Edexcel further maths cp1

This set of vocabulary flashcards covers essential terminology, definitions, and standard results from complex numbers, matrices, series, and vectors found in the Edexcel Further Mathematics Core Pure 1 curriculum.

Complex Number

A number written in the form a + bi, where a and b are real numbers and i is the square root of -1.

Imaginary Number

A number of the form bi, where b is a real number.

Complex Conjugate

For a complex number z = a + bi, the conjugate z* is defined as a - bi.

Argand Diagram

A geometric representation of complex numbers where the x-axis is the real axis and the y-axis is the imaginary axis.

Modulus

The distance from the origin to a complex number on an Argand diagram, denoted |z| and calculated as the square root of (x^2 + y^2).

Argument

The angle between the positive real axis and the line joining the complex number to the origin, measured anticlockwise in radians.

Discriminant

The part of the quadratic formula (b^2 - 4ac) used to determine the nature of the roots of a quadratic equation.

Conjugate Pair

The occurrence of non-real complex roots of a polynomial with real coefficients; if z is a root, then z* is also a root.

Sum of Natural Numbers (Σr)

A standard result defined as n(n + 1) / 2.

Volume of Revolution (x-axis)

The volume formed by rotating a curve y=f(x) through 2π radians about the x-axis, calculated as π∫y^2 dx.

Identity Matrix

A square matrix denoted by I, where elements on the leading diagonal are 1 and all other elements are 0.

Singular Matrix

A matrix with a determinant of 0, meaning it has no inverse.

Determinant (2x2 Matrix)

The scalar value calculated as (ad - bc) for a 2x2 matrix with elements a, b, c, d.

Invariant Point

A point that remains in its original position after a specific linear transformation.

Mathematical Induction

A four-step proof method involving a Basis step, an Assumption step, an Inductive step, and a Conclusion.

Scalar Product (Dot Product)

The product of two vectors a and b defined as |a||b|cosθ, or a1b1 + a2b2 + a3b3.

Direction Vector

A vector that defines the path or orientation of a straight line in 3D space.

Skew Lines

Two straight lines in 3D space that are not parallel and do not intersect.

Transpose Matrix

The matrix resulting from interchanging the rows and columns of an existing matrix.

Area Scale Factor

Represented by the determinant of a transformation matrix M, it indicates the factor by which an area changes under a linear transformation.