CSEC Additional Mathematics Syllabus 2026

This chapter covers fundamental polynomial operations, factorization techniques, and the application of the Remainder and Factor Theorems to analyze polynomial expressions.

Learn to convert quadratic functions to vertex form, determine their maximum or minimum values, and accurately sketch their graphs.

Explore the nature of roots, solve reducible quadratic equations, understand root relationships, and solve simultaneous linear and non-linear equations.

Master algebraic and graphical methods to determine solution sets for both quadratic inequalities and rational inequalities.

Perform addition, subtraction, multiplication, and rationalization of denominators involving surd expressions.

Apply the laws of indices to solve exponential equations involving a single unknown, including those reducible to linear or quadratic forms.

Understand the fundamental relationship between indices and logarithms, and simplify complex expressions using the core laws of logarithms.

Solve various logarithmic equations, use logarithms to solve exponential equations, and apply them to transform non-linear relationships into linear forms.

Define sequences, understand their notation, and learn to determine specific terms given the general formula for the nth term.

Define series as the sum of sequence terms, use summation notation, and identify the characteristics distinguishing arithmetic and geometric series.

Derive general terms and sums for arithmetic and geometric series, analyze their convergence or divergence, and apply these concepts to solve real-world problems.

Students will learn to determine the equation of a straight line in various forms, such as y=mx+c or ax+by+c=0.

Students will determine if lines are parallel or mutually perpendicular using their gradients.

Students will find the point where two straight lines intersect by solving their equations simultaneously.

Students will write the equation of a circle in standard and general forms, including (x+f)²+(y+g)²=r² and x²+y²+2fx+2gy+c=0.

Students will determine the centre and radius of a circle given its equation.

Students will derive equations for tangents and normals at specific points on a circle.

Students will find the point(s) where a straight line intersects a circle using algebraic methods.

Learn to interpret the derivative as the gradient of a tangent to a curve, including its formal definition as a limit and standard notation.

Master the fundamental rules for differentiating powers of x, trigonometric functions, sums, and multiples of functions.

Apply the chain rule for composite functions and the product and quotient rules for differentiating more complex algebraic and trigonometric expressions.

Determine the equations of tangent and normal lines to a curve at a given point using the first derivative.

Understand the derivative as a rate of change, calculate second derivatives, and apply these concepts to kinematics and related rates.

Students will distinguish between qualitative, quantitative, discrete, and continuous data types.

Students will calculate quartiles, percentiles, range, interquartile range, and semi-interquartile range from raw and grouped data.

Students will represent numerical data using stem-and-leaf diagrams and box-and-whisker plots, interpreting and comparing their advantages.

Students will calculate and interpret measures of central tendency and dispersion for ungrouped and grouped data.

Students will define and distinguish between experiment, outcome, sample space, and event, understanding the concept of probability.

Students will calculate the probability of an event using classical probability and relative frequency when outcomes are equally likely.