← Further Maths syllabus

Northern IrelandFurther Maths

Unit 1: Pure Mathematics

11 dot points across 11 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

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.
A CCEA GCSE Further Mathematics answer on algebraic manipulation and algebraic fractions, covering simplifying by factorising, the four operations on fractions, solving fractional equations, and writing algebraic proofs in the compulsory Pure unit.
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.
A CCEA GCSE Further Mathematics answer on coordinate geometry, covering the gradient and equation of a line, parallel and perpendicular conditions, the distance and midpoint, the equation of a circle, and the tangent to a circle in the compulsory Pure unit.
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.
A CCEA GCSE Further Mathematics answer on differentiation, covering the power rule, the second derivative, tangents and normals, finding and classifying stationary points, increasing and decreasing functions, and optimisation in the compulsory Pure unit.
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.
A CCEA GCSE Further Mathematics answer on functions and graphs, covering composite and inverse functions, domain and range, and the translations, reflections and stretches that transform graphs in the compulsory Pure unit.
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.
A CCEA GCSE Further Mathematics answer on integration, covering the reverse-power rule, the constant of integration, finding a function from its derivative, evaluating definite integrals, and finding the area under a curve in the compulsory Pure unit.
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.
A CCEA GCSE Further Mathematics answer on logarithms and exponentials, covering the relationship between index and log form, the laws of logarithms, and solving exponential equations using logs in the compulsory Pure unit.
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.
A CCEA GCSE Further Mathematics answer on matrices and transformations, covering matrix arithmetic, the identity matrix, multiplying matrices, and using 2x2 matrices to represent rotations, reflections, enlargements and combined transformations in the compulsory Pure unit.
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.
A CCEA GCSE Further Mathematics answer on polynomials, covering the factor theorem and remainder theorem, factorising cubics, dividing polynomials, and solving cubic equations in the compulsory Pure unit.
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.
A CCEA GCSE Further Mathematics answer on quadratic theory, covering completing the square, the discriminant and the nature of roots, solving quadratic and simultaneous quadratic equations, and solving quadratic inequalities in the compulsory Pure unit.
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.
A CCEA GCSE Further Mathematics answer on surds and indices, covering simplifying surds, rationalising denominators including conjugates, and the full index laws with zero, negative and fractional powers in the compulsory Pure unit.
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.
A CCEA GCSE Further Mathematics answer on trigonometry, covering the sine and cosine rules, the area formula, exact values, the tan and Pythagorean identities, and solving trigonometric equations across an interval in the compulsory Pure unit.
12 min answer →