Component 1 and 2: Pure Mathematics
Proof, Algebra and functions, Coordinate geometry in the (x,y) plane, Sequences and series, Trigonometry, Exponentials and logarithms, Differentiation, Integration, Numerical methods, Vectors.
Component 3
Section A: Statistics
Statistical sampling, Data presentation and interpretation, Probability, Statistical distributions, Statistical hypothesis testing.
Section B: Mechanics
Quantities and units in mechanics, Kinematics, Forces and Newton’s laws and Moments.
| Component | Assessment | Duration | Weighting |
|---|---|---|---|
| 1: Pure Mathematics 1 | Written exam | 2h | 33.3% |
| 2: Pure Mathematics 2 | Written exam | 2h | 33.3% |
| 3: Statistics and Mechanics | Written exam | 2h | 33.3% |
Year 12
Half Term 1 (Sept-Nov)
Half Term 2 (Nov – Dec)
Half Term 3 (Jan – Feb)
Half Term 4 (Feb – March)
Half Term 5 (April – May)
Half Term 6 (May – July)
Half Term 1 (Sept-Nov)
Focus and Topic
- Algebra and Functions
Core Knowledge
- Algebraic Expressions
- Quadratics
- Equations and Inequalities
Core Skills
- Manipulate algebraic expressions: expand, factorise, simplify
- Apply laws of indices and work with surds, including rationalising denominators
- Solve quadratic equations by:
factorising, completing the square, quadratic formula - Understand and use the discriminant
- Sketch and interpret quadratic graphs
- Solve linear and quadratic inequalities, representing solutions graphically
- Solve simultaneous equations (linear-linear and linear-quadratic)
- Apply graph transformations and interpret intersections
- Model and solve real-world problems using algebra and quadratics
- Develop core algebraic reasoning and problem-solving skills
Assessment
- Students will be assessed on their ability to manipulate algebraic expressions accurately, including using indices and surds. They must solve quadratic equations using various methods and interpret the discriminant.
- Sketching and interpreting quadratic graphs, solving inequalities (both linear and quadratic), and representing solutions graphically will also be assessed.
- Students should demonstrate competence in solving simultaneous equations, particularly linear-quadratic combinations.
- Understanding and applying basic graph transformations, as well as interpreting points of intersection, will form part of the assessment.
- Overall, the focus will be on algebraic fluency, graphical understanding, and problem-solving using these core techniques.
- Edexcel Unit Test
Half Term 2 (Nov – Dec)
Focus and Topic
Graphs and Functions
Core Knowledge
- Cubic functions (y = ax³ + bx² + cx + d)
- Quartic functions (y = ax⁴ + bx³ + cx² + dx + e)
- Reciprocal functions (y = a/x and y = a/x²)
- Asymptotes (vertical and horizontal)
- Points of intersection (f(x) = g(g))
- Effect of transformations on coordinates and asymptotes • Equations of lines: y = mx + c, ax + by + c = 0, and y – y₁ = m(x – x₁)
- Gradient formula: m = (y₂ – y₁) / (x₂ – x₁)
- Distance formula: d = √[(x₂-x₁)² + (y₂-y₁)²]
- Midpoint formula
- Parallel condition: m₁ = m₂
- Perpendicular condition: m₁ × m₂ = -1
- Linear modeling frameworks • Standard circle equation: (x – a)² + (y – b)² = r²
- Center (a, b) and radius r
- Expanded form: x² + y² + 2gx + 2fy + c = 0
- Circle Theorems:
- – Angle in a semi-circle is 90°
- – Perpendicular bisector of a chord passes through center
- – Radius is perpendicular to tangent at contact
- Tangents and Normals
- Intersections and the discriminant
Core Skills
- Sketch and interpret cubic/quartic graphs, identifying intercepts and repeated roots.
- Sketch reciprocal graphs, identifying coordinate axes behavior and asymptotes.
- Find coordinates of intersection points by solving simultaneous equations.
