Perbandingan Kurikulum Indonesia Dan Singapura

Dosen Pengampu: Beni Ashyar, M. Pd

Oleh : Kelompok 6/ TMT 3B

A.

KONDISI PENDIDIKAN DI SINGAPURA 1

Singapura merupakan salah satu negara yang pendidikannya, perekonomian, teknologi, dan sumber daya manusia yang maju di dunia, terutama di Asia Tenggara. Oleh karena itu, Singapura menjadi salah satu negara tujuan untuk menuntut ilmu.Selama bertahun-tahun, Singapura telah berkembang dari sistem pendidikan ala Inggris yang tradisional menjadi sistem pendidikan yang bertujuan untuk memenuhi kebutuhan individual dan mengembangkan bakat peserta didik. Keunggulan sistem pendidikan di Singapura terletak pada kebijakan dua bahasa ( Bahasa Inggris dan bahasa ibu yaitu: Melayu/Mandarin/Tamil) dan kurikulum yang lengkap dimana inovasi dan semangat kewirausahaan menjadi hal yang sangat diutamakan. Para individu menunjukkan bakat-bakat yang berkaitan satu sama lain dan kemampuan untuk bertahan dalam lingkungan yang penuh dengan persaingan, dan dipersiapkan untuk sebuah masa depan yang lebih cerah. Sistem pendidikan di Singapura meliputi: 1. Sekolah Dasar & Menengah Secara umum, lamanya pendidikan dasar di Singapura sama dengan di Indonesia yaitu enam (6) tahun, terdiri dari program dasar selama empat (4) tahun dan diikuti oleh program orientasi selama dua (2) tahun. Pada akhir tahun keenam, pelajar akan mengikuti ujian PSLE (Primary School Leaving Examination). Kurikulum yang diajarkan lebih memfokuskan pada pengajaran bahasa Inggris, bahasa ibu seperti Cina, Melayu atau Tamil , serta pelajaran matematika, pengetahuan alam, musik, seni rupa dan kerajinan tangan, olahraga dan pendidikan sosial. Setelah lulus ujian PSLE, pelajar meneruskan ke sekolah menengah dengan kurikulum ‘O’ Level selama empat (4) tahun atau ‘N’ Level selama lima (5) tahun, sesuai dengan kemampuan individu. Kurikulum ini mencakup bahasa Inggris, bahasa ibu seperti Cina, Melayu atau Tamil , serta pelajaran matematika, science dan humanities. Pada tahun ketiga, pelajar dapat memilih untuk mengambil kelas kesenian, science, ilmu tata niaga atau jurusan teknik. Ujian akhir yaitu Singapore - Cambridge General Certificate of Education ‘Ordinary’ (GCE ‘O’ Level ) atau ‘Normal’ (GCE ‘N’ Level ). ). Melalui kurikulum ini, pelajar dilatih

dan diajarkan cara berpikir kritis. Normal adalah kursus empat tahun menjelang ujian Normal2

tingkat (N-level), dengan kemungkinan tahun kelima diikuti oleh tingkat O-. Normal dibagi menjadi Normal (Akademik) dan Normal (Teknis ). Pada tahun 2004, Departemen Pendidikan

mengumumkan bahwa siswa yang dipilih dalam kegiatan normal akan memiliki kesempatan untuk duduk untuk ujian O-level secara langsung tanpa terlebih dahulu mengambil ujian N-tingkat. .

2. Pra-Universitas ( Junior College) Setelah menyelesaikan ujian GCE ‘O’ Level , untuk mempersiapkan diri memasuki kurikulum universitas, pelajar dapat memilih mendaftar ke Pra-Universitas ( Junior College) atau langsung ke ITE ( Institutes of Technical Education ) atau Politeknik. Pra-Universitas atau yang lebih dikenal dengan sebutan Junior College atau disingkat JC ini berdurasi dua (2) tahun. Kurikulum terdiri dari dua (2) pelajaran wajib yaitu general paper dan salah satu dari bahasa ibu (Cina, Melayu atau Tamil ), serta maksimum empat (4) pelajaran dari tingkat ‘A’ Level . Selesai dari JC , pelajar akan memperoleh Singapore - Cambridge General Certificate of

Education ‘Advanced’ (GCE ‘A’ Level ) dan dapat melanjutkan ke tahun pertama universitas di

Singapura. 3. ITE (Institutes Of Technical Education ) & Politeknik Untuk pelajar yang telah menyelesaikan ujian GCE ‘O’ Level atau GCE ‘N’ Level , pilihan lainnya selain daripada masuk ke JC , adalah ITE dan Politeknik. Keduanya memiliki durasi belajar selama tiga (3) tahun pada tingkat Diploma; yang membedakan adalah persyaratan untuk mendaftar, Politeknik memiliki persyaratan masuk yang lebih tinggi dibanding ITE. Kebanyakan pelajar Indonesia mendaftar ke Politeknik dibandingkan ke ITE. 4. Universitas Negeri Singapura sebagai pusat pendidikan tersier menawarkan kesempatan belajar berbeda, karena didukung oleh fasilitas pendidikan dan teknologi yang canggih. Pendidikan tersier di Singapura mempunyai dedikasi mempersiapkan para pelajar di dalam menghadapi masa depan mereka. Di Singapura terdapat tiga (3) universitas negeri yang menawarkan program Bachelor , Master hingga PhD; dengan syarat penerimaan yang sangat kompetitif dan juga beasiswa dengan kontrak kerja setelah kelulusan.

