TUGAS KPM SMP ‘PERBANDINGAN KURIKULUM INDONESIA DAN SINGAPURA’ Dosen Pengampu: Beni Ashyar, M. Pd Oleh : Kelompok 6/ TMT 3B Nama anggota kelompok : 1. Ade restu pratama (3214113033) 2. Anisiatul lailiyah (3214113047) 3. Bella maristha cahya retnani (3214113055) 4. Dyas eko eviani (3214113062) SEKOLAH TINGGI AGAMA ISLAM NEGERI TULUNGAGUNG 2012 1 A. KONDISI PENDIDIKAN DI SINGAPURA 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 2 dan diajarkan cara berpikir kritis. Normal adalah kursus empat tahun menjelang ujian Normaltingkat (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. Aspek yang dibandingkan Perbandingan Pendidikan Indonesia Pendidikan agama, PKN, B. Indonesia, Matematika, IPA, IPS, Penjaskes, Muatan Lokal Singapura B. inggris, matematika, Sains, Bahasa Ibu, Geografi, Fisika, Biologi, Sejarah, B. Perancis, B. Jepang. SD, Sekolah Lanjutan, Junior College centeroes Institut 1 Kurikulum Mata Pelajaran 2 Sistem Pendidikan Segi kelembagaan dan masa belajar. Tk 2 thn, SD 6 thn, SMP 3 thn, SMA 3 thn, Perguruan Tinggi 4 thn 3 Pembiayaan Pendidikan 4 5 Usia normal memasuki sekolah Tujuan Pendidikan Nasional 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 6-12 thn 7-13 thn 6 7 Bahasa Nasional Evaluasi Mencerdaskan kehidupan bangsa dan mengembangkan manusia Indonesia seutuhnya, yaitu manusia yang beriman dan bertaqwa terhadap Tuhan Yang Maha Esa dan berbudi pekerti luhur, memiliki pengetahuan dan keterampilan, kesehatan jasmani dan rohani, kepribadian yang mantap serta rasa tanggung jawab kemasyarakatan dan kebangsaan. Bahasa Indonesia Ujian naik kelas berdasarkan nilai harian, sikap, dan Ujian semester, Ujian Nasional. Bertujuan untuk mendidik anak masingmasing potensi perlu untuk menemukantalenta dan untuk mengenimbangkan dalam dirinya semangat untuuk belajar Bahasa Inggris SD = Prinigry School leaving exaniination Sekolah lanjutan = general Certificare of education Cordinary C. Perbandingan Kurikulum Matematika Tingkat Menengah Indonesia dan Singapura. 1. Singapura O LEVEL MATHEMATICS 5 Secondary One Topics/SubTopics 1. Numbers and Algebra Numbers and the four operations Content Ratio, rate and Proportion 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 representation and formulae • using letters to represent numbers • interpreting notations: * ab as a × b • 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) * Ratios involving rational numbers writing a ratio in its simplest form average rate problems involving ratio and rate 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. 2𝑥 3(𝑥−5) (−2)(3𝑥−5) + 4𝑥 − 3 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 and inequalities solving linear equations in one unknown (including fractional coefficients) • solving simple inequality (e.g. 3𝑥 ≤ 5) • solving simple fractional equations that can be reduced to linear equations, e.g. 𝑥 3 + 𝑥−2 4 =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/outcomes 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 Content 1. Numbers and Algebra Ratio, rate and Include: Proportion • map scales (distance and area) 7 Algebraic manipulation • direct and inverse proportion Include: • expansion of the product of algebraic expressions • changing the subject of a formula • finding the value of an unknown quantity in a given formula • recognising and applying the special products ∗ (𝑎 ± 𝑏)2 = 𝑎2 ± 2ab + 𝑏 2 • factorisation of algebraic expressions of the form ∗ 𝑎2 𝑥 2 −𝑏 2 𝑦 2 • multiplication and division of simple algebraic fractions, e.g. ∗( 3𝑎 4𝑏 2 5𝑏 )( ) 4 • addition and subtraction of algebraic fractions with linear or quadratic denominator, e.g. ∗ 1 𝑥−2 + 2 𝑥−3 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 : • use of n(A∪ B) = n(A) + n(B) − n(A∩ B) 2. Geometry and Measurement 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. Statistics and Probability 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 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 Content 1. Numbers and Algebra Numbers and the four 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 = ± (𝑥 − 𝑝)𝑧 + 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 Solutions of equations Include: and inequalities • solving quadratic equations in one unknown by: ∗ use of formula ∗ completing the square for y = 𝑥 2 + px + q ∗ graphical methods • solving fractional equations that can be reduced to quadratic equations, e.g. ∗ Applications of mathematics in practical situations Matrices 6 𝑥+4 =𝑥+3 • solving linear inequalities in one unknown, and representing the solution set on the number line Include: • problems derived from practical situations such as ∗ 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. 