- Apply/sketch functional transformations: f(x+a), f(x)+a, f(ax), af(x).
- Calculate exact new coordinate positions following transformations.
- Fluidly transition between different mathematical forms of a straight-line equation.
- Calculate gradients, midpoints, and exact lengths of line segments.
- Construct equations of parallel and perpendicular lines from geometric constraints.
- Solve coordinate geometry problems involving areas of triangles, quadrilaterals, and intersections.
- Interpret the real-world contextual meaning of gradients and y-intercepts in models.
- Identify center and radius from standard and expanded circle equations.
- Complete the square for both x and y variables to determine circular properties.
- Apply circle theorems to solve analytical coordinate geometry problems.
- Find the equation of a tangent or normal to a circle at a given coordinate.
- Determine the number of intersection points between a line and a circle using simultaneous equations and the discriminant.
Assessment
- Students will be assessed on their conceptual understanding of graph shapes, roots, and asymptotic behavior.
- They must sketch curves accurately from factored forms, showing where a graph crosses or touches an axis.
- Transforming functions will be tested both algebraically and graphically from unlabelled sketches.
- Precision in using formal geometric language (e.g., ‘translation by vector’, ‘stretch parallel to…’) is required.
- This chapter presents a high algebraic demand; assessments heavily reward precision in completing the square with fractional or negative coefficients.
- A primary assessment focus is the application of geometric circle properties to find exact linear equations of tangents and normals.
- Students must use the discriminant accurately to determine line-circle intersection states.
- Clear, logical geometric justifications are required at every phase of a multi-step coordinate proof
Half Term 3 (Jan – Feb)
Focus and Topic
- Algebraic Methods
- Proof, Fractions and Polynomials
- Algebra and Functions
- The Binomial Expansion
- Trigonometry
- Trigonometric Ratios
Core Knowledge
- Simplifying algebraic fractions by factorising numerators and denominators.
- Polynomial division algorithm for dividing polynomials by linear terms (x ± p).
- The Factor Theorem: if f(p) = 0, then (x – p) is a factor of f(x).
- Definitions and structures of mathematical proof: Proof by Deduction, Proof by Exhaustion, and Disproof by Counter-example.
- Pascal’s Triangle structures and patterns for finding expansion coefficients.
- Factorial notation (n!) and the mathematical definition of combinatorial combinations (nCr).
- The general Binomial Expansion formula for expanding (a + bx)ⁿ where n is a positive integer.
- Concept of binomial approximation and valid intervals.
- The Sine Rule: a/sin A = b/sin B = c/sin C.
- The Cosine Rule: a² = b² + c² – 2bc cos A.
- Trigonometric triangle area formula: Area = 0.5 ab sin C.
- Periodic nature and key coordinates of basic Sine, Cosine, and Tangent graphs.
- The ‘ambiguous case’ of the sine rule.
Core Skills
- Divide a cubic or quartic polynomial by a linear factor.
- Use the Factor Theorem to find unknown coefficients and completely factorise polynomials.
- Construct rigorous algebraic proofs by deduction to show structural properties (e.g., proving a statement holds for all even or odd integers).
- Use proof by exhaustion or provide single valid counter-examples to break down false generalisations.
- Efficiently evaluate combinations using factorial logic or calculator operations.
- Expand expressions of the form (a + bx)ⁿ up to specified powers of x (e.g., x³ or x⁴).
- Isolate and calculate individual coefficients of specific terms within large expansions without executing full expansions.
- Utilize partial binomial expansions to calculate numerical approximations of complex roots or decimals (e.g., approximating 1.02¹⁰).
- Solve non-right-angled triangle parameters using sine and cosine rules.
- Recognize and compute both valid solutions in ambiguous geometric configurations (where two distinct triangles can be formed).
- Sketch and interpret trigonometric curves from 0° to 360° (or corresponding radian intervals).
- Transform trigonometric profiles accurately given structural parameter adjustments like y = f(x) + a or y = f(ax).
Assessment
- Students will be assessed on algebraic precision during multi-step polynomial operations.
