Northern Ireland · CCEASyllabus
Maths syllabus, dot point by dot point
Every dot point in the Northern Ireland 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.
A2 1 Pure Mathematics
Module overview →- How do the chain, product and quotient rules let us differentiate any combination of functions, including implicitly?Differentiating exponential, logarithmic and trigonometric functions, the chain, product and quotient rules, implicit differentiation, and connected rates of change.13 min answer →
- How do we describe, combine and invert functions, and split a rational expression into partial fractions?Functions, domain and range, composite and inverse functions, the modulus function and modulus equations, and expressing a rational function as partial fractions.13 min answer →
- How do substitution, integration by parts and partial fractions let us integrate harder functions and solve differential equations?Integrating standard functions, integration by substitution and by parts, integrating with partial fractions, and forming and solving differential equations by separating the variables.13 min answer →
- How do we locate roots and estimate areas when exact methods fail?Locating roots by a sign change, iterative methods including the Newton-Raphson method and fixed-point iteration, and the trapezium rule for estimating a definite integral.12 min answer →
- How do parametric equations describe a curve through a parameter, and how do we convert and differentiate them?Curves defined parametrically, converting between parametric and Cartesian form, and finding the gradient of a parametric curve using the chain rule.12 min answer →
- How do we prove a mathematical statement is always true, or show it is false?Methods of proof, including proof by deduction, proof by exhaustion, disproof by counter-example, and proof by contradiction.12 min answer →
- How do arithmetic and geometric series sum, and how does the binomial expansion extend to any power?Arithmetic and geometric sequences and series and their sums, the sum to infinity of a convergent geometric series, and the binomial expansion for any rational power with its validity condition.13 min answer →
- How do radians, the compound and double-angle formulae and the harmonic form extend trigonometry?Radian measure with arc length and sector area, the reciprocal and inverse trigonometric functions, the compound-angle and double-angle identities, and the form for solving equations.13 min answer →
- How do vectors extend to three dimensions, and how do we measure distances and angles between them?Three-dimensional vectors in component form, the magnitude and distance between points in space, the scalar (dot) product and the angle between two vectors, and the condition for perpendicular vectors.12 min answer →
A2 2 Applied Mathematics
Module overview →- How does knowing one event has happened change the probability of another?Conditional probability, the conditional probability formula, the multiplication rule for dependent events, the test for independence, and using tree diagrams and two-way tables.12 min answer →
- How do friction and moments govern the equilibrium and motion of bodies, including on inclined planes?Resolving forces in two dimensions, the friction model with the coefficient of friction, motion and equilibrium on an inclined plane, and the moment of a force with the conditions for the equilibrium of a rigid body.13 min answer →
- How do we use a sample to test a claim about a population, and decide whether to reject it?The structure of a hypothesis test, the null and alternative hypotheses, the significance level and critical region, one-tailed and two-tailed tests, and carrying out a binomial hypothesis test.13 min answer →
- How do we analyse projectile motion in two dimensions and motion with a varying acceleration?Projectile motion resolved into horizontal and vertical components, the range, time of flight and maximum height, and using calculus to relate displacement, velocity and acceleration when the acceleration varies with time.13 min answer →
- How does the normal distribution model continuous data, and how do we calculate probabilities from it?The normal distribution and its parameters, standardising to the standard normal variable Z, finding probabilities and values from the distribution, and the normal approximation to the binomial distribution.13 min answer →
AS 1 Pure Mathematics
Module overview →- How do indices, surds, quadratics and polynomials let us manipulate and solve algebraic expressions?The laws of indices and surds, completing the square and the quadratic formula, the discriminant, simultaneous equations, inequalities, and polynomial manipulation including the factor and remainder theorems.13 min answer →
- How do equations describe straight lines, circles and the shapes of common graphs?The equation of a straight line and conditions for parallel and perpendicular lines, the equation of a circle and its key properties, and sketching and transforming standard curves.13 min answer →
- How does differentiation measure the gradient of a curve and locate its turning points?Differentiation from first principles, differentiating powers of , the gradient of a curve, tangents and normals, increasing and decreasing functions, and locating and classifying stationary points.13 min answer →
- How do exponential functions and logarithms describe growth and let us solve equations with the variable in the power?Exponential functions and the number , the laws of logarithms and the relationship between exponentials and logarithms, solving equations of the form , and using logarithms to linearise data.13 min answer →
- How does integration reverse differentiation and let us find areas under curves?Integration as the reverse of differentiation, indefinite integrals with a constant of integration, the definite integral and its evaluation, and finding the area under a curve.12 min answer →
- How does the binomial theorem expand powers of a bracket, and how are series described and summed?The binomial expansion of for positive integer using binomial coefficients, and sequences and series described by sigma notation and recurrence.12 min answer →
- How do trigonometric ratios, identities and graphs let us model and solve angle problems?The trigonometric ratios and their graphs, the sine and cosine rules and the area of a triangle, the identities and , and solving trigonometric equations.13 min answer →
- How do vectors represent quantities with magnitude and direction in two dimensions?Two-dimensional vectors in component and unit-vector form, the magnitude and direction of a vector, addition and scalar multiplication, position vectors, and using vectors in geometric problems.12 min answer →
AS 2 Applied Mathematics
Module overview →- How do we summarise, display and interpret a set of data?Measures of central tendency and spread, calculating the mean, median, mode, range, interquartile range, variance and standard deviation, displaying data with histograms and box plots, and identifying outliers.13 min answer →
- How do Newton's laws relate the forces on a body to its acceleration?Forces as vectors, modelling assumptions, Newton's three laws, the equation , weight, normal reaction, tension and the motion of connected particles.13 min answer →
- How do the equations of motion and motion graphs describe a body moving in a straight line?Displacement, velocity and acceleration for motion in a straight line, the equations of motion for constant acceleration, motion under gravity, and interpreting displacement-time and velocity-time graphs.12 min answer →
- How do we calculate the probability of single and combined events?Probability of an event, mutually exclusive and independent events, the addition and multiplication rules, Venn diagrams and tree diagrams, and the probability of complementary events.12 min answer →
- How do we model the probabilities of a discrete random variable, and when does the binomial distribution apply?Discrete random variables and their probability distributions, the binomial distribution and its conditions, calculating binomial probabilities, and the mean of a binomial distribution.13 min answer →
- How do we collect a sample that fairly represents a population?Populations, samples and the census, sampling units and the sampling frame, and the main sampling methods including random, systematic, stratified, quota and opportunity sampling with their advantages and limitations.11 min answer →