 CSEC 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 of the Caribbean societies is 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 precursors for this dynamic world.
AIMS
 make Mathematics relevant to the interests and experiences of students by helping them to recognise Mathematics in the local and global environment;
 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;
 help students develop positive attitudes, such as openmindedness, resourcefulness, persistence and a spirit of enquiry;
 prepare students for the use of Mathematics in further studies;
 help students foster a ‘spirit of collaboration’, with their peers and others within the wider community;
 help students apply the knowledge and skills acquired to solve problemsin everyday situations; and,
 integrate Information Communications, and Technology (ICT) tools and skills in the teaching and learning processes.
Course Content

SECTION 1 – NUMBER THEORY AND COMPUTATION GENERAL OBJECTIVES 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.
 Lesson 1 – Distinguish among sets of numbers
 Lesson 2 – Compute powers of real numbers of the form 𝓍 𝑎 , where 𝑎 ∈ ℚ
 Lesson 3 – Evaluate numerical expressions using any of the four basic operations on real numbers
 Lesson 4 – Convert among fractions, per cents and decimals
 Lesson 5 – List the set of factors and multiples of a given integer
 Lesson 6 – Compute the H.C.F. or L.C.M. of two or more positive integers
 Lesson 7 – State the value of a digit of a numeral in a given base
 Lesson 8 – Convert from one set of units to another
 Lesson 9 – Express a value to a given number of a) significant figures and b) decimal places
 Lesson 10 – Use properties of numbers and operations in computational tasks
 Lesson 11 – Write any rational number in scientific notation
 Lesson 12 – Calculate any fraction or percentage of a given quantity
 Lesson 13 – Express one quantity as a fraction or percentage of another
 Lesson 14 – Compare quantities
 Lesson 15 – Order a set of real numbers
 Lesson 16 – Compute terms of a sequence given a rule
 Lesson 17 – Derive an appropriate rule given the terms of a sequence
 Lesson 18 – Divide a quantity in a given ratio
 Lesson 19 – Solve problems involving concepts in number theory and 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 realworld problems.
 Lesson 1 – Calculate a) discount, b) sales tax, c) profit and d) loss
 Lesson 2 – Calculate a) percentage profit and b) percentage loss
 Lesson 3 – Express a profit, loss, discount, markup and purchase tax, as a percentage of some value
 Lesson 4 – Solve problems involving marked price, selling price, cost price, profit, loss or discount
 Lesson 5 – Solve problems involving payments by instalments as in the case of hire purchase and mortgages
 Lesson 6 – Solve problems involving simple interest
 Lesson 7 – Solve problems involving compound interest
 Lesson 8 – Solve problems involving appreciation and depreciation
 Lesson 9 – Solve problems involving measures and money
 Lesson 10 – 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 realworld problems.
 Lesson 1 – Explain concepts relating to sets
 Lesson 2 – Represent a set in various forms
 Lesson 3 – List subsets of a given set
 Lesson 4 – Determine elements in intersections, unions and complements of sets
 Lesson 5 – Describe relationships among sets using set notation and symbols
 Lesson 6 – Draw Venn diagrams to represent relationships among sets
 Lesson 7 – Use Venn diagrams to represent the relationships among sets
 Lesson 8 – 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 realworld problems.
 Lesson 1 – Convert units of length, mass, area, volume, capacity
 Lesson 2 – Use the appropriate SI unit of measure for area, volume, capacity, mass, temperature and time (24hour clock) and other derived quantities
 Lesson 3 – Determine the perimeter of a plane shape
 Lesson 4 – Calculate the length of an arc of a circle
 Lesson 5 – Estimate the area of plane shapes
 Lesson 6 – Calculate the area of polygons and circles
 Lesson 7 – Calculate the area of a sector of a circle
 Lesson 8 – Calculate the area of a triangle given two sides and the angle they form
 Lesson 9 – Calculate the area of a segment of a circle
 Lesson 10 – Calculate the surface area of solids
 Lesson 11 – Calculate the volume of solids
 Lesson 12 – Solve problems involving the relations among time, distance and speed
 Lesson 13 – Estimate the margin of error for a given measurement
 Lesson 14 – Use scales and scale drawings to determine distances and areas
 Lesson 15 – Solve problems involving measurement

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 realworld problems; and, 4. understand the four levels/scales of measurement that inform the collection of data.
 Lesson 1 – Differentiate between sample and population attributes
 Lesson 2 – Construct a frequency table for a given set of data
 Lesson 3 – Determine class features for a given set of data
 Lesson 4 – Construct statistical diagrams
 Lesson 5 – Determine measures of central tendency for raw, ungrouped and grouped data
 Lesson 6 – Determine when it is most appropriate to use the mean, median and mode as the average for a set of data
 Lesson 7 – Determine the measures of dispersion (spread) for raw, ungrouped and grouped data
 Lesson 8 – Use standard deviation to compare sets of data
 Lesson 9 – Draw cumulative frequency curve (Ogive)
 Lesson 10 – Analyse statistical diagrams
 Lesson 11 – Determine the proportion or percentage of the sample above or below a given value from raw data, frequency table or cumulative frequency curve
 Lesson 12 – Identify the sample space for simple experiment
 Lesson 13 – Determine experimental and theoretical probabilities of simple events
 Lesson 14 – Determine experimental and theoretical probabilities of simple events

