sylabus (kelas x) rev (mht)

8/6/2019 Sylabus (Kelas X) Rev (MHT)

1/21

PEMERINTAH PROPINSI DAERAH KHUSUS IBUKOTA JAKARTA

DINAS PENDIDIKAN

SEKOLAH BERTARAF INTERNASIONAL

SYLLABUS OF SBI CURRICULUM

School : Senior HighSubject : MATHEMATICSGrade/Program : XSemester : 1

COMPETENCE STANDARD1. Understand number systems and how to use them in applied problems or real-life situation

BASICCOMPETENCE

INDICATORLEARNINGMATERIAL

ACTIVITY OFLEARNING

ASSESMENT TIME RESOURSES

1.1 Know naturalnumbers,integers, primenumbers,common factorsand multiples,rational andirrationalnumbers;describe

sequences,patterns usingwords and nthterm.

Using : naturalnumbers, integers,prime numbers,

Using : common

factors and multiples,rational and irrationalnumbers, realnumbers, numbersequences, recognize

patterns in sequnces Using :Language,

notation and VennDiagrams to describesets and representrelationships betweensets

Number, setnotation andlangujage

Identify a number from adescription of itsproperties, for example,which numbers than 50has 3 and 5 as a factorsand is a multiple of 9

Investigate Goldbachsconjecture

Square tables are placedin a row so that 6 peoplecan sit around 2 tables, 8people can sit around 3tables, and so on. Howmany people can sitaround n tables?

Quiz 4 x 45 Self-made modul

www.cie.org.uk.


2/21


3/21

BASICCOMPETENCE


ACTIVITY OFLEARNING

ASSESMENT TIME RESOURSES

2.2. Work out

algebraic

operations relatesto indices,surdsand logarithm

Simplify algebraic

expresions involving

indices, surds andlogarithm

Prove simple

properties aboutindices, surds andlogarithm

Use concepts of indices,

surds and logarithm to solve

problems.

Prove about simpleproperties ofindices,surds andlogarithm

Technique :

I

ndividual work G

roup work

Exam

Instrument:

Quiz

Writtentest :Multiple choiceand essay

4 x45Resourses

MathBook by

Karren M Self-

made modul

CDe-dukasi.net


4/21


5/21

BASICCOMPETENCE


ACTIVITY OF LEARNING ASSESMENT TIME RESOURSES

symmetry and vertex ofquadratic function graphsand coefficients of quadratic

functions. Determine axis of symmetry

and vertex of quadraticfunction graphs usingformulae of the functions.

Draw graphs of quadratic

function using result offunction formulae analys

Identify positive definit and

negative definit of quadraticfunction based on graph

Draw graph of simplealgebraic functions usingrelations between variablevalue and function value

3.3. Using properties

and rules ofquadraticequations andinequalities

Determine roots ofquadratic equations

Find the solutions ofquadratic inequalities

Quadraticequation andinequalitieso Solution of

quadraticequations

o Solution of

quadraticinequalities

Find the roots of quadratic

equation by factorise

Find the roots of quadratic

equation by formulae

Find the solution of quadraticinequalities.

Find the meaning of

geometrice of quadraticequation solutions andinequalities solutions byusing graph quadraticequations

Describe the meaning of

geometrice of quadraticequation and quadraticinequalities solutions

Technique :

Individual work

Group work

Exam

Instrument:

Quiz

Writtentest :Multiple

choiceand essay

4 x45Resourses

MathBook byKarren M

Self-

made modul

CDe-dukasi.net


6/21

BASICCOMPETENCE



Use formulae of sum

and product of roots ofthe equations.

formulae ofsum and productof roots of the

quadraticequations.

Compute sum and product of

roots of quadratic equationsolutions

Determine the relationshipsbetween sum and product ofroots with coefisient ofquadratic equations

Conclude the relationships

between sum and product ofroots with the coeficient ofquadratic equations.

Proving formulae of sum

and product of quadraticequation roots.

Use the formulae of sum and

product of quadratic equationroots in computing

Technique :

I

ndividual work G

roup work

Exam

Instrument:

Quiz


choiceand essay

4 x45Resourses

MathBook by

Karren M Self-

made modul

CDe-dukasi.net

Distinguish kind ofquadratic equation roots

Kinds ofquadratic equationroots

Distinguish kind of quadraticequation roots throughexamples

Investigate relation between

kind of roots of quadraticequation and discriminantvalue.

