Back to Northern Ireland Maths
Northern Ireland · CCEAQ&A
MathsQ&A by dot point
A short Q&A bank for every Northern Ireland 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.
A2 1 Pure Mathematics
- Differentiating exponential, logarithmic and trigonometric functions, the chain, product and quotient rules, implicit differentiation, and connected rates of change.4Q&A pairs
- Functions, domain and range, composite and inverse functions, the modulus function and modulus equations, and expressing a rational function as partial fractions.6Q&A pairs
- Integrating standard functions, integration by substitution and by parts, integrating with partial fractions, and forming and solving differential equations by separating the variables.4Q&A pairs
- 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.4Q&A pairs
- Curves defined parametrically, converting between parametric and Cartesian form, and finding the gradient of a parametric curve using the chain rule.4Q&A pairs
- Methods of proof, including proof by deduction, proof by exhaustion, disproof by counter-example, and proof by contradiction.5Q&A pairs
- 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.4Q&A pairs
- 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.3Q&A pairs
- 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.3Q&A pairs
A2 2 Applied Mathematics
- Conditional probability, the conditional probability formula, the multiplication rule for dependent events, the test for independence, and using tree diagrams and two-way tables.3Q&A pairs
- 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.3Q&A pairs
- 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.3Q&A pairs
- 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.3Q&A pairs
- 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.3Q&A pairs
AS 1 Pure Mathematics
- 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.4Q&A pairs
- 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.4Q&A pairs
- 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.3Q&A pairs
- 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.3Q&A pairs
- 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.5Q&A pairs
- The binomial expansion of for positive integer using binomial coefficients, and sequences and series described by sigma notation and recurrence.4Q&A pairs
- The trigonometric ratios and their graphs, the sine and cosine rules and the area of a triangle, the identities and , and solving trigonometric equations.3Q&A pairs
- 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.3Q&A pairs
AS 2 Applied Mathematics
- 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.4Q&A pairs
- Forces as vectors, modelling assumptions, Newton's three laws, the equation , weight, normal reaction, tension and the motion of connected particles.4Q&A pairs
- 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.6Q&A pairs
- 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.3Q&A pairs
- Discrete random variables and their probability distributions, the binomial distribution and its conditions, calculating binomial probabilities, and the mean of a binomial distribution.4Q&A pairs
- 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.4Q&A pairs