Pure Mathematics Key Terms

vectors

vectors is a method cue for Trigonometry in context. Use it when working on "E9 Use trigonometric functions to solve problems in context, including problems involving vectors, kinematics and forces." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

graph

graph is a method cue for Exponential functions. Use it when working on "F1 Know and use the function a^x and its graph, where a is positive; know and use the function e^x and its graph." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

exponential model

exponential model is a method cue for Exponential gradient and modelling. Use it when working on "F2 Know that the gradient of e^(kx) is equal to ke^(kx) and hence understand why the exponential model is suitable in many applications." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

know

know is a method cue for Logarithmic functions. Use it when working on "F3 Know and use the definition of log_a x as the inverse of a^x, where a is positive and x >= 0; know and use the function ln x and its graph; know and use ln x as the inverse function of e^x." 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 Laws of logarithms. Use it when working on "F4 Understand and use the laws of logarithms, including log_a x + log_a y = log_a(xy), log_a x - log_a y = log_a(x/y), and k log_a x = log_a(x^k), including cases such as k = -1 and k = -1/2." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

solve

solve is a method cue for Exponential equations. Use it when working on "F5 Solve equations of the form a^x = b." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

logarithmic graphs

logarithmic graphs is a method cue for Logarithmic graphs. Use it when working on "F6 Use logarithmic graphs to estimate parameters in relationships of the form y = ax^n and y = kb^x, given data for x and y." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

growth

growth is a method cue for Exponential growth and decay. Use it when working on "F7 Understand and use exponential growth and decay; use exponential models in contexts such as continuous compound interest, radioactive decay, drug concentration decay and population growth; consider limitations and refinements of exponential models." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

derivative

derivative is a method cue for Derivative concept. Use it when working on "G1 Understand and use the derivative of f(x) as the gradient of the tangent to y = f(x) at a general point; understand the gradient of the tangent as a limit and as a rate of change; sketch the gradient function for a given curve; understand second derivatives; differentiate from first principles for small positive integer powers of x and for sin x and cos x; understand and use the second derivative as the rate of change of gradient, including links to convex and concave sections and points of inflection." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

differentiate

differentiate is a method cue for Differentiation techniques. Use it when working on "G2 Differentiate x^n for rational values of n and related constant multiples, sums and differences; differentiate e^(kx), a^(kx), sin kx, cos kx, tan kx and related sums, differences and constant multiples; understand and use the derivative of ln x." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

gradients

gradients is a method cue for Applications of differentiation. Use it when working on "G3 Apply differentiation to find gradients, tangents and normals, maxima and minima, stationary points and points of inflection; identify where functions are increasing or decreasing." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

product rule

product rule is a method cue for Product, quotient and chain rules. Use it when working on "G4 Differentiate using the product rule, quotient rule and chain rule, including problems involving connected rates of change and inverse functions." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

differentiate

differentiate is a method cue for Implicit and parametric differentiation. Use it when working on "G5 Differentiate simple functions and relations defined implicitly or parametrically, for first derivative only." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

modelling

modelling is a method cue for Differential equation construction. Use it when working on "G6 Construct simple differential equations in pure mathematics and in context, including contexts such as kinematics, population growth and modelling the relationship between price and demand." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

Fundamental Theorem of Calculus

Fundamental Theorem of Calculus is a method cue for Fundamental Theorem of Calculus. Use it when working on "H1 Know and use the Fundamental Theorem of Calculus." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

integrate

integrate is a method cue for Integration techniques. Use it when working on "H2 Integrate x^n excluding n = -1 and related sums, differences and constant multiples; integrate e^(kx), 1/x, sin kx, cos kx and related sums, differences and constant multiples." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

definite integrals

definite integrals is a method cue for Definite integration and areas. Use it when working on "H3 Evaluate definite integrals; use a definite integral to find the area under a curve and the area between two curves." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

integration

integration is a method cue for Integration as limit of a sum. Use it when working on "H4 Understand and use integration as the limit of a sum." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

substitution

substitution is a method cue for Integration by substitution and parts. Use it when working on "H5 Carry out simple cases of integration by substitution and integration by parts; understand these methods as inverse processes of the chain and product rules respectively, with substitution limited to cases where one substitution leads to an integrable function and integration by parts excluding reduction formulae." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

partial fractions

partial fractions is a method cue for Integration using partial fractions. Use it when working on "H6 Integrate using partial fractions that are linear in the denominator." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

separable variables

separable variables is a method cue for First order differential equations. Use it when working on "H7 Evaluate the analytical solution of simple first order differential equations with separable variables, including finding particular solutions, where separation of variables may require factorisation involving a common factor." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

limitations

limitations is a method cue for Differential equation interpretation. Use it when working on "H8 Interpret the solution of a differential equation in the context of solving a problem, including identifying limitations of the solution and links to kinematics." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

roots

roots is a method cue for Root location. Use it when working on "I1 Locate roots of f(x) = 0 by considering changes of sign of f(x) in an interval of x on which f(x) is sufficiently well behaved; understand how change of sign methods can fail." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

Newton-Raphson

Newton-Raphson is a method cue for Iterative methods and Newton-Raphson. Use it when working on "I2 Solve equations approximately using simple iterative methods; draw associated cobweb and staircase diagrams; solve equations using the Newton-Raphson method and other recurrence relations of the form x_(n+1) = g(x_n); understand how such methods can fail." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

numerical integration

numerical integration is a method cue for Numerical integration. Use it when working on "I3 Understand and use numerical integration of functions, including the trapezium rule and estimating the approximate area under a curve and limits that it must lie between." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.

numerical methods

numerical methods is a method cue for Numerical methods in context. Use it when working on "I4 Use numerical methods to solve problems in context." and state the specific calculation, notation, or reasoning role it plays rather than treating it as a loose label.