Conclude relation between

kinds of quadratic equation

roots and discriminant value.

Analyse kind of roots of

quadratic equations.

Technique :

Individual work

Group work

Exam

Instrument:

Quiz Written

test :Multiple

choiceand essay

2 x45Resourses

MathBook byKarren M

Self-made modul

CDe-dukasi.net


7/21

BASICCOMPETENCE



3.4. Make algebraicmanipulation in

computing relatesto equation andquadraticinequalities

Make quadratic

equation whose itsroots is given.

Determinesolutions of equationsthat can be changed tobe quadratic equationand inequalities

Make

quadratic equationwhose its roots isgiven

Solution ofother equationinvolvingquadraticsequation.

Make quadratic

equation whose its roots isgiven

Make quadratic equationwhose the roots related withother quadratic equations.

Identify equations that can

be changed in quadraticequation.

Solve equations thatcan be changed in quadraticequation or quadraticinequalities.

Technique :

I

ndividual work G

roup work

Exam

Instrument:

Quiz


choiceand essay

4 x45Resourses

MathBook by

Karren M Self-

made modul

CDe-dukasi.net

3.5. Design model ofmath of problemsrelates toequation andquadraticinequalities.

Design math modelrelated to mathproblems, other subjector daily problemsrelates to equation orquadratic function.

Usingequations andquadratic functionsin solvingproblems.

Identification daily problemsrelated to equations andquadratic functions.

Distinguish math model ofmath problems, otherssubject or daily living relatesto equation or quadraticfunctions.

Technique :

Individual work

Group work

Exam

Instrument: Quiz


choiceand essay

4 x45Resourses

MathBook byKarren M

Self-made modul

CDe-dukasi.net


8/21

BASICCOMPETENCE



3.6. Solve math modelof problemsrelate to

equations andquadraticfunctions and itsinterpretations

Solve math modelof problems relates toequations and quadratic

functions and itsinterpretations

Interpret solutionsof math problems, othersubject or daily livingproblems relate toequation or quadraticfunctions.

Applyequation andquadratic function

in solvingproblems.

Solve math model ofmath problems, other subjector daily living relates to

equation or quadraticfunctions.

Interpret solutions ofmath problems, other subjector daily living problems relateto equation or quadraticfunctions.

Technique :

I

ndividual work G

roup work

Exam

Instrument:

Quiz


choiceand essay

4 x45Resourses

MathBook by

Karren M Self-

made modul

CDe-dukasi.net

COMPETENCE STANDARD :

4. Solve problems involving linear equations system and inequalities of one unknown variable


9/21

BASICCOMPETENCE



4.1. Solve linearequation systemsand mixed

equation systemsand quadratic intwo variables

Find the solution of two

variables linear equationsystem.

Equation andinequalities systems

Linear equation

system in twovariables

Linear equationsystem in threevariables

Identify steps of solvinglinear equation systems in

two variables. Use linear equation systems

to solve problems

Technique :

I

ndividual work G

roup work

Exam

Instrument:

Quiz


2 x45Resourses

MathBook by

Karren M Self-

made modul

CDe-dukasi.net

Determine solutions of

linear equation systems

in three variables.

Identify steps of solvinglinear equation systems in

three variables Use linear equation systems

in three variables to solveproblems

4 x 45

Find the solution of linearmixed equation systemand quadratic in twovariables

Identify steps of solutions

linear mixed equationsystems and quadratic in twovariables.

Use linear miixed equationsystems and quadratic in twovariables to solve problems

4 x 45

4.4. Design math

model of problemsrelate to liniearequation systems.

Identify problems related

to linear equationsystems.

Make math model

related to linear equationsystemst

Apply linearequation systems intwo and threevariables

Identify daily problems

related to linear equationsystems

Conclude math problems of

math problems,other subjector daily living relate linearequation systems

2 x 45


10/21

BASICCOMPETENCE



4.5. Solve math model

relate to linierequation system

and theinterpretation

Find the solution of math

model related to linierequation system

Interpret the solution setof linier equation system

Apply linier

equation system intwo and three

variables

Solve math model of math

problems , other subjectproblems or daily living

relate to linier equationsystem.

Interpret solution of math

problems , other subjectproblems or daily livingproblems relate to linierequation system.

