Tag: G3

Outline of how students progress in each main topic from Secondary 1 to Secondary 4. The topics are grouped by the three main strands: Number and Algebra, Geometry and Measurement, and Statistics and Probability.

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Number and Algebra

Secondary 1

• Numbers and Operations
  • Prime factorization, HCF, LCM, and roots
  • Negative numbers, integers, rational and real numbers
  • Approximation and estimation
• Ratio and Proportion
  • Basic concepts and problems
• Percentage
  • Increasing/decreasing values, reverse percentages
• Rate and Speed
  • Average and constant speeds
• Algebraic Expressions and Formulae
  • Simplifying, evaluating, and translating expressions
• Functions and Graphs
  • Linear functions and gradients
• Equations and Inequalities
  • Solving and formulating linear equations

Secondary 2

• Ratio and Proportion
  • Direct and inverse proportion, map scales
• Algebraic Expressions and Formulae
  • Expansion, factorization, and quadratic expressions
• Functions and Graphs
  • Quadratic functions and their graphs
• Equations and Inequalities
  • Solving inequalities, simultaneous equations, and quadratic equations

Secondary 3 & 4

• Numbers and Operations
  • Standard form, laws of indices
• Functions and Graphs
  • Sketching quadratic and power functions
• Equations and Inequalities
  • Quadratic equations, completing the square, and fractional equations
• Set Language and Notation
  • Set operations and Venn diagrams
• Matrices
  • Operations and applications

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Geometry and Measurement

Secondary 1

• Angles, Triangles, and Polygons
  • Angle properties, symmetry in polygons
• Mensuration
  • Area of parallelograms and trapeziums, volume of prisms and cylinders

Secondary 2

• Congruence and Similarity
  • Congruent and similar figures, proportionality
• Pythagoras’ Theorem and Trigonometry
  • Use of Pythagoras’ theorem, trigonometric ratios
• Mensuration
  • Volume of pyramids, cones, and spheres

Secondary 3 & 4

• Congruence and Similarity
  • Scale drawings, ratios of areas and volumes
• Properties of Circles
  • Tangents, angle properties
• Pythagoras’ Theorem and Trigonometry
  • Extension to obtuse angles, sine and cosine rules
• Mensuration
  • Arc length, sector area, and radian measures
• Coordinate Geometry
  • Gradient, length, and equations of straight lines
• Vectors in Two Dimensions
  • Representation, magnitude, and operations

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Statistics and Probability

Secondary 1

• Data Handling and Analysis
  • Basics of tabulation and interpretation of graphs (e.g., bar graphs, line graphs)

Secondary 2

• Data Handling and Analysis
  • Advanced statistical diagrams (e.g., histograms, stem-and-leaf plots)
  • Measures of central tendency (mean, mode, median)
• Probability
  • Basic probability of single events

Secondary 3 & 4

• Data Handling and Analysis
  • Quartiles, percentiles, cumulative frequency diagrams
  • Measures of spread (range, standard deviation)
• Probability
  • Combined events, tree diagrams, and probability rules (addition and multiplication)

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Breakdown of the O-Level Additional Mathematics syllabus (Syllabus Code 4049) into its main sections:

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1. Algebra

1. Quadratic Functions:
   • Completing the square to find maximum/minimum values.
   • Conditions for a quadratic function to always be positive or negative.
   • Using quadratic functions for modeling.
2. Equations and Inequalities:
   • Solving quadratic equations and inequalities.
   • Analyzing conditions for intersections and tangents between lines and curves.
   • Representing solutions on a number line.
3. Surds:
   • Operations on surds, including rationalization.
   • Solving equations involving surds.
4. Polynomials and Partial Fractions:
   • Factor and remainder theorems for solving polynomial equations.
   • Partial fractions for specific types of denominators.
5. Binomial Expansion:
   • Expanding binomials using the binomial theorem for positive integer powers.
6. Exponential and Logarithmic Functions:
   • Properties and laws of exponents and logarithms.
   • Solving equations and using these functions for modeling.

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2. Geometry and Trigonometry

1. Trigonometric Functions, Identities, and Equations:
   • Trigonometric functions for angles of any magnitude (degrees or radians).
   • Graphs of trigonometric functions.
   • Trigonometric identities and their simplifications.
   • Solving trigonometric equations within specified intervals.
   • Using trigonometric models for real-world problems.
2. Coordinate Geometry in Two Dimensions:
   • Conditions for lines to be parallel or perpendicular.
   • Midpoints, areas of rectilinear figures, and equations of circles.
   • Transforming relationships to linear forms for graph interpretation.
3. Proofs in Plane Geometry:
   • Properties of parallel lines, triangles, quadrilaterals, and circles.
   • Congruent and similar triangles.
   • Tangent-chord and midpoint theorems.

