rancangan pengajaran tahunan t.4 2012

7/31/2019 Rancangan Pengajaran Tahunan T.4 2012

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4/1-

6/1/2012

Chapter 1:

Standard

Form

1.1 Understand anduse the concept

of significant

figure

Students will be able to:

i. round off positive numbers to a given number ofsignificant figures when the numbers are:

greater than 1

a) less than 1ii. perform operations of addition, subtraction,

multiplication and division, involving a few

numbers and state the answer in specific

significant figuresiii.solve problems involving significant figure

- contextual-working out mentally- finding all possible

solutions

- identifying relations

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13/1/2012

1.2 Understandand use the concept

of standard form to

solve problem

i. state positive numbers in standard form when thenumbers are:

a) greater than or equal to 10b) less than 1

ii. convert numbers in standard form to singlenumbers

iii. perform operations of addition, subtraction,multiplication and division, involving any two

numbers and state the answers in standard form

iv. solve problems involving numbers in standardform

- working out mentally- identifying relations

16/1-

20/1/2011

Chapter 2:

Quadratic

Expressions

and

Equations

2.1 Understand the

concept of Quadratic

Expression

i. Identify quadratic expressionsii. Form quadratic expressions by multiplying any

two linear expressions

iii. Form quadratic expressions based on specificsituations

- classifying- arranging

sequentially

- translating

-


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2.2 Factorization

quadratic expression

i Factorise quadratic expressions of the form

ax2

+bx+c=0, where b= 0 or c= 0

ii Factorise quadratic expressions of the formpx2

q,

p

and qare the perfect squares

30/1/-

03/2/2012

2.3 Understand the

concept of Quadratic

Equation

iii Factorise quadratic expressions of the form ax2

+

bx+

c, where a, band cnot equal to zero

iv Factorise quadratic expressions containing

coefficients

with common factors

i. Identify quadratic equations with one unknownii. Write quadratic equations in general form i.e.

ax2

+ bx+ c= 0

iii. Form quadratic equations based on specificsituations

- arrangingsequentially

- arrangingsequentially

- classifying- translating

-

6/2-

12/2/2012

concept of Roots of

quadratic equations

i. determine the solutions for quadratic equationsby:

a) trial and error methodb) factorization

iii. solve problems involving quadratic equation- comparing &

differentiating

finding all possible

solutions

13/2-

17/2/2012

Chapter 3:

Sets

3.1 Understand the

concept of Set i. sort given objects into groupsii. define sets by

a)descriptionsb)using set notation

- makinggeneralizations

- working out mentallyclassifying

-


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iii identify whether a given object is an element of a

set

and use the symbol or

iv. represent sets by using Venn diagrams

v. list the elements and state the number of elements

of a set

vi. determine whether a set is an empty set

vii. determine whether two sets are equal

-comparing and

differentiating

20/2-

24/2/12

3.2 Understand and

use the concept of

Subset, universal set

and the complement

of a set

i. determine whether a given set is a subset of aspecific set and use the symbol or .

ii. represent subset by using Venn diagramiii.list the subsets for a specific setiv. illustrate the relationship between set and

universal set using Venn diagram

v. determine the complement of a given setvi.determine the relationship between set, subset,

universal set and the complement of a set

- classifying- finding all possible

solutions

- drawing diagrams- identifying relations- interpreting

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10/3/2011

3.3 Perform

Operations on set

i. determine the intersection ofa) two setsb) three setsand use the symbol

ii. represent the intersection of sets using Venndiagram

iii.state the relationship betweena) BA andAb) BA and B

iv.determine the complement of the intersection ofsets

v. solve problems involving the intersection of sets.vi.determine the union of

a) two setsb) three setsand use the symbol

vii.represent the union of sets using Venn diagramviii. state the relationship between

a) BA andAb) BA and B

- comparing anddifferentiating

- drawing diagrams- identifying relations- interpreting- translating- making

generalization

-


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Week 11

ix.determine the complement of the union of setsx. solve problems involving the union of setsxi.determine the outcome of combined operations

on sets

xii. solve problems involving combined operations on

sets

UJIAN PERTENGAHAN PENGGAL 1 [27/2-

8/3/2012]