3

B. PERBANDINGAN PENDIDIKAN SINGAPURA DAN INDONESIA Pendidikan formal Singapura dimulai dari tingkat kindergarten kemudian primary school, secondary school, pre university, ITE, university. Pendidikan diIndonesia juga di mulai dari TK (kindergarten), Sekolah Dasar dan Sekolah Menengah, sekolah menengah terdiri dari Sekolah Menengah Pertama (SMP) dan Sekolah Menengah Atas (SMA), kemudian Universitas. Lamanya jenjang pendidikan kindergarten yaitu selama dua tahun sama seperti TK di Indonesia. Pendidikan berikutnya yaitu Primary School jika di Indonesia adalah Sekolah Dasar, lamanya jenjang pendidikan ini adalah 6 tahun. Kemudian jenjang berikutnya adalah Secondary School yang ditempuh selama 4 sampai 5 tahun tergantung pada tingkat kemampua siswa. Di Singapura jenjang pendidikan menengah tidak dibedakan seperti di Indonesia menjadi SMP dan SMA yang masing-masing ditempuh selama 3 tahun. Setelah selesai dari jenjang pendidikan Secondary School jenjang berikutnya adalah Pre-University bagi siswa yang akan melanjutkan ke university. Pre-university dilaksanakan selama dua tahun. Bagi siswa yang tidak ingin melanjutkan ke University, setelah selesai Primary school mereka dapat langsung melanjutkan ke ITE dan politeknik yang dilaksanakan selama 3 tahun. Berbeda dengan Di Indonesia, setelah selesai jenjang pendidikan SMA atau sederajat, mereka langsung bisa melanjutkan ke Universitas. Di Singapura juga mengadakan Ujian Nasional bagi setiap siswa yang akan melanjutkan ke jenjang pendidikan berikutnya sama halnya dengan di Indonesia. Bedanya, UN di Singapura tidak menentukan kelulusan karena menurut pemerintah Singapura, setiap orang punya kesempatan sama untuk melanjutkan pendidikan. Sedangkan jika Di Indonesia, Ujian nasional adalah penentu kelulusan dengan menentukan nilai minimum. Jadi jika siswa mendapatkan nilai dibawah nilai minimum maka mereka dinyatakan tidak lulus dan harus mengikuti ujian ulang. Sebenarnya di Singapura juga menetapkan nilai minimum untuk setiap pelajaran jika siswa mendapatkan nilai dibawah minimum mereka tetap lulus. Namun dalam ijazah akan terdapat nilai merah jika tidak ingin nilai merah di ijazah meraka harus mengulang satu tahun di kelas yang sama.

4

No. 1

Aspek yang dibandingkan Kurikulum Mata Pelajaran

Perbandingan Pendidikan Indonesia

Singapura

Pendidikan agama, PKN, B.

B. inggris, matematika,

Indonesia, Matematika, IPA, IPS,

Sains, Bahasa Ibu,

Penjaskes, Muatan Lokal

Geografi, Fisika, Biologi, Sejarah, B. Perancis, B. Jepang.

2

3

Sistem Pendidikan

Tk 2 thn,

SD,

Segi kelembagaan dan masa

SD 6 thn, SMP 3 thn,

Sekolah Lanjutan,

belajar.

SMA 3 thn,

Junior College centeroes

Perguruan Tinggi 4 thn

Institut

Pembiayaan Pendidikan

Sekolah

negeri

dibiayai

oleh

Semua

sekolah

tingkat

pemerintah

dasar di biayai

Sekolah suasta hanya mendapatkan

oleh pemerintah

subsidi

Sekolah lanjutan Junior College di subsidi Pemerintah

4

Usia normal memasuki

6-12 thn

7-13 thn

Mencerdaskan kehidupan bangsa

Bertujuan untuk

dan mengembangkan manusia

mendidik anak masing-

Indonesia seutuhnya, yaitu

masing potensi perlu

manusia yang beriman dan

untuk menemukan-

bertaqwa terhadap Tuhan Yang

talenta dan untuk

Maha Esa dan berbudi pekerti

mengenimbangkan dalam

luhur, memiliki pengetahuan dan

dirinya semangat untuuk

keterampilan, kesehatan jasmani

belajar

sekolah 5

Tujuan Pendidikan Nasional

dan rohani, kepribadian yang mantap serta rasa tanggung jawab kemasyarakatan dan kebangsaan. 6

Bahasa Nasional

Bahasa Indonesia

Bahasa Inggris

7

Evaluasi

Ujian naik kelas berdasarkan nilai

SD = Prinigry School

harian, sikap, dan Ujian semester,

leaving exaniination

Ujian Nasional.

Sekolah lanjutan = general Certificare of education Cordinary

C. Perbandingan Kurikulum Matematika Tingkat Menengah Indonesia dan Si ngapura. 1.

Singapura O LEVEL MATHEMATICS

5

Secondary One Topics/SubTopics 1.

Content

Numbers and Algebra

Numbers and the four

• primes and prime factorisation

operations

• finding HCF and LCM, squares, cubes, square roots and cube

roots by prime factorisation • negative numbers, integers, rational numbers, real numbers and

their four operations • calculations with the use of a calculator • representation and ordering of numbers on the number line • use of the symbols <, >, =, = • approximation and estimation (including rounding off numbers to

a required number of decimal places or significant figures, estimating the results of computation, and concepts of rounding and truncation errors) Ratio, rate and



Ratios involving rational numbers

Proportion



writing a ratio in its simplest form



average rate



problems involving ratio and rate

Percentage

• expressing one quantity as a percentage of another • comparing two quantities by percentage • percentages greater than 100% • increasing/decreasing a quantity by a given percentage • reverse percentages • problems involving percentages

Speed

• concepts of speed, uniform speed and average speed • conversion of units (e.g. km/h to m/s) •problems involving speed, uniform speed and average speed

Algebraic

• using letters to represent numbers

representation and

• interpreting notations:

formulae

* ab as a × b *

 as a ÷ b 

• evaluation of algebraic expressions and formulae • translation of simple real-world situations into algebraic

expressions • recognising and representing number patterns (including finding

an algebraic expression for the nth term) Algebraic manipulation

addition and subtraction of linear algebraic expressions • simplification of linear algebraic expressions, e.g.

