Pure Mathematics key terms

deduction

deduction is a method cue for Proof. Use it when working on "A1 Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof including proof by deduction and proof by exhaustion; use disproof by counter example; use proof by contradiction including proof of the irrationality of sqrt(2), the infinity of primes and application to unfamiliar proofs." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

indices

indices is a method cue for Laws of indices. Use it when working on "B1 Understand and use the laws of indices for all rational exponents." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

surds

surds is a method cue for Surds. Use it when working on "B2 Use and manipulate surds, including rationalising the denominator." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

quadratic

quadratic is a method cue for Quadratic functions. Use it when working on "B3 Work with quadratic functions and their graphs; use the discriminant including the conditions for real and repeated roots; complete the square; solve quadratic equations including solving quadratic equations in a function of the unknown." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

simultaneous equations

simultaneous equations is a method cue for Simultaneous equations. Use it when working on "B4 Solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

inequalities

inequalities is a method cue for Inequalities. Use it when working on "B5 Solve linear and quadratic inequalities in a single variable and interpret such inequalities graphically, including inequalities with brackets and fractions; express solutions through correct use of and and or, or through set notation; represent linear and quadratic inequalities graphically." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

polynomials

polynomials is a method cue for Polynomial and rational expression manipulation. Use it when working on "B6 Manipulate polynomials algebraically, including expanding brackets and collecting like terms, factorisation and simple algebraic division; use the factor theorem; simplify rational expressions including by factorising and cancelling, and algebraic division by linear expressions only." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

functions

functions is a method cue for Graphs of functions. Use it when working on "B7 Understand and use graphs of functions; sketch curves defined by simple equations including polynomials, the modulus of a linear function, y = a/x and y = a/x^2 including their vertical and horizontal asymptotes; interpret algebraic solution of equations graphically; use intersection points of graphs to solve equations; understand and use proportional relationships and their graphs." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

composite functions

composite functions is a method cue for Composite and inverse functions. Use it when working on "B8 Understand and use composite functions, inverse functions and their graphs." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

understand

understand is a method cue for Transformations of function graphs. Use it when working on "B9 Understand the effect of simple transformations on the graph of y = f(x), including sketching associated graphs y = af(x), y = f(x) + a, y = f(x + a), y = f(ax), and combinations of these transformations." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

rational functions

rational functions is a method cue for Partial fractions. Use it when working on "B10 Decompose rational functions into partial fractions, with denominators not more complicated than squared linear terms and with no more than three terms, and numerators constant or linear." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

functions

functions is a method cue for Functions in modelling. Use it when working on "B11 Use functions in modelling, including consideration of limitations and refinements of the models." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

straight line

straight line is a method cue for Straight line coordinate geometry. Use it when working on "C1 Understand and use the equation of a straight line, including the forms y - y1 = m(x - x1) and ax + by + c = 0; use gradient conditions for two straight lines to be parallel or perpendicular; use straight line models in a variety of contexts." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

circle

circle is a method cue for Circle coordinate geometry. Use it when working on "C2 Understand and use the coordinate geometry of the circle including the equation of a circle in the form (x - a)^2 + (y - b)^2 = r^2; complete the square to find the centre and radius; use circle properties including the angle in a semicircle, the perpendicular from the centre to a chord, and the radius perpendicular to a tangent." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

parametric equations

parametric equations is a method cue for Parametric equations. Use it when working on "C3 Understand and use the parametric equations of curves and conversion between Cartesian and parametric forms." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

parametric equations

parametric equations is a method cue for Parametric modelling. Use it when working on "C4 Use parametric equations in modelling in a variety of contexts." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

binomial expansion

binomial expansion is a method cue for Binomial expansion. Use it when working on "D1 Understand and use the binomial expansion of (a + bx)^n for positive integer n; use the notations n!, nCr and binomial coefficients; link to binomial probabilities; extend to any rational n including use for approximation; be aware that the expansion is valid for |bx/a| < 1, with proof not required." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

sequences

sequences is a method cue for Sequences. Use it when working on "D2 Work with sequences including those given by a formula for the nth term and those generated by a simple relation of the form x_(n+1) = f(x_n); work with increasing, decreasing and periodic sequences." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

series

series is a method cue for Sigma notation. Use it when working on "D3 Understand and use sigma notation for sums of series." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

arithmetic sequence

arithmetic sequence is a method cue for Arithmetic sequences and series. Use it when working on "D4 Understand and work with arithmetic sequences and series, including the formulae for nth term and the sum to n terms." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

geometric sequence

geometric sequence is a method cue for Geometric sequences and series. Use it when working on "D5 Understand and work with geometric sequences and series, including formulae for the nth term and the sum of a finite geometric series; use the sum to infinity of a convergent geometric series, including the use of |r| < 1 and modulus notation." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

sequences

sequences is a method cue for Sequences and series in modelling. Use it when working on "D6 Use sequences and series in modelling." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

sine

sine is a method cue for Trigonometric definitions and radians. Use it when working on "E1 Understand and use the definitions of sine, cosine and tangent for all arguments; use the sine and cosine rules; use the area of a triangle in the form 1/2 ab sin C; work with radian measure, including use for arc length and area of sector." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

radians

radians is a method cue for Small angle approximations. Use it when working on "E2 Understand and use the standard small angle approximations of sine, cosine and tangent, including sin theta approximately theta, cos theta approximately 1 - theta^2/2, and tan theta approximately theta where theta is in radians." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

graphs

graphs is a method cue for Trigonometric functions and exact values. Use it when working on "E3 Understand and use the sine, cosine and tangent functions, their graphs, symmetries and periodicity; know and use exact values of sin and cos for 0, pi/6, pi/4, pi/3, pi/2, pi and multiples thereof, and exact values of tan for 0, pi/6, pi/4, pi/3, pi and multiples thereof." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

secant

secant is a method cue for Reciprocal and inverse trigonometric functions. Use it when working on "E4 Understand and use the definitions of secant, cosecant and cotangent and of arcsin, arccos and arctan; understand their relationships to sine, cosine and tangent, their graphs, ranges and domains." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

tan

tan is a method cue for Trigonometric identities. Use it when working on "E5 Understand and use tan theta = sin theta / cos theta; understand and use sin^2 theta + cos^2 theta = 1, sec^2 theta = 1 + tan^2 theta, and cosec^2 theta = 1 + cot^2 theta." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

double angle

double angle is a method cue for Compound and double angle formulae. Use it when working on "E6 Understand and use double angle formulae; use formulae for sin(A +/- B), cos(A +/- B) and tan(A +/- B); understand geometrical proofs of these formulae; understand and use expressions for a cos theta + b sin theta in equivalent forms r cos(theta +/- alpha) or r sin(theta +/- alpha)." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

quadratic equations

quadratic equations is a method cue for Trigonometric equations. Use it when working on "E7 Solve simple trigonometric equations in a given interval, including quadratic equations in sin, cos and tan and equations involving multiples of the unknown angle." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

proof

proof is a method cue for Trigonometric proofs. Use it when working on "E8 Construct proofs involving trigonometric functions and identities." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.