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The guiding principles of the Mathematics syllabus direct that Mathematics as taught in Caribbean schools should be relevant to the existing and anticipated needs of Caribbean society, related to the abilities and interests of Caribbean students and aligned with the philosophy of the educational system.
These principles focus attention on the use of Mathematics as a problem solving tool, as well as on some of the fundamental concepts which help to unify Mathematics as a body of knowledge. The syllabus explains general and unifying concepts that facilitate the study of Mathematics as a coherent subject rather than as a set of unrelated topics.
Every citizen needs basic computational skills (addition, subtraction, multiplication and division) and the ability to use these mentally to solve everyday problems. All citizens should recognise the importance of accuracy in computation as the foundation for deductions and decisions based on the results. In addition, the citizen should have, where possible, a choice of mathematical techniques to be applied in a variety of situations.
This syllabus aims to:
- help students appreciate the use of mathematics as a form of communication;
- help students acquire a range of mathematical techniques and skills and to foster and maintain the
awareness of the importance of accuracy;
- make Mathematics relevant to the interests and experiences of students by helping them to recognise Mathematics in their environment;
- cultivate the ability to apply mathematical knowledge to the solution of problems which are meaningful to students as citizens;
- help students cultivate the ability to think logically and critically;
- help students develop positive attitudes, such as open-mindedness, self-reliance, persistence and a
spirit of enquiry;
- prepare students for the use of Mathematics in further studies;
- help students develop an appreciation of the wide application of Mathematics and its influence in
the development and advancement of civilisation;
- help students become increasingly aware of the unifying structure of Mathematics.
SECTION 1: NUMBER THEORY AND COMPUTATION On completion of this Section, students should: 1.demonstrate computational skills; 2.be aware of the importance of accuracy in computation; 3.appreciate the need for numeracy in everyday life; 4.demonstrate the ability to make estimates fit for purpose; 5.understand and appreciate the decimal numeration system; 6.appreciate the development of different numeration systems; 7.demonstrate the ability to use rational approximations of real numbers; 8.demonstrate the ability to use number properties to solve problems; and, 9.develop the ability to use patterns, trends and investigative skills.
- distinguish among sets of numbers;
- compute powers of real numbers of the form 𝓍𝑎,where𝑎∈ℚ;
- evaluate numerical expressionsusing any of the four basic operations onreal numbers;
- convert among fractions, percentsand decimals
- list the set of factors andmultiples of a giveninteger
- compute the H.C.F. or L.C.M. of two or more positive integers;
- state the value of a digit ofa numeral ina givenbase;
- convert from one set of units to another;
- express a value to a given number of:(a)significant figures;and,(b)decimal places.
- use properties of numbers and operations in computational tasks;
- write any rational number in scientific notation;
- calculate any fraction or percentage of a given quantity
- express one quantity as a fraction or percentage of another;
- compare quantities;
- order a set of real numbers
- computetermsof a sequence given a rule
- derive an appropriate rule given the terms of a sequence Copy
- divide a quantity in a given ratio; and,
- solve problems involving concepts in number theoryand computation
SECTION 2: CONSUMER ARITHMETIC On completion of this Section, students should: 1.develop the ability to perform the calculations required in normal business transactions, and in computing their own budgets; 2.appreciate the need for both accuracy and speed in calculations; 3.appreciate the advantages and disadvantages of different ways of investing money; 4.appreciate that business arithmetic is indispensable in everyday life; and,5.demonstrate the ability to use concepts in consumer arithmetic to describe, model and solve real-world problems.
- calculate:(a)discount;(b)sales tax;(c)profit;and,(d)loss;
- calculate(a)percentage profit;and,(b)percentage loss;
- express a profit, loss, discount, markup and purchase tax, as a percentage of some value;
- solve problems involving marked price, selling price, cost price, profit, loss or discount;
- solve problems involving payments by instalmentsas in the case of hire purchase and mortgages;
- solve problems involving simple interest;
- solve problems involving compound interest;
- solve problems involving appreciation and depreciation;
- solve problems involving measures and money;and,
- solve problems involving:(a)rates and taxes; (b)utilities;(c)invoices and shopping bills; (d)salaries and wages;and,(e)insurance and investments.
SECTION 3: SETS On completion of this Section, students should: 1.demonstrate the ability to communicate using set language and concepts; 2.demonstrate the ability to reason logically; and, 3.appreciate the importance and utility of sets in analysing and solving real-world problems.