) (2)(35)  4 23  3(5 2

• factorisation of linear algebraic expressions of the form

* ax + ay (where a is a constant) * ax + bx + kay + kby (where a, b and k are constants) Functions and graphs

cartesian coordinates in two dimensions • graph of a set of ordered pairs • linear relationships between two variables (linear functions) • the gradient of a linear graph as the ratio of the vertical change

6

to the horizontal change (positive and negative gradients) Solutions of equations

solving linear equations in one unknown (including fractional

and inequalities

coefficients) • solving simple inequality (e.g.

3  ≤ 5)

• solving simple fractional equations that can be reduced to linear

equations, e.g. 

  − = 3  

• formulating a linear equation in one unknown to solve problems

2.

Geometry and Measurement

Angles, triangles and

right, acute, obtuse and reflex angles, complementary and

Polygons

supplementary angles, vertically opposite angles, adjacent angles on a straight line, adjacent angles at a point, interior and exterior angles • angles formed by two parallel lines and a transversal:

corresponding angles, alternate angles, interior angles • properties of triangles and special quadrilaterals • classifying special quadrilaterals on the basis of their properties • angle sum of interior and exterior angles of any convex polygon • properties of regular pentagon, hexagon, octagon and decagon • properties of perpendicular bisectors of line segments and angle

bisectors • construction of simple geometrical figures from given data

(including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractors, where appropriate Mensuration

area of parallelogram and trapezium • problems involving perimeter and area of composite plane

figures (including triangle and circle) • volume and surface area of cube, cuboid, prism and cylinder • conversion between cm2 and m2 , and between cm3 and m3 • problems involving volume and surface area of composite solids

3.

Statistics and Probability

Data handling

data collection methods such as: * taking measurements * conducting surveys * classifying data * reading results of observations/outcom es of events • construction and interpretation of: table,bar graph,pictogram,line graph,pie

chart,histogram purposes and use, advantages and disadvantages of the different forms of statistical representations • drawing simple inference from statistical diagrams

Exclude histograms with unequal intervals.

Secondary two Topics/SubTopics 1.

Content

Numbers and Algebra

Ratio, rate and

Include:

Proportion

• map scales (distance and area)

7

• direct and inverse proportion

Algebraic manipulation

Include: • expansion of the product of algebraic expressions • changing the subject of a fo rmula • finding the value of an unknown quantity in a given formula • recognising and applying the special products

∗ ( ± )=  ± 2ab +   • factorisation of algebraic expressions of the form

∗   − • multiplication and division of simple algebraic fractions, e.g.

∗ ()() • addition and subtraction of algebraic fractions with linear or

quadratic denominator, e.g.

   ∗ − − Functions and graphs

Include: • graphs of linear equations in two unknowns • graphs of quadratic functions and their properties

Solutions of equations

Include: • solving simultaneous linear equations in two unknowns by

∗ substitution and elimination methods ∗ graphical method • solving quadratic equations in one unknown by factorisation • formulating a pair of linear equations in two unknowns or a

quadratic equation in one unknown to solve problems Set language and

• Include:

Notation

• use of set language and the following notation • Venn diagrams

Exclude :

∪ B) = n( A) + n(B) − n( A∩ B)

• use of n( A 2.


Congruence and

Include:

Similarity

• congruent figures as figures that are identical in shape and size • matching sides and angles of two congruent polygons • similar figures as figures that have the same shape but different

sizes • properties of similar polygons: • enlargement and reduction of a plane figure by a scale factor • scale drawings • solving simple problems involving similarity and congruence Pythagoras’ theorem

Include: • use of Pythagoras’ theorem • determining whether a triangle is right-angled given the lengths

of three sides Mensuration

Include: • volume and surface area of pyramid, cone and sphere

3.

Data analysis

Statistics and Probability Include: • interpretation and analysis of:

∗ dot diagrams ∗ stem-and-leaf diagrams • mean, mode and median as averages • purposes and use of mean, mode and median • calculation of the mean for grouped data

8

Probability

Include: • probability as a measure of chance • probability of single events (including listing all the possible

outcomes in a simple chance situation to calculate the probability)

Secondary Three/Four Topics/SubTopics 1.

Content

Numbers and Algebra


Include:

operations

• examples of very large and very small numbers such as mega/

million (10 6 ), giga/ billion (109 ), tera/ trillion (1012 ), micro (10−6 ), nano (10−9 ) and pico (10 −12 ) • use of standard form A × 10n , where n is an integer, and

1 ≤ A < 10 • positive, negative, zero and fractional indices • laws of indices

Functions and graphs

Include: • sketching of the graphs of quadratic functions given in the form

∗ y = ± (  ) + q ∗ y = ± ( x − a)( x − b) • graphs of functions of the form y = axn

where n = −2, −1, 0, 1, 2, 3, and simple sums of not more than three of these • graphs of exponential functions y = kax where a is a positive

integer • estimation of gradients of curves by drawing tangents


Include:

and inequalities

• solving quadratic equations in one unknown by:

∗ use of formula ∗ completing the square for y =  + px + q ∗ graphical methods • solving fractional equations that can be reduced to quadratic

equations, e.g.

6 =3 ∗ + • solving linear inequalities in one unknown, and representing the

solution set on the number line Applications of

Include:

mathematics in

• problems derived from practical situations such as

practical situations

∗ utilities bills ∗ hire-purchase ∗ simple interest and compound interest ∗ money exchange • use of data from tables and charts • interpretation and use of graphs in practical situations • drawing graphs from given data • distance-time and speed-time graphs

Exclude the use of the terms percentage profit and percentage loss. Matrices

Include: • display of information in the form of a matrix of any order • interpreting the data in a given matrix • product of a scalar quantity and a matrix • problems involving the calculation of the sum and product

9

(where appropriate) of two matrices Exclude: • matrix representation of geometrical transformations • solving simultaneous linear equations using the inverse matrix

Method 2.


