve and y-axis7. find area bounded by curve and line/another curve8. find the volume of revolution - SMTP

(e.g.limiting process of rectangles or trapeziums) used to find area under the curve

Topics for Term 3 Test 5(a) Integration(b) Partial Fractions

(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

For SMTP:Volume of Revolution

*no clear mentioning of (5a) and (2 – “f(x)” notation)

In Wks/hrs1 week

Time frameTerm 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

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 motionTranslate the motion of pendulum using v-t graphsConsider real world factors influencing motion (for e.g. air

Suggestions:

Inquiring Learning:

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]

Suggestions:

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

Summative Assessment: Term 3 Test 6

Online resources: Using calculus in

kinematics KinematicsPrint 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

11

Hwa Chong Institution Subject/Programme : Mathematics

Scheme of Work 2015 Level : Secondary 4

acceleration of a particle moving in a straight line with variable.

distance travelled on 3rd sec (for example)

resistance) and link to terminal velocity for skydiving

“distance travelled on 3rd sec”

Time allocated Content/ Learning Outcomes

Suggested Curriculum of Parallel/s

Learning Activities Assessment/Feedback Resources

In Wks/hrs1 Week

Time frameTerm 3 Week 6

Core:Probability I (Unit 1/Probability)

At the end of the topic, students will be able to1. 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 non-mutually 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

10. illustrate law of total probability using Venn

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 gamesConnect probability to expected value of variable and concept of calculation of average with frequency of dataUse probability tree and conditional probability to analyse the chances of winning in the Game of CrapInterpret Gross Domestic Product (GDP) using confidence interval

Identity:

Suggestions:

Inquiry Learning :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 non-mutually exclusive events, and between independent and dependent events and use probability tree to illustrate probability problems.

Suggestions:

Formative Asssessment : Student video record their

experiment of tossing a coin and establish the connection between probability, binomial theorem and probability tree.

Student write a mathematical reflective jounrnal after reading this article Parking Lot

Summative Assessment: Term 3 Test 6

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

12

Hwa Chong Institution Subject/Programme : Mathematics

Scheme of Work 2015 Level : Secondary 4

diagram Discuss the ills of gambling and the impact on family especially loansharksUsing 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

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Hwa Chong Institution Subject/Programme : Mathematics

Scheme of Work 2015 Level : Secondary 4

Time allocated Content/ Learning Outcomes

Suggested Curriculum of Parallel/s

Learning Activities Assessment/Feedback Resources

In Wks/hrs1.5 weeks

Time frameTerm 3 Week 8 to Week 9

Core:Vectors I (Unit 1/Vectors in Two Dimensions)

At the end of the topic, students will be able to1. use notations such as

.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

vector as .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 vectors9. solve geometric problems

using vector, e.g. computing area ratios, proving parallelogram, trapezium and other special types of quadrilaterals, collinearity etc.

Connection:Relate to Physics problems involving resolution of vectorsRelate to Arithmetic concept of negative numbers as numbers with directionRelate to unit vector as a basic unit

Compare and contrast method in Coordinate Geometry to Vector method in proving geometrical problems

Compare the different notations used in Coordinate Geometry, Matrices, and Vectors

Extend the concept of vectors to find dot product and scalar product

Suggestions:

Inquiring Learning:Students use the Vector Applets and Resultant Vector represent graphically the sum and difference of two vectors and a multiple of a vector.

Suggestions:

Formative Asssessment :(s) Pop-quiz to access mastery of

concepts

Summative Assessment: EOY Exam

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

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Hwa Chong Institution Subject/Programme : Mathematics

Scheme of Work 2015 Level : Secondary 4

10. Calculate dot product and explain the significance – SMTP

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