RAN PENG MT 6A

RANCANGAN PENGAJARAN/PEMBELAJRAN

SCHEME OF WORK

PRA-U2 MATHEMATICS T 2012TERM /

WEEK

THEMELEARNING

AREAINTENDED OUTCOME LEARNING LEARNING DAN TEACHING ACTIVITIES /

TECHNIQUESNOTEPEDAGOGY

Semester11st Week

IntegrationIntegral

of a function

Integration

techniques1.To determine the antiderivative of a function

f(x) by reversing the process of differentiation.

2.To obtain the integral of a function making use

of the integrals of x n , e x, sin x, cos x, sec 2 x.

3.Carrying out integration of kf(x) and f(x) (g(x).

4.To obtain the integral of a function in the form

{f(x)} r f (x), where r is a rational number.

1.Revising integration by reversing the process of

differentiation,

the integrals of x n , e x, sin x, cos x, sec 2 x,

the integrals of kf(x) and f(x) (g(x). Exercises and

discussions.

2.Investigating the integral of a function in the form

{f(x)} r f (x), where r is rational number. Exercises and

discussions.Obeying the law

Carefulness

Rationality

Honesty

Diligence

Determinations

Cleanliness

Patience

ResponsibilityDirective

Mastery

Metacognitive

Penyediaan JSI, soalan, skema PS1 bermula. Mesyuarat Kelab dan Permainan , Pendaftaran keahlian.

2nd week5.To obtain the integral of a function using

substitutions.

6.To obtain the integral of a rational function by

means of decomposition into partial fractions.

7.To obtain the integral of a function using

integration by parts.3. Introducing integration by means of substitutions.4.Introducing the techniques of integration of a rational

function by means of decomposition into partial fractions

Exercises and discussions.

5.Introducing the techniques of integration of a product of

function two function by means of integration by parts.


Meraikan pelajar cemerlang PMR, Pelancaran Program Peningkatan Akademik Perfect Score Milikku . Kem Kecemerlangan.

3th WeekIntegrationDefinite integrals

Trapezium

rule

Applications

of integration1.Evaluating definite integrals of a function.

2.Evaluating the approximate value of a definite

integral of a function using trapezium rule.

3.To determine the plane area between a curve

and x - axis.

4.To determine the plane area between a curve

and y - axis.

5.To determine the plane area between two

curves.

1.Introducing definite integrals of a function as a process of

summation of the area of strips. the skill of evaluating

the definite integrals with change of variable,

approximate method for evaluating a definite integral

by the trapezium rule. Exercises and discussions.

2.Revising the application of integration to find the plane

area of the region between curve and x - axis, curve and

y - axis and area of the region between two curves.


Kem kecemerlangan STPM

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4th WeekIntegrationApplications

of integration6.To determine the volume of revolution of a

curve about the x - axis.

7.To determine the volume of revolution of a

curve about the y - axis.3.Revising the application of integration to find the volume of

revolution of a plane area enclosed by a section of a curve

and the x - axis about the x - axis. a plane area enclosed

by a section of a curve and the y - axis about the y axis,Obeying the law

Carefulness

Rationality

HonestyDirective

Mastery

Metacognitive

8. To determine the volume of revolution of a

curve about the line x = k.

a plane area enclosed by two curves about x- axis / y -axis.


4.Revising integration and discussing various type of

problems. Exercises and discussions.Diligence Determinations

Cleanliness

PatienceResponsibility

Merenras Desa

5th WeekCuti Berganti, ,Cuti Peristiwa, Cuti Tahun Baru Cina

6th WeekDifferential

EquationsDifferential Equations

First order DE with separable variables.

1.To identify the order of a differential equation.

2.To identify the degree of a differential

equation.

3.To determine the differential equation from the

general solution .

4.To identify the differential equation of the first

order and first degree with separable variables.1.Introduction of differential equation, order of differential

equation, degree of differential equation, solution of

differential equation, general solution and particular solution,

family of curves of the solution. Exercises and discussions.

First order

Homogeneous DE

5.To obtain the general solution and particular

solution for the differential equations of the first

order and first degree with separable

variables .

6.To identify the first order homogeneous

differential equations.

2. Introduction of first order differential equation with separable

variables and the skill of solving. Exercises and discussions.

Pra Kejohanan Olahraga, Minggu Anti Dadah, Kursus Motivasi Sahsiah Pra-U

7th Week7.To obtain the general solution and particular

solution for the first order homogeneous

differential equations .