Congruence and

Include:

Similarity

• determining whether two triangles are

∗ congruent ∗ similar • ratio of areas of similar plane figures • ratio of volumes of similar solids

Properties of circles

Include: • symmetry properties of circles:

bisects the angle between the tangents • angle properties of circles:

∗ angle in a semicircle is a right angle ∗ angle between tangent and radius of a circle is a right angle ∗ angle at the centre is twice the angle at the circumference ∗ angles in the same segment are equal ∗ angles in opposite segments are supplementary Trigonometry

Include: • use of trigonometric ratios (sine, cosine and tangent) of acute

angles to calculate unknown sides and an gles in right-angled triangles • extending sine and cosine to obtuse angles • use of the formula

  

for the area of a triangle

• use of sine rule and cosine rule for any triangle • problems in 2 and 3 dimensions including those involving angles

of elevation and depression and bearings Exclude calculation of the angle between two planes or of the angle between a straight line and a plane Mensuration

Include: • arc length and sector area as fractions of the circumference and

area of a circle • area of a segment • use of radian measure of angle (including conversion between

radians and degrees) • problems involving the arc length, sector area of a circle and

area of a segment Coordinate geometry

Include: • finding the gradient of a straight line given the coordinates of two

points on it • finding the length of a line segment given the coordinates of its

end points • interpreting and finding the equation of a straight line graph in

the form y = mx + c • geometric problems involving the use of coo rdinates

Exclude: • condition for two lines to be parallel or perpendicular • midpoint of line segment • finding the area of quadrilateral given its vertices

Vectors in two

Include:

Dimensions

10

• use of notations:

→ ,a, → ,|| (),  

• directed line segments • translation by a vector • position vectors • magnitude of a vector

() as√   

• use of sum and difference of two vectors to express given

vectors in terms of two coplanar vectors • multiplication of a vector by a scalar • geometric problems involving the use of vectors

Exclude: • expressing a vector in terms of a unit vector • midpoint of line segment • solving vector equations with two unknown parameters 3.


Data analysis

Include: • quartiles and percentiles • range, interquartile range and standard deviation as measures

of spread for a set of data • interpretation and analysis of:

∗ cumulative frequency diagrams ∗ box-and-whisker plots • calculation of the standard deviation for a set of data (grouped

and ungrouped) • using the mean and standard deviation to compare two sets of

Data Probability

Include: • probability of simple combined events (including using possibility

diagrams and tree diagrams, where appropriate) • addition and multiplication of probabilities • mutually exclusive events and independent events

∪

Exclude use of P( A B) = P( A) + P(B) − P( A∩B)

N(A) LEVEL MATHEMATICS N(A) Secondary One Topics/SubTopics 1.

Content

Numbers and Algebra


Include:

operations

• primes and prime factorisation • finding HCF and LCM, squares, cubes, square roots and cube

roots by prime factorisation • negative numbers, integers, rational numbers, real numbers and

their four operations • calculations with the use of a calculator • representation and ordering of numbers on the number line • use of the symbols <, >, ≤, ≥ • approximation and estimation (including rounding off numbers to

a required number of decimal places or significant figures, estimating the results of computation, and concepts of rounding and truncation errors) Ratio, rate and

Include:

proportion

• comparison between two or more quantities by ratio • relationship between ratio and fraction

11

• dividing a quantity in a given ratio • ratios involving rational numbers • equivalent ratios • writing a ratio in its simplest form • average rate • problems involving ratio and rateinteger • estimation of gradients of curves by drawing tangents

Percentage

Include: • expressing percentage as a fraction or decimal • expressing one quantity as a percentage of another • comparing two quantities by percentage • percentages greater than 100% • increasing/decreasing a quantity by a given percentage • finding percentage increase/decrease • reverse percentages • problems involving percentages

Speed

Include: • relationships between distance, time and speed • writing speed in different units (e.g. km/h, m/min, m/s and cm/s) • conversion of units (e.g. km/h to m/s) • calculation of speed, distance or time given the other two

quantities • concepts of speed, uniform speed and average speed • problems involving speed, uniform speed and average speed

Algebraic

Include:

representation and


formulae


∗ ab as a × b • evaluation of algebraic expressions and formulae • translation of simple real-world situations into algebraic


an algebraic expression for the nth term) Algebraic manipulationAlgebraic

Include:

manipulation

• addition and subtraction of linear algebraic expressions • simplification of linear algebraic expressions, e.g.

∗ − 2(3 x − 5) + 4 x 2.



Include:

polygons

• right, acute, obtuse and reflex angles, co mplementary and


corresponding angles, alternate angles, interior angles Mensuration

Include: • area of parallelogram and trapezium • problems involving perimeter and area of composite plane

figures (including triangle and circle) • volume and surface area of cube, cuboid, prism and cylinder • conversion between cm2 and m2, and between cm3 and m3

∗

• problems involving volume and surface area of composite solids tangents from an

12

external point are equal in length

∗ the line joining an external point to the centre of the circle bisects the angle between the tangents • angle properties of circles:

∗ angle in a semicircle is a right angle ∗ angle between tangent and radius of a circle is a right angle ∗ angle at the centre is twice the angle at the circumference ∗ angles in the same segment are equal ∗ angles in opposite segments are supplementary 3.


Data handling

Include: • data collection methods such as:

∗ taking measurements ∗ conducting surveys ∗ classifying data ∗ reading results of observations/outcomes of events • construction and interpretation of: table, bar graph,pictogram,etc • purposes and use, advantages and disadvantages of the different

forms of statistical representations • drawing simple inference from statistical diagrams

Exclude histograms with unequal intervals.