Technique :

I

ndividual work G

roup work

Exam

Instrument:

Quiz


4 x45Resourses

MathBook by

Karren M Self-

made modul

CDe-dukasi.net

4.6. Determine onevariable rational,irrational and

absolut

inequalities

Find the solution ofabsolute equation

Find the solution ofirational equation

Find the solution ofone variable rationalinequalities

Find the solution of

one variable irrationalinequalities

Find the solution ofone variable absoluteinequalities

Find the solution of

one variable absoluteinequalities

rational inequalities eqution and

inequalities ofirrational

eqution andinequalities ofabsolute

Using one variableinequalities to solveproblems

Solutions of one variable

irrational and absoluteequation

Solutions of one variable

rational, irrational andabsolute inequalities

Technique :

Individualwork

Group work

Exam

Instrument:

Quiz

Written

test :Multiplechoice

and essay

4 x45Resourses Math

Book byKarren M

Self-

made modul

CD

e-dukasi.net


11/21

BASICCOMPETENCE



4.7. Design math

model ofproblems relate to

one variableinequalities

Identification problemsinvolving one variableinequalities

Design math model ofproblems relate to onevariable inequalities

Applying one

variable inequalitiesin algebraic

fractions.

Identification problems related

to one variable inequalities.

Formulate math model of

math problems or othersubject problems related toone variable inequalities

Technique :

I

ndividual work G

roup work

Exam

Instrument:

Quiz


4 x45Resourses

MathBook by

Karren M Self-

made modul

CDe-dukasi.net

4.8. Solve math model

relate to onevariableinequalities andits interpretation.

Find the solution of math

problems relate to onevariable inequalities inalgebraic fractions.

Interpret solution of

problems relate toinequalities in onevariables in algebraicfractions.

Apply one variableinequalities inalgebraic fractions.

Solve math model of math

problems or other subjectrelate to one variableinequalities

Interpret solution of math

problems or other subjectrelate to one variableinequalities.

Technique :

Individual work

Group work

Exam

Instrument:

Quiz

Writtentest :

Multiple choiceand essay

2 x45Resourses Math

Book byKarren M

Self-

made modul

CDe-dukasi.net


12/21

PEMERINTAH PROPINSI DAERAH KHUSUS IBUKOTA JAKARTA

DINAS PENDIDIKAN

SEKOLAH BERTARAF INTERNASIONAL

SYLLABUS OF SBI CURRICULUM

School : Senior HighSubject : MATHEMATICSGrade/Program : XSemester : 2

STANDARD COMPETENCY:5. Using math logic in problem solving related to compound sentences and sentence wit quantor.

BASIC

COMPETENCE INDICATOR TOPIC LEARNING ACTIVITY ASSESSMENT

TIME

ALLOCATION RESOURCES

5.1. Determining truthvalue ofcompoundsentence andsentence withquantor

Determining truth

value of sentence withquantor

Determiningnegation of sentencewith quantor

Determining truthvalue of compoundsentence

Determining

negation of compoundsentence

Math Logic

Preposition and itstruth value

Preposition withquantor

Negation ofpreposition

Compoundpreposition

Truth value and itsnegationo Conjunction

o Disjunction

o Implication

Distinguishing preposiition andnot preposition

Determining truth value of a

preposition

Determining negation of a

preposition

Identifying compoundsentence in form ofconjunction, disjunction andimplication

Constructing truth value ofcompound sentence in form ofconjunction, disjunction andimplication in the form of table

Determining truth value ofcompound sentence in form ofconjunction, disjunction andimplication

Constructing negation ofcompound sentence in form ofconjunction, disjunction andimplication in the form of table

Task type:

Individual task

Group task

Test

Instrument type:

Quiz

MultipleChoice test

Essaytest

8 x 45 Resources:

MathBook byKarren M

Self-made modul

Learning CD MAFIA

e-dukasi.net


13/21

BASICCOMPETENCE

INDICATOR TOPIC LEARNING ACTIVITY ASSESSMENTTIME

ALLOCATIONRESOURCES

Identifying daily sentencewhich related to compoundsentence

Identifying relation between

implication with converse,inverse and its contraposition

Determining converse, inverseand contraposition ofimplication

5.2. Formulatingpreposition whichis equivalent togiven compoundsentense orpreposition withquantor

Checking equivalencybetween to compoundpreposition orpreposition withquantor

Proving equivalencybetween to compoundpreposition orpreposition withquantor

Constructingpreposition which isequivalent tocompound prepositionor preposition withquantor

