Further Pure Mathematics
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Pearson Edexcel IGCSE の学習者向けの無料Further Pure Mathematics学習ノート。各章のリンクから、要点・例題・練習問題への導線にアクセスできます。
Logarithmic functions and indices
Indices and the functions a^x and log_b x
Laws of logarithms and change of base
Exponential and logarithmic equations
Surds and rationalising the denominator
The quadratic function
Factorising and completing the square
The discriminant and the nature of roots
Functions of the roots alpha and beta
Forming equations with given roots
Identities and inequalities
Simple algebraic division
The factor and remainder theorems
Cubic equations and factorising cubics
One linear and one quadratic simultaneous equations
Linear and quadratic inequalities
Graphs and linear programming
Graphs of polynomials
Rational functions with linear denominators and asymptotes
Solving equations by graphical methods
Linear inequalities in two variables and linear programming
Series and the binomial series
Sigma notation
Arithmetic series
Geometric series and sum to infinity
Binomial series for positive integer n
Binomial series for rational n and validity
Scalar and vector quantities
Vector addition, subtraction and scalar multiples
Components, resolved parts and the vectors i and j
Magnitude, unit vectors and position vectors
Dividing a line in a given ratio with vectors
Collinearity, parallel lines and concurrency
Rectangular Cartesian coordinates
Distance between two points and gradient
The point dividing a line in a given ratio
The straight line and its equation
Parallel and perpendicular lines
Calculus
Differentiating powers of x, sin ax, cos ax and e^(ax)
Product, quotient and function of a function rules
Tangents and normals to y = f(x)
Stationary points, maxima and minima
Rates of change and connected rates of change
Integration and areas under and between curves
Volumes of revolution about the coordinate axes
Simple linear kinematics
Trigonometry
Radian measure, arc length and area of sector
Trigonometric ratios of any magnitude and their graphs
Sine and cosine formulae and area of a triangle
Problems in two and three dimensions
Trigonometric identities
Addition formulae
Solving trigonometric equations in a given interval
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