N(A) Secondary Two Topics/SubTopics

Content

1 Numbers and Algebra Ratio, rate and

Include:

proportion

• map scales (distance and area) • direct and inverse proportion


Include: • expansion of the product of two linear algebraic expressions • factorisation of linear algebraic expressions of the form

∗ ax + ay (where a is a constant) • recognising and applying the special products

∗ ( ± )= a2 ± 2ab +   • factorisation of algebraic expressions of the form

∗   − • multiplication and division of simple algebraic fractions, e.g.• factorisation of

algebraic expressions of the form • multiplication and division of simple algebraic fractions, e.g. • addition and subtraction of algebraic fractions with linear or


∗ ()() Functions and graphs

Include: • cartesian coordinates in two dimensions • graph of a set of ordered pairs • linear relationships between two variables (linear functions) • the gradient of a linear graph as the ratio of the vertical change

to the horizontal change (positive and n egative gradients) • graphs of linear equations in two unknowns


Include:

and inequalities

• solving linear equations in one unknown (including fractional

coefficients) • solving simple inequality (e.g. 3 x ≤ 5 )

13

• solving simple fractional equations that can be reduced to linear

equations, e.g.

∗   −  =3 N(A) Secondary Two Topics/SubTopics 1.

Content

Numbers and Algebra • solving simultaneous linear equations in two unknowns by

∗ substitution and elimination methods ∗ graphical method • formulate a linear equation in one unknown or a pair of linear

equations in two unknowns to solve problems 2.



Include:

polygons

• properties of triangles and special quadrilaterals • classifying special quadrilaterals on the basis of their properties • angle sum of interior and exterior angles of any convex polygon • properties of regular pentagon, hexagon, octagon and decagon • properties of perpendicular bisectors of line segments and angle


(including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractors, where appropriate Congruence and

Include:

similarity

• congruent figures as figures that are identical in shape and size • matching sides and angles of two congruent polygons

Mensuration

Include: • volume and surface area of pyramid, cone and sphere

3.


Data analysis

Include: • interpretation and analysis of:

∗ dot diagrams ∗ stem-and-leaf diagrams • mean, mode and median as averages • purposes and use of mean, mode and median • calculation of the mean for grouped data.

Probability


outcomes in a simple chance situation to calculate the probability)

N(A) Secondary Three/Four Topics/SubTopics

Content

Certain parts of the syllabus have been underlined. These will only be tested in Section B

of Paper 2 of the GCE ‘N’ Level (Syllabus A) examinations. 1.

Numbers and Algebra


nclude:

operations

• examples of very large and very small numbers such as mega/

106), giga/ billion ( 109 ), tera/ trillion (10 ), micro (10−6), nano (10−9) and pico (10−) million (

14

• use of standard form A ×

10 , where n is an integer, and

1 ≤ A < 10 • positive, negative, zero and fractional indices • laws of indices


Include: • expansion of the product of algebraic expressions • changing the subject of a fo rmula • finding the value of an unknown quantity in a given formula • addition and subtraction of algebraic fractions with linear or


   ∗ − − Functions and graphs

Include: • graphs of quadratic functions and their properties

∗ positive or negative coefficient of   ∗ maximum and minimum points ∗ symmetry • sketching of the graphs of quadratic functions given in the form

∗ y = ± (  ) + q

  where n = −2, −1, 0, 1,

• graphs of functions of the form y = a

2, 3, and simple sums of not more than three of th ese • graphs of exponential functions y =

  where a is a positive

integer • estimation of gradients of curves by drawing tangents

N(A) Secondary Three/Four Topics/SubTopics

Content

Certain parts of the syllabus have been underlined. These will only be tested in Section B

of Paper 2 of the GCE ‘N’ Level (Syllabus A) examinations. 1.

Numbers and Algebra


Include: • solving quadratic equations in one unknown by

∗ factorisation ∗ use of formula ∗ completing the square for y =  + px + q ∗ graphical methods • solving fractional equations that can be reduced to quadratic

equations, e.g.

6 =3 ∗ + • formulate a quadratic equation in one unknown to solve

Problems Applications of

Include:

mathematics in

• problems derived from practical situations such as

practical situations

∗ utilities bills ∗ hire-purchase ∗ simple interest and compound interest ∗ money exchange • use of data from tables and charts • interpretation and use of graphs in practical situations • drawing graphs from given data • distance-time and speed-time graphs

Exclude the use of the terms percentage profit and percentage loss. 2 Geometry and Measurement Congruence and

Include:

15

similarity

• similar figures as figures that have the same shape but different

sizes • properties of similar polygons:

∗ corresponding angles are equal ∗ corresponding sides are proportional • enlargement and reduction of a plane figure by a scale factor • scale drawings • solving simple problems involving similarity and congruence

Properties of circles

Include: • symmetry properties of circles:

∗ equal chords are equidistant from the centre ∗ the perpendicular bisector of a chord passes through the centre

∗ tangents from an external point are equal in length ∗ the line joining an external point to the centre of the circle bisects the angle between the tangents • angle properties of circles:

∗ angle in a semicircle is a right angle ∗ angles in the same segment are equal ∗ angles in opposite segments are supplementary Pythagoras’ theorem

Include:

and trigonometry

• use of Pythagoras’ theorem • determining whether a triangle is right-angled given the lengths

of three sides • use of trigonometric ratios (sine, cosine and tangent) of acute

angles to calculate unknown sides and an gles in right-angled triangles • extending sine and cosine to obtuse angles • use of the formula

  for the area of a triangle 

• use of sine rule and cosine rule for any triangle • problems in 2 and 3 dimensions including those involving

angles of elevation and depression and bearings Exclude calculation of the angle between two planes or of the angle between a straight line and a plane. Mensuration

Include: • arc length and sector area as fractions of the circumference and

area of a circle • area of a segment • use of radian measure of angle (including conversion between

radians and degrees) • problems involving the arc length, sector area of a circle and

area of a segment Coordinate geometry

Include: • finding the gradient of a straight line given the coordinates of two

points on it • finding the length of a line segment given the coordinates of its

end points • interpreting and finding the equation of a straight line graph in

the form y = mx + c • geometric problems involving the use of coo rdinates

Exclude: • condition for two lines to be parallel or perpendicular • midpoint of line segment • finding the area of quadrilateral given its vertices

16

3 Statistics and Probability Data analysis

Include: • quartiles and percentiles • range, interquartile range and standard deviation as measures of

spread for a set of data • interpretation and analysis of:

∗ cumulative frequency diagrams ∗ box-and-whisker plots • calculation of the standard deviation for a set of data (grouped

and ungrouped) • using the mean and standard deviation to compare two sets of

Data Probability

Include: • probability of simple combined events (including using possibility

diagrams and tree diagrams, where appropriate) • addition and multiplication of probabilities • mutually exclusive events and independent events

∪

Exclude use of P( A B) = P( A) + P(B) − P( A∩B) .

