Back to Northern Ireland Further Maths
Northern Ireland · CCEAQ&A
Further MathsQ&A by dot point
A short Q&A bank for every Northern Ireland Further Maths syllabus dot point. Each question and answer is drawn directly from our worked dot-point page, so you can scan key concepts before opening the long-form answer.
Unit 1: Pure Mathematics
- Manipulate algebraic expressions and algebraic fractions: simplify, add, subtract, multiply and divide them, solve equations involving them, and construct simple algebraic proofs.1Q&A pairs
- 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.1Q&A pairs
- Differentiate polynomials: find first and second derivatives, find gradients, tangents and normals, locate and classify stationary points, and solve optimisation problems.0Q&A pairs
- Use function notation: form composite functions, find inverse functions, state domain and range, and apply transformations to the graphs of functions.1Q&A pairs
- Integrate polynomials: find indefinite integrals with a constant of integration, evaluate definite integrals, and use definite integration to find the area under a curve.0Q&A pairs
- 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.1Q&A pairs
- Use matrices: add, subtract and multiply matrices, use the identity matrix, and apply 2x2 matrices to describe and combine transformations of the plane.0Q&A pairs
- Work with polynomials: apply the factor theorem and the remainder theorem, factorise cubics, and solve polynomial equations of degree three.1Q&A pairs
- 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.0Q&A pairs
- Use surds and the laws of indices: simplify surds, rationalise denominators, and apply the index laws including zero, negative and fractional indices.0Q&A pairs
- 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.1Q&A pairs
Unit 2: Mechanics
- 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.2Q&A pairs
- 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.0Q&A pairs
- 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.0Q&A pairs
- Model motion in a straight line with constant acceleration: use the suvat equations and interpret displacement-time and velocity-time graphs.0Q&A pairs
- Use calculus in kinematics: differentiate to move from displacement to velocity to acceleration, and integrate to reverse the process, for motion with variable acceleration.0Q&A pairs
- 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.0Q&A pairs
- 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.1Q&A pairs
- 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.0Q&A pairs
Unit 3: Statistics
- Analyse bivariate data: draw and interpret scatter graphs, describe correlation, find and use a regression line, and understand interpolation and extrapolation.0Q&A pairs
- 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.0Q&A pairs
- Calculate probabilities: use the addition and multiplication laws, mutually exclusive and independent events, tree diagrams, and conditional probability.1Q&A pairs
- Use the binomial distribution: identify when it applies, calculate probabilities of r successes in n trials, and find its mean and variance.0Q&A pairs
- Use the normal distribution: recognise its bell shape and symmetry, standardise values with the z-score, and find probabilities using the standard normal table.0Q&A pairs
- Use the Poisson distribution: identify when it applies, calculate probabilities of r events given a mean rate, and use its mean and variance.0Q&A pairs