Further Mathematics Support Programme
MEI Mechanicsa –Suggested Scheme of Work (2017-2018)
This template shows how Integral Resourcesand FMSP FM videoscan be used to support Further Mathematics students and teachers.
This is for the optional Mechanicscomponent of AS Further Mathematics – you will need to deliver another optional element Further Pure alongside this. This content makes up 33⅓% of the MEI AS Further Mathematics content.
It is examined in AS level paper Y411 and in A level paper Y431.
/Teacher access to the Integral Resources (integralmaths.org/2017/) for Further Mathematics is available free of charge to all schools/colleges that register with the Further Mathematics Support Programme: furthermaths.org.uk.
This will include access to the FM videos. A single student login will also be included so that teachers can give students direct access to the FM videos.
/ Individual student access to the full range of Integral Resources andtheFM videos for Further Mathematics is available at a cost of £30 per student or via a full school/college subscription to Integral. Teachers will get access to the management system so they can monitor their students' progress: furthermaths.org.uk/fm-videos.
Integral Resourcesinclude a wide range of resources for both teacher and student use in learning and assessment. Interactive resources and ideas for using technology are featured throughout. Sample resources are available via:integralmaths.org/2017/.
FM videosare available for individual components of AS and A level Further Mathematics. There will be around 4-5 videos of 5-10 minutes in length for each section in Integral. The intention of these videos is that they are sufficient to introduce students to the concepts so that they can learn the material by working through appropriate examples. FM videosare ideal for schools/colleges teaching Further Mathematics with small groups and/or limited time allocation. They are also useful to support less experienced teachers of Further Mathematics. See furthermaths.org.uk/fm-videos.
Scheduling will depend on circumstances, but the template breaks the study intotopic sections.Each section corresponds to one set of videos and may be allocated approximately equal time – this would equate to approximately one week of teaching time for a single teacher delivering the complete AS course. Further information on scheduling can be found at furthermaths.org.uk/offering-fm.FMSP Area Coordinators will be able to offer additional guidance if needed: furthermaths.org.uk/regions.
OCR AS Mechanics – Suggested Scheme of Work (2017-2018)
Date / Topic / Specification statements / Integral Resources / Exercises & AssessmentIntegral Resources / FM videos / Notes / Other resources
Mechanics basic principles / MEI_FM_Mecha / ► Introduction, overview and assumed knowledge / 1.1 Units
1.2 Modelling
1.3 Forces
1.4 Newton’s Laws
1.5 SUVAT equations
1.6 Resolving
1.7 Equilibrium of forces / These videos cover the fundamental concepts from A level Mechanics.
Work, energy & power 1: Work & energy /
- Understand the language relating to work, energy
energy, potential energy, conservative force,dissipative force, driving force, resistive force, power of a force, power developed by a vehicle.
- Be able to calculate the work done by a forcewhich moves along its line of action.
- Be able to calculate the work done by a force
- Be able to calculate kinetic energy and gravitational potential energy.
- Understand when the principle of conservation of
appropriately.
- Understand and use the work-energy principle.
- Exercise level 1
- Exercise level 2
- Section test E1
- Exercise level 3 (Extension)
1.2 Kinetic energy
1.3 The work-energy principle
1.4 Potential energy
1.5 Conservation of energy / In an examination question ‘the power developed by a car’ (or a bicycle or train engine) means the useful, or available, power. It is the power of the driving force; it is not the power developed by the engine, some of which is lost in the system.
Zero work is done by a force acting
perpendicular to displacement.
E.g. the maximum height of a projectile, a
particle sliding down a smooth curved surface,
a child swinging on a rope.
The total work done by all the external forces
acting on a body is equal to the increase in the
kinetic energy of the body.
E.g. a particle sliding down a rough curved
surface
Work, energy & power 2: Power /
- Understand and be able to use the definition of power (the rate at which a force does work).
- Use average power time = work done/time elapsed
- Use the relationship between power, the tractive force and velocity (?=??) to solve problems.
- Consider motion on an inclined plane.
- Work out the maximum velocity or speed of a body
- Exercise level 1
- Exercise level 2
- Section test E2
- Exercise level 3 (Extension)
2.2 Power, force and velocity
2.3 Motion on inclined planes
I_FM_Mecha / ► Work, energy and power / ► Work, energy and power: Topic assessment
Forces and Moments /
- Know that a particle is in equilibrium under aset of concurrent forces if and only if theirresultant is zero.
- Be able to draw a force diagram for a rigid body, in cases where the particle model is not appropriate
- Understand that a system of forces can have aturning effect on a rigid body. e.g. a lever
- Know the meaning of the term couple
- Be able to calculate the moments about a fixedaxis of forces acting on a body.
- Take account of a given couple when taking moments.
- Understand and be able to apply the conditionsfor equilibrium of a rigid body
- Be able to derive and use the result that a body on a
on the point of slipping if
- Be able to identify whether equilibrium will be broken by sliding or toppling. e.g. a cuboid on an inclined plane.
