Specification points
OCR A Level Further Mathematics B (MEI) H645
528 points in 10 topics, with OCR's codes and titles.
Grade boundaries·OCR command words
Codes and titles are read by a script from OCR's published specification and have not been checked by a person. What each point covers is in the specification itself: OCR’s specification.
Y420 Core Pure
- Y420.1 Core pure: proof
- Y420/Pp4 Proof by induction for formulae
- Y420/Pp5 Proof by induction for any given result
- Y420.2 Core pure: complex numbers
- Y420/Pj1 Language of complex numbers
- Y420/Pj2 Quadratics with real coefficients
- Y420/Pj3 Conjugate pairs of complex roots
- Y420/Pj4 Arithmetic with complex numbers
- Y420/Pj5 Complex number equal to zero
- Y420/Pj6 Radians and complex numbers
- Y420/Pj7 Modulus-argument form
- Y420/Pj8 Multiplying and dividing in modulus-argument form
- Y420/Pj9 Argand diagrams and conjugates
- Y420/Pj10 Sums and products on an Argand diagram
- Y420/Pj11 Loci on an Argand diagram
- Y420/Pj12 De Moivre's theorem
- Y420/Pj13 Multiple angle formulae and series by de Moivre
- Y420/Pj14 Exponential form of a complex number
- Y420/Pj15 Nth roots of a complex number
- Y420/Pj16 Formula for nth roots
- Y420/Pj17 Sum of nth roots is zero
- Y420/Pj18 Multiplication as a transformation on an Argand diagram
- Y420/Pj19 Roots of unity on an Argand diagram
- Y420/Pj20 Complex numbers in geometry
- Y420.3 Core pure: matrices and transformations
- Y420/Pm1 Adding and multiplying matrices
- Y420/Pm2 Zero, identity and equal matrices
- Y420/Pm3 Matrix multiplication: associative, not commutative
- Y420/Pm4 Matrices of linear transformations
- Y420/Pm5 Successive transformations and matrix products
- Y420/Pm6 Invariant points and lines
- Y420/Pm7 Determinants and singular matrices
- Y420/Pm8 Determinant as area scale factor
- Y420/Pm9 Determinant as volume scale factor
- Y420/Pm10 Determinant of a product
- Y420/Pm11 Inverse matrices
- Y420/Pm12 Calculating inverse matrices
- Y420/Pm13 Using inverse matrices
- Y420/Pm14 Inverse of a product of matrices
- Y420/Pm15 3 × 3 determinant and inverse without a calculator
- Y420.4 Core pure: vectors and 3-D space
- Y420/Pv1 Scalar product
- Y420/Pv2 Vector and cartesian equations of a plane
- Y420/Pv3 Normal vectors to a plane
- Y420/Pv4 Arrangements of three planes
- Y420/Pv5 Three simultaneous equations by inverse matrix
- Y420/Pv6 Angle between two planes
- Y420/Pv7 Vector product in component form
- Y420/Pv8 Alternative form of the vector product
- Y420/Pv9 Equation of a line in 2-D and 3-D
- Y420/Pv10 Angle between two lines
- Y420/Pv11 How lines in 3-D can meet or not
- Y420/Pv12 Parallel, skew or intersecting lines
- Y420/Pv13 Distances between parallel and skew lines
- Y420/Pv14 Intersection of a line and a plane
- Y420/Pv15 Angle between a line and a plane
- Y420/Pv16 Distance from a point to a line
- Y420/Pv17 Distance from a point to a plane
- Y420.5 Core pure: algebra
- Y420/Pa1 Roots and coefficients of polynomials
- Y420/Pa2 Transforming roots of equations
- Y420.6 Core pure: series
- Y420/Ps1 Summing series: standard formulae and differences
- Y420/Ps2 Summing series using partial fractions
- Y420/Ps3 Maclaurin series
- Y420/Ps4 Convergence of Maclaurin series
- Y420/Ps5 Maclaurin series of standard functions