8.To obtain the general solution and particular

solution for the differential equations which

can be transformed into differential equations

of the types variables separable or

homogeneous equations.3. Introduction of first order homogenous differential equation

and the skill of solving. Exercises and discussions.

4. Introduction to first order differential equation which can be

solved by substitution. Exercises and discussions.

Problems Invollving Differential Equation9.To sketch a family of solution curves.

10.To solve mechanical and physical problems

which can be modeled by differential

equations5. Introduction of physical and mechanical problems involving

differential equation, and the skill of solving. Exercises and

exercises. Revising differential equation , doing

revision exercise and discussions

TERM /

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8thWeekTrigonometrySolution of a

TriangleDua and Three Dimensional

Problems1. To obtain the solution of a triangle using the

sine rule.

2. To investigate the ambiguity case when using

the sine rule.

3. To obtain the solution of a triangle using the

cosine rule.

4. To obtain the area of a triangle.

5. To solve problems involving triangles.6.To draw normal from a point to a plane and

orthogonal projection of a straight line onto a

plane.

7.To identify the angle between a straight line

and a plane. 8. To identify the angle between two intersecting

planes.

9. To identify the angle between two skew lines.1.Revising the sine rule and investigate the ambiguity case.

2. Revising the cosine rule.

3. Derive the formula of the area of a triangle .

Introduction of Herons formula.

4. Discussing problems involving triangle, exercise and


Carefulness

Rationality

Honesty

Diligence

Determinations

Cleanliness

Patience

Responsibility

Directive

Mastery

Metacognitive

10.To draw normal from a point to a plane and

orthogonal projection of a straight line onto a

plane.

11.To identify the angle between a straight line

and a plane.

12. To identify the angle between two intersecting planes.

13. To identify the angle between two skew lines. 14.To solve problems involving 3 dimensional

geometry objects.

1.Introduction of normal, orthogonal projection of a straight line

onto a plane, angle between a straight line and a plane,

angle between two intersecting planes, angle between two

skew lines.

2. Doing exercise and discussions.

Kem Kepimpinan Pelajar

Penyemakan JSU peperiksaan Sumatif 1

9thWeekPeperiksaan Sumatif 1

10thWeekTrigonometryThree Dimensional

Problems

1.To sketch the 3 dimensional diagram from the given

information.

2. To solve problems in three dimension involving

bearing of a point.

3. Introducing the skill of sketching 3 dimensional positon

diagrams.

4. Discussing miscellaneous problems in 3 dimensions.

TrigonometryCircular

Measure1.To state the relationship between degree and

radian.

2.To convert degrees to radians and vice versa.

3.To determine the length of a circular arc and

area of a circular sector.

4.To determine the radius and the angle

subtends by an arc at the centre of a circle.1.Revision of definition of radian, relationship between radian

and degree, derivation of the formulae for length of arc and

area of sector .

2. Discussing problems involving length of arc and area of sector.

11thWeekCuti Pertengahan Semester 1

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12thWeekTrigonometryTrigonometric ratio & formulae1.To define the 6 trigonometric ratios using pairs

of sides of a right angled triangle.

2.To express the value of a trigonometric ratio of

any angle in term of ratio of acute angle.

3.To write down the 3 trigonometric formulae

that are derived from Pythagoras theorem.

4.To simplify a trigonometric expression and to

prove a trigonometric identity using the

formulae.1.Revision of 6 trigonometric ratios using pairs of sides of a

right angled triangle and the skill to evaluate the value of a

trigonometric ratio of any angle in term of ratio ofacute angle.

2. Derivation of the 3 trigonometric formulae using Pythagoras

theorem. Using the formulae to simply an expression and to

prove the trigonometric identities. Doing exercise and

discussions.

Obeying the law

Carefulness

Rationality

Honesty

Diligence

Determinations

Cleanliness

Patience


Mastery

Metacognitive

The Compound

angle formulae5.To derive the compound angle formulae.

6.To evaluate a trigonometric expression using

the compound angle formulae.

7.To simplify a trigonometric expression and to

prove a trigonometric identity using the

compound angle formulae, double angle

formulae, half angle formulae.

8. To simplify a trigonometric expression and to

prove a trigonometric identity using the factor

formulae. 3. Derivation of the compound angle formulae

4. Revision of the double angle and half angle formulae.

Doing exercise and discussions.

5. Derivation of the factor formulae and using the factor

formulae.

6. Exercise and discussing problems involving factor formulae.

7. Discussing miscellaneous problems involving various

type of trigonometric formulae.

