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Further Mathematics Support Programme OCR M2 – Scheme of Work Template - 2016-2017 This template is part of a series designed to assist with planning and delivery of further mathematics courses. It shows how Integral Resources and Live Interactive Lectures can be used to support students and teachers. Integral Resources Integral Resources Live Interactive Lectures Teacher-level access to the Integral Resources (integralmaths.org/) for Further Pure and Applied units is available free of charge to all schools/colleges that register with the Further Mathematics Support Programme: www.furthermaths.org.uk/ Student-level access to the Integral Resources and the Live Interactive Lectures for Further Mathematics is available at a moderate cost via: www.furthermaths.org.uk/lilfm Integral Resources include a wide range of resources for both teacher and student use in learning and assessment. A selection of these are suggested in the template below. Sample resources are available via: http://integralmaths.org/help/info.php. Live Interactive Lectures are available for individual Further Pure and Applied units and take place in the spring and autumn terms. LIL FM is ideal for schools/colleges teaching Further Mathematics with small groups and/or limited time allocation. It is also useful to support less experienced teachers of Further Mathematics. See www.furthermaths.org.uk/lilfm Scheduling will depend on circumstances, but the template below breaks the module down into 7 sections which may be allocated approximately equal time. Each section corresponds to one Live Interactive Lecture (LIL) and these take place fortnightly to supplement the teaching and tutorial support in schools/colleges and students' own independent study. FMSP Area Coordinators will be able to offer additional guidance if needed. See www.furthermaths.org.uk/regions OCR M2 – Scheme of Work Template - 2016-2017 Topic Specification statements Suggested Integral Resources Motion of projectiles model the motion of a projectile as a particle moving with constant acceleration and understand any limitations of this model use horizontal and vertical equations of motion to solve problems on the motion of projectiles, including finding the magnitude and direction of the velocity at a given time or position, the range on a horizontal plane and the greatest height reached derive and use the Cartesian equation of the trajectory of a projectile, including problems in which the initial speed and/or angle of projection may be unknown ► OCR_M2 / ► The motion of projectiles / ► The motion of projectiles 1: Introduction understand the concept of the work done by a force, and calculate the work done by a constant force when its point of application undergoes a displacement ► OCR_M2 / ► Work, energy and power / ► Work, energy and power 1: Introduction Work, energy and power Projectiles teaching activities Additional exercise Assessment (Integral Resources) Live Interactive Lecture Other resources Motion of projectiles PhET simulation: Projectile motion nrich: Model solutions Section Test P1 nrich: Dam Busters 1 ► OCR_M2 / ► The motion of projectiles / ► The motion of projectiles 2: General equations Trajectory teaching activities Additional exercise Section Test P2 ► OCR_M2 / ► The motion of projectiles The motion of projectiles topic assessment Work, energy and nrich: Powerfully power fast nrich: Go Spaceship Go not necessarily parallel to the force (use of the scalar product is not required) understand the concepts of gravitational potential energy and kinetic energy, and use appropriate formulae understand and use the relationship between the change in energy of a system and the work done by the external forces, and use in appropriate cases the principle of conservation of energy use the definition of power as the rate at which a force does work, and use the relationship between power, force and velocity for a force acting in the direction of motion solve problems involving, for example, the instantaneous acceleration of a car moving on a hill with resistance Energy and power teaching activities Additional exercise Section Test W1 ► OCR_M2 / ► Work, energy and power / ► Work, energy and power 2: Potential energy Energy teaching activities Additional exercise Section Test W2 ► OCR_M2 / ► Work, energy and power Rigid bodies 1: Moments calculate the moment of a force about a point in two dimensional situations only (understanding of the vector ► OCR_M2 / ► Rigid bodies / ► Rigid bodies 1: Moments Moments teaching activities Work, energy and power topic assessment Rigid bodies 1: PhET simulation: Moments Balancing act Rigid bodies 2: Rigid bodies in equilibrium Centres of mass nature of moments is not required) use the principle that, under the action of coplanar forces, a rigid body is in equilibrium if and only if (i) the vector sum of the forces is zero, and (ii) the sum of the moments of the forces about any point is zero solve problems involving the equilibrium of a single rigid body under the action of coplanar forces, including those involving toppling or sliding (problems set will not involve complicated trigonometry) use the result that the effect of gravity on a rigid body is equivalent to a single force acting at the centre of mass of the body identify the position of the centre of mass of a uniform body using considerations of symmetry use given information about the position of the centre of mass of a triangular lamina and other simple shapes Additional exercise Section Test R1 / ► OCR_M2 / ► Rigid bodies / ► Rigid bodies 2: Rigid bodies in equilibrium Equilibrium teaching activities Additional exercise / ► OCR_M2 / ► Centres of mass / ► Centres of mass 1: Finding the centre of mass Centres of mass teaching activities Additional exercise ► OCR_M2 / ► Centres of mass / ► Centres of mass 2: Centres of mass of special shapes Rigid bodies 2: Rigid bodies in equilibrium Section Test R2 ► OCR_M2 / ► Rigid bodies Rigid bodies topic assessment Centres of mass nrich: Overarch 1 nrich: Overarch 2 Section Test CoM1 (including those listed in the List of Formulae) determine the position of the centre of mass of a composite rigid body by considering an equivalent system of particles (in simple cases only, e.g. a uniform Lshaped lamina or a hemisphere abutting a cylinder) Notes and examples Section Test CoM2 ► OCR_M2 / ► Centres of mass Impulse and restitution recall and use Newton’s experimental law and the definition of coefficient of restitution, the property 0 ≤ 𝑒 ≤ 1 and the meaning of the terms ‘perfectly elastic’ (e= 1) and ‘inelastic’ (e=0) use Newton’s experimental law in the course of solving problems that may be modelled as the direct impact of two smooth spheres or as the direct impact of a smooth sphere with a fixed plane surface recall and use the definition of impulse as change of momentum (in one dimension only, restricted to ‘instantaneous’ events, so ► OCR_M2 ► Impulse and restitution / ► Impulse and restitution 1: Newton's law of impact Centres of mass topic assessment Impulse and restitution PhET simulation: Collision lab nrich: Whoosh Collisions (Geogebra) Collisions teaching activities Additional exercise Section Test I1 that calculations involving force and time are not included) ► OCR_M2 / ► Impulse and restitution Circular motion understand the concept of angular speed for a particle moving in a circle, and use the relation v = rw understand that the acceleration of a particle moving in a circle with constant speed is directed towards the centre of the circle, and use the formulae rw2 and v2/r solve problems which can be modelled by the motion of a particle moving in a horizontal circle with constant speed / ► OCR_M2 / ► Circular motion / ► Circular motion 1: Motion in a horizontal circle Impulse and restitution topic assessment Circular motion PhET simulation: Ladybug revolution Circular motion teaching activities Additional exercise Section Test C1 ► OCR_M2 / ► Circular motion Circular motion topic assessment Consolidation and revision FMSP - Revision Videos The study plans available on Integral Resources refer to Mechanics 2 for OCR (Cambridge Advanced Level Mathematics) (ISBN 9780521549011). Other textbooks covering this course may be available, and Integral Mathematics Resources does not endorse any particular set of textbooks.