- Y420.7 Core pure: calculus
- Y420/Pc1 Improper integrals
- Y420/Pc2 Volumes of revolution
- Y420/Pc3 Mean value of a function
- Y420/Pc4 Partial fractions in integration
- Y420/Pc5 Differentiating inverse trigonometric functions
- Y420/Pc6 Integrals giving inverse trigonometric functions
- Y420.8 Core pure: polar coordinates
- Y420/PP1 Polar coordinates
- Y420/PP2 Sketching polar curves
- Y420/PP3 Area enclosed by a polar curve
- Y420.9 Core pure: hyperbolic functions
- Y420/Pa3 Hyperbolic functions and their graphs
- Y420/Pa4 Hyperbolic identity cosh² − sinh² = 1
- Y420/Pa5 Differentiating and integrating hyperbolic functions
- Y420/Pa6 Inverse hyperbolic functions
- Y420/Pa7 Logarithmic forms of inverse hyperbolic functions
- Y420/Pa8 Integrals giving inverse hyperbolic functions
- Y420.10 Core pure: differential equations
- Y420/Pp19 Defining variables to model a situation
- Y420/Pp20 Forming differential equations from descriptions
- Y420/Pp21 Language of kinematics and relationships
- Y420/Pp22 Differential equations in modelling
- Y420/Pc7 General and particular solutions
- Y420/Pc8 When to use an integrating factor
- Y420/Pc9 Finding an integrating factor
- Y420/Pc10 Solving with an integrating factor
- Y420/Pc11 Homogeneous second order equations
- Y420/Pc12 Cases of the auxiliary equation
- Y420/Pc13 Non-homogeneous second order equations
- Y420/Pc14 Particular integrals
- Y420/Pc15 Simple harmonic motion equation
- Y420/Pc16 Damped oscillations
- Y420/Pc17 Interpreting damped oscillation models
- Y420/Pc18 Coupled differential equations
Y421 Mechanics Major
- Y421.1 Mechanics major: dimensional analysis
- Y421/Mq1 Dimensions in terms of M, L and T
- Y421/Mq2 Dimensionless quantities
- Y421/Mq3 Units from dimensions
- Y421/Mq4 Changing units
- Y421/Mq5 Checking consistency with dimensions
- Y421/Mq6 Finding unknown indices by dimensional analysis
- Y421/Mq7 Models from dimensional analysis
- Y421.2 Mechanics major: forces
- Y421/Md1 Friction and normal contact force
- Y421/Md2 Total contact force and friction
- Y421/Md3 Friction model F ≤ μR
- Y421/Md4 Body on a rough slope
- Y421/Md5 Newton's laws with friction
- Y421/Md6 Resolving forces
- Y421/Md7 Resultant of concurrent forces
- Y421/Md8 Equilibrium under concurrent forces
- Y421/Md9 Closed force figures in equilibrium
- Y421/Md10 Solving equilibrium problems
- Y421/Md11 Force diagrams for rigid bodies
- Y421/Md12 Turning effect of forces
- Y421/Md13 Couples
- Y421/Md14 Moments about an axis
- Y421/Md15 Equilibrium of a rigid body
- Y421/Md16 Sliding or toppling
- Y421.3 Mechanics major: work, energy and power
- Y421/Mw1 Language of work, energy and power
- Y421/Mw2 Work done along a line of action
- Y421/Mw3 Work done at an angle
- Y421/Mw4 Kinetic energy
- Y421/Mw5 Gravitational potential energy
- Y421/Mw6 Conservation of energy
- Y421/Mw7 Work-energy principle
- Y421/Mw8 Power as rate of doing work
- Y421.4 Mechanics major: momentum and impulse
- Y421/Mi1 Impulse as a vector
- Y421/Mi2 Linear momentum as a vector
- Y421/Mi3 Impulse-momentum equation
- Y421/Mi4 Conservation of linear momentum
- Y421/Mi5 Direct impact assumptions
- Y421/Mi6 Momentum in direct impacts
- Y421/Mi7 Newton's experimental law and coefficient of restitution
- Y421/Mi8 Perfectly inelastic impacts (e = 0)