Mesyuarat Panitia 2

13th WeekTrigonometryTrigonometric Equations1.To solve the trigonometric equations using

trigonometric formulae.

2.To express a sin( + b cos( in the forms

r sin( ( ( () and r cos( ( ( () .

3.To determine the maximum and minimum

values of the functions in the form

a sin( + b cos(4.To solve the equation in the form

a sin( + b cos( = c by substitution t = tan (/2

and using the forms r sin( ( ( () and

r cos( ( ( () .

5.To solve trigonometric inequalities.1.Revising the inverse process of determining an angle given

the value of one of the trigonometric ratios through sketch

graphs. Discussing the solutions of an equation in a given

range, types of trigonometric equations. Exercise and

discussions.

2.Introduction of the function a sin( + b cos( which can be

expressed in the forms r sin( ( ( () and r cos( ( ( (),

the maximum and minimum values of the functions in the

form a sin( + b cos( , method to solve equation of the form

a sin( + b cos( = c. Exercise and discussions .

3.Introduction of trigonometric inequalities, solving

trigonometric inequalities using graphical method and

analytical method.

4.Revision, doing revision exercise and discussions.

Peperiksaan Percubaan Bertulis MUET

Program Kemasyarakatan.

14th WeekDeductive

Geometry

Euclidean Axiom

Angle1.To write Euclidean axioms that are related to

geometry.

2.To determine an angle using the properties of

angles at a point, angles related to parallel

lines, and angles of a triangle.1. Introduction of Euclidean axiom that are related to

geometry, difference between axiom and theorem.

2. Introduction of angle definition, of angles at a point, angles

related to parallel lines, and angles of a triangle. Exercise

and discussions.

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14th WeekDeductive

Geometry

Polygon

Triangle 3.To determine the interior angle and number of

sides of a polygon.

4.To prove two triangles are congruent.3.Revision of properties related to a polygon. Exercise.

4.Introduction of congruent triangles, theorem related to

congruent triangles. Exercise and discussions. Determinations

Cleanliness

Patience


Mastery

Metacognitive

5.To solve problems involving triangles and

parallel lines .

6.To solve problems involving angle bisector.5.Revision of theorem related to ratio and triangle, internal

angle bisector and external angle bisector, mid-point of two

sides of a triangle. Exercise and discussions.Obeying the law

Carefulness

Rationality

Quadrilateral

7.To solve problems involving the mid-point

theorem.

8.To prove two triangles are similar.

9.To prove the properties of a plane figure using

properties of similar triangle.

10.To prove the properties of a plane figure

using properties of parallelogram, rhombus,

rectangle and square.6.Introduction of similar triangles, properties related to similar

triangles, theorems related to similar triangles. Exercise and

discussions.

7.Revision of properties related to a parallelogram, rhombus,

rectangle and square. Exercise and discussions.

.Honesty

Diligence

Ujian Percubaan Speaking MUET

15th WeekCircle1.To prove the theorems about angles in a circle.

2.To prove properties of a plane figures using

theorems about angles in a circle.

3.To prove the theorems about cyclic

quadrilaterals. .


theorems about cyclic quadrilaterals.

5.To prove the theorems about chords and

tangents.


theorems about chords and tangents.

7.To solve various type of problems involving

plane geometry.1.Revision of properties of angle in a circle, theorems about

angles in a circle, theorems about cyclic quadrilaterals.

Exercise and discussions.

2.Revision of properties of chords in a circle, theorems about

chords in a circle, properties of tangents to a circle,

theorems about tangents to a circle. Exercise and

discussions

3.Revision of deductive geometry, doing revision exercise and

discussions.

16th WeekVectorVector and its notations.1.To differential between scalar quantities and

vector quantities.

2.To state the position vector of a point in the

form of i and j.1.Revision of definition of a vector, notations, unit vector, equal

vectors, parallel vectors, equivalent vectors, position vectors,

magnitude and direction of a vector. Exercise and

discussions.

Equivalent

Vector

3.To identify parallel vectors and equal vectors.

4.To determine the magnitude and the direction

of a vector.

5.To determine a unit vector in the directn of a.

6.To determine an equivalent vector from the

magnitude and direction. 2.Revision of operation on vectors, vector addition, triangle

law, parallelogram law, vector subtraction, multiplication of

a vector by a scalar. Exercise and discussions.

3.Revision of vector in Cartesian form.

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16th WeekVectorVector addition7.To express a vector as a combination of two

vectors using vector addition.

8.To show 3 given points are collinear.

9.To show 4 given points form a parallelogram.