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.
 Lesson 1 – Use symbols to represent numbers, operations, variables and relations
 Lesson 2 – Translate between algebraic symbols and worded expressions
 Lesson 3 – Evaluate arithmetic operations involving directed numbers
 Lesson 4 – Simplify algebraic expressions using the four basic operations
 Lesson 5 – Substitute numbers for variables in algebraic expressions
 Lesson 6 – Evaluate expressions involving binary operations (other than the four basic operations)
 Lesson 7 – Apply the distributive law to factorise or expand algebraic expressions
 Lesson 8 – Simplify algebraic fractions
 Lesson 9 – Use the laws of indices to manipulate expressions with integral indices
 Lesson 10 – Solve linear equations in one unknown
 Lesson 11 – Solve simultaneous linear equations, in two unknowns, algebraically
 Lesson 12 – Solve a simple linear inequality in one unknown
 Lesson 13 – Change the subject of formulae
 Lesson 14 – Factorise algebraic expressions
 Lesson 15 – Rewrite a quadratic expression in the form 𝑎(𝑥 + ℎ)2 +k
 Lesson 16 – Solve quadratic equations algebraically
 Lesson 17 – Solve word problems
 Lesson 18 – Solve a pair of equations in two variables when one equation is quadratic or nonlinear and the other linear
 Lesson 19 – Prove two algebraic expressions to be identical
 Lesson 20 – Represent direct and inverse variation symbolically
 Lesson 21 – 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, tabular or pictorial form; and, 3. appreciate the usefulness of concepts in relations, functions and graphs to solve realworld problems.
 Lesson 1 – Explain basic concepts associated with relations
 Lesson 2 – Represent a relation in various ways
 Lesson 3 – State the characteristics that define a function
 Lesson 4 – Use functional notation
 Lesson 5 – Distinguish between a relation and a function
 Lesson 6 – Draw graphs of linear functions
 Lesson 7 – Determine the intercepts of the graph of linear functions
 Lesson 8 – Determine the gradient of a straight line
 Lesson 9 – Determine the equation of a straight line
 Lesson 10 – Solve problems involving the gradient of parallel and perpendicular lines
 Lesson 11 – Determine from coordinates on a line segment a) the length and b) the coordinates of the midpoint
 Lesson 12 – Solve a pair of simultaneous linear equations in two unknowns graphically
 Lesson 13 – Represent the solution of linear inequalities in one variable using a) set notation, b) the number line and c) graph
 Lesson 14 – Draw a graph to represent a linear inequality in two variables
 Lesson 15 – Use linear programming techniques to graphically solve problems involving two variables
 Lesson 16 – Derive the composition of functions
 Lesson 17 – State the relationship between a function and its inverse
 Lesson 18 – Derive the inverse of a function
 Lesson 19 – Evaluate a function 𝑓(𝑥) at a given value of x
 Lesson 20 – Draw and use the graph of a quadratic function to identify its features b) an element of the domain that has given image, b) the image of a give element in the domain, c) the maximum or minimum value of the function and d) the equation of the axis of symmetry
 Lesson 21 – Interpret the graph of a quadratic function to determine a) the interval of the domain for which 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
 Lesson 22 – Determine the equation of the axis of symmetry and the maximum or minimum value of a quadratic function expressed in the form 𝑎(𝑥 + ℎ)2 +k
 Lesson 23 – Sketch the graph of a quadratic function expressed in the form 𝑦 = 𝑎(𝑥 + ℎ)2 + 𝑘 and determine the number of roots
 Lesson 24 – Draw graphs of nonlinear functions
 Lesson 25 – interpret graphs of functions
 Lesson 26 – Solve problems involving graphs of linear and nonlinear 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 realworld problems; and, 5. appreciate the power of trigonometrical methods in solving authentic problems.
 Lesson 1 – Explain concepts relating to geometry
 Lesson 2 – Draw and measure angles and line segments accurately using appropriate instruments
 Lesson 3 – Construct lines, angles, and polygons using appropriate instruments
 Lesson 4 – Identify the type(s) of symmetry possessed by a given plane figure
 Lesson 5 – 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
 Lesson 6 – Identify the type(s) of symmetry possessed by a given plane figure
 Lesson 7 – Represent translations in a plane using vector
 Lesson 8 – Determine and represent the location of a) the image of an object under a transformation; and b) an object given the image under a transformation
 Lesson 9 – State the relationship between an object and its image in the plane under geometric transformations
 Lesson 10 – Describe a transformation given an object and its image
 Lesson 11 – Locate the image of an object under a combination of transformations
 Lesson 12 – Use Pythagoras’ theorem to solve problems
 Lesson 13 – Define the trigonometric ratios of acute angles in a right triangle
 Lesson 14 – Relate objects in the physical world to geometric objects
 Lesson 15 – Apply the trigonometric ratios to solve problems
 Lesson 16 – Use the sine and cosine rules to solve problems involving triangles
 Lesson 17 – 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 realworld 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.
 Lesson 1 – Explain concepts associated with vectors
 Lesson 2 – Simplify expressions involving vectors
 Lesson 3 – Write the position vector of a point 𝑃(𝑎, 𝑏) as 𝑂𝑃⃗= (𝑎/𝑏) where 𝑂 is the origin (0,0)
 Lesson 4 – Determine the magnitude of a vector
 Lesson 5 – Determine the direction of a vector
 Lesson 6 – Use vectors to solve problems in geometry
 Lesson 7 – Explain basic concepts associated with matrices
 Lesson 8 – Solve problems involving matrix operations
 Lesson 9 – Evaluate the determinant of a ‘2 x 2’ matrix
 Lesson 10 – Define the multiplicative inverse of a nonsingular square matrix
 Lesson 11 – Obtain the inverse of a nonsingular ‘2 x 2’ matrix
 Lesson 12 – Determine a ‘2 x 2’ matrix associated with a specified transformation
 Lesson 13 – Use matrices to solve simple problems in Arithmetic, Algebra and Geometry