- Y421/Mi9 Newton's experimental law in direct impacts
- Y421/Mi10 Modelling direct impacts
- Y421/Mi11 Perfectly elastic impacts (e = 1)
- Y421/Mi12 Kinetic energy loss in impacts
- Y421/Mi13 Oblique impact assumptions
- Y421/Mi14 Restitution in oblique impacts
- Y421/Mi15 Oblique impact with a smooth plane
- Y421/Mi16 Oblique impact between two bodies
- Y421/Mi17 Energy loss in oblique impacts
- Y421.5 Mechanics major: circular motion
- Y421/Mr1 Language of circular motion
- Y421/Mr2 Forces in circular motion
- Y421/Mr3 Centripetal acceleration
- Y421/Mr4 Horizontal circular motion
- Y421/Mr5 Circular motion with non-uniform speed
- Y421/Mr6 Tangential acceleration
- Y421/Mr7 Motion in a vertical circle
- Y421/Mr8 Leaving circular motion
- Y421.6 Mechanics major: Hooke’s law
- Y421/Mh1 Language of elasticity
- Y421/Mh2 Hooke's law
- Y421/Mh3 Stiffness and modulus of elasticity
- Y421/Mh4 Tension in elastic strings and springs
- Y421/Mh5 Equilibrium with elastic strings
- Y421/Mh6 Elastic potential energy
- Y421/Mh7 Energy methods with elastic strings
- Y421/Mh8 Limits of Hooke's law
- Y421.7 Mechanics major: centre of mass
- Y421/MG1 Centre of mass of particles
- Y421/MG2 Centre of mass by symmetry
- Y421/MG3 Centres of mass of standard shapes
- Y421/MG4 Centre of mass of composite bodies
- Y421/MG5 Centre of mass and equilibrium
- Y421/MG6 Volume of revolution
- Y421/MG7 Centre of mass of solids of revolution
- Y421/MG8 Centre of mass of compound solids
- Y421/MG9 Centre of mass of a lamina by calculus
- Y421/MG10 Equilibrium using centres of mass found by calculus
- Y421.8 Mechanics major: vectors and variable forces
- Y421/Mk1 Kinematics language in 2 and 3 dimensions
- Y421/Mk2 Extending kinematics to 2 and 3 dimensions
- Y421/Mv1 Motion under constant acceleration with vectors
- Y421/Mv2 Modelling with position, velocity and acceleration vectors
- Y421/Mv3 Eliminating a parameter from position vectors
- Y421/Mv4 Interpreting the path equation
- Y421/Mv5 Cartesian equation of a path
- Y421/Mv6 Range on an inclined plane
- Y421/Mv7 Maximum range on an inclined plane
- Y421/Mv8 Differential equations for variable acceleration
- Y421/Mv9 Verifying solutions for variable acceleration
- Y421/Mv10 Particular solutions from initial conditions
- Y421/Mv11 Recognising SHM in non-standard form
- Y421/Mv12 Simple harmonic motion equation
Y422 Statistics Major
- Y422.1 Statistics major: sampling
- Y422/Sx1 Sample size in experimental design
- Y422/Sx2 Why sampling is necessary
- Y422/Sx3 Advantage of random samples
- Y422.2 Statistics major: discrete random variables
- Y422/SR1 Discrete probability functions
- Y422/SR2 Expectation of a discrete variable
- Y422/SR3 Variance of a discrete variable
- Y422/SR4 Expectation of a linear function
- Y422/SR5 Variance of a linear function
- Y422/SR6 Linear combinations of independent variables
- Y422/SR7 When to use a discrete uniform model
- Y422/SR8 Discrete uniform probabilities
- Y422/SR9 Mean and variance of a discrete uniform distribution
- Y422/SR10 When to use a binomial model
- Y422/SR11 When to use a Poisson model
- Y422/SR12 Poisson and binomial as alternative models
- Y422/SR13 Poisson probabilities
- Y422/SR14 Mean and variance of a Poisson distribution