Equivalency oftwo compopundpreposition

Tautology andContradiction

Identifying compoundprepositions which areequivalent

Checking equivalencybetween to compoundpreposition or preposition with

quantor

Proving equivalency between

to compound preposition orpreposition with quantor usingproperties of math logic

Identifying characteristics of

tautology and contradictionfrom truth table

Checking whether a

compound preposition is atautology or contradiction ornone of them

Task type:

Individual task

Group task

Test

Instrument type:

Quiz

MultipleChoice test

Essaytest

4 x 45 Resources:

MathBook byKarren M

Self-made modul

Learnin

g CD MAFIA e-

dukasi.net


14/21

BASICCOMPETENCE


ALLOCATIONRESOURCES

5.3. Using principlesof math logicwhich related tocompound

preposition andpreposition withquantor in makingconclusion andproblem solving

Checking validity ofconcluding prepositionusing principles of mathlogic

Determining conclusionof some premises given

Making conclusiono Ponens Mode

o Tolens Mode

o Syllogism

Identifying how to makeconclusion from someexamples given

Formulating how to makeconclusion based onimplication methods (ponensmode, tolens mode andsyllogism)

Checking validity of makingconclusion

Constructing valid conclusionbased on some premisesgiven.

Task type:

Individual task

G

roup task T

est

Instrument type:

Quiz

MultipleChoice test

Essaytest

4 x 45 Resources:

MathBook byKarren M

Self-made modul

Learning CD MAFIA

e-dukasi.net


15/21

STANDARD COMPETENCY:

6. Using trigonometric ratio, function, equation and identity in problem solving.

BASICCOMPETENCE


ALLOCATION

RESOURCES

6.1. Doing algebraicmanipulation intechnicalcalculation whichrelates totrigonometricratio, function,equation andidentity

Determining valueof trigonometricratio in right-angledtriangle

Determining valueof trigonometricratio of specialangles

Determining value

of trigonometricratio of angles in allquadrants

Trigonometry

Trigonometric ratio inright-angled triangle

Value of trigonometricratio of special angle

Trigonometric ratio ofangles in all quadrants

Calculating ratio of trianglesides which has fixedangles, but different lengthof sides.

Defining the meaning oftrigonometric ratio in right-angled triangle.

Determining value oftrigonometric ratio of anglesin right-angled triangle.

Investigating value oftrigonometric ratio in specialangles.

Using trigonometric ratiovalue in special angle tosolve problems.

Deriving formula oftrigonometric ratio of anangle on Cartesian plane

Calculating value oftrigonometric ratio onCartesian plane

Investigating relationbetween trigonometric ratioof angles in all quadrants.

Determining value oftrigonometric ratio of anglesin all quadrants

Task type:

Individual task

Group task

Test

Instrument type:

Quiz

MultipleChoice test

Essaytest

10 x 45 Resources:

MathBook byKarren M

Self-made modul

Learning CD MAFIA

e-dukasi.net


16/21

BASICCOMPETENCE


ALLOCATION

RESOURCES

6.2. Constructingmathematicalmodel of problemrelated totrigonometricratio, function,equation andidentity

Drawing graph ofsimpletrigonometricfunction.

Solving simpletrigonometricfunction.

Proving simpletrigonometricidentity.

Solving calculationusing sine andcosine rules.

Calculating area oftriangle with givencomponents.

Trigonometric function

and its graph

Simple trigonometricequation.

Trigonometric identity

Sine rule and Cosinerule.

Formula of areaof triangle

Determining value oftrigonometric function

Drawing graph of

simple trigonometricfunction.

Determining solution

of simple trigonometricequation.

Constructing realtionbetween trigonometricratio of an angle.

Proving simple

trigonometric identity byusing formula of relationbetween trigonometricratio

Identifying problemsin calculating angles orsides in a t riangle.

Constructing sine ruleand cosine rule.

Using sine and cosine

rules in problem solving ofcalculating side or angle ina triangle.

Identifying problem incalculating area of triangle.

