Specification points
OCR A-level Mathematics A H240
236 points in 7 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.
OT1 Mathematical argument, language and proof
OT2 Mathematical problem solving
- OT2.1 Recognising mathematical structure in problems
- OT2.2 Extended arguments for unstructured problems
- OT2.3 Interpreting solutions in context
- OT2.4 Numerical methods where analytic solution fails
- OT2.5 Evaluating accuracy and limitations of solutions
- OT2.6 The problem-solving cycle
- OT2.7 Using and constructing mathematical diagrams
OT3 Mathematical modelling
1 Pure Mathematics
- 1.01 Proof
- 1.01a Proof
- 1.01b Logical connectives
- 1.01c Disproof by counter-example
- 1.01d Proof by contradiction
- 1.02 Algebra and Functions
- 1.02a Indices
- 1.02b Surds
- 1.02c Simultaneous equations
- 1.02d Quadratic functions
- 1.02e Completing the square
- 1.02f Solving quadratic equations
- 1.02g Inequalities
- 1.02h Expressing solutions with 'and', 'or' and set notation
- 1.02i Graphs of linear and quadratic inequalities
- 1.02j Polynomials
- 1.02k Simplifying rational expressions
- 1.02l The modulus function
- 1.02m Curve sketching
- 1.02n Sketching polynomial curves
- 1.02o Sketching reciprocal curves and asymptotes
- 1.02p Interpreting solutions graphically
- 1.02q Solving equations with intersection points
- 1.02r Proportional relationships and graphs
- 1.02s Graph of the modulus of a linear function
- 1.02t Modulus equations and inequalities graphically
- 1.02u Functions
- 1.02v Inverse and composite functions
- 1.02w Graph transformations
- 1.02x Combinations of graph transformations
- 1.02y Partial fractions
- 1.02z Models in context
- 1.03 Coordinate Geometry in the x–y Plane
- 1.03a Straight lines
- 1.03b Parallel and perpendicular lines
- 1.03c Straight-line models
- 1.03d Circles
- 1.03e Centre and radius of a circle
- 1.03f Circle properties in coordinate geometry
- 1.03g Parametric equations of curves
- 1.03h Parametric equations in context
- 1.04 Sequences and Series
- 1.04a Binomial expansion
- 1.04b Link to binomial probabilities
- 1.04c Binomial expansion for rational powers
- 1.04d Validity of the binomial expansion
- 1.04e Sequences
- 1.04f Increasing, decreasing and periodic sequences
- 1.04g Sigma notation
- 1.04h Arithmetic sequences
- 1.04i Geometric sequences
- 1.04j Sum to infinity of a geometric series
- 1.04k Modelling
- 1.05 Trigonometry
- 1.05a sin, cos and tan for all arguments
- 1.05b Sine and cosine rules
- 1.05c Area of a triangle using sine
- 1.05d Radians, arc length and sector area
- 1.05e Small angle approximations
- 1.05f Graphs of the basic trigonometric functions
- 1.05g Exact trigonometric values
- 1.05h Inverse and reciprocal trigonometric ratios
- 1.05i Graphs of inverse and reciprocal trigonometric functions
- 1.05j Trigonometric identities
- 1.05k Identities with sec, cosec and cot
- 1.05l Further trigonometric identities
- 1.05m Geometric proofs of trigonometric formulae
- 1.05n Harmonic form: R cos(θ ± α)
- 1.05o Trigonometric equations
- 1.05p Proof involving trigonometric functions
- 1.05q Trigonometric functions in context
- 1.06 Exponentials and Logarithms
- 1.06a Properties of the exponential function
- 1.06b Gradient of eᵏˣ
- 1.06c Properties of the logarithm
- 1.06d The function ln x and its graph
- 1.06e ln x as the inverse of eˣ
- 1.06f Laws of logarithms
- 1.06g Equations involving exponentials
- 1.06h Reduction to linear form
- 1.06i Modelling using exponential functions
- 1.07 Differentiation
- 1.07a Gradients
- 1.07b Gradient of a tangent as a limit
- 1.07c Sketching the gradient function
- 1.07d Second derivatives
- 1.07e Second derivative as rate of change of gradient
- 1.07f Convex and concave curves
- 1.07g Differentiation from first principles
- 1.07h Differentiating sin x and cos x from first principles
- 1.07i Differentiation of standard functions
- 1.07j Differentiating exponentials
- 1.07k Differentiating trigonometric functions
- 1.07l Derivative of ln x
- 1.07m Tangents, normals, stationary points, increasing and decreasing functions
- 1.07n Stationary points: maxima and minima
- 1.07o Increasing and decreasing functions
- 1.07p Points of inflection
- 1.07q Techniques of differentiation
- 1.07r The chain rule and connected rates of change
- 1.07s Parametric and implicit differentiation