- Y422/SR15 Sum of independent Poisson variables
- Y422/SR16 When to use a geometric model
- Y422/SR17 Geometric probabilities
- Y422/SR18 Mean and variance of a geometric distribution
- Y422.3 Statistics major: bivariate data
- Y422/Sb1 Bivariate data and choice of axes
- Y422/Sb2 Scatter diagrams
- Y422/Sb3 Scatter diagrams from software
- Y422/Sb4 Calculating the pmcc
- Y422/Sb5 When to test with the pmcc
- Y422/Sb6 Hypothesis tests using the pmcc
- Y422/Sb7 The pmcc as an effect size
- Y422/Sb8 Spearman's rank correlation coefficient
- Y422/Sb9 Hypothesis tests with Spearman's coefficient
- Y422/Sb10 Choosing between r and rₛ
- Y422/Sb11 Least squares regression line
- Y422/Sb12 Using a regression line to estimate
- Y422/Sb13 Regression lines y on x and x on y
- Y422/Sb14 Checking model fit
- Y422/Sb15 Relationship between the two regression lines
- Y422.4 Statistics major: chi-squared tests
- Y422/Sb16 Contingency tables
- Y422/SH1 Chi-squared test for contingency tables
- Y422/SH2 Interpreting chi-squared contingency table results
- Y422/SH3 Chi-squared goodness of fit tests
- Y422/SH4 Interpreting chi-squared goodness of fit results
- Y422.5 Statistics major: continuous random variables
- Y422/SR19 Continuous random variables as models
- Y422/SR20 Probability density functions
- Y422/SR21 Properties and graphs of pdfs
- Y422/SR22 Mean and variance from a pdf
- Y422/SR23 Mode and median from a pdf
- Y422/SR24 Cumulative distribution functions
- Y422/SR25 Pdf from a cdf
- Y422/SR26 Median and percentiles from a cdf
- Y422/SR27 Linear combinations of random variables
- Y422/SR28 Normal distribution as a model
- Y422/SR29 Linear combinations of Normal variables
- Y422/SR30 The Normal distribution as an approximation: the Central Limit Theorem
- Y422/SR31 Normal probability plots
- Y422/SR32 Normal distribution in confidence intervals
- Y422.6 Statistics major: inference
- Y422/SI1 Estimating a population mean
- Y422/SI2 Estimating a population variance
- Y422/SI3 Sample mean as a random variable
- Y422/SI4 Standard error of the mean
- Y422/SI5 Sample mean from a Normal population
- Y422/SI6 The Central Limit Theorem
- Y422/SI7 Confidence intervals: meaning and language
- Y422/SI8 Width of a confidence interval
- Y422/SI9 Confidence interval for a population mean
- Y422/SI10 Paired samples
- Y422/SI11 Confidence interval for a paired difference
- Y422/SI12 Confidence intervals from software
- Y422/SI13 Decisions using confidence intervals
- Y422/SH5 Wilcoxon signed rank test for a median
- Y422/SH6 Test for a mean using Normal or t distribution
- Y422.7 Statistics major: simulation
- Y422/SZ1 Simulating distributions with spreadsheets
- Y422/SZ2 Simulations to estimate probabilities
Y431 Mechanics Minor
- Y431.1 Mechanics minor: dimensional analysis
- Y431/Mq1 Dimensions in terms of M, L and T
- Y431/Mq2 Dimensionless quantities
- Y431/Mq3 Units from dimensions
- Y431/Mq4 Changing units
- Y431/Mq5 Checking consistency with dimensions
- Y431/Mq6 Finding unknown indices by dimensional analysis
- Y431/Mq7 Models from dimensional analysis
- Y431.2 Mechanics minor: forces
- Y431/Md1 Friction and normal contact force
- Y431/Md2 Total contact force and friction
- Y431/Md3 Friction model F ≤ μR
- Y431/Md4 Body on a rough slope
- Y431/Md5 Newton's laws with friction