10.To determine vector in Cartesian form.

Patience

Responsibility

Obeying the law

Carefulness

RationalityDirective

Mastery

Metacognitive

17th Week

Scalar Product11.To define the scalar product of two vectors.

12.To determine the scalar product of two

vectors in Cartesian form.

13.To determine whether the two given vectors

are perpendicular.

14.To determine the angle between two vectors.

15.To use the scalar product of two vectors to

find the angle between two straight line and

to show two given lines are parallel.

4.Introduction of scalar product, basic properties of sclar

product of two vectors, scalar product in cartesion form,

angle between two straight lines, perpendicular lines.

Exercise and discussions

Honesty

Diligence

Patience

Responsibility

18th Week

Peperiksaan Sumatif 2

Ujian Speaking MUET

20th WeekApplication of vector

Displacement,

velocity, acceleration.

Resultant velocity and Relative velocity16 To prove geometrical results using vectors.

17.To derive velocity and acceleration from

position vectors.

18.To derive position vector from velocity and

velocity from acceleration.

19.To determine the resultant velocities and

resultant forces using graphical method

and using calculation method.

20.To determine relative velocity using velocities

triangle.

21.To determine relative velocity using vector

subtraction.

24.To solve various types of problems involving

vector.5.Introduction of vector application to prove geometrical

results, altitudes of any triangle are convergent, cosine rule,

perpendicular bisectors of the sides of a triangle are

convergent, diagonals of a parallelogram bisect each other.

Exercise and discussions

6.Introduction of velocities and accelerations as a derivative of

position vectors and the inverse derivative of accelerations

and velocities. Exercise and discussions.

7.Introduction of resultant velocities, resultant forces, to find

the resultant velocities and resultant forces using graphical

method and calculation method. Exercise and discussions.

21st WeekVectorResultant velocity and Relative velocity22.To determine the nearest distance between

two moving bodies.

23.To determine whether collision of two moving

bodies will occur.

8.Introduction of relative velocity, triangle of velocities, course,

track, drift, air speed, ground speed. Exercise and

discussions.

9.Introduction of relative position, the nearest distance

between two moving bodies, collision path of two

moving bodies, time of collision. Exercise and discussions

Data DescriptionData

1.To differential between discrete and

continuous data. 1.Revision of types of data, discrete data, continuous data,

ungrouped data and grouped data.

Representation of Data

2.To differential between ungrouped data and

grouped data.

3.To construct and interpret stemplots. 2.Introduction of stem plots, back-to-back stem plots,

histogram with equal class width, histogram with

different class width. Exercise and discussions.

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22ndWeek23rd Week

Cuti Pertengahan TahunKursus JPAM

Semester 2

24th Week

Data DescriptionRepresentation of Data

4.To construct and interpret histogram with equal

class width and with different class width.

5.To construct frequency curve, frequency

polygon and cumulative frequency curve.3.Revision of tabulation of data, frequency distribution, relative

frequency distribution, class intervals, class limits, class

boundaries, class width, frequency polygon, frequency

curve, relative frequency curve, cumulative frequency /

relative frequency curve. Exercise and discussions.Obeying the law

Carefulness

Rationality

Honesty

DiligenceDirective

Mastery

Metacognitive

Measures of Location

6.To state the three types of measurement

Used to measures of location.

7.To determine mean of ungrouped data and

mean of grouped data.

8.To determine mean using coding method.

9.To determine median of ungrouped data

and median of grouped data.

10.To determine median using cumulative

frequency curve and from a histogram.4. Advantages and disadvantages of mean, median and mode,

mean of ungrouped data, mean of grouped data, coding

method. Exercise and discussions.

5. Revision of the method of finding media of ungrouped data,

median of grouped data using the method of proportion;

using cumulative frequency curve; using histogram.


DeterminationsCleanliness

Responsibility

Data DescriptionMeasures of Dispersion11.To determine mode of ungrouped data

and mode of grouped data.

12.To determine range in a set of data.

13.To determine the first quartile and third

quartile of ungrouped data.

14.To determine interquartile range and semi-

interquartile range for ungrouped data

15.To determine the first quartile and third

quartile of grouped data.6.Revision of the method of finding mode of ungrouped data,

mode of grouped data using the method of proportion;

using histogram. Exercise and discussions.7.Revision of the measures of dispersion, range, quartile for

ungrouped data, meted of finding first quartile and third

quartile, interquartile range and semi-interquartile range

for ungrouped data; using method of proportion,

cumulative frequency curve and histogram to find

quartile, interquartile range and semi- interquartile range

for grouped data. Exercise and discussions.

