Mathematics P1 + P4

Completing the square, Discriminant and nature of roots, Conditions for tangency, Quadratic inequalities, Line meeting a curve, Equations reducible to quadratic form, Range of a quadratic function, Resolving forces into components, Equilibrium of coplanar forces, Resultant force magnitude and direction, Forces on an inclined plane, Friction and limiting equilibrium, Tension in strings

Domain and range, One-one functions and restricted domains, Composite functions, Inverse functions and their graphs, Translations stretches and reflections, Combined transformations, The constant acceleration equations, Vertical motion under gravity, Two particles meeting, Velocity-time graphs, Displacement from area under a graph, Multi-stage journeys

Length midpoint and gradient, Parallel and perpendicular lines, Equation of a circle, Tangents and chords of a circle, Intersection of a line and a circle, Problems with triangles and rectangles, Differentiating displacement and velocity, Integrating acceleration and velocity, Constants of integration from initial conditions, Maximum velocity and instantaneous rest, Motion defined in separate intervals, Total distance travelled

Radian measure, Arc length and sector area, Areas of segments and composite regions, Graphs and exact values of sin cos and tan, Inverse trigonometric functions, Proving trigonometric identities, Solving trigonometric equations, Trigonometric modelling, Newton's second law F = ma, Weight and normal reaction, Motion on a rough horizontal plane, Motion up and down an inclined plane, Motion in a resisting medium, Multi-stage motion with changing forces

Binomial expansion and particular coefficients, Arithmetic progressions, Geometric progressions, Sum to infinity and convergence, Combined AP and GP problems, Progressions in real-life contexts, Light inextensible string over a smooth pulley, Pulley at the edge of a table, Particles on two inclined planes, Tension and common acceleration, Motion after a particle hits the ground, Friction in connected systems

Differentiating powers of x and the chain rule, Tangents and normals, Increasing and decreasing functions, Stationary points and their nature, Maximum and minimum problems, Connected rates of change, Momentum and impulse, Conservation of momentum in direct collisions, Particles coalescing, Particles separating after impact, Successive collisions, Momentum combined with friction and gravity