- explain concepts relating to sets;
- represent a set in various forms;
- list subsets of a given set;
- determine elements in intersections, unions and complements of sets;
- describe relationships among sets using set notation and symbols;
- drawVenn diagrams to represent relationships among sets;
- use Venn diagrams to representtherelationships among sets;and,
- solve problems in Number Theory, Algebra and Geometry using concepts in Set Theory.
SECTION 4: MEASUREMENT On completion of this Section, students should: 1.understand that the attributes of geometrical objects can be quantified using measurement; 2.appreciate that all measurements are approximate and that the relative accuracy of a measurement is dependent on the measuring instrument and the measurement process; and,3.demonstrate the ability to use concepts in measurement to model and solve real-world problems.
- convert units of length,mass, area, volume, capacity;
- use the appropriate SI unit of measure for area, volume, capacity, mass, temperature and time (24-hour clock) and other derived quantities;
- determine the perimeter of a plane shape;
- calculate the length of an arc of a circle;
- estimate the area of plane shapes;
- calculate the area of polygonsandcircles;
- calculate the area of a sector of a circle;
- calculatethe area of a trianglegiven two sides and the angle they form;
- calculate the area of a segment of a circle;
- calculate the surface area ofsolids;
- calculate the volume of solids;
- solve problems involvingthe relations amongtime, distance and speed;
- estimate the margin of error for a given measurement;
- use scalesand scale drawings to determine distances and areas;and,
- solve problems involvingmeasurement.
SECTION 5: STATISTICS On completion of this Section, students should: 1.appreciate the advantages and disadvantages of the various ways of presenting and representing data; 2.appreciate the necessity for taking precautions in collecting, analysing and interpreting statistical data, and making inferences; 3.demonstrate the ability to use concepts in statistics and probability to describe, model and solve real-world problems; and, 4.understand the four levels/scales of measurement that inform the collection of data.
- differentiate between sample and population attributes;
- construct a frequency table for a given set of data;
- determine class features for a given set of data;
- construct statistical diagrams;
- determine measures of central tendency for raw, ungrouped andgrouped data;
- determine when it is most appropriate to use the mean, median and mode as the average for a set of data;
- determinethe measures of dispersion (spread) for raw, ungrouped and grouped data;
- use standard deviation to compare sets of data;
- draw cumulative frequency curve (Ogive);
- analyse statistical diagrams;
- determine the proportion or percentage of the sample above or below a given value from raw data, frequency table or cumulative frequency curve;
- identify the sample space for simple experiment;
- determine experimental and theoretical probabilities of simple events;and,
- make inference(s) from statistics.
SECTION 6: ALGEBRA On completion of this Section, students should: 1.appreciate the use of algebra as a language and a form of communication; 2.appreciate the role of symbols and algebraic techniques in solving problems in mathematics and related fields; and,3.demonstrate the ability to reason with abstract entities.
- use symbols to represent numbers, operations, variables and relations;
- translate between algebraic symbols and worded expressions;
- evaluatearithmetic operations involving directed numbers;
- simplify algebraic expressions usingthe four basic operations;
- substitute numbers for variablesin algebraic expressions;
- evaluate expressions involvingbinary operations (other than the four basic operations);
- applythe distributive law to factorise or expand algebraic expressions;
- simplify algebraic fractions;
- use the laws of indices to manipulate expressions withintegralindices;
- solve linear equations in one unknown;
- solve simultaneous linear equations,in two unknowns,algebraically;
- solve a simple linear inequality in one unknown;
- change the subject of formulae;
- factorise algebraic expressions;
- rewrite a quadratic expression
- solve quadratic equationsalgebraically
- solve word problems;
- solvea pair of equations in two variables when one equation is quadratic or non-linear and the other linear
- provetwo algebraic expressions to be identical;
- represent direct andinverse variation symbolically;and,
- solve problems involving direct variation and inverse variation.
SECTION 7: RELATIONS, FUNCTIONS AND GRAPHS On completion of this Section, students should: 1.appreciate the importance of relations in Mathematics; 2.appreciate that many mathematical relations may be represented in symbolic form, tabular or pictorial form; and, 3.appreciate the usefulness of concepts in relations, functions and graphs to solve real-world problems.