- Y431/Md6 Resolving forces
- Y431/Md7 Resultant of concurrent forces
- Y431/Md8 Equilibrium under concurrent forces
- Y431/Md9 Closed force figures in equilibrium
- Y431/Md10 Solving equilibrium problems
- Y431/Md11 Force diagrams for rigid bodies
- Y431/Md12 Turning effect of forces
- Y431/Md13 Couples
- Y431/Md14 Moments about an axis
- Y431/Md15 Equilibrium of a rigid body
- Y431/Md16 Sliding or toppling
- Y431.3 Mechanics minor: work, energy and power
- Y431/Mw1 Language of work, energy and power
- Y431/Mw2 Work done along a line of action
- Y431/Mw3 Work done at an angle
- Y431/Mw4 Kinetic energy
- Y431/Mw5 Gravitational potential energy
- Y431/Mw6 Conservation of energy
- Y431/Mw7 Work-energy principle
- Y431/Mw8 Power as rate of doing work
- Y431.4 Mechanics minor: momentum and impulse
- Y431/Mi1 Impulse as a vector
- Y431/Mi2 Linear momentum as a vector
- Y431/Mi3 Impulse-momentum equation
- Y431/Mi4 Conservation of linear momentum
- Y431/Mi5 Direct impact assumptions
- Y431/Mi6 Momentum in direct impacts
- Y431/Mi7 Newton's experimental law and coefficient of restitution
- Y431/Mi8 Perfectly inelastic impacts (e = 0)
- Y431/Mi9 Newton's experimental law in direct impacts
- Y431/Mi10 Modelling direct impacts
- Y431/Mi11 Perfectly elastic impacts (e = 1)
- Y431/Mi12 Kinetic energy loss in impacts
- Y431.5 Mechanics minor: centre of mass
- Y431/MG1 Centre of mass of particles
- Y431/MG2 Centre of mass by symmetry
- Y431/MG3 Centres of mass of standard shapes
- Y431/MG4 Centre of mass of composite bodies
- Y431/MG5 Centre of mass and equilibrium
Y432 Statistics Minor
- Y432.1 Statistics minor: sampling
- Y432/Sx1 Sample size in experimental design
- Y432/Sx2 Why sampling is necessary
- Y432/Sx3 Advantage of random samples
- Y432.2 Statistics minor: discrete random variables
- Y432/SR1 Discrete probability functions
- Y432/SR2 Expectation of a discrete variable
- Y432/SR3 Variance of a discrete variable
- Y432/SR4 Expectation of a linear function
- Y432/SR5 Variance of a linear function
- Y432/SR6 Linear combinations of independent variables
- Y432/SR7 When to use a discrete uniform model
- Y432/SR8 Discrete uniform probabilities
- Y432/SR9 Mean and variance of a discrete uniform distribution
- Y432/SR10 When to use a binomial model
- Y432/SR11 When to use a Poisson model
- Y432/SR12 Poisson and binomial as alternative models
- Y432/SR13 Poisson probabilities
- Y432/SR14 Mean and variance of a Poisson distribution
- Y432/SR15 Sum of independent Poisson variables
- Y432/SR16 When to use a geometric model
- Y432/SR17 Geometric probabilities
- Y432/SR18 Mean and variance of a geometric distribution
- Y432.3 Statistics minor: bivariate data
- Y432/Sb1 Bivariate data and choice of axes
- Y432/Sb2 Scatter diagrams
- Y432/Sb3 Scatter diagrams from software
- Y432/Sb4 Calculating the pmcc
- Y432/Sb5 When to test with the pmcc
- Y432/Sb6 Hypothesis tests using the pmcc
- Y432/Sb7 The pmcc as an effect size
- Y432/Sb8 Spearman's rank correlation coefficient
- Y432/Sb9 Hypothesis tests with Spearman's coefficient
- Y432/Sb10 Choosing between r and rₛ
- Y432/Sb11 Least squares regression line
- Y432/Sb12 Using a regression line to estimate
- Y432/Sb13 Regression lines y on x and x on y
- Y432/Sb14 Checking model fit
