Maths (Year 12)
See Year 12s Maths ‘Schedule of Learning’ for the 2025/26 academic year
| Topic Pure & Mechanics | Sub-topic | Topic Pure & Statistics | Sub-topic |
|---|---|---|---|
| Quadratics | – Factorising quadratics and solving equations – Quadratic Graphs – The discriminant – Completing the square | Algebraic Expressions | – Algebraic Manipulation – Laws of Indices – Manipulation of Surds |
| Equations and Inequalities | – Solve simultaneous equations linear and quadratic – Solve linear and quadratic inequalities, including in set notation – Interpret and represent linear and quadratic inequalities graphically | Algebraic Methods | – Use algebraic division – Know and apply the factor theorem -Fully factorise a cubic expression -Construct mathematical proofs using algebra |
| Graphs and Transformations | -Sketch cubic, quartic and reciprocal graphs – Use intersection points of graphs to solve | Algebraic Methods | – use methods of proof including by deduction, exhaustion and disproof by counter-example |
| Graphs and Transformations | – Transformations of graphs | The Binomial Expansion | – use Pascal’s triangle to find coefficients – use combinations and factorial notation – understand and be able to use the binomial expansion of (a + bx)n for positive integer n – be able to find an unknown coefficient of a binomial expansion. |
| Vectors | – use vectors in 2D -Calculate the magnitude and direction of a vector -use vectors to solve geometric problems and problems in context | The Binomial Expansion | – be able to find an unknown coefficient of a binomial expansion. ‘-Understand and use the equation of a straight line -Form the equation of a straight line |
| Vectors | -understand and be able to use position vectors -be able to calculate the distance between two points represented by position vectors -be able to use vectors to solve problems in pure mathematics and in context, (including forces). | Straight Line Graphs | -Understand and use the equation of a straight line -Form the equation of a straight line -Parallel and Perpendicular lines |
| Differentiation | -understand differentiation from first principles for small positive integer powers of x -Use the derivative to solve problems involving gradients, tangents and normals -be able to find the second derivative of a function | Straight Line Graphs | -Be able to use straight line models in a variety of contexts |
| Differentiation | -be able to sketch the gradient function for a given curve -find stationary points of a function and determine their nature | Data Collection | -This topic should be taught using the large data set as it is important students are really familiar with the data included in it. -understand and be able to use the terms ‘population’ and ‘sample’ -know how to use samples to make informal inferences about the population -be able to describe advantages and disadvantages of sampling compared to census -understand and be able to use sampling techniques |
| Differentiation | -model real life situations with differentiation | Data Collection | -be able to describe advantages and disadvantages of sampling techniques -be able to select or critique sampling techniques in the context of solving a statistical problem -understand that different samples can lead to different conclusions about the population |
| Integration | -be able to integrate x^n (excluding n = −1), and related sums, differences and constant multiples. -be able to evaluate definite integrals | Measures of Location and Spread | -Measures of Central Tendency including Mean, Median and Mode -Measures of Location including quartiles and percentiles -Measures of Spread including range, IQR and IPR -Variance and Standard Deviation -Coding -Students are expected to know the different notation for population summary statistics (μ,σ^2,σ) and sample summary statistics (x ̄,s^2,s) |
| Integration | -be able to use a definite integral to find the area under a curve. | Representations of Data and Correlation | -Calculate and interpret outliers -Box Plots and cumulative frequency diagrams -Histograms -Comparing data |
| Exponentials and Logarithms | -Sketch graphs of the form y=a^x , y=e^x and complete transformations of these graphs -Differentiate e^kx and understand why this result is important -Use and interpret models that use exponential functions -know and be able to use the function ln x and its graph | Representations of Data and Correlation | -Draw and interpret scatter diagrams – Interpret correlation and causation -Interpret coefficients of a linear regression line -Understand when a regression line can be used for predictions |
| Exponentials and Logarithms | -understand and use the laws of logarithms -be able to solve equations of the form a^x=b -be able to use logarithmic graphs to estimate parameters in relationships of the form y=ax^n and y=kb^x, given data for x and y -understand and be able to use exponential growth and decay in modelling, giving consideration to limitations and refinements of exponential models | Circles | -find the midpoint of a line segment -Understand and use the equation of a circle – Find points of intersection between a line and circle – know and use the properties of chords and tangents |
| Modelling in Mechanics | -understand the concept of a mathematical model. -be familiar with commonly-made assumptions when using mechanical models -Know SI units quantities and derived quantities used in Mechanics -Know the difference between scalar and vector quantities | Circles | – Use circle properties to solve problems on coordinate grids |
| Constant Acceleration | -Understand and interpret displacement – time graphs -Understand and interpret velocity-time graphs -Derive the constant acceleration formulae and use them solve problems -Use the constant acceleration formulae to solve problems involving vertical motion under gravity | Trigonometric Ratios | -Use the cosine and sine rules -When using the sine rule the ambiguous case should be covered. – Area of a triangle using the sine rule – understand and be able to use the sine, cosine and tangent functions; their graphs, symmetries and periodicity. |
| Constant Acceleration | -recognise when it is appropriate to use the suvat formulae for constant acceleration; -be able to solve kinematics problems using constant acceleration formulae | Trigonometric Ratios | -Area of a triangle using the sine rule – understand and be able to use the sine, cosine and tangent functions; their graphs, symmetries and periodicity. |
