Topik dan Subtopik Matematika Singapura (Secondary School)

Untuk dijadikan bahan perbandingan, di bawah ini adalah topik dan subtopik mata pelajaran Matematika di negara Singapura untuk secondary school (sama dengan kelas VII s.d. X di Indonesia).

Topik dan subtopik ini diambil dari 4 seri buku Mathematics Matters (Express) karangan Sin Kwai Meng dan Chip Wai Lung. Buku ini telah mendapat pengesahan dari SEAB (Singapore Education and Assessment Board). Selain itu, buku ini dipersiapkan pula sebagai materi acuan untuk persiapan ujian O’Level yang diselenggarakan oleh Cambridge University UK.

MATHEMATICS MATTERS 1
(untuk kelas VII)

CHAPTER 1: INTEGERS
1.1 Prime Numbers and Prime Factorisation
1.2 Highest Common Factor (HCF)
1.3 Lowest Common Multiple (LCM)
1.4 Negative Numbers
1.5 Integers
1.6 Squares and Square Roots
1.7 Cubes and Cube Roots

CHAPTER 2: REAL NUMBERS
2.1 Basic Law of Addition and Multiplication
2.2 Rational Numbers
2.3 Real Numbers
2.4 Approximation (Rounding Off)
2.5 Significant Figures
2.6 Estimation

CHAPTER 3: ALGEBRAIC EXPRESSIONS AND NUMBER PATTERNS
3.1 Algebraic Notation
3.2 Evaluating Algebraic Expressions and Formulae
3.3 Forming Algebraic Expressions and Formulae
3.4 Number Patterns

CHAPTER 4: LINEAR ALGEBRAIC EXPRESSIONS
4.1 Algebraic Terms
4.2 Adding and Subtracting Algebraic Expressions
4.3 Factorisation

CHAPTER 5: EQUATIONS AND INEQUALITIES
5.1 Equations
5.2 Equivalent Equations
5.3 Solving Equations
5.4 Equations with Fractional Coefficients
5.5 Fractional Equations
5.6 Simple Inequalities
5.7 Equivalent Inequalities
5.8 Evaluation of Formulae
5.9 Algebraic Word Problem

CHAPTER 6: RATE, RATIO AND PERCENTAGE
6.1 Rate and Speed
6.2 Ratio and Proportion
6.3 Percentage

CHAPTER 7: INTRODUCTION TO GEOMETRY
7.1 Line Segment, Line and Angle
7.2 Perpendicular Lines
7.3 Parallel Lines
7.4 Angle Properties and Straight Lines
7.5 Angle Properties Related to Parallel Lines

CHAPTER 8: POLYGONS
8.1 Triangles
8.2 Quadrilateral
8.3 Angle Properties of a Polygon

CHAPTER 9: AREA AND PERIMETER
9.1 Perimeter and Area of Polygon
9.2 Circumference and Area of a Circle
9.3 More Problems on Area and Perimeter

CHAPTER 10: VOLUME AND SURFACE AREA
10.1 Prism and Cylinder
10.2 Nets of Solids
10.3 Volume and Surface Area of Prism and Cylinder
10.4 More Word Problems on Volume and Surface Area

CHAPTER 11: GRAPHS OF LINEAR FUNCTIONS
11.1 The Coordinate Plane
11.2 Linear Functions and Graphs
11.3 Gradient of a Linear Graphs
11.4 Applications of Linear Graphs

CHAPTER 12: STATISTICS
12.1 Collection and Presentation of Data
12.2 Line Graph
12.3 Bar Graph
12.4 Pie Chart
12.5 Pictogram
12.6 Frequency Table
12.7 Histogram

MATHEMATICS MATTERS 2
(untuk kelas VIII)

CHAPTER 1: ALGEBRAIC MANIPULATION
1.1 Special Algebraic Rules
1.2 Expanding Products
1.3 Expanding Products Using the Special Rules
1.4 Factorisation Using the Special Rules
1.5 Factorisation Using the Cross-Multiplication Method
1.6 Multiplying and Dividing Simple Algebraic Fractions
1.7 Adding and Subtracting Algebraic Fractions

CHAPTER 2: QUADRATIC EQUATIONS
2.1 Solving Quadratic Equations
2.2 Solving Word Problems Involving Quadratic Equations

CHAPTER 3: ALGEBRAIC FORMULAE
3.1 Manipulating Variables in Equations
3.2 Changing the Subject of a Formla
3.3 More Algebraic Manipulatin

CHAPTER 4: SIMULTANEOUS LINEAR EQUATIONS
4.1 Elimination Method
4.2 Substitution Method
4.3 Graphical Method
4.4 Word Problems about Simultaneous Equations

CHAPTER 5: GRAPHS OF QUADRATICS FUNCTIONS
5.1 Graphs of Quadratic equations

CHAPTER 6: DIRECT AND INVERSE PROPORTIONS
6.1 Direct Proportion
6.2 Inverse Proportion
6.3 More Problems on Proportion

CHAPTER 7: SETS
7.1 The Idea of a Set
7.2 Intersection and Union of Sets
7.3 Universal Sets

CHAPTER 8: CONGRUENCY AND SIMILARITY
8.1 Congruent Figures
8.2 Similar Figures
8.3 Map Scales
8.4 Scale Drawings