19/3-

23/3/2012

Chapter 4:

Mathematical

Reasoning

4.1 Understand the

concept of Statement

i. determine whether a given sentence is astatement

ii. determine whether a given statement is true orfalse

iii.

construct true or false statement using givennumbers and mathematical symbols

- Classifying- Working out

mentally

- Translating- Interpreting

-

4.2 Understand the

concept of

Quantifiers all and

some

i. construct statements using quantifiera) allb) some

ii. determine whether a statement that contains thequantifier all is true or false

iii. determine whether a statement can begeneralized to cover all cases by using the

quantifier all

iv.

construct a true statement using the quantifierall or some given an object and a property

- Working outmentally

- Identifying relations-

26/3-

30/3/2012

4.3 Perform

Operations Involving

the words not or

no statements

i. change the truth value of a given statement byplacing the word not into the original statement

ii. identify two statements from a compoundstatement that contains the word and

iii. of two statements with the word or form acompound statement by combining two given

statements using the word and

iv. identify two statement from a compoundstatement that contains the word or

v. form a compound statement by combining two

- working out mentallyclassifying -


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given statements using the word or

vi. determine the truth value of a compoundstatement which is the combination of two

statements with the word and

vii. determine the truth value of a compoundstatement which is the combination

4.4 Understand the

concept of

Implication

i. identify the antecedent and consequent of animplication ifp, then q

ii. write two implications from a compoundstatement containing if and only if

iii. construct mathematical statements in the form ofimplication:

a) Ifp, then qb) pif and only ifq

iv. determine the converse of a given implicationv. determine whether the converse of an

implication is true or false

- working out mentallyclassifying -

2/4-

5/4/2012

4.5 Understand the

concept of Argument

i. identify the premise and conclusion of a givensimple argument

ii. make a conclusion based on two given premisesfor:

a) Argument Form Ib) Argument Form IIc) Argument Form III

iii. complete an argument given a premise and theconclusion

- Classifying- Making inferences -

4.6 Understand and

use the concept of

Deduction and

Induction

i. determine whether a conclusion is made through:a) reasoning by deductionb) reasoning by induction

ii. make a conclusion for a specific case based on agiven general statement, by deduction

iii. make a generalization based on the pattern of anumerical sequence, by induction

iv. use deduction and induction in problem solving

- classifying- making inferences- making

generalization

- looking for patterns- making analogy

-


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10/4-

13/4/2012

Chapter 5:

The Straight

Line

5.l Understant the

concept of gradient of

a straight line

i.determine the vertical and horizontal distancesbetween two given points on a straight line

ii. determine the ratio of vertical distance to

horizontal distance

- Interpreting -

5.2 Understant the

concept of gradient of

a straight line in

Cartesian coordinates

i. derive the formula for the gradient of a straightline

ii. calculate the gradient of a straight line passingthrough two points

iii. determine the relationship between the value ofthe gradient and the:

a) steepnessb) direction of inclinationof a straight line

- interpreting- classifying -

16/4-

20/4/2012

5.3 Understand the

concept of intercept

i. determine the x-intercept and they-intercept of astraight line

ii. derive the formula for the gradient of a straightline in terms of the x-intercept and they-intercept

iii. perform calculations involving gradient x-intercept andy-intercept

- interpreting -

23/4-

27/4/2012

5.4Understand and

use the concept of

Equation of a straight

line

i. draw the graph given an equation of the formy =mx+ c

ii. determine whether a given point lies on a specificstraight line

iii. write the equation of the straight line given thegradient andy-intercept

iv. determine the gradient and y-intercept of thestraight line which equation is of the form:

a)y = mx+ c

b) ax+ by= c

v. find the equation of the straight line which:a) is parallel to the x-axisb) is parallel to they-axisc) passes through a given point and has a

specific gradient

d) passes through two given points

- drawing diagrams- comparing and

differentiating

- working out mentally

-


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vi. find the point of the intersection of two straightlines by:

a) drawing the two straight linese) solving simultaneous equations

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30/4/2012

5.5 Understand and

use the concept of

Parallel line

i. verify that two parallel lines have the samegradient and vice versa

ii. determine from the given equations whether twostraight lines are parallel

iii. find the equation of the straight line which passesthrough a given point and is parallel to another

straight line

iv. solve problems involving equations of straightlines


2413/6-

22/6/2012

Chapter 6:Statistics

6.1 Understand theconcept of class

Interval

i. complete the class interval for a set of data givenone of the class intervals

ii. determine:a) the upper limit an lower limitb) the upper boundary and lower boundaryof a class in a group data

iii. calculate the size of a class interval

- working out mentallyclassifying- making inferences

-

iv. determine the class interval, given a set of dataand the numbers of classes

v. determine a suitable class interval for a given setof data


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i. construct a frequency table for given set of data6.2Understand and

use the concept of

Mode and mean of

grouped data

i. determine the modal class from the frequency table

of grouped data

ii. calculate the midpoint of a classiii. verify the formula for the mean of grouped dataiv. calculate the mean from the frequency table of

grouped data

v. discuss the effect of the size of class interval onthe accuracy of the mean for a specific set of

grouped data

- Interpreting- Working out

mentally

-Making inferences- Identifying relations

-

6.3 represent and

interpret data in

histograms with class

intervals

i. draw a histogram based on the frequency table ofa grouped data

ii. interpret information from given histogramiii. solve problems involving histogramsiv.

- drawing diagrams- interpreting -

25/6-29/6/

6.4Represent and

interpret data in

Frequency polygons

to solve problem

i. draw the frequency polygon based on:a) a histogramb) a frequency table

ii. interpret information from a given frequencypolygon

iii. solve problems involving frequency polygon

- drawing diagrams- interpreting -

6.5 Understand the

concept of

Cumulative frequency

i. construct the cumulative frequency table for:a) ungrouped datab) grouped data

ii. draw the ogive for:a) ungrouped datab) grouped data

- working out mentally- drawing diagrams -

25/6-

29/6/2012

6.6Understand and

use the concept of

Measures of

dispersion

i. determine the range of a set dataii. determine:

a) the medianb) the first quartilec) the third quartiled) the interquartile rangefrom the ogive

iii. interpret information from an ogiveiv. solve problems involving data representations

and measures of dispersion

- interpreting- identifying relations -

Chapter 7: 7.1Understand the i.determine whether an outcome is a possible - Finding all possible -


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Probability I concept of Sample

space

outcome of an experiment

ii.list all the possible outcomes of an experiment:a) from activitiesb) by reasoning

iii determine the sample space of an experiment

iv write the sample space by using set notations

solutions

02/7-

6/7/2012

7.2 Understand the

concept of Events

i.identify the elements of a sample space whichsatisfy given conditions

ii.list all the elements of a sample which satisfy certainconditions using set notations

iii determine whether an event is possible for a

sample space

- Finding all possiblesolutions

-

7.3Understand and

use the concept of

Probability of an

event

i.find the ratio of the number of times an eventoccurs to the number of trials

ii.find the probability of an event from a big enoughof trials

iii calculate the expected number of times an event

will occur, given the probability of the use event and

number of trials

iii. problems involving probabilityiv. solve predict the occurrence of an outcome

and make a decision based on known information

v.

- identifying relations -

09/7-13/7/2012

Chapter 8:

Circles III

8.1 Understand and

use the concept of

Tangents of a circle

i.identify tangents to a circleii.make inference that the tangent to a circle is a

straight line perpendicular to the radius that passes

through the contact point

iii construct the tangent to a circle passing through a

point:

a) on the circumference of the circleb) outside the circle

iv. determine the properties related to two tangents to

a circle from a given point outside the circle

v. solve problems involving tangents to a circle

-Working out mentally-Drawing diagrams-Identifying relations

-

8.2 Understand and

use the properties of

Angle between

tangent and chord

i. identify the angle in the alternate segment whichis subtended by the chord through the contact