- Y432/Sb15 Relationship between the two regression lines
- Y432.4 Statistics minor: chi-squared tests
- Y432/Sb16 Contingency tables
- Y432/SH1 Chi-squared test for contingency tables
- Y432/SH2 Interpreting chi-squared contingency table results
- Y432/SH3 Chi-squared goodness of fit tests
- Y432/SH4 Interpreting chi-squared goodness of fit results
Y433 Modelling with Algorithms
- Y433.1 Modelling with algorithms: algorithms
- Y433/AA1 What an algorithm is
- Y433/AA2 Interpreting algorithms in different formats
- Y433/AA3 Repairing and adapting algorithms
- Y433/AA4 Algorithmic complexity
- Y433/AA5 Proving algorithms correct or incorrect
- Y433/AA6 Heuristics
- Y433/AA7 Quick sort and other sorting algorithms
- Y433/AA8 Counting comparisons and swaps in sorting
- Y433/AA9 Reasoning about sorting algorithms
- Y433/AA10 Bin packing algorithms
- Y433/AA11 Comparisons in packing algorithms
- Y433.2 Modelling with algorithms: networks
- Y433/AN1 Graphs and their language
- Y433/AN2 Modelling with graphs
- Y433/AN3 Networks as weighted graphs
- Y433/AN4 Modelling with networks
- Y433/AN5 Kruskal's and Prim's algorithms
- Y433/AN6 Dijkstra's algorithm
- Y433/AN7 Complexity of network algorithms
- Y433/AN8 Activity-on-arc networks
- Y433/AN9 Critical path analysis
- Y433/AN10 Networks as transmission systems
- Y433/AN11 Cuts and their capacity
- Y433/AN12 Maximum flow/minimum cut theorem
- Y433/AN13 Exploring network algorithms with software
- Y433.3 Modelling with algorithms: linear programming
- Y433/AL1 Language of linear programming
- Y433/AL2 Formulating linear programmes
- Y433/AL3 Standard form of an LP
- Y433/AL4 Slack variables and augmented form
- Y433/AL5 Integer solutions to LPs
- Y433/AL6 Network problems as LPs
- Y433/AL7 Feasible regions in 2-D
- Y433/AL8 Graphical solution of 2-D LPs
- Y433/AL9 Modifying constraints or objective
- Y433/AL10 Integer LPs solved graphically
- Y433/AL11 Visualising 3-D LPs
- Y433/AL12 The simplex algorithm
- Y433/AL13 Geometric basis of the simplex method
- Y433/AL14 Two-stage simplex method
- Y433/AL15 Equality constraints as two inequalities
- Y433/AL16 Negative variables and minimisation in LPs
- Y433/AL17 Methods for solving large LPs
- Y433/AL18 Interpreting LP software output
Y434 Numerical Methods
- Y434.1 Numerical methods: use of technology
- Y434/NQ1 Spreadsheets for numerical methods
- Y434/NQ2 Iterating with a calculator
- Y434.2 Numerical methods: errors
- Y434/NU1 Errors in arithmetic operations
- Y434/NU2 Error in a function of x
- Y434/NU3 Order of operations and errors
- Y434/NU4 Limited precision in computers
- Y434/NU5 Subtracting nearly equal quantities
- Y434/NU6 Rounding and chopping
- Y434/NU7 Convergence and order of convergence
- Y434/NU8 Error analysis to improve solutions
- Y434.3 Numerical methods: solution of equations
- Y434/Ne1 Graphs of root-finding methods
- Y434/Ne2 Solving equations to required accuracy
- Y434/Ne3 Merits and failures of root-finding methods
- Y434/Ne4 Order of convergence of iterations
- Y434/Ne5 Relaxation of fixed point iteration
- Y434.4 Numerical methods: numerical differentiation
- Y434/Nc1 Forward and central difference estimates
- Y434/Nc2 Accuracy of central differences
- Y434.5 Numerical methods: numerical integration
- Y434/Nc3 Numerical integration to required accuracy