- 1.07t Constructing differential equations
- 1.08 Integration
- 1.08a Fundamental theorem of calculus
- 1.08b Indefinite integrals
- 1.08c Integrating exponentials and trigonometric functions
- 1.08d Definite integrals and areas
- 1.08e Area between a curve and the x-axis
- 1.08f Area between two curves
- 1.08g Integration as the limit of a sum
- 1.08h Integration by substitution
- 1.08i Integration by parts
- 1.08j Use of partial fractions in integration
- 1.08k Differential equations with separable variables
- 1.08l Interpreting the solution of a differential equation
- 1.09 Numerical Methods
- 1.09a Sign change methods
- 1.09b Failure of change of sign methods
- 1.09c Formal iterative methods
- 1.09d Newton–Raphson and other recurrence methods
- 1.09e Failure of iterative methods
- 1.09f Numerical integration
- 1.09g Use numerical methods in context
- 1.10 Vectors
- 1.10a Vectors
- 1.10b Vectors in three dimensions
- 1.10c Magnitude and direction of vectors
- 1.10d Basic operations on vectors
- 1.10e Position vectors
- 1.10f Distance between points
- 1.10g Problem solving using vectors
- 1.10h Vectors in kinematics
2 Statistics
- 2.01 Statistical Sampling
- 2.01a Statistical sampling
- 2.01b Informal inference from samples
- 2.01c Sampling techniques
- 2.01d Choosing and critiquing sampling techniques
- 2.02 Data Presentation and Interpretation
- 2.02a Single variable data
- 2.02b Area in a histogram as frequency
- 2.02c Bivariate data
- 2.02d Informal interpretation of correlation
- 2.02e Correlation does not imply causation
- 2.02f Measures of average and spread
- 2.02g Calculations of mean and standard deviation
- 2.02h Outliers and cleaning data
- 2.02i Choosing data presentation techniques
- 2.02j Dealing with missing data, errors and outliers
- 2.03 Probability
- 2.03a Mutually exclusive and independent events
- 2.03b Probability
- 2.03c Conditional probability
- 2.03d Conditional probability from first principles
- 2.03e Modelling with probability
- 2.04 Statistical Distributions
- 2.04a Discrete probability distributions
- 2.04b Binomial distribution as a model
- 2.04c Binomial probabilities with a calculator
- 2.04d Normal approximation parameters
- 2.04e The normal distribution
- 2.04f Normal distribution probabilities with a calculator
- 2.04g Normal distribution, histograms, mean and standard deviation
- 2.04h Selecting an appropriate distribution
- 2.05 Statistical Hypothesis Testing
- 2.05a The language of hypothesis testing
- 2.05b Hypothesis test for the proportion in a binomial distribution
- 2.05c Samples, inference and significance level
- 2.05d Hypothesis test for the mean of a normal distribution
- 2.05e Carrying out and interpreting a normal mean test
- 2.05f Hypothesis test using Pearson’s correlation coefficient
- 2.05g Hypothesis tests with Pearson's correlation coefficient
3 Mechanics
- 3.01 Quantities and Units in Mechanics
- 3.01a SI units
- 3.01b Derived quantities and units
- 3.01c Unit for moment
- 3.02 Kinematics
- 3.02a Language of kinematics
- 3.02b Graphical representation
- 3.02c Displacement–time and velocity–time graphs
- 3.02d Constant acceleration
- 3.02e Constant acceleration formulae with vectors
- 3.02f Non uniform acceleration
- 3.02g Calculus with vectors in two dimensions
- 3.02h Gravity
- 3.02i Projectile motion model and its limitations
- 3.03 Forces and Newton’s Laws
- 3.03a Newton’s first law
- 3.03b Applying Newton's first law
- 3.03c Newton’s second law
- 3.03d Newton's second law with vector forces
- 3.03e Newton's second law with resolved forces
- 3.03f Weight
- 3.03g Gravitational acceleration g
- 3.03h Newton’s third law
- 3.03i Normal reaction force
- 3.03j Smooth contact model
- 3.03k Equilibrium and straight-line motion problems
- 3.03l Newton's third law with resolved forces
- 3.03m Equilibrium of a particle
- 3.03n Equilibrium problems in two dimensions using vectors
- 3.03o Connected particles and smooth pulleys
- 3.03p Applications of vectors in a plane
- 3.03q Motion in a plane under a variable force
- 3.03r Frictional forces
- 3.03s Contact force between rough surfaces
- 3.03t Coefficient of friction
- 3.03u Static equilibrium on a rough surface
- 3.03v Motion on a rough surface
- 3.04 Moments
- 3.04a Statics
- 3.04b Equilibrium of a rigid body
- 3.04c Moments in static contexts