- A key focus is the ability to show complete mathematical arguments—marks are heavily weighted towards fully factorising expressions without relying on trial-and-error values.
- Proof questions will strictly assess structural clarity; students must conclude statements cleanly with definitive algebraic conclusions and accurate notation.
- Assessment centers on binomial fluency, evaluating how reliably students execute expansions involving negative or fractional values inside brackets.
- Students must demonstrate absolute care with brackets when coefficients are algebraic expressions (e.g., expanding pairs like (2 – 3x)⁵).
- Problem-solving tasks will evaluate the ability to work backwards—using a given coefficient to solve for an unknown constant within the initial binomial form.
- Students will be evaluated on navigating complex, multi-step geometric problem spaces (e.g., advanced bearings or contextual elevation puzzles).
- Assessments target spatial reasoning—specifically spotting when to apply the ambiguous case of the sine rule without explicit prompting.
- High accuracy is required when tracking transformed trigonometric coordinates, local maxima/minima, and altered vertical asymptotic intervals
Half Term 4 (Feb – March)
Focus and Topic
- Trigonometry
- Trigonometric Identities and Equations
- Vectors
Core Knowledge
- Fundamental trigonometric
- identities: tan x ≡ sin x / cos x and sin² x + cos² x ≡ 1.
- Principal values and secondary values of inverse trigonometric functions.
- Structure of trigonometric equations within specific intervals (e.g., 0° ≤ x < 360° or -180° < x ≤ 180°).
- Methods for solving hidden quadratics in sin x or cos x.
- Definition of scalar and vector quantities; representation using bold type, underlined notation (u), or directed line segments (AB).
- Magnitude and direction of a vector, and the concept of a unit vector.
- Position vectors relative to an origin O, and displacement vectors between two distinct coordinates.
- Algebraic representation using base component unit vectors (i and j) and column vectors.
Core Skills
- Simplify complex trigonometric expressions and prove identity proofs using fundamental definitions.
- Solve linear trigonometric equations by mapping principal values onto the CAST diagram or trig graphs to find all valid interval solutions.
- Solve quadratic trigonometric equations by factorising or using the quadratic formula, safely rejecting values outside [-1, 1].
- Solve equations with modified arguments (e.g., sin 2x or cos(x + 30°)) by adjusting the interval boundaries systematically.
- Perform scalar multiplication, vector addition, and vector subtraction both algebraically and graphically.
- Calculate the magnitude of a vector using Pythagoras’ theorem: |xi + yj| = √(x² + y²).
- Calculate the direction of a vector using trigonometry, paying careful attention to the correct quadrant.
- Construct geometric proofs to show lines are parallel (scalar multiples) or points are collinear.
- Model real-world situations (such as forces or constant velocity displacements) using 2D vector systems.
Assessment
- Students will be assessed on their capacity to handle multi-step algebraic substitutions using trigonometric identities fluidly.
- A heavy focus will be placed on finding *all* solutions within a given interval—marks are routinely lost for missing values or including extraneous values outside the range.
- Proof questions require a rigorous left-hand side (LHS) to right-hand side (RHS) progression; jumping steps or treating identities as equations will be penalised.
- The assessment will focus on both computational precision and geometric vector reasoning.
- Students must demonstrate competence converting fluidly between column vector form and i, j base unit form.
- Problem-solving tasks will target the application of vectors to context-based modeling (e.g., finding a resultant force or relative position), requiring exact surd form magnitudes.
- Rigorous geometric proof notation when describing vector pathways (e.g., expressing vector paths in terms of a and b) is highly scrutinized.
Half Term 5 (April – May)
Focus and Topic
- Calculus
- Differentiation
- Integration
- Exponentials and Logarithms
Core Knowledge
- Definition of the derivative from first principles as the limit as h approaches 0 of [f(x+h) – f(x)] / h.
- The derivative function dy/dx or f'(x) representing the gradient of a curve.
- Differentiation rules for power functions: d/dx(xn) = nxⁿ⁻¹.