- Y434/Nc4 Order of midpoint, trapezium and Simpson's rules
- Y434.6 Numerical methods: approximations to functions
- Y434/Nf1 Newton's forward difference interpolation
- Y434/Nf2 Interpolating polynomials
Y435 Extra Pure
- Y435.1 Extra pure: recurrence relations
- Y435/Xs1 Modelling with recurrence relations
- Y435/Xs2 Language of recurrence relations
- Y435/Xs3 Long-run behaviour of recurrence relations
- Y435/Xs4 Verifying solutions of recurrences
- Y435/Xs5 First order homogeneous recurrences
- Y435/Xs6 First order non-homogeneous recurrences
- Y435/Xs7 Second order homogeneous recurrences
- Y435/Xs8 Second order non-homogeneous recurrences
- Y435/Xs9 Properties of solutions of recurrences
- Y435.2 Extra pure: groups
- Y435/XS1 Language and notation of sets
- Y435/XS2 Sets of numbers and their properties
- Y435/Xa1 Group axioms and language
- Y435/Xa2 Examples of groups and group tables
- Y435/Xa3 Cyclic groups and generators
- Y435/Xa4 Order of a group and of an element
- Y435/Xa5 Subgroups
- Y435/Xa6 Lagrange's theorem
- Y435/Xa7 Same underlying structure in different situations
- Y435/Xa8 Isomorphisms between groups
- Y435.3 Extra pure: matrices
- Y435/Xm1 Eigenvalues and eigenvectors
- Y435/Xm2 Characteristic equation of a matrix
- Y435/Xm3 Diagonalising a matrix
- Y435/Xm4 Powers of a matrix by diagonal form
- Y435/Xm5 Cayley–Hamilton theorem
- Y435/Xm6 Eigenvectors in transformations
- Y435.4 Extra pure: multivariable calculus
- Y435/Xc1 Surfaces defined by z = f(x, y)
- Y435/Xc2 Contours and sections of surfaces
- Y435/Xc3 First order partial derivatives
- Y435/Xc4 Partial derivatives and their notation
- Y435/Xc5 Surfaces defined by g(x, y, z) = c
- Y435/Xc6 Grad and normal vectors
- Y435/Xc7 Normal lines and tangent planes
Y436 Further Pure with Technology
- Y436.1 Further pure with technology: investigation of curves
- Y436/TC1 Plotting families of curves with software
- Y436/TC2 Using CAS with curves
- Y436/TC3 Vocabulary of curves
- Y436/TC4 Properties of curves
- Y436/TC5 Converting cartesian, polar and parametric forms
- Y436/TC6 Gradient of a tangent to a curve
- Y436/TC7 Chords, tangents and normals
- Y436/TC8 Arc length
- Y436/TC9 Envelopes of families of curves
- Y436/TC10 Limits and properties of curves
- Y436/TC11 Asymptotes
- Y436/TC12 Cusps
- Y436.2 Further pure with technology: exploring differential equations
- Y436/Tc1 Software solutions of differential equations
- Y436/Tc2 Tangent fields from software
- Y436/Tc3 Spreadsheets for differential equations
- Y436/Tc4 Verifying solutions of differential equations
- Y436/Tc5 Particular solutions and families
- Y436/Tc6 Sketching tangent fields
- Y436/Tc7 Step-by-step numerical solution of differential equations
- Y436/Tc8 Step length and accuracy
- Y436/Tc9 Runge–Kutta methods: underlying ideas
- Y436/Tc10 Solving with Runge–Kutta methods
- Y436.3 Further pure with technology: number theory
- Y436/TT1 Programs for number theory problems
- Y436/TT2 Limitations of short programs
- Y436/TT3 Unique prime factorisation
- Y436/TT4 Modular arithmetic
- Y436/TT5 Fermat's little theorem
- Y436/TT6 Euler's totient function and theorem
- Y436/TT7 Wilson's theorem
- Y436/TT8 Pythagorean triples
- Y436/TT9 Pell's equation
- Y436/TT10 Other Diophantine equations