Seychelles S5 School Syllabus - Mathematics (IGCSE)

This syllabus is based on the Cambridge IGCSE Mathematics (0580) syllabus, adapted for use in Seychelles. S5 students typically follow either the Core or Extended curriculum. The Core content is for students targeting grades G-C, while the Extended content is for students targeting grades D-A*. The Extended curriculum includes all the Core content. Students are allowed to use scientific calculators in all papers.

Number

• Natural Numbers, Integers, Prime Numbers, etc.: Students work with various types of numbers, including natural numbers, integers, prime numbers, square and cube numbers, common factors and multiples, rational and irrational numbers, and real numbers. They also learn about reciprocals and express numbers as products of prime factors. Finding the lowest common multiple (LCM) and highest common factor (HCF) is also covered.
• Sets and Venn Diagrams: Students learn the notation and language of sets and use Venn diagrams to represent relationships between sets. The Extended curriculum covers more advanced set theory concepts.
• Powers and Roots: Calculations involving squares, square roots, cubes, cube roots, and other powers and roots of numbers are included.
• Directed Numbers: Students use directed numbers in practical situations like temperature changes and flood levels.
• Fractions, Decimals, and Percentages: The syllabus covers the language and notation of fractions, decimals, and percentages, including conversions between these forms. The Extended curriculum includes converting recurring decimals to fractions.
• Ordering Quantities and Magnitude: Students order quantities by magnitude and use symbols like =, <, >, ≤, ≥.
• Indices: Understanding and using indices (including fractional, negative, and zero indices) and the rules of indices are part of the syllabus.
• Standard Form: Students use standard form (A x 10ⁿ) and perform calculations with numbers in standard form.
• Four Rules of Calculation: The four rules (addition, subtraction, multiplication, and division) are applied to calculations with whole numbers, decimals, and fractions, including mixed numbers and improper fractions. Correct order of operations and use of brackets are emphasized.
• Estimation, Approximation, and Rounding: Making estimates of numbers, quantities, and lengths, giving approximations to specified numbers of significant figures and decimal places, and rounding off answers are covered.
• Upper and Lower Bounds: Students determine appropriate upper and lower bounds for data given to a specified accuracy. The Extended curriculum includes finding bounds for solutions to problems.
• Ratio and Proportion: Understanding and applying ratio and proportion, including direct and inverse proportion, are included. Calculating average speed and using ratio and scales in practical situations are also covered. The Extended curriculum includes increasing and decreasing quantities by a given ratio.
• Percentages: Calculating percentages of quantities, expressing one quantity as a percentage of another, and calculating percentage increase or decrease are included. The Extended curriculum includes reverse percentages.
• Calculator Use and Accuracy Checks: Efficient calculator use and applying appropriate checks of accuracy are emphasized.
• Time Calculations: Calculations involving 24-hour and 12-hour clocks, reading clocks, dials, and timetables are covered.
• Money and Currency Conversion: Calculations using money and converting between currencies are included.
• Personal and Household Finance: Solving problems involving earnings, simple interest, and compound interest are covered. Extracting data from tables and charts is also included. The Extended curriculum includes exponential growth and decay in relation to population and finance.

Algebra and Graphs

• Algebraic Representation and Substitution: Using letters to express generalized numbers and expressing basic arithmetic processes algebraically are covered. Substituting numbers for words and letters in formulae and rearranging formulae are also included. The Extended curriculum includes constructing and rearranging more complex formulae and equations.
• Manipulating Directed Numbers and Brackets: Manipulating directed numbers, using brackets, and extracting common factors are included. Expanding products of algebraic expressions is also covered, with the Extended curriculum including products of more than two brackets.
• Algebraic Fractions: The Extended curriculum covers manipulating and simplifying algebraic fractions.
• Indices: Using and interpreting positive, negative, and zero indices and the rules of indices are covered. The Extended curriculum includes fractional indices.
• Linear Equations and Inequalities: Deriving and solving linear equations in one unknown and simultaneous linear equations in two unknowns are included. The Extended curriculum includes solving simultaneous equations involving one linear and one quadratic equation, and solving linear inequalities.
• Quadratic Equations: The Extended curriculum covers deriving and solving quadratic equations by factorization, completing the square, and using the formula.
• Number Sequences: Continuing number sequences, recognizing patterns, finding the nth term of linear, quadratic, and cubic sequences are included. The Extended curriculum includes exponential sequences and combinations of different sequence types.
• Proportion: The Extended curriculum covers expressing direct and inverse proportion algebraically.
• Functions: The Extended curriculum covers function notation, inverse functions, and composite functions.
• Graphs: Interpreting and using graphs in practical situations, drawing graphs from data, and constructing tables of values are covered. Solving linear and quadratic equations graphically is also included. The Extended curriculum includes kinematics graphs, calculating distance traveled as area under a speed-time graph, and graphs of exponential growth and decay. Recognizing, sketching, and interpreting graphs of various functions (linear, quadratic, cubic, reciprocal, and exponential) are also part of the Extended curriculum.
• Gradients and Tangents: The Extended curriculum covers estimating gradients of curves by drawing tangents and understanding the concept of a derived function. Applying differentiation to gradients, turning points, and distinguishing between maxima and minima are also included.
• Linear Programming: The Extended curriculum covers representing inequalities graphically and using this to solve simple linear programming problems.