Deriving formula ofarea of a triangle

Using formula of areamof triangle in problem

Task type:

Individual task

Group task

Test

Instrument type:

Quiz

MultipleChoice test

Essaytest

12 x 45 Resources:

MathBook byKarren M

Self-made modul

Learning CD MAFIA

e-dukasi.net


17/21

BASICCOMPETENCE


ALLOCATION

RESOURCES

solving

6.3. Solvingmathematicalmodel of problemrelated totrigonometricratio, function,equation, identityand itsinterpretation

Identifyingproblems relatedto trigonometricratio, function,equation, andidentity

Constructing

mathematicalmodel which isrelated totrigonometricratio, function,equation, andidentity

Determiningsolution ofmathematicalmodel which isrelated to

trigonometricratio, function,equation, andidentity

Interpreting

the solution ofproblem related totrigonometricratio, function,equation, andidentity

Usingtrigonometric ratio

Identifying problemsrelated to t rigonometricratio, function, equation,and identity

Constructing

mathematical model whichis related to trigonometric

ratio, function, equation,and identity

Solving mathematical

model which is related totrigonometric ratio,function, equation, andidentity

Interpreting the solution of

problem related totrigonometric ratio,function, equation, andidentity

Task type:

Individual task

Group task

Test

Instrument type:

Quiz

MultipleChoice test

Essaytest

8 x 45 Resources:

MathBook byKarren M

Self-made modul

Learning CD MAFIA

e-dukasi.net


18/21


19/21

STANDARD COMPETENCY:

7. Determining position, distance and value of angle which relate to points, lines and planes in 3-Dimension.

BASICCOMPETENCE


ALLOCATIONRESOURCES

7.1. Determiningposition,distance andvalue of angle in3-Dimension(solid)

Determining position

of point and line on aplane


of point, line and plane ina solid

Determining positionbetween two lines in asolid

Determining positionof line and plane in a solid


between two planes in asolid.

3-Dimension

Introductionto solids

Position ofpoint, line andplane in a solid

Identifying shapes ofsolids

Identifying parts of asolid

Investigating positionbetween parts of a solid

Describing positionbetween parts of a solid

Task type:

Individual task

Group task

Test

Instrument type:

Quiz

MultipleChoice test

Essaytest

4 x 45 Resources:

MathBook byKarren M

Self-made modul

Learning CDMAFIA

e-dukasi.net

7.2. Determiningdistance frompoint to line andpoint to plane in3-dimension

Determining distance

from a point to a line in asolid

Determining distancefrom a point to a plane ina solid

Determining distance

between two lines in asolid *)

Distance ina solid

Defining the meaning ofdistance between a point, aline and a plane in a solid

Calculating distance

from a point to a line in asolid

Calculating distance from a

point to a plane in a solid

Calculating distance

between two lines in a solid*)

Task type:

Individual task

G

roup task T

est

Instrument type:

Quiz

MultipleChoice test

Essaytest

10 x 45 Resources:

MathBook byKarren M

Self-made modul

Learning CDMAFIA

e-dukasi.net


20/21

BASICCOMPETENCE


ALLOCATIONRESOURCES

7.3. Determiningvalue of anglebetween line and

plane andbetween twoplanes in 3-dimension (solid)

Determining value ofangle between two lines ina solid

Determining value ofangle between line andplane in a solid

Determining value ofangle between two planesin a solid

Angles in asolid

Defining the meaning ofpoint, line and plane in a

solid

Drawing angle betweentwo lines in a solid

Calculating value ofangle between two lines in asolid

Drawing value of anglebetween line and plane in asolid

Calculating value ofangle between line and planein a solid

Drawing angle betweentwo planes in a solid

Calculating value ofangle between two planes ina solid

Task type:

Individual task

Group task

Test

Instrument type:

Quiz

MultipleChoice test

Essaytest

10 x 45 Resources:

MathBook by

Karren M Self-

made modul

Learning CDMAFIA

e-dukasi.net


21/21

STANDARDS COMPETENCES:

8. Understanding number systems and how to use them in applied problems or real-life situation

BASICCOMPETENCE INDICATOR LEARNINGMATERIAL ACTIVITY OFLEARNING ASSESMENT TIME RESOURSES

8.1. Using given datato solve problemson personal andhouseholdfinance involvingearnings, simpelinterest, discount,profit and loss

Using personaland householdfinance, involvingearnings, simpleineterst, discount,profit and loss

Personaland householdfinance

Solve simple

problems, using practicalexamples where possible,taking information frompublished tablesoradvertisements.

Worksheet

6 x 45 Self-made modul

www.cie.org.uk.

sylabus (kelas x) rev (mht)

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