Course Content

CSEC Mathematcis SBA

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 𝓍 𝑎 , where 𝑎 ∈ ℚ ;
 Evaluate numerical expressions using any of the four basic operations on real numbers;
 Convert among fractions, per cents and decimals;
 List the set of factors and multiples of a given integer;
 Compute the H.C.F. or L.C.M. of two or more positive integers;
 State the value of a digit of a numeral in a given base;
 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;
 Compute terms of a sequence given a rule;
 Derive an appropriate rule given the terms of a sequence;
 Divide a quantity in a given ratio;
 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.
 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 instalments as 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;
 Solve problems involving: (a) rates and taxes; (b) utilities; (c) invoices and shopping bills; (d) salaries and wages; (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.
 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;
 Draw Venn diagrams to represent relationships among sets;
 Use Venn diagrams to represent the relationships among sets;
 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.
 Convert units of length, mass, area, volume, capacity;
 Use the appropriate SI unit of measure for area, volume, capacity, mass, temperature and time (24hour 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 polygons and circles;
 Calculate the area of a sector of a circle;
 Calculate the area of a triangle given two sides and the angle they form;
 Calculate the area of a segment of a circle;
 Calculate the surface area of solids;
 Calculate the volume of solids;
 Solve problems involving the relations among time, distance and speed;
 Estimate the margin of error for a given measurement;
 Use scales and scale drawings to determine distances and areas;
 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.
 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 and grouped data;
 Determine when it is most appropriate to use the mean, median and mode as the average for a set of data;
 Determine the 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;
 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;
 Evaluate arithmetic operations involving directed numbers;
 Simplify algebraic expressions using the four basic operations;
 Substitute numbers for variables in algebraic expressions;
 Evaluate expressions involving binary operations (other than the four basic operations);
 Apply the distributive law to factorise or expand algebraic expressions;
 Simplify algebraic fractions;
 Use the laws of indices to manipulate expressions with integral indices;
 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 equations algebraically;
 Solve word problems;
 Solve a pair of equations in two variables when one equation is quadratic or nonlinear and the other linear;
 Prove two algebraic expressions to be identical;
 Represent direct and inverse variation symbolically;
 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 realworld 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;
 Determine the 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 coordinates on a line segment: (a) the length; (b) the coordinates of the midpoint.
 Solve a pair of simultaneous linear equations in two unknowns graphically;
 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;
 Use linear programming techniques to graphically solve problems involving two variables;
 Derive the composition of functions;
 State the relationship between a function and its inverse;
 Derive the inverse of a function;
 Evaluate a function 𝑓(𝑥) at a given value of 𝑥;
 Draw and use the graph of a quadratic function to identify its features;
 Interpret the graph of a quadratic function;
 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;
 Sketch the graph of a quadratic function expressed in the form 𝑦 = 𝑎(𝑥 + ℎ)2 + 𝑘 and determine the number of roots;
 Draw graphs of nonlinear functions;
 Interpret graphs of functions;
 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 real world problems; and, 5. appreciate the power of trigonometrical methods in solving authentic problems.
 Explain concepts relating to geometry;
 Draw and measure angles and line segments accurately using appropriate instruments;
 Construct lines, angles, and polygons using appropriate instruments;
 Identify the 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 a plane using vectors;
 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.
 State the relationship between an object and its image in the plane under geometric transformations;
 Describe a transformation given an object and its image;
 Locate the image of an object under a combination of transformations;
 Use Pythagoras’ theorem to solve problems;
 Define the trigonometric ratios of acute angles in a right triangle;
 Relate objects in the physical world to geometric objects;
 Apply the trigonometric ratios to solve problems;
 Use the sine and cosine rules to solve problems involving triangles;
 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.
 Explain concepts associated with vectors;
 Simplify expressions involving vectors;
 Write the position vector of a point;
 Determine the magnitude of a vector;
 Determine the direction of a vector;
 Use vectors to solve problems in geometry;
 Explain basic concepts associated with matrices;
 Solve problems involving matrix operations;
 Evaluate the determinant of a ‘2 x 2’ matrix;
 Define the multiplicative inverse of a nonsingular square matrix;
 Obtain the inverse of a nonsingular ‘2 x 2’ matrix;
 Determine a ‘2 x 2’ matrix associated with a specified transformation;
 Use matrices to solve simple problems in Arithmetic, Algebra and Geometry.