- Equations of tangents and normals to a curve at a given point.
- Turning points (local maxima and minima) where dy/dx = 0.
- Second derivatives (d²y/dx²) and structural classification criteria for turning points.
- Integration as the structural inverse process of differentiation.
- Indefinite integrals and the absolute necessity of the arbitrary constant of integration (+ c).
- Integration rules for power functions: ∫ xⁿ dx = (xⁿ⁺¹) / (n + 1) for n ≠ -1.
- Fundamental Theorem of Calculus: evaluating definite integrals between two limits [a, b].
- Geometric meaning of a definite integral as the area bounded by a curve, the x-axis, and specified vertical lines.
- The mathematical nature and shape of exponential functions y = a^x and the natural exponential function y = e^x.
- Exponential growth and decay models (e.g., population growth, radioactive decay).
- The definition of a logarithm as the inverse function of an exponential: log_a(n) = x is equivalent to a^x = n.
- The laws of logarithms: log_a(xy) = log_a(x) + log_a(y), log_a(x/y) = log_a(x) – log_a(y), and log_a(x^k) = k log_a(x).
- The natural logarithm ln x (logarithm to the base e) and change of base logic.
- Linearisation of non-linear laws: transforming y = ax^n into log y = log a + n log x, and y = ab^x into log y = log a + x log b.
Core Skills
- Prove the derivative of simple functions (e.g., x² or x³) from first principles.
- Differentiate algebraic polynomials and functions with fractional or negative indices.
- Find the exact linear equations of tangents and normals to a curve at a specified coordinate.
- Locate stationary points on a curve and mathematically classify them as maximums or minimums using the second derivative test.
- Set up optimization problems from geometric or real-world profiles and use calculus to determine maximum or minimum values.
- Integrate terms with fractional, negative, or multiple polynomial component indices.
- Find the specific equation of a curve given dy/dx and a boundary coordinate point to evaluate the constant ‘c’.
- Evaluate definite integrals accurately without calculator assistance to produce exact numerical solutions.
- Calculate the exact area enclosed between a curve, the x-axis, and boundary lines.
- Handle area calculations where parts of the curve fall below the x-axis by breaking integrals down into separate positive intervals.
- Sketch exponential curves and their transformations, explicitly displaying y-intercepts and horizontal asymptotes.
- Fluidly apply the laws of logarithms to simplify, expand, or condense multi-term algebraic expressions.
- Solve equations of the form a^x = b by taking logarithms of both sides, and solve more complex variations containing hidden quadratics (e.g., e^2x – 5e^x + 6 = 0).
- Interpret coefficients and solve constraints within exponential growth and decay context problems.
- Plot non-linear experimental data onto log-log or log-linear coordinate configurations, and use the gradient and intercept of the resulting straight line to determine unknown constants
Assessment
- Assessment centers on algebraic manipulation accuracy, especially expanding and simplifying functions into differentiable indices form.
- First principles questions strictly evaluate the structured layout of limit notation—omitting ‘lim as h approaches 0’ steps will lead to a penalty.
- Students must demonstrate logical reasoning when setting up equations for Optimization contexts and explicitly use analytical tests to justify maximum/minimum states rather than relying on sketches.
- Students will be assessed heavily on arithmetic and algebraic precision during substitution phases of definite integration.
- Forgetting the constant of integration (+ c) in indefinite problems is a recurring penalty point.
- High demand is placed on drawing a preliminary sketch to spot area contributions below the x-axis, as evaluating a single combined definite integral across crossing points results in cancellations and an incorrect net area answer.
- Assessment centers heavily on algebraic fluency with logarithmic manipulation and exact values.
- Students must demonstrate proper handling of boundary constraints in real-world contexts (e.g., recognizing that time t ≥ 0 and identifying initial states at t = 0).
- Linearisation questions place high demand on spatial and analytical accuracy—students must clearly show how a curve’s parameters map directly to y = mx + c to earn full marks.
