**Maths Index**

- a cos x ± b sin x
- Algebra
- factorising
- expanding one or more brackets
- Algebraic
- long division
- factorising
- Arc length
- Area
- between a curve and the x-axis
- between a curve and the y-axis
- between a parametric curve
- sector
- segment
- triangle
- Argand diagram
- Arithmetic Progression (Series)
- Asymptotes
- horizontal and vertical

- Cast Diagram
- Chain rule
- Change of sign
- Circle equation
- Cofactor, matrix
- Completing the square
- Complex Numbers
- argument
- Argand diagram
- equations
- locus
- modulus
- Composite functions
- Compound angles
- Compound interest
- Connected rates of change
- Cosecant
- Cosine Rule
- Cotangent
- Cubic
- graphs
- Curve, gradient
- Curve Sketching
- cubic graphs
- quadratic graphs
- reciprocal graphs

- Definite integrals
- De Moivre’s Theorem
- Derivative, second order
- Determinant of a matrix
- Difference of two Squares
- Differential
- second
- Differential equations
- first order separable type
- forming
- separable
- Differentiation
- chain rule
- connected rates of change
- product rule
- quotient rule
- reciprocal function
- Differentiation of
- ax
^{n} - exponential functions a
^{x} - exponential functions e
^{x} - implicit functions
- log functions
- sec(x), cosec(x), cot(x)
- trigonometric functions
- Discriminant
- Distance
- between points
- Division
- algebraic
- algebraic long division
- Double-angle formula
- Domain

- e
^{x} - Equations
- complex numbers
- linear equations
- simultaneous equations
- quadratic equations
- Even functions
- Expanding
- brackets
- Exponential
- differential: See
*differentiation of* - functions and graphs
- integration: See
*Integrals of the form* - Exponents

- Factorising (Factoring)
- difference of two squares
- grouping
- quadratics
- Factor theorem
- Fractions
- partial
- simplifying algebraic
- Functions
- composite
- domain
- increasing, decreasing
- inverse
- modulus
- notation
- range

- Geometric Progression (series)
- Gradient of
- curve
- parallel lines
- perpendicular lines
- straight lines (line segment)
- Graphs
- cubic
- quadratic
- reciprocal
- transformations

- Identity
- identity or equation – what’s the difference?
- Imaginary numbers
- Implicit functions
- differentiation
- Indices
- Inequalities
- double
- linear
- modulus
- quadratic
- Integral
- definite
- Integrals of the form
- ax
^{n} - (ax + b)
^{n} - exponential: e
^{x}, e^{ax}and e^{(ax+b)} - f ‘(x) / f(x)
- f ‘(x) e
^{f(x)} - f [g(x)] g ‘(x)
- reciprocal: 1/x and 1/(ax + b)
- trigonometric functions
- Integration
- by parts
- change of variable
- definite
- equation of a curve given dy/dx
- general methods
- partial fractions type
- substitution
- Integration – applications
- area bounded by a curve and x-axis
- area between a curve and the y-axis
- area between a parametric curve
- Inverse
- function
- trigonometric functions
- Iteration
- iteration – fixed point
- Newton-Raphson

- Linear transformations, matrices
- Line
- equation of
- gradient of
- mid-point
- Locus – complex plane
- Logarithms
- change of base
- differential – see
*differentiation of* - rules
- simplifying and expanding
- simultaneous equations
- Long Division
- algebraic

- Matrices
- addition and subtraction
- cofactor
- determinant 3×3
- inverse
- linear transformations
- minors
- multiplication
- transpose
- Maximum and minimum – see
*stationary points* - Mid-point of a line
- Modelling curves
- Modulus Functions

- Newton-Raphson
- Normal
- to a curve
- to parametric curves
- Numerical methods for equations
- change of sign
- graphical
- iteration
- Newton-Raphson
- Numerical methods for integration
- trapezium rule

- Quadrant Rule
- Quadratic Equations – solution by:-
- completing the square
- discriminant
- factorising
- formula
- sum and product of roots
- Quadratic Expressions
- completing the square
- factorising
- Quadratic Graphs
- sketching
- Quotient rule

- Radians
- Range
- Rationalising
- surds
- Reciprocal
- function of dy/dx
- graphs
- Reflection – see
*transformations* - Roots
- discriminant – quadratic equations
- Rotation – see
*transformations*

- Secant
- Sector – area
- Segment – area
- Sequences
- recurrence relationships
- nth term
- Sequences and Series
- Series
- arithmetic
- binomial
- geometric
- sum of – sigma notation
- Simultaneous Equations
- elimination method
- substitution method
- Sine rule
- Small angles
- Stationary points
- Stretch – see
*transformations* - Surds

- Tangent
- to a circle
- to a curve
- to a parametric curve
- t-substitution
- Terms
- Transformations
- graphs
- Translation see
*transformations* - Trapezium rule
- Trigonometric identities / equations
- 1) basic
- 2) Pythagorean
- 3) compound angles
- 4) double angles
- 5) half angles
- 6) triple angles
- 7) harmonic
- Trigonometric functions
- differential – see
*differentiation of* - integration – see
*integrals of the form* - inverse (arcsin, arccos, arctan)
- small angles
- Trigonometric ratios
- Trigonometry
- applications
- cosine rule
- graphs and transformations
- right angled triangles
- sine rule