N(T) LEVEL MATHEMATICS N(T) Secondary One Topics/SubTopics 1.

Content

Numbers and Algebra


Include:

operations

• negative numbers, integers, and their four operations • four operations on fractions and decimals (including negative

fractions and decimals) • calculations with the use of a calculator, including squares,

cubes, square roots and cube roots • representation and ordering of numbers on the number line • use of the symbols <, >, ≤, ≥ • rounding off numbers to a required number of decimal places or

significant figures • estimating the results of computation

Ratio

Include: • comparison between two or more quantities by ratio • dividing a quantity in a given ratio • ratios involving fractions and decimals • equivalent ratios • writing a ratio in its simplest form • problems involving ratios

Percentage

Include: • expressing percentage as a fraction or decimal • finding the whole given a percentage part • expressing one quantity as a percentage of another • comparing two quantities by percentage • percentages greater than 100% • finding one quantity given the percentage and the other quantity • increasing/decreasing a quantity by a given percentage • finding percentage increase/decrease • problems involving percentages

Algebraic


17

representation and


formulae

* ab as a × b *

 as a ÷ b 

• evaluation of algebraic expressions and formulae • translation of simple real-world situations into algebraic


an algebraic expression for the nth term) 2.



Include:

Polygons

• right, acute, obtuse and reflex angles, co mplementary and


corresponding angles, alternate angles, interior angles Mensuration

Include: • area of triangle • area and circumference of circle • area of parallelogram and trapezium • problems involving perimeter and area of composite plane

figures • visualising and sketching cube and cuboid (including use of

nets to visualise the surface area of these solids) • volume and surface area of cube and cuboid • conversion between cm2 and m2, and between cm3 and m3 • problems involving volume and surface area of composite

Solids 3.


Data handling

Include: • data collection methods such as:

∗ taking measurements ∗ conducting surveys ∗ classifying data ∗ reading results of observations/ outcomes of events • construction and interpretation of:table,bar graph,pictogram,etc • purposes and use, advantages and disadvantages of the

different forms of statistical representations • drawing simple inference from statistical diagrams

Exclude histograms with unequal intervals

N(T) Secondary Two Topics/SubTopics

Content

1 Numbers and Algebra Ratio

Include: • rates and average rates (including the concepts of speed and

average speed) • conversion of units


Include: • addition and subtraction of linear algebraic expressions • simplification of linear algebraic expressions, e.g.


Include: • cartesian coordinates in two dimensions

18

• graph of a set of ordered pairs • linear relationships between two variables (linear functions) • the gradient of a linear graph as the ratio of the vertical change

to the horizontal change (positive and negative gradients) Solutions of equations

Include: • solving linear equations in one unknown (including fractional

coefficients) • formulating a linear equation in one unknown to solve problems

2 Geometry and Measurement Angles, triangles and

Include:

quadrilaterals

• properties of triangles and special quadrilaterals • classifying special quadrilaterals on the basis of their properties • properties of perpendicular bisectors of line segments and angle


(including perpendicular bisectors and angle bisectors) using compasses, rulers, set squares and protractors where appropriate Exclude properties of polygons. Congruence, similarity

Include:

and transformations

• congruent figures as figures that are identical in shape and size • matching sides and angles of two congruent polygons • similar figures as figures that have the same shape but different

sizes • properties of similar polygons:

* corresponding angles are equal * corresponding sides are proportional Pythagoras’ theorem

Include: • use of Pythagoras‘ theorem • determining whether a triangle is right-angled given the lengths

of three sides Mensuration

Include: • visualising and sketching prism and cylinder (including use of

nets to visualise the surface area of these solids) • volume and surface area of prism and cylinder

3 Statistics and Probability Data analysis

Include: • interpretation and analysis of dot diagrams • purposes and use of averages: mean, mode and median • calculations of mean, mode and median for a set of ungrouped

Data Probability


outcomes in a simple chance situation to calculate the probability) Exclude probability of combined events: P( A and B), P( A or B). 4 Integrative Contexts Problems derived from

Include:

practical real-life

• practical situations such as

situations

* profit and loss

(The content should be

* simple interest and compound interest

distributed over 3

* household finance (earnings, expenditures, budgeting, etc.)

years, from Sec 2 to

* payment/ subscription rates (hire-purchase, utilities bills,

19

Sec 4)

etc.) * money exchange * time schedules (including 24-hour clock) and time zone variation * designs (tiling patterns, models/structures, maps and plans, packagings, etc.) * everyday statistics (sport/ game statistics, household and market surveys, etc.) • tasks involving:

* use of data from tables and charts * interpretation and use of graphs in practical situations * drawing graphs from given data * creating geometrical patterns and designs * interpretation and use of quantitative information Exclude use of the terms percentage profit and percentage loss.

N(T) Secondary Three/Four Topics/SubTopics 1.

