Integral Section List for OCR Specification

Transcription

1 Integral Section List for OCR Specification 161 Sections are listed below, covering all of AS/A level Mathematics and Further Mathematics, categorised by Module and Topic Module Topic Section Name OCR Core 1 Algebra Quadratics Inequalities Polynomials Coordinate geometry Points and straight lines Circles Differentiation Graphs of nth power functions Investigating shapes of curves Applications of differentiation Graphs and transformations Some important graphs Graphs and transformations Transforming graphs Revision Topics GCSE revision Surds and indices Surds Indices OCR Core 2 Algebra Exponentials and logarithms Factors and remainders Integration Finding areas The trapezium rule Series Sequences Arithmetic sequences and series Geometric sequences and series The binomial expansion Trigonometry Trigonometric functions and graphs Identities and equations The sine and cosine rules Radians

2 OCR Core 3 Algebra and functions Successive transformations Functions Exponential growth and decay The modulus function Differentiation and integration Extending the techniques Exponentials and logarithms The chain rule The product and quotient rules Volumes of revolution Numerical methods Solving equations numerically Simpson's rule Trigonometry Trigonometric functions and identities Further trigonometric equations OCR Core 4 Algebra The binomial expansion Rational functions and algebraic division Partial fractions Differential equations Forming and solving differential equations Differentiation and integration Trigonometric functions Implicit differentiation Integration techniques Integration by parts Integration by substitution or inspection Parametric equations Using parametric equations Parametric differentiation Vectors Vectors in two and three dimensions Scalar products OCR Decision 1 Algorithms Sorting algorithms Packing algorithms Further networks The route inspection problem The travelling salesperson problem Graphs Definitions and problem solving Linear programming Formulating and solving graphically The simplex method Networks Minimum connector problems Shortest paths OCR Decision 2 Critical path analysis Critical paths Resource allocation Dynamic programming to dynamic programming Game theory to game theory Matchings Matching problems Allocation problems Network flows Maximising flow in a network Extending the labelling procedure

3 OCR Further Pure 1 Complex numbers Matrices Roots of polynomials Series and induction OCR Further Pure 2 Calculus Hyperbolic functions Maclaurin series Numerical methods Polar coordinates Rational functions OCR Further Pure 3 Complex numbers Differential equations Groups Vectors Equations and geometrical representation Modulus and argument Determinants and inverses of 2x2 matrices Matrix transformations Determinants and inverses of 3x3 matrices Quadratic and cubic equations Summing series Mathematical induction Inverse trigonometric functions Integration using trigonometric functions Reduction formulae to hyperbolic functions The inverse hyperbolic functions Finding and using Maclaurin series Series and integrals Solving equations Polar coordinates and curves The area of a sector Partial fractions Graphs of rational functions Further graphs The polar and exponential forms de Moivre's theorem Complex numbers and trigonometry First order differential equations Second order equations More second order equations to groups Subgroups Isomorphisms Lines and planes The vector product Using the vector product

4 OCR Mechanics 1 Force in one dimension Horizontal motion Vertical motion Motion under gravity Force in two dimensions Resolving forces Friction Force using vectors Combining and splitting forces General motion in a straight line Using calculus Interacting objects Newton's third law Momentum Velocity and acceleration Using graphs Constant acceleration OCR Mechanics 2 Centres of mass Finding the centre of mass Centres of mass of special shapes Circular motion Motion in a horizontal circle Impulse and restitution Newton's law of impact Rigid bodies Moments Rigid bodies in equililbrium The motion of projectiles General equations OCR Mechanics 3 Circular motion Circular motion with variable speed Elastic strings and springs Hooke's law Work and energy Impulse and momentum Working in two dimensions Linear motion with variable forces Differential equations Oscillations Simple harmonic motion Mechanical oscillations Small oscillations of a simple pendulum Rigid bodies Systems of rigid bodies OCR Statistics 1 Correlation and regression Correlation Regression Discrete random variables Probability distributions The binomial and geometric distributions Expectation and variance Probability Introducing probability Permutations and combinations Working with data Representing data Measures of location Measures of spread

5 OCR Statistics 2 Continuous random variables Probability density functions Expectation and variance Hypothesis tests Sampling Continuous variables Discrete variables Errors in hypothesis testing The normal distribution More on the normal distribution The Poisson distribution Approximating distributions OCR Statistics 3 Chi-squared tests Testing for goodness of fit Contingency tables Confidence intervals and tests Confidence intervals Using the t-distribution Continuous random variables Distribution functions Functions of variables Linear combinations Two or more random variables Testing for differences Tests on unpaired samples Tests and confidence intervals