LC Applied Maths study plan

Derive and apply the five constant-acceleration equations to vertical and horizontal projectile problems without looking at notes

Resolve forces on inclined planes and connected particles (pulleys, tow-bars) into components and write the equations of motion

Construct free-body diagrams for at least ten standard configurations and label every reaction force explicitly

Convert fluently between displacement-time, velocity-time and acceleration-time graphs, including area and gradient interpretation

Apply Newton's second law with variable forces, including friction proportional to normal reaction

Set up and solve differential equations of motion for velocity-dependent resistance using separation of variables

Use impulse and momentum conservation for collisions and explosions in one dimension

Compute work, kinetic energy and power in problems where force varies with position

State and apply the conditions for equilibrium of a rigid body in two dimensions

Take moments about a chosen point to eliminate unknown reactions and solve ladder, beam and hinge problems

Resolve reactions at supports for uniformly and non-uniformly loaded beams, including point loads

Analyse toppling versus sliding for a block on an incline by comparing moment and friction criteria

Derive centripetal acceleration for uniform circular motion and apply it to conical pendulum and banked-track problems

Solve vertical circular motion problems using energy conservation and identify where tension or normal reaction vanishes

Set up simple harmonic motion equations from restoring-force assumptions and extract amplitude, period and phase

Apply Newton's law of gravitation to satellite orbits, escape velocity and Kepler's third law

Link simple harmonic motion to calculus by differentiating displacement to obtain velocity and acceleration

Solve oscillation problems involving damping or phase shift using trigonometric identities

Differentiate and integrate standard functions and apply the chain, product and quotient rules accurately

Use calculus to find maxima, minima and rates of change in applied mechanics contexts

Evaluate definite integrals using substitution and integration by parts, including trigonometric integrands

Compute areas under curves, volumes of revolution and centroids of simple laminas by integration

Solve first-order separable differential equations arising from motion and growth models

Interpret a definite integral as an accumulated quantity and justify the limits chosen in applied problems

Compute probabilities using the addition and multiplication rules, including conditional probability and independence checks

Apply the binomial, Poisson and normal distributions and decide which model fits a given scenario, stating assumptions

Calculate and interpret mean, variance and standard deviation, and standardise normal variables to use tables

Set up and interpret hypothesis tests and confidence intervals for a mean or proportion

Complete two full timed papers under exam conditions and mark them strictly against a scheme

Rank recurring error types by frequency and rework the five costliest mistakes from scratch

Rehearse time allocation per domain to match the 30/20/20/15/15 weighting

Memorise and self-test the full formula sheet, including moment of inertia, SHM and distribution formulae