11–12Mathematics Extension 2 11–12 Syllabus

Solve problems involving velocity and acceleration expressed in terms of displacement, and acceleration expressed in terms of velocity

Examine Newton’s three laws of motion, including force, acceleration, action and reaction under a constant and non-constant force

Recognise that forces are vector quantities, analyse concurrent forces on a body by resolving them into perpendicular components and use vector projections to determine how much of a given force acts in a given direction in both 2D and 3D contexts

Describe simple harmonic motion using displacement, velocity, acceleration, force, amplitude and period

Determine equations for simple harmonic motion when given graphs of acceleration, velocity or displacement in terms of time

Model and solve problems involving simple harmonic motion using relevant formulas and graphs

Derive the equations of motion for a particle travelling, without resistance, in a straight line with constant and variable acceleration and use the equations of motion to solve problems

Analyse and solve problems relating to motion on a smooth inclined plane by resolving forces into components parallel and perpendicular to the inclined plane

Solve motion problems involving a single smooth pulley and a smooth inclined plane where a body hangs vertically or lies on a smooth horizontal or inclined plane

Derive an expression for velocity as a function of time of a particle moving in a straight line and in the absence of external forces, except for a resistance oppositely directed to the motion and with a magnitude proportional to a power of the speed

Derive an expression for velocity as a function of displacement of a particle moving in a straight line and in the absence of external forces, except for a resistance oppositely directed to the motion and with a magnitude proportional to a power of the speed

Derive an expression for displacement as a function of time of a particle moving in a straight line and in the absence of external forces, except for a resistance oppositely directed to the motion and with a magnitude proportional to a power of the speed

Solve problems, excluding those with pulley systems, involving a particle moving in a straight line subject to a resistance oppositely directed to the motion and with a magnitude proportional to a power of the speed

Define the terminal velocity of a particle falling through a medium as the constant velocity the particle reaches when the resistance of the medium prevents further acceleration

Solve vertical resisted motion problems using the expressions derived for acceleration, velocity and displacement, including finding the maximum height reached by a particle projected vertically upwards and the time taken to reach this maximum height, and finding the time taken for a particle to return to the level from which it was projected and its terminal velocity

Distinguish between the shape of the trajectory of a projectile moving under the influence of gravity and with negligible resistance and the shape of the trajectory of a projectile moving under the influence of gravity subject to resistance whose magnitude is proportional to the speed

Establish and use the equations for acceleration for a projectile moving under the influence of gravity, projected at an angle to the horizontal, and subject to a resistance whose magnitude is proportional to the speed, to solve problems