Coordinate Geometry

• Cartesian Coordinates: Demonstrating familiarity with Cartesian coordinates in two dimensions is covered.
• Gradient of a Straight Line: Finding the gradient of a straight line is included. The Extended curriculum includes calculating the gradient from the coordinates of two points.
• Length and Midpoint of a Line: The Extended curriculum covers calculating the length and midpoint of a line segment from the coordinates of its endpoints.
• Equation of a Straight Line: Interpreting and obtaining the equation of a straight line in the form y = mx + c is included.
• Parallel and Perpendicular Lines: Determining the equation of a straight line parallel to a given line is covered. The Extended curriculum includes finding the gradient of parallel and perpendicular lines and the equation of a perpendicular line.

Geometry

• Geometrical Terms: Using and interpreting geometrical terms related to points, lines, angles, parallel lines, bearings, perpendicular lines, similarity, and congruence are covered. Vocabulary of triangles, quadrilaterals, circles, polygons, and simple solid figures, including nets, is also included.
• Measuring and Drawing: Measuring and drawing lines and angles and constructing triangles are covered.
• Scale Drawings: Reading and making scale drawings are included.
• Similar Figures: Calculating lengths of similar figures is covered. The Extended curriculum includes relationships between areas and volumes of similar figures.
• Congruent Shapes: Recognizing congruent shapes is included. The Extended curriculum includes congruence criteria for triangles (SSS, ASA, SAS, RHS).
• Symmetry: Recognizing rotational and line symmetry in two dimensions is covered. The Extended curriculum includes symmetry properties of prisms, pyramids, cylinders, cones, and circles.
• Angle Properties: Calculating unknown angles using various geometrical properties (angles at a point, angles on a straight line, parallel lines, triangles, quadrilaterals, regular polygons, angles in a semicircle, and angle between tangent and radius) is included. The Extended curriculum includes angle properties of irregular polygons, angles at the center and circumference of circles, angles in the same segment, angles in opposite segments, cyclic quadrilaterals, and the alternate segment theorem.

Mensuration

• Units of Measurement: Using and converting between units of mass, length, area, volume, and capacity are covered.
• Perimeter and Area: Calculations involving the perimeter and area of rectangles, triangles, parallelograms, trapeziums, and compound shapes are included.
• Circles: Calculations involving the circumference and area of a circle, arc length, and sector area are covered.
• Surface Area and Volume: Calculations involving the surface area and volume of cuboids, prisms, cylinders, spheres, pyramids, and cones are included. Formulae for spheres, pyramids, and cones are provided in the questions.
• Compound Shapes: Calculations involving the areas and volumes of compound shapes are covered.

Trigonometry

• Bearings: Interpreting and using three-figure bearings is included.
• Pythagoras' Theorem and Trigonometric Ratios: Applying Pythagoras' theorem and the sine, cosine, and tangent ratios for acute angles in right-angled triangles is covered. The Extended curriculum includes solving problems in two dimensions involving angles of elevation and depression.
• Trigonometric Graphs and Equations: The Extended curriculum includes recognizing, sketching, and interpreting graphs of simple trigonometric functions and solving simple trigonometric equations.
• Sine and Cosine Rules: The Extended curriculum covers using the sine and cosine rules for any triangle and the formula for the area of a triangle (½absinC).
• 3D Trigonometry: The Extended curriculum includes solving trigonometrical problems in three dimensions.

Vectors and Transformations

• Vectors: Describing translations using vectors, adding and subtracting vectors, and multiplying a vector by a scalar are covered. The Extended curriculum includes calculating the magnitude of a vector, representing vectors by directed line segments, expressing vectors in terms of two coplanar vectors, and using position vectors.
• Transformations: Reflecting and rotating simple plane figures and constructing translations and enlargements are covered. Recognizing and describing reflections, rotations, translations, and enlargements are also included. The Extended curriculum includes positive, fractional, and negative scale factors for enlargements.

Probability

• Probability of a Single Event: Calculating the probability of a single event as a fraction, decimal, or percentage is covered.
• Probability Scale: Understanding and using the probability scale from 0 to 1 is included.
• Complementary Events: Understanding that the probability of an event occurring is 1 minus the probability of the event not occurring is covered.
• Relative Frequency: Understanding relative frequency as an estimate of probability and calculating expected frequency are included.
• Combined Events: Calculating the probability of simple combined events using possibility diagrams, tree diagrams, and Venn diagrams is covered. The Extended curriculum includes conditional probability using Venn diagrams, tree diagrams, and tables.

Statistics

• Data Collection and Tabulation: Collecting, classifying, and tabulating statistical data are covered.
• Interpreting Data: Reading, interpreting, and drawing simple inferences from tables and statistical diagrams, comparing sets of data, and appreciating restrictions on drawing conclusions are included.
• Statistical Diagrams: Constructing and interpreting bar charts, pie charts, pictograms, stem-and-leaf diagrams, simple frequency distributions, histograms with equal intervals, and scatter diagrams are covered. The Extended curriculum includes histograms with unequal intervals.
• Mean, Median, Mode, and Range: Calculating the mean, median, mode, and range for individual and discrete data and distinguishing between their purposes are included.
• Grouped Data: The Extended curriculum includes calculating an estimate of the mean for grouped and continuous data and identifying the modal class.
• Cumulative Frequency: The Extended curriculum covers constructing and using cumulative frequency diagrams, estimating and interpreting the median, percentiles, quartiles, and interquartile range, and constructing and interpreting box-and-whisker plots.
• Correlation: Understanding positive, negative, and zero correlation with reference to a scatter diagram is included.
• Lines of Best Fit: Drawing, interpreting, and using lines of best fit by eye are covered.