Year 11 Mathematics Advanced Notes

These flashcards cover key concepts and formulas from Year 11 Mathematics Advanced, including algebra, functions, trigonometry, and more.

Expanding

The process of distributing terms, for example, a(b + c) = ab + ac.

Factorising

Rewriting an expression as a product of its factors, such as ax + ay = a(x + y).

Quadratics

Expressions of the form x² + (a+b)x + ab can be written as (x+a)(x+b).

Difference of squares

An expression of the form x² − a² can be factored as (x−a)(x+a).

Indices laws

Rules governing exponents, e.g., x^a × x^b = x^(a+b).

Surds

Expressions containing a root that cannot be simplified to remove the root.

Rationalising

The process of removing a surd from the denominator by multiplying the numerator and the denominator by the surd.

Linear equations

Equations of the form ax + b = 0, solved by collecting like terms and isolating x.

Quadratic formula

x = (−b ± √(b² − 4ac)) / 2a, used to find the roots of a quadratic equation.

Functions

A relationship where each input has a single output, commonly written as f(x).

Domain

The set of all possible input values (x-values) for a function.

Range

The set of all possible output values (y-values) of a function.

Gradient (m)

The slope of the line in a linear function, represented as y = mx + c.

Sine Rule

a/sinA = b/sinB = c/sinC, used to relate the lengths of sides of a triangle to the sines of its angles.

Cosine Rule

c² = a² + b² − 2ab cosC, used to find unknown sides or angles in triangles.

Amplitude

The maximum distance from the central axis of a wave, represented in functions like y = a sinx.

Period

The length of one complete cycle of a periodic function, such as sin and cos with a period of 2π.

Exponential growth/decay

Describes processes that increase or decrease by a fixed percentage over time, expressed as A = P(1+r)^t.

Distance between points

Calculated using the formula: d = √[(y2 - y1)² + (x2 - x1)²].