Saint Vincent and the Grenadines Form 5 Subjects (CSEC) - Mathematics > Mathematics

This course covers the CSEC Mathematics syllabus as outlined by the Caribbean Examinations Council (CXC). It is designed to equip students with the mathematical skills and knowledge relevant to the needs of Caribbean society and to prepare them for further studies and careers in various fields.

Core Topics:

• Computation: This section focuses on developing fundamental computational skills and understanding place value, performing operations with real numbers, converting between fractions, percentages, and decimals, expressing values to significant figures or decimal places, using scientific notation, calculating fractions and percentages of quantities, comparing quantities using ratios, dividing quantities in given ratios, and solving problems involving fractions, decimals, percentages, ratios, rates, proportions, and arithmetic mean.
• Number Theory: This section covers sets of numbers (natural, whole, integers, rational, irrational, real), sequences, factors and multiples, square numbers, even and odd numbers, prime and composite numbers, ordering real numbers, generating terms of sequences, deriving rules for sequences, identifying subsets, listing factors and multiples, computing H.C.F. and L.C.M., understanding place value in different bases, and using number properties to solve problems.
• Consumer Arithmetic: This section focuses on practical applications of mathematics in everyday business transactions and personal finance. It includes calculating discount, sales tax, profit and loss, expressing these as percentages, solving problems involving marked price, cost price, percentage profit/loss/discount, hire purchase, mortgages, simple and compound interest, appreciation and depreciation, measures and money, rates and taxes, utilities, invoices, shopping bills, salaries and wages, insurance, and investments.
• Sets: This section introduces set theory, including concepts like set membership, cardinality, finite and infinite sets, universal set, empty set, complement, subsets, equal and equivalent sets, intersection, disjoint sets, and union. Students learn to represent sets in different forms, describe relationships among sets, list subsets, determine elements in intersections, unions, and complements, construct and interpret Venn diagrams, and solve problems using Venn diagrams and set theory concepts.
• Measurement: This section covers calculating perimeters and areas of various shapes (polygons, circles, and combinations), arc length, sector area, surface area and volume of solids (prism, cylinder, cone, sphere, cube, and cuboid), converting units of measurement, using SI units, solving problems involving time, distance, and speed, estimating margins of error, and using maps and scale drawings. Optional objectives include calculating the area of a triangle given two sides and the included angle and calculating the area of a segment of a circle.
• Statistics: This section focuses on data analysis and probability. It includes differentiating between types of data, constructing frequency tables, determining class features, constructing and interpreting statistical diagrams (pie charts, bar charts, line graphs, histograms, frequency polygons), determining measures of central tendency (mean, median, mode), determining measures of dispersion (range, interquartile range, semi-interquartile range), constructing cumulative frequency tables and curves (Ogives), determining proportions and percentages from data, identifying sample spaces, determining experimental and theoretical probabilities, and making inferences from statistics.
• Algebra: This section covers using symbols in algebra, translating between algebraic and verbal phrases, performing operations with directed numbers and algebraic expressions, substituting numbers for symbols, performing binary operations, applying the distributive law, simplifying algebraic fractions, using laws of indices, solving linear equations and inequalities, solving simultaneous linear equations, changing the subject of formulae, factorizing algebraic expressions, solving quadratic equations, and solving word problems. An optional objective includes solving pairs of equations where one is quadratic or non-linear and the other is linear.
• Relations, Functions, and Graphs: This section covers concepts related to relations and functions, representing relations in various ways, using functional notation, distinguishing between relations and functions, drawing and interpreting graphs of linear and quadratic functions, determining intercepts and gradients, solving systems of linear equations graphically, representing solutions of linear inequalities, and working with composite and inverse functions. Optional objectives include linear programming, sketching graphs of quadratic functions, and interpreting distance-time and speed-time graphs.
• Geometry and Trigonometry: This section covers geometric concepts, constructions, properties of lines, angles, polygons, circles, congruent and similar figures, and solids. It also includes transformations (translations, reflections, rotations, enlargements), using Pythagoras' theorem, trigonometric ratios, sine and cosine rules, bearings, and solving problems involving heights and distances in two and three dimensions.
• Vectors and Matrices: This section introduces vector and matrix operations, including addition, subtraction, scalar multiplication, magnitude, position vectors, and using vectors to solve geometric problems. It also covers matrix concepts, operations, determinants, inverses, and using matrices to represent transformations and solve problems in arithmetic, algebra, and geometry.