CHAPTER 9: PYTHAGORAS’ THEOREM
9.1 Pythagoras’ Theorem

CHAPTER 10: MENSURATION
10.1 Pyramids and Cones
10.2 Spheres

CHAPTER 11: STATISTICS
11.1 The Dot Diagram and Stem-and-Leaf Diagram
11.2 Mean, Median and Mode
11.3 Types of Averages
11.4 Mean for Grouped Data

CHAPTER 12: PROBABILITY
12.1 Definition of Probability
12.2 Probability as Relative Frequency
12.3 Probability of Events with Equally Likely Outcomes

MATHEMATICS MATTERS 3
(untuk kelas IX)

CHAPTER 1: INDICES
1.1 Index Notation
1.2 Addition of Indices
1.3 subtraction of Indices
1.4 Multiplication of Indices
1.5 Products and Fractions of Index Forms
1.6 Zero and Negative Indices
1.7 Fractional Indices
1.8 Standard Form
1.9 Use of Prefixes for Very Large and Very Small Numbers
1.10 Rounding Off and Truncation Errors

CHAPTER 2: COORDINATE GEOMETRY
2.1 Length of a Line Segment
2.2 Gradient of a Straight Line
2.3Equation of a Straight Line

CHAPTER 3: TRIGONOMETRY
3.1 Trigonometric Ratios
3.2 Right-Angled Triangles
3.3 Applications of Trigonometrical Ratios
3.4 More Examples Involving Height and Distance

CHAPTER 4: QUADRATIC EQUATIONS
4.1 Perfect Square
4.2 Completing the Square
4.3 Solving Quadratic Equatins by Using a Formula
4.4 Solving Quadratic Equation by Using a Graphical Method
4.5 Solving Fractional Equations
4.6 Problems Leading to Quadratic Equations

CHAPTER 5: INEQUALITIES
5.1 Inequalities
5.2 Representing Inequalities on the Number LIne
5.3 Properties of Inequalities
5.4 Solving Inequalities
5.5 Word PRoblems Involving Inequalities

CHAPTER 6: MATHEMATICS IN PRACTICAL SITUATIONS
6.1 Simple Interest
6.2 Compound Interest
6.3 Hire Purchase
6.4 Profit and Loss
6.5 Taxation
6.6 Money Exchange
6.7 Utilities Bill

CHAPTER 7: GRAPHS IN PRACTICAL SITUATIONS
7.1 Graphs in Practical Situations
7.2 Rate of Change
7.3 Distance-Time Graph
7.4 Speed-Time Graph
7.5 Area Under Speed-Time Graph

CHAPTER 8: CONGRUENT AND SIMILAR TRIANGLES
8.1 Congruent Triangles
8.2 Similar Triangles
8.3 Area of Similar Figures
8.4 Volumes of Similar Solids

CHAPTER 9: THE CIRCLE AND ITS ARC, SECTOR AND SEGMENT
9.1 The Circle: A Review of Area and Circumference
9.2 Arc Length
9.3 Area of Sector
9.4 Area of Segment
9.5 The Radian
9.6 Arc Length and Area of Sector

CHAPTER 10: SYMMETRY PROPERTIES OF A CIRCLE
10.1 Symmetry Properties of a Circle

CHAPTER 11: ANGLE PROPERTIES OF A CIRCLE
11.1 Angle Properties of a Circle
11.2 Angle in a Semicircle and Angles in Opposite Segments

CHAPTER 12: STATISTICS
12.1 Cumulative Frequency
12.2 Percentiles, Quartiles and the Interquartile Range
12.3 Estimating the Quartiles for a Set of Data
12.4 The Box-and-Whisker Plot
12.5 Measures of Spread
12.6 Using the Mean and Standard Deviation to Compare Two Sets of Data

MATHEMATICS MATTERS 4
(untuk kelas X)

CHAPTER 1: TRIGONOMETRY: THE SIN AND COSINE RULES
1.1 Trigonometrical Ratios of an Obtuse Angle
1.2 The Sine Rule
1.3 The Cosine Rule
1.4 Area of Triangle

CHAPTER 2: TRIGONOMETRY II
2.1 Bearings
2.2 Problems on Bearings
2.3 Three Dimensional Problems

CHAPTER 3: VECTORS
3.1 Vectors as Directed Line Segments
3.2 Position Vectors and Column Vectors
3.3 More Vectors Problems

CHAPTER 4: GRAPHS
4.1 Sketching Quadratic Functions of Special Forms
4.2 Gradient of a Graph
4.3 Solving Equations Using Graphs

CHAPTER 5: MATRICES
5.1 Matrix Addition and Subtraction
5.2 Scalar Multiplication of Matrices
5.3 Multiplication of Matrices
5.4 More Problems Involving Matrix Products

CHAPTER 6: PROBABILITIES OF COMBINED EVENTS
6.1 A Review of Probability Concepts
6.2 More About Probability
6.3 Probability of Combined Events

Bagian akhir dari buku Mathematics Matters 4 ini berisi review tentang materi-materi berikut:
Arithmetic and Algebra
Geometry and Mensuration
Trigonometry and Bearing
Graphs
Probability and Statistics
Sets, Matrices and Vectors

Ygn. 101009

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