 CAPE Training, CXC Training
 0 (Registered)

RATIONALE
The Caribbean society is an integral part of an everchanging world. The impact of globalisation on most societies encourages this diverse Caribbean region to revisit the education and career opportunities of our current and future citizens. A common denominator is for Caribbean societies to create among its citizens a plethora of quality leadership with the acumen required to make meaningful projections and innovations for further development. Further, learning appropriate problemsolving techniques, inherent to the study of mathematics, is vital for such leaders. Mathematics promotes intellectual development, is utilitarian and applicable to all disciplines. Additionally, its aesthetics and epistemological approaches provide solutions fit for any purpose. Therefore, Mathematics is the essential tool to empower people with the knowledge, competencies and attitudes which are required for academia as well as quality leadership for sustainability in this dynamic world.
AIMS
This syllabus aims to:
 improve on the mathematical knowledge, skills and techniques with an emphasis on accuracy;
 empower students with the knowledge, competencies and attitudes which are precursors for academia as well as quality leadership for sustainability in the dynamic world;
 provide students with the proficiencies required to model practical situations and provide workable solutions in their respective fields of work and study;
 develop competencies in critical and creative thinking, problem solving, logical reasoning, modelling, team work, decision making, research techniques and information communication and technology for lifelong learning;
 nurture desirable character qualities that include selfconfidence, selfesteem, ethics and emotional security;
 make Mathematics interesting, recognisable and relevant to the students locally, regionally and globally.
Course Content

MODULE 1: FOUNDATIONS OF MATHEMATICS On completion of this Module, students should: 1.acquire competency in the application of algebraic techniques; 2.appreciate the role of exponential or logarithm functions in practical modelling situations; 3.understand the importance of relations functions and graphs in solving realworld problems; 4.appreciate the difference between a sequence and a series and their applications; 5.appreciate the need for accuracy in performing calculations; 6.understand the usefulness of different types of numbers.

2.Coordinate Geometry

3.Functions, Graphs, Equations and Inequalities
 combine components of linear and quadratic functions to sketch their graphs;
 determine the solutions of a pair of simultaneous equations where one is linear and the other is nonlinear;
 apply solution techniques of equations to solve real life problems
 determine the solution set for linear and quadratic inequalities
 solve equations and inequalities involving absolute linear functions;
 determine an invertible section of a function;
 evaluate the composition of functions for a given value of 𝑥.

4.Logarithms and Exponents
 apply the laws of indices to solve exponential equations in one unknown;
 identify the properties of exponential and logarithmic functions
 simplify logarithmic expressions using the laws of logarithm;
 identify the relationship between exponents and logarithms;
 convert between the exponential and logarithmic equations;
 apply the laws of logarithms to solve equations involving logarithmic expressions;
 solve problems involving exponents and logarithms.

5.Remainder and Factor Theorem

6.Sequences and Series

7.Matrices and Systems of Equations

8.Trigonometry

MODULE 2: STATISTICS On completion of this Module, students should: 1.understand the concept of randomness and its role in sampling and collection, description and analysis of data; 2.appreciate that the numerical and graphical representation of data is an important part of data analysis; 3.understand the concept of probability and its applications to realworld situations; 4.appreciate dataanalysis processes for applications to realworld situations.

2.Presentation of Data

3.Measures of Location and Spread
 select measures of location for appropriate data types
 determine measures of location for ungrouped data;
 determine estimates for measures of location for grouped data
 Select measures ofspread for appropriate data types.
 determine measures of spread for ungrouped data
 determine estimates for measures of spread for grouped data;

4.Permutations and Combinations

5.Probability,Probability Distributions and Regression
 distinguish among the terms experiment, outcome, event, sample space;
 apply basic rules of probability;
 explain the meaning of calculated probability values;
 investigate random variables;
 calculate probabilities from discrete probability distribution table;
 solve problems involving the binomial distribution;
 determine characteristics of a Normal distribution;
 determine percentages of a population within desired limits of standard deviation;
 investigate linear regression;
 evaluate correlation coefficient given summary statistics
 interpret the value of the correlation coefficient;
 draw an estimated regression line on a scatter plot
 determine the equation of a regression line using summary statistics;
 Use statistics to solve realworld problems;
 interpret results of statistical calculations.

MODULE 3: CALCULUS On completion of this Module, students should: 1.develop curiosity in the study of limits and continuity; 2.appreciate the importance of differentiation and integration in analysing functions and graphs; 3.enjoy using calculus as a tool in solving realworld problems.
 1.Limits and Continuity – describe the limiting behaviourof a function of 𝑥, as 𝑥approaches a given number;
 use limit notation
 evaluate limits using simple limit theorems;
 apply factorisation to expressions whose limits are indeterminate
 apply the concept of left and righthanded limits to continuity
 identify the points for which a function is discontinuous

2.Differentiation
 relate the derivative of a function with the gradient at a point on that function
 use notations for the first derivative of a function, y = f(x);
 differentiate polynomials;
 differentiate expressions involving sine and cosinefunctions
 apply the chain rule in the differentiation of composite functions
 differentiate exponential and logarithmic functions;
 differentiate products and quotients;
 determine the stationary point(s) of a given function
 obtain the second derivative of a function;
 investigate the nature of the stationary points;

3.Application of Differentiation
 apply the concept of the derivative to rate of change
 solve problems involving rates of change;
 use the sign of the derivative to investigate where a function is increasing or decreasing;
 solve problems involving stationary points
 apply the concept of stationary (critical) points to curve sketching;
 find the first partial derivative of a function of two variables;
 solve problems involving differentiation;

4.Integration
 defineintegration as the reverse process of differentiation
 compute indefinite integrals of polynomials;
 integrate expressions that involve trigonometric functions;
 integrate functions of the form1𝑝(𝑥), where 𝑝(𝑥)is a linear polynomial;
 integrate composite functions by substitution;
 compute definite integrals;
 apply integration to determine the area between a curve and a straight line;
 solve first order differential equations
 solve problems involving integration;