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AQA Level 2 Further Maths (8365) — revision checklist

AQA · L2 8365
57 spec points
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Board and spec code confirmed against AQA 8365 · registry checked 2026-07-11How this checking works

Scope: Tracks the registered 8365 topic-content leaves.

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0% green0/57 rated green

NNumber

0/3
  • Knowledge and use of numbers and the number system including fractions, decimals, percentages, ratio, proportion and order of operations

    N1NotesQuestions

  • The product rule for counting

    N2NotesQuestions

  • Manipulation of surds, including rationalising the denominator; the use of surds in exact calculations

    N3NotesQuestions

AAlgebra

0/22
  • The basic processes of algebra, including use of the associative, commutative and distributive laws

    A1NotesQuestions

  • Definition of a function; notation f(x)

    A2NotesQuestions

  • Domain and range of a function

    A3NotesQuestions

  • Composite functions (the result of two or more functions acting in succession)

    A4NotesQuestions

  • Inverse functions (domains chosen for f to make f one-one)

    A5NotesQuestions

  • Expanding brackets and collecting like terms

    A6NotesQuestions

  • Expand (a + b)^n for positive integer n; use of Pascal's triangle

    A7NotesQuestions

  • Factorising

    A8NotesQuestions

  • Manipulation of rational expressions: use of + - x / for algebraic fractions with numeric, linear or quadratic denominators

    A9NotesQuestions

  • Use and manipulation of formulae and expressions

    A10NotesQuestions

  • Use of the factor theorem for rational values of the variable for polynomials

    A11NotesQuestions

  • Completing the square

    A12NotesQuestions

  • Drawing and sketching of functions; interpretation of graphs (linear, quadratic, exponential y = ab^x and y = ab^-x, functions restricted to no more than 3 domains)

    A13NotesQuestions

  • Solution of linear and quadratic equations (by factorisation, graph, completing the square or formula)

    A14NotesQuestions

  • Algebraic and graphical solution of simultaneous equations in two unknowns, where the equations could both be linear or one linear and one second order

    A15NotesQuestions

  • Algebraic solution of linear equations in three unknowns

    A16NotesQuestions

  • Solution of linear and quadratic inequalities

    A17NotesQuestions

  • Index laws, including fractional and negative indices and the solution of equations

    A18NotesQuestions

  • Algebraic proof

    A19NotesQuestions

  • Using nth terms of sequences; limiting value of a sequence as n approaches infinity

    A20NotesQuestions

  • nth terms of linear sequences

    A21NotesQuestions

  • nth terms of quadratic sequences

    A22NotesQuestions

CGCoordinate Geometry (2 dimensions only)

0/9
  • Know and use the definition of a gradient

    CG1NotesQuestions

  • Know the relationship between the gradients of parallel and perpendicular lines

    CG2NotesQuestions

  • Use Pythagoras' theorem to calculate the distance between two points

    CG3NotesQuestions

  • Use ratio to find the coordinates of a point on a line given the coordinates of two other points, including the midpoint

    CG4NotesQuestions

  • The equation of a straight line: y = mx + c and y - y1 = m(x - x1) and other forms, including interpretation of the gradient and y-intercept

    CG5NotesQuestions

  • Draw a straight line from given information

    CG6NotesQuestions

  • Understand that x^2 + y^2 = r^2 is the equation of a circle with centre (0, 0) and radius r; application of circle geometry facts

    CG7NotesQuestions

  • Understand that (x - a)^2 + (y - b)^2 = r^2 is the equation of a circle with centre (a, b) and radius r

    CG8NotesQuestions

  • The equation of a tangent at a point on a circle

    CG9NotesQuestions

CCalculus

0/9
  • Know that the gradient function dy/dx gives the gradient of the curve and measures the rate of change of y with respect to x

    C1NotesQuestions

  • Know that the gradient of a function is the gradient of the tangent at that point

    C2NotesQuestions

  • Differentiation of kx^n where n is an integer, and the sum of such functions

    C3NotesQuestions

  • The equation of a tangent and normal at any point on a curve

    C4NotesQuestions

  • Increasing and decreasing functions

    C5NotesQuestions

  • Understand and use the notation d2y/dx2; know that it measures the rate of change of the gradient function

    C6NotesQuestions

  • Use of differentiation to find maxima and minima points on a curve

    C7NotesQuestions

  • Using calculus to find maxima and minima in simple problems

    C8NotesQuestions

  • Sketch/interpret a curve with known maximum and minimum points

    C9NotesQuestions

MMatrix Transformations (all calculations restricted to 2x2 or 2x1 matrices)

0/4
  • Multiplication of matrices (2x2 by 2x2 or by 2x1), and multiplication by a scalar

    M1NotesQuestions

  • The identity matrix I (2x2 only)

    M2NotesQuestions

  • Transformations of the unit square in the x-y plane, represented by a 2x2 matrix (rotations of 90/180/270 about the origin, reflections in x=0, y=0, y=x, y=-x, enlargements centred on the origin)

    M3NotesQuestions

  • Combination of transformations using matrix multiplication

    M4NotesQuestions

GGeometry

0/10
  • Knowledge of perimeter, area, surface area and volume of standard shapes; angle properties of parallel/intersecting lines, triangles, quadrilaterals and polygons; and understand and use circle theorems

    G1NotesQuestions

  • Understand and construct geometrical proofs using formal arguments

    G2NotesQuestions

  • Sine and cosine rules in scalene triangles; area of a triangle = 1/2 ab sinC

    G3NotesQuestions

  • Use of Pythagoras' theorem in 2D and 3D; recognise Pythagorean triples

    G4NotesQuestions

  • Apply trigonometry and Pythagoras' theorem to 2 and 3 dimensional problems, including the angle between a line and a plane and between two planes

    G5NotesQuestions

  • Sketch and use graphs of y = sin x, y = cos x and y = tan x for angles of any size

    G6NotesQuestions

  • Use the definitions of sin, cos and tan for any positive angle up to 360 degrees (measured in degrees only)

    G7NotesQuestions

  • Knowledge and use of 30, 60, 90 triangles and 45, 45, 90 triangles

    G8NotesQuestions

  • Know and use tan = sin / cos and sin^2 + cos^2 = 1

    G9NotesQuestions

  • Solution of simple trigonometric equations in given intervals

    G10NotesQuestions

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