MEI_FM_Mecha / ► Forces / ► Forces 2: Sliding and toppling /
- Exercise level 1
- Exercise level 2
- Section test F1
- Exercise level 1
- Exercise level 2
- Section test F2
1.2: Moments and couples
1.3: Equilibrium of a rigid body
1.4: Ladders
1.5: Sliding and toppling / Prerequisites for this section are understanding different types of forces such as weight, tension, thrust , normal reaction
frictional force, resistance.
Students also need to have studied frictional forces and know about limiting equilibrium and that
They need to know how to resolve, find resultants and apply Newton’s laws of motion.
Work out moments both as the product of force and perpendicular distance of the axis from the line of action of the force, and by
first resolving the force into components.
MEI_FM_Mecha / ► Forces / ► Forces: Topic assessment
Centres of Mass /
- Be able to find the centre of mass of a system ofparticles of given position and mass, in 1, 2 and 3-dimensions.
- Know how to locate centre of mass by appeal tosymmetry.
- Know the positions of the centres of mass of a
- Be able to find the centre of a mass of a compositebody by considering each constituent part as a particle
- Be able to use the position of the centre of mass in
- situations involving the equilibrium of a rigid body.E.g. a suspended object.
- Exercise level 1
- Exercise level 2
- Section test C1
1.2: Centre of mass of a lamina
1.3: Centre of mass of a triangular lamina
1.4: Centre of mass of composite bodies 2D
1.5: Centre of mass of composite bodies 3D
1.6: Centres of mass and equilibrium / .
Composite bodies may be formed by the addition or subtraction of parts.
Where a composite body includes parts whose centre of mass the
learner is not expected to know or be able to find, the centre of mass will be
given.
For the purpose of calculating its moment, the weight of a body can be taken as acting through its centre of mass.
MEI_FM_Mecha / ► Centre of mass / ► Centre of mass: Topic assessment
Impulse & momentum 1 /
- Be able to calculate the impulse of a forceas a vector and in component form.
- Understand and use the concept of linear
- Understand and use the impulse-momentum
- Understand and use the principle that asystem subject to no external force hasconstant total linear momentum and that
- Understand the term direct impact and the
- assumptions made when modelling direct
- Be able to apply the principle of conservation of linear
bodies. / MEI_FM_Mecha / ► Impulse and momentum / ► Impulse and momentum 1: Introduction /
- Exercise level 1
- Exercise level 2
- Section test I1
- Exercise level 3 (Extension)
1.2: Impulse
1.3: Conservation of momentum
1.4: Momentum and impulse in 2D / Impulse = force × time over which it acts
The total impulse of all the external forces acting on a body is equal to the change in momentum of the body.
Use of relative velocity in one dimension isrequired.
The impulse of a finite external force (e.g. friction) acting over a very short period of time (e.g. in a collision) may be regarded as negligible.
Application to collisions, coalescence and a body
dividing into one or more parts.
Impulse & momentum 2 /
- Know the meanings of Newton’s Experimental Law
direct impact.
- Understand the significance of e = 0 (The bodies coalesce.
- Be able to apply Newton’s Experimental Law inmodelling direct impacts.
- Be able to model situations involving direct impact
Newton’s Experimental Law.
- Understand the significance of e = 1. (The collision is perfectly elastic and kinetic energy is conserved.)
- Understand when KE is notconserved and find the loss.
- Exercise level 1
- Exercise level 2
- Section test I2
- Exercise level 3 (Extension)
2.2: Loss of energy due to impact
2.3: Successive impacts of spheres
2.4: Successive impacts of a sphere with a smooth plane / Newton’s Experimental Law is:
the speed of separation is e x the speed of approach
where e is known as the coefficient
of restitution.
MEI_FM_Mecha / ► Impulse and momentum / ► Impulse and momentum: Topic assessment
Dimensional Analysis /
- Be able to find the dimensions of a quantity in terms of M, L and T, and understand that some quantities are dimensionless.
- Understand and be able to use the relationship between the units of a quantity and its dimensions.
- Be able to change the units in which a quantity isgiven.
- Be able to use dimensional analysis to check the consistency of a relationship.
- Use dimensional analysis to determine unknownindices in a proposed formula.
- Use a model based on dimensional analysis
- Exercise level 1
- Exercise level 2
- Section test D1
1.2: Dimensional consistency
1.3: Determining indices in a proposed formula
1.4: Modelling using dimensional analysis / Know the dimensions of angle and frequency. Work out without further
guidance the dimensions of density (mass per unit volume), pressure
(force per unit area) and other.
Deduce the dimensions of an unfamiliar quantity from a given relationship.
E.g. to find the value of a
dimensionless constant.
E.g. to investigate the effect of a
percentage change in some of the
variables.
MEI_FM_Mecha / ► Dimensional analysis / ► Dimensional analysis: Topic assessment
PRCv1.0 16/04/2019