Content

Numbers and Algebra


Include:

operations

• use of index notation for integer powers: • examples of very large and very small numbers such as mega/

million (106 ), giga/ billion ( 109 ), tera/ trillion ( 1012 ), micro (10−6 ), nano (10−9) and pico ( 10−12) • use of standard form A × 10 , where n is an integer, and

1 ≤ A < 10 Exclude: • use of the terms ‘rational numbers’, ‘irrational numbers’ and ‘real numbers’ • primes and prime factorisation • fractional indices and surds

Ratio and proportion

Include: • map scales (distance and area) • direct and inverse proportion


Include: • expansion of the product of two linear algebraic expressions • multiplication and division of simple algebraic fractions, e.g. • changing the subject of a simple formula • finding the value of an unknown quantity in a given formula • factorisation of linear algebraic expressions of the form

∗ ax + ay (where a is a constant) ∗ ax + bx + kay + kby (where a, b and k are constants) • factorisation of quadratic expressions of the form x 2 + px + q

Exclude: • use of special products:

(a ± b)2 = a2 ± 2ab + b2 a2 − b2 = (a + b)(a − b) • factorisation of algebraic expressions of the form

∗ a2 x 2 − b2 y 2 ∗ a2 ± 2ab + b2 ∗ ax 2 + bx + c , where a ≠ 1 • addition and subtraction of algebraic fractions

20


Include: • graphs of linear equations in two unknowns • graphs of quadratic functions and their properties

∗ positive or negative coefficient of x 2 ∗ maximum and minimum points ∗ symmetry Exclude sketching of graphs of quadratic functions. Solutions of equations

Include: • solving simple fractional equations that can be reduced to linear

equations, e.g. • solving simultaneous linear equations in two unknowns by

* substitution and elimination methods * graphical method • solving quadratic equations in one unknown by use of formula • formulating a quadratic equation in one unknown or a pair of

linear equations in two unknowns to solve problems Exclude solving quadratic equations by: • method of completing the square • graphical methods

2 Geometry and Measurement Congruence, similarity

Include:

and transformations

• drawing on square grids the following transformations of simple

plane figures

∗ reflection about a given horizontal or vertical line ∗ rotation about a given point through multiples of 90o clockwise/anticlockwise

∗ translation represented by a given translation arrow ∗ enlargement by a simple scale factor such as , 2 and 3, given the centre of enlargement • scale drawings

Exclude: • use of coordinates • negative scale factors

Symmetry, tessellations

Include:

and projections

• line and rotational symmetry of plane fi gures • order of rotational symmetry • identifying the unit figure(s) of a tessellation and continuing a

tessellation • orthographic projection drawings, including plan (top view), front,

left and right views Exclude symmetry of solids. Pythagoras’ theorem

Include:

and trigonometry

• use of trigonometric ratios (sine, cosine and tangent) of acute

angles to calculate unknown sides and an gles in right-angled triangles (including problems involving angles of elevation and depression) for the area of a triangle (extending sine to obtuse angles) Exclude: • sine rule and cosine rule • bearings

Mensuration

Include: • visualising and sketching pyramid, cone and sphere (including

21

use of nets to visualise the surface area of these solids, where applicable) • volume and surface area of pyramid, cone and sphere • arc length and sector area as fractions of the circumference

and area of a circle Exclude the radian measure of angle. 3 Statistics and Probability Data analysis

Include: • percentiles, quartiles, range and interquartile range • interpretation and analysis of cumulative frequency diagrams

4 Integrative Contexts Problems derived from

Include:

practical real-life

• practical situations such as

situations

* profit and loss

(The content should be

* simple interest and compound interest

distributed over 3

* household finance (earnings, expenditures, budgeting, etc.)

years, from Sec 2 to

* payment/ subscription rates (hire-purchase, utilities bills,

Sec 4)

etc.) * money exchange * time schedules (including 24-hour clock) and time zone variation * designs (tiling patterns, models/structures, maps and plans, packagings, etc.) * everyday statistics (sport/ game statistics, household and market surveys, etc.) • tasks involving:

* use of data from tables and charts * interpretation and use of graphs in practical situations * drawing graphs from given data * creating geometrical patterns and designs * interpretation and use of quantitative information Exclude use of the terms percentage profit and percentage loss.

2.

Indonesia Kelas VII, Semester 1 Standar kompetensi

Kompetensi Dasar

Bilangan Memahami sifatoperasi hitung bilangan dan penggunaannya dalam pemecahan masalah

Melakukan operasi hitung bilangan bulat dan pecahan Menggunakan sifat-sifat operasi hitung bilangan bulat dan pecahan dalam pemecahan masalah

Aljabar Memahami bentuk aljabar, persamaan dan pertidaksamaan linear satu variabel

Mengenali bentuk aljabar dan unsur-unsurnya Melakukan operasi pada bentuk aljabar Menyelesaikan persamaan linear satu variabel Menyelesaikan pertidaksamaan linear satu variabel

Menggunakan bentuk aljabar persamaan dan

Membuat model matematika dari masalah yang

pertidaksamaan linear satu variabel, dan

berkaitan dengan persamaan dan pertidaksamaan

perbandingan dalam pemecahan masalah

linear satu variabel Menyelesaikan model matematika dari masalah yang berkaitan dengan persamaan dan pertidaksamaan

22

linear satu variabel Menggunakan konsep aljabar dalam pemecahan masalah aritmetika sosial yang sederhana Menggunakan perbandingan untuk pemecahan masalah

Kelas VII, Semester 2 Standar Kompetensi

Konsep Dasar

Aljabar Menggunakan konsep himpunan dan diagram venn dalam pemecahan masalah

Memahami pengertian dan notasi himpunan, serta penyajiannya Memahami konsep himpunan bagian Melakukan operasi irisan, gabungan, kurang (difference), dan komplemen pada himpunan Menyajikan himpunan dengan diagram venn Menggunakan konsep himpunan dalam penyelesaian masalah

Geometri Memahami hubungan garis dengan garis,

Menentukan hubungan antara dua garis,

garis dengan sudut, sudut dengan sudut,

serta besar dan jenis sudut

serta menentukan ukurannya

Memahami sifat-sifat sudut yang terbentuk jika dua garis berpotongan atau dua garis sejajar berpotongan dengan garis lain Melukis sudut Membagi sudut

Memahami konsep segiempat dan segitiga dan serta menentukan ukurannya

Mengidentifikasisifat-sifat segitiga berdasarkan sisi dan sudutnya Mengidentifikasi sifat-sifat persegi panjang, persegi, trapesium, jajargenjang, belah ketupat, dan layang-layang Menghitung keliling dan luas bangun segitiga dan segi empat serta menggunakannya dalam pemecahan masalah Melukis segitiga, garis tinggi, garis bagi, garis berat, dan garis sumbu

Kelas VIII, Semester 1 Standar Kompetensi

Kompetensi Dasar

Aljabar 1.