- explain basic concepts associated with relations;
- represent a relation in various ways;
- state the characteristics that define a function
- use functional notation;
- distinguish between a relation and a function
- draw graphs of linear functions
- determinethe intercepts of the graph of linear functions;
- determine the gradient of a straight line;
- determine the equation of a straight line;
- solve problems involving the gradient of parallel and perpendicular lines;
- determine from co-ordinates on a line segment: (a)the length;and,(b)the co-ordinates of themidpoint.
- solvea pair of simultaneous linear equations in two unknownsgraphically;
- represent the solution of linear inequalities in one variable using:(a)set notation;(b)the number line;and,(c)graph.
- draw a graph to represent a linear inequality in two variables Copy
- use linear programming techniques tographicallysolveproblems involving two variables
- derive the composition of functions;
- state the relationship between a function and its inverse;
- derive the inverse of a function
- evaluatea function 𝑓(𝑥)at a given value of 𝑥;
- draw and use the graph of a quadratic function to identify its features:(a)an element of the domain that hasa given image;(b)the image of a given element in the domain;(c)the maximum or minimum value of the function;and,(d)the equation of the axis of symmetry.
- interpret the graph of a quadratic function to determine: (a)the interval of the domain for which the elements of the range may be greater than or less than a given point;(b)an estimate of the value of the gradient at a given point;and,(c)intercepts of the function.
- determine the equation of theaxis of symmetryand themaximum or minimum value of a quadratic function expressed in the form𝑎(𝑥+ℎ)2+𝑘;
- sketch the graph of a quadratic function expressed in the form 𝑦=𝑎(𝑥+ℎ)2+𝑘and determine the number of roots;
- draw graphs of non-linear functions;
- interpret graphs of functions;and,
- solve problems involving graphs of linear and non-linear functions.
SECTION 8: GEOMETRY AND TRIGONOMETRY On completion of this Section, students should: 1.appreciate the notion of space as a set of points with subsets of that set (space) having properties related to other mathematical systems; 2.understand the properties and relationship among geometrical objects; 3.understand the properties of transformations; 4.demonstrate the ability to use geometrical concepts to model and solve real world problems; and, 5.appreciate the power of trigonometrical methods in solving authentic problems.
- explainconcepts relating to geometry
- draw and measure angles and line segments accurately using appropriate instruments
- construct lines, angles, and polygons using appropriate instruments;
- identifythe type(s) of symmetry possessed by a given plane figure;
- solve geometric problems using properties of:(a)lines, angles, and polygons; (b)congruent triangles;(c)similar figures;(d)faces, edges and vertices of solids;and,(e)classes of solids.
- solve geometric problems using properties of circles and circle theorems
- represent translations in aplane using vectors
- determine and represent the location of:(a)the image of an objectunder a transformation;and,(b)an object given the image under a transformation.
- statethe relationship between an object and its image in the plane undergeometric transformations;
- describea transformation given an object and its image
- locatethe image of an objectunder a combination of transformations;
- use Pythagoras’ theorem to solve problems;
- definethe trigonometric ratios of acute angles in a right triangle;
- relate objects in the physical world to geometric objects
- applythe trigonometric ratios to solve problems
- usethe sine and cosine rules to solveproblems involving triangles;and
- solve problems involving bearings.
SECTION 9: VECTORS AND MATRICES On completion of this Section, students should: 1.demonstrate the ability to use vector notation and concepts to model and solve real-world problems; 2.develop awareness of the existence of certain mathematical objects, such as matrices, that do not satisfy the same rules of operation as the real number system; and,3.appreciate the use of vectors and matrices in representing certain types of linear transformations in the plane.
- explain concepts associated with vectors
- simplify expressions involving vectors;
- write the position vector ofa point
- where 𝑂is the origin (0,0);
- determinethe magnitude of a vector;
- determine the direction of a vector;
- use vectors tosolve problems in geometry;
- explain basic concepts associated with matrices;
- solve problems involving matrix operations
- evaluatethe determinant of a ‘2 x 2’ matrix
- define the multiplicative inverse of anon-singular square matrix;
- obtain the inverse of a non-singular ‘2 x 2’ matrix;
- determinea‘2 x 2’ matrix associated with aspecified transformation;and,
- usematrices to solve simple problems inArithmetic, Algebra and Geometry.
- GUIDELINES FOR THE SCHOOL-BASED ASSESSMENT