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3. Calculus

1. Differentiation:
   • Derivatives as gradients and rates of change.
   • Rules for differentiating functions, including products, quotients, and compositions.
   • Applications to tangents, normals, and optimization problems.
   • Using second derivatives to identify maxima, minima, and inflection points.
2. Integration:
   • Integration as the reverse process of differentiation.
   • Definite integrals for areas under curves.
   • Applications to displacement, velocity, and acceleration problems in straight-line motion.

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4. Additional Assessment Notes

• The syllabus emphasizes reasoning, problem-solving, and the application of mathematical models.
• Use of calculators is allowed, and candidates are expected to provide accurate solutions with appropriate working.
• The syllabus prepares students for further studies in mathematics, particularly A-Level H2 Mathematics.

Here is a summary of the G3 Secondary 2 Mathematics syllabus, organized by its three main strands: Number and Algebra, Geometry and Measurement, and Statistics and Probability.

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Number and Algebra

1. Ratio and Proportion:
   • Map scales (distance and area).
   • Direct and inverse proportions.
2. Algebraic Expressions and Formulae:
   • Expansion of products of algebraic expressions.
   • Changing the subject of a formula.
   • Simplifying expressions using standard algebraic identities:
     • \((a+b)^2=a^2+2ab+b^2 \),
     • \((a−b)^2= a^2 – 2ab + b^2 \),
     • \(a^2−b^2=(a+b)(a−b)\).
   • Factorization of quadratic expressions.
   • Operations with algebraic fractions, including addition, subtraction, multiplication, and division.
3. Functions and Graphs:
   • Quadratic functions: Graphs, properties (e.g., maximum and minimum points, symmetry), and interpretations.
4. Equations and Inequalities:
   • Solving inequalities and representing solutions on the number line.
   • Solving simultaneous linear equations using substitution, elimination, and graphical methods.
   • Solving quadratic equations through factorization.

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Geometry and Measurement

1. Congruence and Similarity:
   • Properties of congruent and similar figures.
   • Solving problems involving similarity and proportional relationships in triangles and polygons.
2. Pythagoras’ Theorem and Trigonometry:
   • Applications of Pythagoras’ theorem.
   • Trigonometric ratios (sine, cosine, tangent) for solving problems involving right-angled triangles.
3. Mensuration:
   • Volume and surface area of pyramids, cones, and spheres.

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Statistics and Probability

1. Data Handling and Analysis:
   • Interpretation of dot diagrams, histograms, and stem-and-leaf diagrams.
   • Calculation and interpretation of mean, mode, and median.
   • Advantages, disadvantages, and misinterpretation of statistical representations.
2. Probability:
   • Concept of probability as a measure of chance.
   • Calculating probabilities for single events.

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Real-World Applications

The syllabus integrates concepts into real-world contexts, such as financial calculations, interpreting statistical data, and problem-solving involving geometry and algebra.

The G3 Secondary 1 Mathematics syllabus focuses on building a strong foundation in three main strands: Number and Algebra, Geometry and Measurement, and Statistics and Probability. Here is a summary of the key topics covered:

Number and Algebra

1. Numbers and Operations:
   • Prime factorization, HCF, LCM, and operations with integers, rational, and real numbers.
   • Concepts like rounding, estimation, and representing numbers on a number line.
2. Ratio, Proportion, and Percentages:
   • Simplification of ratios, percentage calculations, and solving real-world problems involving ratios and percentages.
3. Rate and Speed:
   • Understanding and calculating average and constant speed, and unit conversions.
4. Algebraic Expressions and Formulae:
   • Simplification, evaluation, and translation of real-world situations into algebraic expressions.
   • Pattern recognition and formulation of algebraic expressions for sequences.
5. Functions and Graphs:
   • Understanding Cartesian coordinates, linear functions, and graph plotting.
6. Equations and Inequalities:
   • Solving linear equations and basic fractional equations, and formulating equations for problem-solving.

Geometry and Measurement

1. Angles, Triangles, and Polygons:
   • Properties of angles, triangles, quadrilaterals, and polygons.
   • Understanding symmetry and constructing geometric figures.
2. Mensuration:
   • Calculations involving area, perimeter, volume, and surface area for composite shapes, prisms, and cylinders.

Statistics and Probability

1. Data Handling and Analysis:
   • Collecting, classifying, and interpreting data using bar graphs, line graphs, pie charts, and tables.
   • Understanding the advantages and limitations of different forms of statistical representation.

Real-World Applications

The syllabus emphasizes solving problems in real-world contexts, such as travel planning, financial calculations, and interpreting data, providing a practical understanding of mathematics.