- When solving equations, steps must be logically shown, and solutions leading to logarithms of negative numbers must be explicitly evaluated and rejected.
Half Term 6 (May – July)
Focus and Topic
- Data Collection
- Measures of Location and Spread
- Representation of Data
- Correlation
- Probability
- Statistical Distributions
- Hypothesis Testing
- Modelling in Mechanics
- Constant Acceleration
- Forces and Motion
- Variable Acceleration
Core Knowledge
- Qualitative vs Quantitative; Discrete vs Continuous variables.
- Sampling methodologies: Simple Random, Systematic, Stratified, Quota, and Opportunity/Convenience sampling.
- Structural properties and variables inside the Edexcel Large Data Set (LDS).
- Types of bias and data cleaning needs
- Central tendency: Mean, Median, Mode.
- Dispersion metrics: Range, Interquartile Range (IQR), Percentiles, Variance, and Standard Deviation (σ).
- Linear coding transformations and its distinct impacts on location vs. spread measures.
- Mathematical rules identifying outliers (e.g., Q3 + 1.5×IQR or 2 standard deviations away from the mean).
- Constructive elements of Box and Whisker plots, Cumulative Frequency charts, and Histograms.
- Frequency density formula for unequal intervals: FD = Frequency / Class Width.
- Comparing data distributions using location alongside spread.
- Explanatory (independent) vs Response (dependent) variables.
- Types of correlation: Positive, Negative, Zero; Linear vs Non-linear patterns.
- PMCC (Product Moment Correlation Coefficient) boundaries [-1, 1].
- Linear Regression lines (y = a + bx) and interpolation/extrapolation validity limitations.
- Venn diagrams, Tree diagrams, and two-way mapping structures.
- Probability axioms: P(A ∪ B) = P(A) + P(B) – P(A ∩ B).
- Conditional probability dependencies.
- Mutual Exclusivity: P(A ∩ B) = 0.
- Statistical Independence criteria: P(A ∩ B) = P(A) × P(B).
- Concept of a discrete random variable and its probability distribution matrix.
- Continuous vs Discrete models.
- Conditions for the Binomial Distribution model: X ~ B(n, p) (fixed trials, independent outcomes, binary states, constant probability).
- Definitions: Population, Parameter, Statistic, Hypothesis (Null H₀ vs Alternative H₁).
- Significance levels, Critical Values, and Critical Regions.
- One-tailed vs Two-tailed testing structures.
- Mechanics concepts: Mass, Weight, Displacement, Velocity, Acceleration, Force.
- Mathematical assumptions: Particle (mass concentrated at a point), Light (zero mass), Rigid (no bending), Smooth (no friction).
- Kinematics parameters in a straight line: s, u, v, a, t.
- Derivations and setups of standard SUVAT equations.
- Vertical motion profiles under constant gravity ($g = 9.8 m/s^2$).
- Velocity-time and Displacement-time graphs.
- Newton’s Three Laws of Motion.
- Force interaction vectors: Weight ($W = mg$), Normal Reaction ($R$), Friction, Tension/Thrust.
- Dynamic equilibrium states vs acceleration profiles.
- Connected bodies configurations (e.g., vehicles towing trailers or basic pulley setups).
- Variable acceleration as a function of time: $a(t), v(t), s(t)$.
- Structural calculus paths: differentiating displacement to find velocity, and velocity to find acceleration.
- Structural calculus paths: integrating acceleration to find velocity, and velocity to find displacement.
Core Skills
- Critically identify and contrast sampling methods given contextual parameters.
- Evaluate sample representations and recognize structural advantages or inherent biases.
- Interpret data contexts using knowledge of the Large Data Set (e.g., handling missing weather indicators like ‘tr’ for trace rain).
- Calculate summary statistics from raw arrays, frequency tables, and grouped frequency profiles.
- Interpolate grouped classes smoothly to evaluate exact medians or specified percentiles.
- Dynamically calculate coded statistics and decode them back to source parameters.
- Evaluate outliers algebraically from specified numerical definitions.