| Constant Acceleration | -be able to solve problems involving vertical motion under gravity. | Trigonometric Identities and Equations | – be able to solve trigonometric equations within a given interval -understand and be able to use tanθ = cosθ/sinθ -Understand and use sin²θ + cos²θ = 1 |
| Forces and Motion | -Draw force diagrams and calculate resultant forces -understand the concept of a force; understand and use Newton’s first law. -understand and be able to use Newton’s second law | Trigonometric Identities and Equations | – be able to solve trigonometric equations within a given interval |
| Forces and Motion | –understand and use Newton’s third law; -Solve problems involving connected particles | Probability | -understand and be able to use mutually exclusive and independent events when calculating probabilities; -be able to make links to discrete and continuous distributions. |
| Variable Acceleration | -be able to use calculus in kinematics to model motion in a straight line for a particle moving with variable acceleration. -understand that gradients of the relevant graphs link to rates of change -know how to find max and min velocities by considering zero gradients and understand how this links with the actual motion (i.e. acceleration = 0). | Statistical Distributions | -understand and be able to use simple, discrete probability distributions, including the binomial distribution; -be able to identify the discrete uniform distribution; -be able to calculate probabilities using the binomial distribution. |
| Variable Acceleration | -be able to use calculus in kinematics to model motion in a straight line for a particle moving under the action of a variable force -understand that the area under a graph is the integral, which leads to a physical quantity -know how to use initial conditions to calculate the constant of integration and refer back to the problem | Hypothesis Testing | -understand and be able to apply the language of statistical hypothesis testing, developed through a binomial model. -understand that a sample is being used to make an inference about the population; -appreciate that the significance level is the probability of incorrectly rejecting the null hypothesis |
| Revision | Hypothesis Testing | -be able to conduct a statistical hypothesis test for the proportion in the binomial distribution and interpret the results in context | |
| Algebraic Methods | -Understand and use proof by contradiction and deduction -Simplify algebraic fractions -Four operations with alegbraic fractions -Convert an impartial fraction into Partial fraction form | Functions and Graphs | –understand what is meant by a modulus of a linear function -be able to sketch graphs of functions involving modulus functions -be able to solve equations and inequalities involving modulus functions -be able to work out the domain and range of functions; -know the definition of a one-one and a many-one mappings; |
| Algebraic Methods and Start Sequences and Series | -Use algebraic division and equating coefficients -understand what is meant by a modulus of a linear function -be able to sketch graphs of functions involving modulus functions -be able to solve equations and inequalities involving modulus functions | Functions and Graphs | -be able to work out the inverse of a function and sketch its graph; -understand the condition for an inverse function to exist. |
| Sequences and Series | -Find the nth term of an arithmetic sequence -Prove and use the formula for the sum of the first n terms of an arithmetic series – Find the nth term of a geometric sequence -Prove and use the formula for the sum of a finite geometric series | Functions and Graphs | -Apply a combination of two (or more) transformations to the same curve -use functions in modelling, including consideration of limitations and refinements of the models. |
| Sequences and Series | – Prove and use the formula for the sum to infinity of a convergent geometric series -Use sigma notation to describe series -Generate sequences from recurrence relations -Model real-life situations with sequences and series | Binomial Expansion | -Expand for any rational constant and determine the range of values for which the expansion is valid – Use partial fractions to expand fractional expressions |
| Radians | – Convert between degrees and radians and apply this to trigonometric graphs and their transformations -Know exact values of angles measured in radians -Find an arc length using radians -Find areas of sectors and segments using radians -Solve trigonometric equations in radians -Use approximate trigonometric values when is small | Numerical Methods | -be able to locate roots of f(x) = 0 by considering changes of sign of f(x); -be able to use numerical methods to find solutions of equations. -understand the principle of iteration; and the need for convergence -be able to use iteration to find terms in a sequence; -be able to sketch cobweb and staircase diagrams; -be able to use cobweb and staircase diagrams to demonstrate convergence or divergence for equations of the form x = g(x). |
| Radians | – Solve trigonometric equations in radians -understand and be able to use the standard small angle approximations for sine, cosine and tangent. | Numerical Methods | -be able to sketch cobweb and staircase diagrams and demonstrate convergence or divergence for equations of the form x = g(x). -be able to solve equations approximately using the Newton-Raphson method -be able to use numerical methods to solve problems in context. |
Exam Board – Edexcel
What will you study?
Units in Algebra, Trigonometry, Statistics and Mechanics
Units in Calculus, Algebra, Trigonometry, Probability and Mechanics
Units in Calculus, Algebra, Trigonometry, Probability and Mechanics
Useful tips and resources
The Year 12 Curriculum covers aspects of Pure Mathematics, Statistics and Mechanics; it’s aim is to build on and extend the work studied at GCSE, as well as introducing new topics. A large part of the Year 12 curriculum centres on modelling and applying Mathematics to real world problems. At A Level, practice is key; we would expect you to spend 10 hours a week including lesson time and homework to be successful at A Level.
Dr Frost Maths
MME Revise
Save My Exams
Physics and Maths Tutor
What super curricular activities can KS5 students engage with at school for your subject?
UKMT Senior Maths Challenge
Hans Woyda Club – Autumn Term
Maths Stretch and Challenge – nrich.maths.org
The Winton Gallery – The Science Museum, London
The Bank of England – Financial History
Bletchley Park – Coding and Alan Turing
The History of Science Museum in Oxford