Mathematics A - H240
19 个单元 · 97 个章节
免费 Mathematics A - H240 学习笔记，适合 Cambridge OCR A Level 学生。每个章节都覆盖一个重点主题，并附例题与可延伸到 thinka app 的练习提示。
Pure Mathematics: Proof
Proof
Pure Mathematics: Algebra and Functions
Indices
Surds
Simultaneous equations
Quadratic functions
Inequalities
Polynomials
The modulus function
Curve sketching
Functions
Graph transformations
Partial fractions
Models in context
Pure Mathematics: Coordinate Geometry in the x–y Plane
Straight lines
Circles
Parametric equations of curves
Parametric equations in context
Pure Mathematics: Sequences and Series
Binomial expansion
Sequences
Sigma notation
Arithmetic sequences
Geometric sequences
Modelling
Pure Mathematics: Trigonometry
sin, cos and tan for all arguments
Sine and cosine rules
Radians
Small angle approximations
Graphs of the basic trigonometric functions
Exact values of trigonometric functions
Inverse and reciprocal trigonometric ratios
Trigonometric identities
Further trigonometric identities
Trigonometric equations
Proof involving trigonometric functions
Trigonometric functions in context
Pure Mathematics: Exponentials and Logarithms
Properties of the exponential function
Gradient of ekx
Properties of the logarithm
Laws of logarithms
Equations involving exponentials
Reduction to linear form
Modelling using exponential functions
Pure Mathematics: Differentiation
Gradients
Differentiation from first principles
Differentiation of standard functions
Tangents, normals, stationary points, increasing and decreasing functions
Techniques of differentiation
Parametric and implicit differentiation
Constructing differential equations
Pure Mathematics: Integration
Fundamental theorem of calculus
Indefinite integrals
Definite integrals and areas
Integration as the limit of a sum
Integration by substitution
Integration by parts
Use of partial fractions in integration
Differential equations with separable variables
Interpreting the solution of a differential equation
Pure Mathematics: Numerical Methods
Sign change methods
Formal iterative methods
Numerical integration
Use numerical methods in context
Pure Mathematics: Vectors
Vectors
Magnitude and direction of vectors
Basic operations on vectors
Position vectors
Distance between points
Problem solving using vectors
Statistics: Statistical Sampling
Statistical sampling
Statistics: Data Presentation and Interpretation
Single variable data
Bivariate data
Measures of average and spread
Calculations of mean and standard deviation
Outliers and cleaning data
Statistics: Probability
Mutually exclusive and independent events
Probability
Modelling with probability
Statistics: Statistical Distributions
Discrete probability distributions
The normal distribution
Selecting an appropriate distribution
Statistics: Statistical Hypothesis Testing
The language of hypothesis testing
Hypothesis test for the proportion in a binomial distribution
Hypothesis test for the mean of a normal distribution
Hypothesis test using Pearson’s correlation coefficient
Mechanics: Quantities and Units in Mechanics
SI units
Mechanics: Kinematics
Language of kinematics
Graphical representation
Constant acceleration
Non uniform acceleration
Gravity
Mechanics: Forces and Newton’s Laws
Newton’s first law
Newton’s second law
Weight
Newton’s third law
Applications of vectors in a plane
Frictional forces
Mechanics: Moments
Statics
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