point of the tangent

ii. verify the relationship between the angle formed

- identifying relations -


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by the tangent and the chord with the angle in the

alternate segment which is subtended by the

chord

iii. perform calculations involving the angle inalternate segment

iv. solve problems involving tangent to a circle andangle in alternate segment

16/7-20/7/2012

8.3 Understand and

use the properties of

common tangents to

solve problem

i. determine the number of common tangentswhich can be drawn to two circles which:

a) intersect at two pointsb) intersect only at one pointc) do not intersect

ii. determine the properties related to the commontangent to two circles which:

a) intersect at two pointsb) intersect only at one pointc) do not intersect

iii. solve problems involving common tangents totwo circles

iv. solve problems involving tangents and commontangent


- Finding all possiblesolutions

- Identifying relations

-

25/7-

29/7/2011

Chapter 9:

Trigonometr

y II

9.1 Values of sin ,

cos and tan

3600 .

i. identify the quadrants and angles in the unitcircle

ii. determine:a) the value ofy-coordinateb) the value ofx-coordinatec) the ratio ofy-coordinate to x-coordinateof several points on the circumference of the unit

circle

iii. verify that, for an angle in quadrant I of the unitcircle:

a) coordinatey sin b) coordinatex cos

-working out mentally- interpreting- identifying relations

-

c)coordinatex

coordinatey

tan


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31/7-

3/8/2012

iv. determine the value of:a) sineb) cosinec) tangentof an angle in quadrant I of the unit circle

v. determine the values of:a) sin b) cos c) tan for 3600

vi. determine whether the values of:a) sineb) cosinec) tangentof an angle in a specific quadrant is positive or

negative

vii. determine the values of sine, cosine and tangentfor special angles

viii.determine the values of the angles in quadrant Iwhich correspond to the values of the angles in

other quadrants

ix. State the relationships between the values of:a) sineb) cosine, andc) tangentof angles in quadrant II, III and IV with their

respective values of the corresponding angle in

quadrant I

x. Find the values of sine, cosine and tangent of theangles between 90 and 360

xi. Find the angles between 0 and 360, given thevalues of sine, cosine and tangent

xii. Solve problems involving sine, cosine andtangent

6/8-

9.2Draw and use

Graphs of sine, cosine

i. draw the graphs of sine, cosine and tangent forangles between 0 and 360

- drawing diagrams- comparing and -


12/13

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10/8/2012 and tangent ii. compare the graphs of sine, cosine and tangentfor angles between 0 and 360

iii. solve problems involving graphs of sine, cosineand tangent

differentiating

- interpreting

13/8-

17/8/2011

Chapter 10:

Angles of

Elevation and

Depression

10.1Understand and

use the concept of

Angle of elevation

and angle of

depression

i. identify:a) the horizontal lineb) the angle of elevationc) the angle of depression

ii. represent a particular situation involvinga) the angle of elevationb) the angle of depression, using diagrams

iii. solve problems involving the angle of elevationand the angle of depression

- working out mentally- drawing diagrams- identifying relations

27/8-4

30/8/2012

Chapter 11:

Lines and

Planes in 3-

dimensions

11.1Understand and

use the concept of

Angle between lines

and planes

i. identify planesii. identify horizontal planes, vertical planes and

inclined planes

iii. sketch a three dimensional shape and identifythe specific planes

iv. identifyv. identify normals to a given planevi. determine the orthogonal projection of a line on

a plane

vii. draw and name the orthogonal projection of lineon plane

viii.determine the angle between a line and a planesolve problems involving the angle between a line

and a plane

- Comparing anddifferentiating

-Working outmentally

- Identifying relations

-

3/9-

15/9/2012

11.2Understand and

the concept of Angle

between two planes

i. identify the line of intersection between twoplanes

ii. draw a line on each plane which is perpendicularto the line of intersection of the two planes at a

point on the line of intersection

iii. determine the angle between two planes on amodel and a given diagram

-working out mentally- drawing diagrams- identifying relations

-


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iv. solve problems involving lines and planes in 3-dimensional shapes

- - Revision

-

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