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. Geometry and Measurement 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 angles in right-angled triangles • extending sine and cosine to obtuse angles 1 • use of the formula 𝑎𝑏𝑠𝑖𝑛𝐶 for the area of a triangle 2 Mensuration Coordinate geometry Vectors in two Dimensions • 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 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 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 coordinates Exclude: • condition for two lines to be parallel or perpendicular • midpoint of line segment • finding the area of quadrilateral given its vertices Include: 10 𝑥 → → • use of notations: (𝑦), ,a, | |,|𝑎| 𝐴𝐵 𝐴𝐵 • directed line segments • translation by a vector • position vectors 𝑥 • magnitude of a vector (𝑦) as√𝑥 2 + 𝑦 2 • 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. 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(A) LEVEL MATHEMATICS N(A) Secondary One Topics/SubTopics Content 1. Numbers and Algebra Numbers and the four 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 Speed Algebraic representation and formulae Algebraic manipulationAlgebraic manipulation 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 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 Include: • using letters to represent numbers • interpreting notations: ∗ ab 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) Include: • addition and subtraction of linear algebraic expressions • simplification of linear algebraic expressions, e.g. ∗ − 2(3x − 5) + 4x 2. Geometry and Measurement Angles, triangles and Include: polygons • right, acute, obtuse and reflex angles, complementary and 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 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. Statistics and Probability 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 Algebraic manipulation 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 ∗ (𝑎 ± 𝑏)2 = a2 ± 2ab + 𝑏 2 • factorisation of algebraic expressions of the form ∗ 𝑎2 𝑥 2 −𝑏 2 𝑦 2 • 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 quadratic denominator, e.g. ∗( 3𝑎 4𝑏 2 Functions and graphs Solutions of equations and inequalities 5𝑏 )( ) 4 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 negative gradients) • graphs of linear equations in two unknowns Include: • solving linear equations in one unknown (including fractional coefficients) • solving simple inequality (e.g. 3x ≤ 5 ) 13 • solving simple fractional equations that can be reduced to linear equations, e.g. 𝑥 𝑥−2 3 4 ∗ + =3 N(A) Secondary Two Topics/SubTopics Content 1. 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. Geometry and Measurement Angles, triangles and 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 bisectors • construction of simple geometrical figures from given data (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. Statistics and Probability 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 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) 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 Numbers and the four nclude: operations • 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 ) 14 Algebraic manipulation • use of standard form A × 10𝑛 , 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 formula • finding the value of an unknown quantity in a given formula • addition and subtraction of algebraic fractions with linear or quadratic denominator, e.g. ∗ Functions and graphs 1 𝑥−2 + 2 𝑥−3 Include: • graphs of quadratic functions and their properties ∗ positive or negative coefficient of 𝑥 2 ∗ maximum and minimum points ∗ symmetry • sketching of the graphs of quadratic functions given in the form ∗ y = ± (𝑥 − 𝑝) 2 + q • graphs of functions of the form y = a𝑥 𝑛 where n = −2, −1, 0, 1, 2, 3, and simple sums of not more than three of these • graphs of exponential functions y = 𝑘𝑎 𝑥 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 Solutions of equations Include: • solving quadratic equations in one unknown by ∗ factorisation ∗ use of formula ∗ completing the square for y = 𝑥 2 + px + q ∗ graphical methods • solving fractional equations that can be reduced to quadratic equations, e.g. ∗ Applications of mathematics in practical situations 2 Geometry and Measurement Congruence and 6 𝑥+4 =𝑥+3 • formulate a quadratic equation in one unknown to solve Problems Include: • problems derived from practical situations such as ∗ 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. Include: 15 similarity Properties of circles Pythagoras’ theorem and trigonometry • 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 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 Include: • 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 angles in right-angled triangles • extending sine and cosine to obtuse angles • use of the formula Mensuration Coordinate geometry 1 2 𝑎𝑏𝑠𝑖𝑛𝐶 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. 