Introduce algebraic notation and basic properties

Practice expanding and simplifying expressions with multiple terms;

Factor simple expressions (e.g., common factor, difference of squares)

Solve linear equations, including those with fractional coefficients

Introduce algebraic manipulation for rearranging formulae

Explore quadratic functions, including standard, vertex, and factored forms

Solve quadratic equations by factorization, completing the square, and quadratic formula

Analyze solutions graphically to interpret roots, turning points, and the parabola’s direction

Solve real-world problems involving quadratic models (e.g., projectile motion)

Define functions and introduce function notation, including domain and range

Identify and sketch graphs of linear, quadratic, cubic, and reciprocal functions

Examine graph transformations (translations, reflections, stretches, and compressions)

Discuss piecewise functions and their applications in real-world scenarios

Perform polynomial division, focusing on long division and synthetic division methods

Apply the factor and remainder theorems to factorize polynomials
 
Simplify rational expressions and solve equations involving rational expressions

Introduce partial fractions with linear denominators and basic applications.

Review laws of exponents and apply them in simplifying expressions

Understand the relationship between exponentials and logarithms as inverses

Solve equations involving exponential and logarithmic terms

Discuss applications of exponential growth and decay in population models, half-life problems, and interest calculations

Convert angles between radians and degrees

Introduce sine, cosine, and tangent functions and their values at standard angles

Solve basic trigonometric equations in degrees and radians

Use right-angle trigonometry to solve triangle problems and apply these skills to real-world applications like elevation and depression

Graph sine, cosine, and tangent functions with amplitude, period, and phase transformations

Explore compound angle formulas (sin(A ± B), cos(A ± B)) and double angle formulas (sin 2A, cos 2A); solve complex trigonometric equations using identities and transformations

Introduce applications in wave and oscillation problems

Review equations of lines (slope-intercept and point-slope forms) and calculate gradients

Work with parallel and perpendicular lines

Find midpoints and lengths of line segments

Introduce the equation of a circle, derive the circle’s properties, and solve geometry problems involving tangents and chords

Define sequences, including arithmetic and geometric sequences

Derive and use formulas for the nth term and sum of arithmetic and geometric sequences

explore the concepts of convergence and divergence
apply series in financial contexts like
installment payments and savings accounts

Introduce the concept of a derivative as a rate of change and define basic rules of differentiation

Differentiate polynomials,
trigonometric, exponential, and logarithmic functions

Find gradients of functions at given
points

Discuss applications in velocity,
acceleration, and optimization problems

Explore product, quotient, and chain rules in differentiation a

Apply higher-order derivatives

Analyze critical points and classify stationary points (maximum, minimum, and point of inflection)

Use differentiation in sketching curves and in solving problems of maxima and minima in physical contexts

Understand integration as the reverse
process of differentiation

Introduce basic techniques for integrating polynomials and simple functions

Interpret integration as finding the area under a curve; solve initial value problems

Explore integration’s use in
calculating displacement, area, and volume

Apply integration techniques including substitution and integration by parts

Solve definite integrals and understand properties of integrals

Calculate areas between curves and solve volume problems using integration

Discuss applications in physics and engineering, including work done by a force

Define probability and introduce key concepts (sample space, events, independence, conditional probability)

Calculate probabilities for single events and combined events

Use Venn diagrams and probability trees to solve problems

Apply probability to real-life contexts such as games and risk assessments.

Introduce discrete random variables and probability distributions

Calculate expectations and variances; explore common distributions like binomial and geometric

Apply distributions to decision-making contexts and problem-solving

Review statistical measures (mean, median, mode, and range)

Interpret cumulative frequency, box plots, and histograms

Introduce standard deviation and variance

Apply these measures to data analysis and compare datasets.

Define correlation and causation, calculate correlation coefficients

Introduce least squares regression and find lines of best fit

Interpret regression lines and make predictions

Discuss real-world applications in economics, biology, and social sciences

Introduce vectors in two and three dimensions

Perform vector addition, subtraction, and scalar multiplication

Calculate magnitudes and directions; solve geometric problems using vectors, including applications in physics and engineering

Define force and its types

Resolve forces into components

Apply Newton’s first law and equilibrium conditions

Solve problems involving forces in static and dynamic contexts

Introduce equations of motion for constant acceleration

Calculate displacement, velocity,
and acceleration in kinematic problems

Apply kinematic equations to real-world scenarios such as projectiles and free-fall motion

Define work, energy, and power

Calculate work done by a force, kinetic energy, and potential energy

Apply conservation of energy in solving problems

Discuss applications in mechanical and physical systems

Review major concepts from each topic

Apply techniques to solve complex, multi-step problems

Practice with past A-level exam questions to build familiarity and confidence.

Conduct a full-length mock exam covering all topics

Review responses and provide feedback

Identify areas for improvement and set goals for further practice and revision

Define momentum and impulse

Understand conservation of momentum in collisions

Solve problems involving elastic and inelastic collisions

Apply concepts to real-world situations like vehicle collisions

Introduce circular motion concepts

Define centripetal force and acceleration

Apply formulas for objects moving in a circular path

Solve problems involving rotation, such as in amusement park rides and planetary motion

Explore numerical methods including Newton-Raphson, iterative methods, and numerical integration

Apply methods to approximate roots and areas

Discuss limitations and applications in computing and engineering

Introduce differential equations as models of real-world phenomena

Solve first-order differential equations with separation of variables

Apply to exponential growth, decay,
and population models

Define parametric equations and convert between parametric and

Cartesian forms sketch graphs of parametric equations

Solve application problems involving parametric motion, such as projectile trajectories.

Explore vector equations of lines and planes

Calculate intersections, angles, and distances between lines and planes

Apply to problems in three-dimensional geometry and engineering contexts

Define complex numbers and perform operations (addition, subtraction, multiplication, division)

Represent complex numbers on an Argand diagram

Introduce polar form and Euler’s formula

Apply complex numbers to electrical engineering and wave problems