- Plot and complete histograms correctly across varying or fractional category widths.
- Contrast distinct statistical distribution shapes (Symmetrical, Positively Skewed, Negatively Skewed).
- Interpret scatter graphs and state the contextual real-world meaning of PMCC values.
- Use linear regression equations to predict parameter states inside data bounds.
- Critically assess the invalidity of extrapolation predictions when projecting outside bounds.
- Translate worded sample criteria into structured Venn layouts.
- Solve complex overlapping conditional probabilities smoothly using equations or diagrams.
- Construct rigorous algebraic tests to definitively confirm independence configurations.
- Construct discrete probability allocation tables ensuring sum of probabilities equals 1.
- Compute exact binomial states using the probability mass function P(X = r).
- Evaluate cumulative binomial inequality thresholds (e.g., P(X ≤ r) or P(X > r)) via calculator cumulative tables.
- Formulate null and alternative hypotheses using correct notation (e.g., H₀: p = 0.4).
- Find the exact critical region for a binomial test using cumulative calculation metrics.
- Conduct a complete test process, comparing sample outcomes against significance margins.
- Translate physical scenarios into simplified mechanical diagrams.
- Select appropriate SI base units ($m, kg, s, N$).
- Evaluate how modeling simplifications modify real-world vector projections.
- Extract kinematics data points and choose the correct SUVAT equation.
- Sketch structured velocity-time graphs, interpreting the gradient as acceleration and area under the curve as total displacement.
- Solve vertical motion problems (e.g., finding maximum height when vertical velocity drops to zero).
- Construct clear, comprehensive Free-Body diagrams showing all active force vectors.
- Set up and resolve equations of motion along a coordinate axis using Newton’s Second Law ($F = ma$).
- Analyze connected bodies systems by looking at components individually or treating them as a single combined mass.
- Apply differentiation techniques to polynomial kinematics expressions.
- Apply definite or indefinite integration, resolving the constant of integration (+ c) using given initial boundary states (e.g., ‘at $t = 0, v = 2$’).
- Find maximum or minimum velocity thresholds by setting acceleration equal to zero ($dv/dt = 0$).
Assessment
- Written questions heavily penalise generic answers; students must frame sampling advantages explicitly within the context provided.
- Specific familiarity with Large Data Set locations, units, and anomalies is systematically tested via multiple-choice or short analytical steps.
- Precision in calculation formulas is highly scrutinized; computational errors when managing grouped tables drop easy marks.
- Students must explicitly demonstrate that linear adjustments like shift operations (adding/subtracting) leave spread metrics (standard deviation) completely unaltered.
- Graphical precision across axis scales is heavily scrutinized.
- Comparisons must be double-layered: students must compare a location parameter (e.g., median) AND a spread parameter (e.g., IQR) using active contextual comparisons to achieve full marks.
- Assessments emphasize clear data definitions (e.g., explaining why correlation does not necessarily imply causation).
- Interpretation of line parameters requires contextual descriptions—students must explain the exact meaning of gradient ‘b’ or intercept ‘a’ relative to the problem environment.
- Marks are primarily allocated to structural setups; calculation work with conditional parameters needs explicit mathematical working.
- Proving independence requires evaluating both sides of the product statement explicitly and comparing values to reach a formal written conclusion.
- Students must explicitly state model structural justifications before using binomial operations in multi-mark problems.
- Directional precision with cumulative inequalities is highly prioritized; errors in rewriting P(X ≥ r) into 1 – P(X ≤ r – 1) are a common penalty point.
- Highest demand for precise wording. Test conclusions must follow a strict two-step pattern: an initial statistical decision based on numbers, followed by a non-assertive, contextual conclusion written in terms of the original problem.
- For two-tailed tests, errors like forgetting to halve the significance level when finding critical regions will result in a loss of marks.
- Assessment centers on validating assumptions. Students must explain how specific modeling keywords dynamically simplify calculations (e.g., explaining that a ‘smooth’ surface means ignoring friction entirely).