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 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 coordinates 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 Probability 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 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 Content 1. Numbers and Algebra Numbers and the four 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 Percentage Algebraic 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 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 • using letters to represent numbers 17 representation and formulae • interpreting notations: * ab as a × b * 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) 2. Geometry and Measurement Angles, triangles and Include: Polygons • right, acute, obtuse and reflex angles, complementary and 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 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. Statistics and Probability 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 Algebraic manipulation Include: • addition and subtraction of linear algebraic expressions • simplification of linear algebraic expressions, e.g. Functions and graphs Include: • cartesian coordinates in two dimensions 18 Solutions of equations 2 Geometry and Measurement Angles, triangles and quadrilaterals Congruence, similarity and transformations Pythagoras’ theorem Mensuration 3 Statistics and Probability Data analysis Probability 4 Integrative Contexts Problems derived from practical real-life situations (The content should be distributed over 3 years, from Sec 2 to • 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) Include: • solving linear equations in one unknown (including fractional coefficients) • formulating a linear equation in one unknown to solve problems Include: • properties of triangles and special quadrilaterals • classifying special quadrilaterals on the basis of their properties • 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, rulers, set squares and protractors where appropriate Exclude properties of polygons. Include: • 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 Include: • use of Pythagoras‘ theorem • determining whether a triangle is right-angled given the lengths of three sides 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 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 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) Exclude probability of combined events: P(A and B), P(A or B). Include: • practical situations such as * profit and loss * simple interest and compound interest * household finance (earnings, expenditures, budgeting, etc.) * 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. Topics/SubTopics Content N(T) Secondary Three/Four 1. Numbers and Algebra Numbers and the four 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 × 10𝑛 , 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 Algebraic manipulation 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 x2 + 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 ∗ a2x2 − b2 y2 ∗ a2 ± 2ab + b2 ∗ ax2 + bx + c , where a ≠ 1 • addition and subtraction of algebraic fractions 20 Functions and graphs Solutions of equations 2 Geometry and Measurement Congruence, similarity and transformations Symmetry, tessellations and projections Pythagoras’ theorem and trigonometry Mensuration Include: • graphs of linear equations in two unknowns • graphs of quadratic functions and their properties ∗ positive or negative coefficient of x2 ∗ maximum and minimum points ∗ symmetry Exclude sketching of graphs of quadratic functions. 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 Include: • 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 Include: • line and rotational symmetry of plane figures • 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. Include: • use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles 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 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 4 Integrative Contexts Problems derived from practical real-life situations (The content should be distributed over 3 years, from Sec 2 to Sec 4) 2. Include: • percentiles, quartiles, range and interquartile range • interpretation and analysis of cumulative frequency diagrams Include: • practical situations such as * profit and loss * simple interest and compound interest * household finance (earnings, expenditures, budgeting, etc.) * payment/ subscription rates (hire-purchase, utilities bills, 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. Indonesia Kelas VII, Semester 1 Standar kompetensi 1. Bilangan Memahami sifatoperasi hitung bilangan dan penggunaannya dalam pemecahan masalah 2. Aljabar Memahami bentuk aljabar, persamaan dan pertidaksamaan linear satu variabel 3. Menggunakan bentuk aljabar persamaan dan pertidaksamaan linear satu variabel, dan perbandingan dalam pemecahan masalah Kompetensi Dasar 1. Melakukan operasi hitung bilangan bulat dan pecahan 1.2 Menggunakan sifat-sifat operasi hitung bilangan bulat dan pecahan dalam pemecahan masalah 2.1 2.2 2.3 2.4 Mengenali bentuk aljabar dan unsur-unsurnya Melakukan operasi pada bentuk aljabar Menyelesaikan persamaan linear satu variabel Menyelesaikan pertidaksamaan linear satu variabel 3.1 Membuat model matematika dari masalah yang berkaitan dengan persamaan dan pertidaksamaan linear satu variabel 3.2 Menyelesaikan model matematika dari masalah yang berkaitan dengan persamaan dan pertidaksamaan 22 linear satu variabel 3.3 Menggunakan konsep aljabar dalam pemecahan masalah aritmetika sosial yang sederhana 3.4 Menggunakan perbandingan untuk pemecahan masalah Kelas VII, Semester 2 Standar Kompetensi 4. 