Mesyuarat Panitia 3, Kursus JPAM

25th WeekData Description

Variance and Standard deviation1.Toderive the formula ( (x- x)2 =( x2 n()2 .

2.To determine the variance and standard

deviation for ungrouped data.


deviation for grouped data.

method. 1.Introduction of the term deviation, deviation from mean,

derivation of the formula ( (x- x)2 =( x2 n()2 , formula for

variance and standard deviation for grouped data and

ungrouped data, method of coding to determine standard

deviation for grouped data. Exercise and discussions.


deviation for ungrouped data using coding

5. To determine the general shape of distribution.

6.To construct and interpret boxplot.

2.Introduction of symmetry and skewness in a data distribution,

bell-shaped, positively skewed and negatively skewed

distribution. Exercise and discussions.

3.Introduction of boxplot, use of boxplot to determine the type

of distribution, and to identify outliers. Exercise and discussions.

4.Revision of data description, doing revision exercise and

discussions.

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25th WeekProbability

Counting and

Set

Permutations and

Combinations1.To determine the number of elements in set A

and A

2.To determine the number of elements in set

A(B , A(B and A(B.

3.To determine the number of elements in set

A(B (C and A(B(C.

4.To determine the number of permutation of n

different objects.

5.To determine the number of permutation of r

different objects chosen from a set of n

different objects.


objects, out of which p of them are the same

objects, q of them another same objects,

r of them another same objects.1.Revision of theory of set, Venn diagram, union and

intersection of sets, counting rules for finite sets,

inclusion-and-exclusion rule, for two or three sets.


2.Introduction of the multiplication principles, permutation of n

different objects, permutation of r different objects chosen

from a set of n different objects, permutation of n objects,

out of which p of them are the same objects, q of them

another same objects, r of them another same objects

and so on, permutation of n objects which are arranged

in a circular arrangement, permutation objects with

conditions.


Obeying the law

Carefulness

Rationality

Honesty

Diligence

DeterminationsPatience Responsibility

CleanlinessDirective

Mastery

Metacognitive


objects which are arranged in a circular

arrangement.

8. To determine the number of permutation

objects with conditions.

9.To determine the number of combination of n

different objects taking r objects each time.

3.Introduction of combination of n different objects taking

r objects each time. Discussing problems involving

combinations.


Mesyuarat Post Mortem PS2

26th WeekProbabilityProbability Theory

1.To determine the probability of an event using

P(A) = n(A)/n(S).

2.To determine the probability of a

complementary event.

3.To determine whether events A and B are

exhaustive.

4.To determine the probability of a composite of

two events.1.Revision of elementary theory of probability, outcomes,

sampling space, event, probability of an event, basic

probability rules, complement of an event, exhaustive events.


2.Introduction of composite events, mutually exclusive events.


Mutually Exclusive Events

Conditional Prob.

Independent Events

Probability Theory

5.To determine whether two events are mutually

exclusive.

6. To determine the probability of a conditional

event.

7.To determine whether two events are

independent.


three events.


events using the tree diagram.

3.Introduction of conditional events and independent ,

complementary events. Exercise and discussions.

4.Introduction of composite events involving three or more

events. Exercise and discussions.

5.Revision of tree diagram and discussion of further probability

problems. Exercise and discussions.

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27th WeekProbabilityMiscellaneous

Problems

10.To solve probability problems using the set

theory, the tree diagram , permutation or

combination.

6.Revision of probability, doing revision exercise and


Carefulness

RationalityHonestyDirective

Mastery

Metacognitive

27th WeekDiscrete

Probability DistributionsDiscrete Random

Variables1.To show a random variable X is a discrete

random variable.

2.To determine probability distribution P(X) of a

discrete random variable.

3.To construct a probability distribution table for

a discrete random variable and sketch the

graph for the distribution.1.Introduction of random variables, discrete random variable,

a discrete probability distribution, probability density function,

graph for the probability distribution. Discussions of

problems involving discrete random variable.


Diligence

Determinations

Cleanliness

Patience

Responsibility

Probability function

4.To determine an unknown in a probability

function.

5.To construct a probability distribution from the

information given.6.To construct a cumulative distribution function

from the probability distribution of a discrete

random variable.

7.To sketch the graph of a cumulative

distribution function of a discrete random

variable.2.Introduction of the cumulative distribution function for a

discrete random variable, the graph for the cumulative

distribution function, the method of finding P(x=k) and

P(a

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