- High priority is placed on directional sign consistency (e.g., choosing upwards as positive, making acceleration due to gravity negative: $a = -9.8 m/s^2$).
- Multiphase motion problems require students to split calculations clearly at points where acceleration changes.
- Free-Body diagrams must be flawless—missing normal reactions or mispointing weight vectors drops immediate marks.
- Connected body systems heavily test a student’s ability to handle simultaneous equations, requiring clear algebraic layouts for tension or acceleration parameters.
- Assessment strictly checks whether students recognize when to use variable calculus vs. constant SUVAT calculations.
- When calculating total distance covered within an interval, students must check for turning points where velocity passes throughzero, as simple definite integration only computes net displacement rather than absolute distance.
Year 13
Half Term 1 (Sept-Nov)
Half Term 2 (Nov – Dec)
Half Term 3 (Jan – Feb)
Half Term 4 (Feb – March)
Half Term 5 (April – May)
Half Term 6 (May – July)
Half Term 1 (Sept-Nov)
Focus and Topic
- Algebraic methods
- Functions and Graphs
- Sequences and Series
- Binomial expansion
- Radians
Core Knowledge
- Proof
- Algebraic Fractions
- Partial Fractions
- Algebraic division
- Modulus function
- Functions and mappings
- Transformations
- Arithmetic and Geometric sequences and series
- Recurrence relationships
- Expanding (1+x) ^n and (a + bx)^n
Core Skills
- Construct rigorous proof.
- Prove algebraic identities.
- Fully factorise the polynomial denominator into distinct linear factors, repeated linear factors, or irreducible quadratics. Identify improper fractions. Partial fraction decomposition,
- Solve for unknown constants
- They learn to work with mappings, composite and inverse functions, domain, range, and graph transformations. Understanding one-to-one functions and modulus graphs is essential.
- In sequences, students handle arithmetic and geometric progressions, using formulae for nth terms and sums, including sums to infinity for convergent series. Sigma notation, recurrence relations, and proof by induction are introduced, reinforcing logical reasoning and algebraic manipulation skills.
- They expand expressions using the binomial theorem for fractional and negative indices, applying series expansions to approximate functions. Skills include identifying valid ranges for expansions and manipulating algebraic series.
- In radians, students convert between degrees and radians, understand arc length and sector area formulas, and apply them in problem-solving. They also explore trigonometric functions in radians, including small angle approximations. These chapters develop precision in algebraic techniques and deepen understanding of trigonometric applications in calculus and geometry.
Assessment
- students are assessed on algebraic manipulation, use of the factor and remainder theorems, simplifying algebraic fractions, and decomposing partial fractions. Proof by deduction and contradiction is key, with emphasis on logical structure, clear reasoning, and correct notation.
- Edexcel Unit test
- Students must interpret mappings, find composite and inverse functions, solve modulus problems, and apply transformations.
- Edexcel Unit test
- In sequences, assessment includes using formulas for arithmetic and geometric series, sigma notation, and proof by induction.
- Edexcel Unit test
- For binomial expansion, students are evaluated on expanding expressions with rational indices and determining validity ranges.
- Edexcel Unit test
- In radians, they must convert units, calculate arc lengths, sector areas, and apply trigonometric functions in radians, including small-angle approximations.
- Edexcel Unit test
Half Term 2 (Nov – Dec)
Focus and Topic
- Exponentials and Logarithms
- Trigonometric Functions
- Trigonometric Identities
- Differentiation
- Numerical Methods
Core Knowledge
- The exponential function e^x and its inverse ln(x).
- Properties and laws of logarithms applied to natural logs.
- Mathematical modeling of growth and decay: y = ae^(bt).
- Linearization of non-linear data equations: y = ax^b becomes log(y) = log(a) + b*log(x); y = ab^x becomes log(y) = log(a) + x*log(b).
- Reciprocal trigonometric functions: sec(x) = 1/cos(x), cosec(x) = 1/sin(x), cot(x) = 1/tan(x).