5. 6. Aljabar Menggunakan konsep himpunan dan diagram venn dalam pemecahan masalah Konsep Dasar 4.1 Memahami pengertian dan notasi himpunan, serta penyajiannya 4.2 Memahami konsep himpunan bagian 4.3 Melakukan operasi irisan, gabungan, kurang (difference), dan komplemen pada himpunan 4.4 Menyajikan himpunan dengan diagram venn 4.5 Menggunakan konsep himpunan dalam penyelesaian masalah Geometri Memahami hubungan garis dengan garis, 5.1 Menentukan hubungan antara dua garis, garis dengan sudut, sudut dengan sudut, serta besar dan jenis sudut serta menentukan ukurannya 5.2 Memahami sifat-sifat sudut yang terbentuk jika dua garis berpotongan atau dua garis sejajar berpotongan dengan garis lain 5.3 Melukis sudut 5.4 Membagi sudut Memahami konsep segiempat dan segitiga 6.1 Mengidentifikasisifat-sifat segitiga dan serta menentukan ukurannya berdasarkan sisi dan sudutnya 6.2 Mengidentifikasi sifat-sifat persegi panjang, persegi, trapesium, jajargenjang, belah ketupat, dan layang-layang 6.3 Menghitung keliling dan luas bangun segitiga dan segi empat serta menggunakannya dalam pemecahan masalah 6.4 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, 1.1 Melakukan operasi aljabar fungsi, dan persamaan garis lurus 1.2 Menguraikan bentuk aljabar kedalam faktorfaktornya 23 1.3 Memahami relasi dan fungsi 1.4 Menentukan nilai fungsi 1.5 Membuat sketsa grafik fungsi alajabar sederhana pada sistem koordinat cartesius 1.6 Menentukan gradien, persamaan dan gerafik garis lurus 2. Memahami sistem persamaan linear2.1 Menyelesaikan sistem persamaan linaer dua dua variabel dan menggunakannya variabel dalam pemecahan masalah 2.2 Membuat model matematika dari masalah yang berkaitan dengan sistem persamaan linear dua variabel 2.3 Menyelesaikan model matematika dari masalah yang berkaitan dengan persaman linear dua variabel dan penafsirannya Geometri dan Pengukuran 3. Menggunakan Teotema Pythagoras3.1 Menggunakan teorema pythagoras untuk dalam pemecahan masalah menentukan panjang sisi-sisi segitiga siku-siku 3.2 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 lingkaran4.1 Menentukan unsur dan bagian-bagian serta ukurannya lingkaran 4.2 Menghitung keliling dan luas lingkaran 4.3 Menggunakan hubungan sudut pusat, panjang busur, luas juring dalam pemecahan masalah 4.4 Menghitung panjang garis singgung persekutuan dua lingkaran 4.5 Melukis lingkaran dalam dan lingkaran luar suatu segitiga 5. Memahami sifat-sifat kubus, balok, 5.1 Mengidentifikasi sifat-sifat kubus, balok, prisma, limas, dan bagian-bagiannya, 24 serta menentukan ukurannya prisma, dan limas serta bagian-bagiannya 5.2 Membuat jaring-jaring kubus, balok, prisma, dan limas 5.3 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 1.1 Mengidentifikasi bangun-bangun datar yang datar dan penggunaannya dalam sebangun dan kongruen pemecahan masalah 1.2 Mengidentifikasi sifat-sifat dan segitiga sebangun dan kongruen 1.3 Menggunakan konsep kesebangunan segitiga dalam pemecahan masalah 2. Memahami sifat-sifat tabung, 2.1 Mengidentifikasi unsur-unsur tabung, kerucut kerucut, dan bola, serta menentukan dan bola ukurannya 2.2 Menghitung luas selimut dan volume tabung, kerucut dan bola 2.3 Memecahkan masalah yang berkaitan dengan tabung, kerucut dan bola Statika dan Peluang 3. Melakukan pengolahan dan penyajian data 3.1 Menentukan rata-rata, median, dan modusdata tunggal serta penafsirannya 3.2 Menyajikandata dalam bentuk tabel dan diagram batang, garis, dan lingkaran 4. Memahami peluang kejadian sederhana 4.1 Menentukan ruang sampel suatu percobaan 4.2 Menentukan peluang suatu kejadian sederhana Kelas IX, Semester 2 Kompetensi Standar Kompetensi Dasar Bilangan 25 5. Memahami sifat-sifat bilangan 5.1 Mengidentifikasi sifat-sifat bilangan berpangkat dan bentuk akar serta berpangkat dan bentuk akar penggunaannya dalam pemecahan 5.2 Melakukan operasi aljabar yang melibatkan masalah sederhana bilangan berpangkat bulat dan bentuk akar 5.3 Memecakan masalah sederhana yang berkaitan dengan bilangan berpangkat dan bentuk akar 6. Memahami barisan dan deret bilangan serta penggunaannya dalam pemecahan masalah 6.1 Menentukan pola barisan bilangan sederhana 6.2 Menentukan suku ke-n barisan aritmetika dan barisan geometri 6.3 Menentukan jyumlah n suku pertama deret aritmetika dan deret geometri 6.4 Memecahkan masalah yang berkaaitan dengan barisan dan deret 7. Memahami sifat-sifat logaritma serta 7.1 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