← Northern Ireland Further Maths
Northern Ireland · CCEASyllabus
Further Maths syllabus, dot point by dot point
Every dot point in the Northern Ireland Further Mathssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.8, Anthropic's latest AI.
Unit 1: Pure Mathematics
Module overview →- How do you simplify, add, subtract and solve algebraic fractions, and prove results algebraically?Manipulate algebraic expressions and algebraic fractions: simplify, add, subtract, multiply and divide them, solve equations involving them, and construct simple algebraic proofs.12 min answer →
- How do you find equations of lines, the equation of a circle, and the tangent to a circle?Use coordinate geometry: find equations of straight lines including parallel and perpendicular lines, use the equation of a circle, and find the equation of a tangent to a circle.12 min answer →
- How do you differentiate polynomials and use the derivative to find gradients, tangents and turning points?Differentiate polynomials: find first and second derivatives, find gradients, tangents and normals, locate and classify stationary points, and solve optimisation problems.13 min answer →
- How do you work with composite and inverse functions, domain and range, and graph transformations?Use function notation: form composite functions, find inverse functions, state domain and range, and apply transformations to the graphs of functions.12 min answer →
- How do you integrate polynomials and use definite integration to find the area under a curve?Integrate polynomials: find indefinite integrals with a constant of integration, evaluate definite integrals, and use definite integration to find the area under a curve.12 min answer →
- How do you use the laws of logarithms to solve exponential equations?Use logarithms and exponentials: apply the laws of logarithms, convert between exponential and logarithmic form, and solve equations of the form a to the power x equals b.11 min answer →
- How do you multiply matrices and use them to describe and combine transformations of the plane?Use matrices: add, subtract and multiply matrices, use the identity matrix, and apply 2x2 matrices to describe and combine transformations of the plane.12 min answer →
- How do you use the factor theorem and the remainder theorem to factorise and solve cubic polynomials?Work with polynomials: apply the factor theorem and the remainder theorem, factorise cubics, and solve polynomial equations of degree three.12 min answer →
- How do you use the discriminant, completing the square and quadratic inequalities in Further Mathematics?Apply quadratic theory: solve quadratics by formula and completing the square, use the discriminant to determine the nature of the roots, and solve quadratic inequalities.12 min answer →
- How do you simplify surds, rationalise denominators and use the laws of indices including negative and fractional powers?Use surds and the laws of indices: simplify surds, rationalise denominators, and apply the index laws including zero, negative and fractional indices.11 min answer →
- How do you solve trigonometric equations and use the sine rule, cosine rule and trigonometric identities?Use trigonometry: apply the sine rule, cosine rule and area formula, use the identities for tan and the Pythagorean identity, and solve trigonometric equations over a given interval.12 min answer →
Unit 2: Mechanics
Module overview →- How do you find the acceleration and tension for connected particles joined by a string over a pulley?Analyse connected particles: model two particles joined by a light inextensible string, including over a smooth pulley, and find the common acceleration and the tension.12 min answer →
- How do you use Newton's laws to relate force, mass and acceleration, including weight and equilibrium?Apply Newton's laws of motion: use F equals ma to relate resultant force, mass and acceleration, work with weight, and analyse particles in equilibrium.12 min answer →
- How do you use the coefficient of friction and the limiting friction model on rough surfaces?Model friction on rough surfaces: use the relationship F is at most mu R, find limiting friction, and analyse motion and equilibrium on rough horizontal surfaces.12 min answer →
- How do you use the constant-acceleration equations and motion graphs to describe motion in a straight line?Model motion in a straight line with constant acceleration: use the suvat equations and interpret displacement-time and velocity-time graphs.12 min answer →
- How do you use calculus to relate displacement, velocity and acceleration when acceleration varies?Use calculus in kinematics: differentiate to move from displacement to velocity to acceleration, and integrate to reverse the process, for motion with variable acceleration.12 min answer →
- How do you use momentum, impulse and the conservation of momentum to analyse collisions?Use momentum and impulse: calculate momentum as mass times velocity, find impulse as change in momentum, and apply conservation of momentum to collisions in a straight line.12 min answer →
- How do you analyse projectile motion by treating the horizontal and vertical components separately?Model projectile motion: resolve initial velocity into horizontal and vertical components, treat horizontal motion at constant velocity and vertical motion under gravity, and find range, time of flight and maximum height.13 min answer →
- How do you use vectors to represent displacement, velocity and force, and find magnitude and direction?Use vectors in mechanics: add and subtract vectors, multiply by a scalar, use component (i and j) form, and find the magnitude and direction of a vector.12 min answer →
Unit 3: Statistics
Module overview →- How do you describe and use the relationship between two variables with correlation and a regression line?Analyse bivariate data: draw and interpret scatter graphs, describe correlation, find and use a regression line, and understand interpolation and extrapolation.12 min answer →
- How do you calculate and interpret the mean, median, standard deviation and other measures of spread?Calculate measures of location and spread: the mean, median and mode, the range and interquartile range, and the variance and standard deviation, including from frequency data.12 min answer →
- How do you use the addition and multiplication laws and conditional probability to solve probability problems?Calculate probabilities: use the addition and multiplication laws, mutually exclusive and independent events, tree diagrams, and conditional probability.12 min answer →
- How do you use the binomial distribution to find probabilities for a fixed number of independent trials?Use the binomial distribution: identify when it applies, calculate probabilities of r successes in n trials, and find its mean and variance.12 min answer →
- How do you use the normal distribution and standardising to find probabilities for continuous data?Use the normal distribution: recognise its bell shape and symmetry, standardise values with the z-score, and find probabilities using the standard normal table.12 min answer →
- How do you use the Poisson distribution to model the number of random events in a fixed interval?Use the Poisson distribution: identify when it applies, calculate probabilities of r events given a mean rate, and use its mean and variance.12 min answer →