- Inverse trigonometric functions: arcsin(x), arccos(x), arctan(x) and their strict principal domains and ranges.
- Fundamental Pythagorean identities: 1 + tan²(x) = sec²(x) and 1 + cot²(x) = cosec²(x).
- Addition formulas: sin(A±B), cos(A±B), tan(A±B).
- Double-angle identities: sin(2A), cos(2A) (three structural variants), tan(2A).
- R-formula expressions: R*cos(��±��) a R*sin(��±��) conversions f linear combinations of sine and cosine.
- Derivatives of standard functions: e^x, ln(x), sin(x), cos(x), tan(x), sec(x), cosec(x), cot(x).
- Differentiation rules: Product Rule, Quotient Rule, and the Chain Rule.
- Parametric differentiation: dy/dx = (dy/dt) / (dx/dt).
- Implicit differentiation for expressions where y cannot be explicitly isolated.
- Rates of change modeling equations involving connected variables.
- Location of roots theorem: If(x) is continuous and changes sign between x=a and x=b, a root exists in [a,b].
- Iterative formulas: x_(n+1) = g(x_n) as a process for finding approximations.
- Convergence behavior:
- Cobweb and staircase diagrams.
- Newton-Raphson formula: x_(n+1) = x_n – f(x_n)/f;(x_n).
Core Skills
- Solve complex equations involving exponential functions and natural logarithms analytically.
- Transform non-linear relationships into linear form using logarithms to estimate parameters from experimental data graphs.
- Set up, manipulate, and solve rate-of-change contextual applications involving real – world growth or decay limits.
- Sketch the graphs of reciprocal and inverse trigonometric functions including all associated asymptotes and turning points.
- Simplify complex trigonometric expressions and construct formal, step-by-step proofs of identities using identities.
- Solve trigonometric equations within specified range intervals, including
- transformations of the argument.
- Apply double-angle and addition formulas to solve complex high-degree trigonometric equations.
- Express expressions of the form a*cos(��) + b*sin(��) a single harmonic term R*cos(��-��).
- Determine the exact maximum or minimum values of composite trigonometric functions and the specific angles where they occur.
- Execute flawless differentiation on highly complex functions using combinations of chain, product, and quotient rules.
- Compute stationary points, tangents, and normals for curves defined parametrically or implicitly.
- Establish mathematical differential relations between connected rates of change using chain rule products.
- Locate intervals containing roots by evaluating sign changes and showing continuity properties explicitly.
- Demonstrate convergence or divergence of an iteration sequence graphically using cobweb or staircase illustrations.
- Apply the Newton-Raphson method to approximate roots of non-linear equations to a specified degree of decimal precision.
Assessment
- TBC
Half Term 3 (Jan – Feb)
Focus and Topic
TBC
Core Knowledge
TBC
Core Skills
TBC
Assessment
TBC
Half Term 4 (Feb – March)
Focus and Topic
TBC
Core Knowledge
TBC
Core Skills
TBC
Assessment
TBC
Half Term 5 (April – May)
Focus and Topic
TBC
Core Knowledge
TBC
Core Skills
TBC
Assessment
TBC
Half Term 6 (May – July)
Focus and Topic
TBC
Core Knowledge
TBC
Core Skills
TBC
Assessment
TBC
Key Info
- Start Date: September 2026
- Awarding Body: Edexcel
- Study Mode: Full Time
- Course Length: 2 Years
Entry Requirements
TBC
Complementary Subjects
Career Opportunities
Employers look for hard-working, self-motivated, and intelligent people to join their staff. Obtaining a Maths A Level shows that you have what it takes. You may not use algebra or probability in your job every day, but the transferable skills of analysis, logic, and problem solving will always come in handy.
Some degree subjects like Physics and Engineering ask for a Maths A Level as part of the entry requirements. Others such as Medicine and Architecture don’t make it a necessity, but they still have a decent amount of mathematical content. If you go in with a Maths A Level, you’ll have a much easier time than those who don’t.