Memahami bentuk aljabar, relasi,

Melakukan operasi aljabar

fungsi, dan persamaan garis lurus Menguraikan bentuk aljabar kedalam faktorfaktornya

23

Memahami relasi dan fungsi Menentukan nilai fungsi Membuat sketsa grafik fungsi alajabar sederhana pada sistem koordinat cartesius Menentukan gradien, persamaan dan gerafik garis lurus 2.

Memahami sistem persamaan linear

Menyelesaikan sistem persamaan linaer dua

dua variabel dan menggunakannya

variabel

dalam pemecahan masalah Membuat model matematika dari masalah yang berkaitan dengan sistem persamaan linear dua variabel Menyelesaikan model matematika dari masalah yang berkaitan dengan persaman linear dua variabel dan penafsirannya

Geometri dan Pengukuran 3.

Menggunakan Teotema Pythagoras

Menggunakan teorema pythagoras untuk

dalam pemecahan masalah

menentukan panjang sisi-sisi segitiga siku-siku Memecahkan masalah pada bangun datar yang berkaitan dengan teorema pythagoras

Kelas VIII, Semester 2 Standar Komperensi

Kompetensi Dasar

Geometri dan pengukuran 4.

Menentukan unsur, bagian lingkaran

Menentukan unsur dan bagian-bagian

serta ukurannya

lingkaran Menghitung keliling dan luas lingkaran Menggunakan hubungan sudut pusat, panjang busur, luas juring dalam pemecahan masalah Menghitung panjang garis singgung persekutuan dua lingkaran Melukis lingkaran dalam dan lingkaran luar suatu segitiga

5.

Memahami sifat-sifat kubus, balok,

Mengidentifikasi sifat-sifat kubus, balok,

prisma, limas, dan bagian-bagiannya,

24

serta menentukan ukurannya

prisma, dan limas serta bagian-bagiannya Membuat jaring-jaring kubus, balok, prisma, dan limas Menghitung luas permukaan dan volume kubus, balok, prisma, dan limas

Kelas IX, Semester 1 Standar Kompetensi

Kompetensi Dasar

Geometri dan Pengukuran 1.

Memahami kesebangunan bangun

Mengidentifikasi bangun-bangun datar yang

datar dan penggunaannya dalam

sebangun dan kongruen

pemecahan masalah Mengidentifikasi sifat-sifat dan segitiga sebangun dan kongruen Menggunakan konsep kesebangunan segitiga dalam pemecahan masalah 2.

Memahami sifat-sifat tabung,

Mengidentifikasi unsur-unsur tabung, kerucut

kerucut, dan bola, serta menentukan

dan bola

ukurannya Menghitung luas selimut dan volume tabung, kerucut dan bola Memecahkan masalah yang berkaitan dengan tabung, kerucut dan bola

Statika dan Peluang 3.

Melakukan pengolahan dan

Menentukan rata-rata, median, dan

penyajian data

modusdata tunggal serta penafsirannya Menyajikandata dalam bentuk tabel dan diagram batang, garis, dan lingkaran

4.

Memahami peluang kejadian

Menentukan ruang sampel suatu percobaan

sederhana Menentukan peluang suatu kejadian sederhana

Kelas IX, Semester 2 Kompetensi Standar

Kompetensi Dasar

Bilangan

25

5.

Memahami sifat-sifat bilangan

Mengidentifikasi sifat-sifat bilangan

berpangkat dan bentuk akar serta

berpangkat dan bentuk akar

penggunaannya dalam pemecahan masalah sederhana

Melakukan operasi aljabar yang melibatkan bilangan berpangkat bulat dan bentuk akar Memecakan masalah sederhana yang berkaitan dengan bilangan berpangkat dan bentuk akar

6.

Memahami barisan dan deret

Menentukan pola barisan bilangan sederhana

bilangan serta penggunaannya dalam pemecahan masalah

Menentukan suku ke-n barisan aritmetika dan barisan geometri Menentukan jyumlah n suku pertama deret aritmetika dan deret geometri Memecahkan masalah yang berkaaitan dengan barisan dan deret

7.

Memahami sifat-sifat logaritma serta

Menghitung nilai logaritma suatu

menyelesaikan permasalahan yang

bilanganMenggunakan sifst-sifat logaritma

berhubungan dengan logaritma

Dari dua tabel di atas nampak perbedaan yang cukup mencolok antara kurikulum ke dua negara dalam tingkat sekolah menengah. Di indonesia fokus materi hanya pada aljabar, geometri dan statistika yang sederhana. Sedangkan di Singapura materi yang disajikan dalam tingkat sekolah menengah lebih rumit, dan tergantung juga pada tingkat sekolah yang di ambil seperti kelas O atau kelas N. Kelas dengan klasifikasi O ditempuh selama 4 tahun sedangkan klasifikasi N ditempuh selama 5 tahun. Walaupun waktu yang ditempuh dalam sekolah menengah lebih lama daripada di Indonesia ternyata materi yang di ajarkan justru lebih banyak dan lebih kompleks. Bahkan ada beberapa materi yang di Indonesia dipelajari dalam tingkat sekolah lanjut (SMA), tetapi di Singapura sudah di ajarkan dalam tingkat menengah seperti trigonometri dan matriks.

26

Perbandingan Kurikulum Indonesia Dan Singapura

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