FSMQ Level 3 (pilot) Dynamics scheme of work
Before starting this Advanced (Level 3) FSMQ students are expected to have acquired the skills and knowledge associated with a Functional Mathematics course at Level 2, or equivalent.
Candidates will also need knowledge of the following.
 Trigonometry: Use of sin, cos and tan (but not the Sine or Cosine rules)

Algebra: Collection of like terms and solution of linear equations such as 3 + 5t = 24 – 5t
Solution of a quadratic equation by at least one of the following methods: use of graphic calculator, use of the formula (which must be memorised): , Factorisation (where appropriate), completion of the square.
A suggested work scheme showing topics and methods to be covered is given below, but the order and time allocations can be varied to suit different groups of students.
Throughout the course, students should learn how to use mathematical models to solve problems, making assumptions to create a simple model of a real situation. Experimental or investigational methods should be used to explore how the mathematical model relates to the actual situation. Modelling will include the appreciation that it is appropriate at times to treat relatively large moving bodies as point masses, that the friction law F =µR is experimental, and that the force of gravity can be assumed to be constant only under certain circumstances. The terms: light, smooth, rough, inextensible, thin and uniform should be introduced as soon as possible and used wherever relevant. Students should be encouraged to comment on the modelling assumptions made, including occasions when terms such as particle, light, inextensible string, smooth surface, and motion under gravity are used.
Topic area 
Content 
Nuffield resource 
Sketching and interpreting kinematics graphs 
Find out what students already know about displacement, speed, velocity and acceleration, and discuss the difference between vector and scalar quantities. Use gradients and area under graphs to solve problems (N.B. Calculus NOT required). Find average speed and average velocity. 
Model the motion 
Motion in one dimension with constant acceleration 
Use graphs to derive the equations , , , Learn these formulae and use them to solve problems involving the position, velocity, speed and acceleration of a particle moving in one dimension with constant acceleration. 
Constant acceleration equations 
Vertical motion under gravity 
Carry out an experiment to verify Galileo's theory regarding vertical motion. Apply the constant acceleration formulae to vertical motion under gravity with the acceleration due to gravity taken as 9.8 ms^{–}^{2}. 
Falling ball 
Runaway train 
Topic area 
Content 
Nuffield resources 
Forces 
Introduce forces. Make an elastoscale and use it to measure and investigate forces. Draw force diagrams (identifying those forces present) and clearly label diagrams, distinguishing between forces and other quantities such as velocity. Include force of gravity W = mg with g = 9.8 (Newton’s Universal Law not required), tensions in strings and rods and resistance.

Measure forces 
Force diagrams 

Newton's Laws 
Introduce Newton’s three laws of motion (for a particle of constant mass). Use knowledge that the resultant force is zero to find unknown forces on bodies which are at rest or moving with constant velocity. (Not resolution of forces or components of forces.) Apply Newton’s second law in the form F = ma to particles moving with constant acceleration. Include finding the acceleration of a body, if the forces acting are specified, or unknown forces if the acceleration is given. 
Newtonian modelling 
Friction 
Carry out an experiment to investigate friction. Discuss limiting friction, the coefficient of friction and the relationship F =μR Use F =μR as a model for dynamic friction to solve problems involving motion on a rough surface. 
Investigating friction 
Solve friction problems 

Projectiles 
Use the equations and to solve problems involving motion of an object under uniform gravity in a vertical plane. Include finding initial speed and/or the angle of projection and modification of the equations to take account of the height of release.
Calculate range, time of flight and maximum height. 
Galileo's projectile model 
Projectile problems 
Topic area 
Content 
Nuffield resources 
Momentum 
Introduce the concept of momentum (momentum = mv). Apply the principle of conservation of momentum to two particles for direct impacts in one dimension. (Note that knowledge of Newton's law of restitution is not required by AQA.) Use Force = rate of change of momentum 
Collisions 
Vectors 
Understanding of a vector; its magnitude and direction. Add and subtract vectors, multiply a vector by a scalar. Magnitude and direction of quantities represented by a vector. Solve problems such as finding the time when a particle is at a specified position or has a specified velocity, or finding the position, velocity or acceleration of a particle at a specified time.
Use the constant acceleration equations in vector form (Note that AQA examinations questions will be set using the column vector notation, and resolution of velocities will not be required.) Use momentum as a vector in two dimensions. Apply Newton’s three laws of motion in two dimensions using vectors. 
Vectors 
Revision 
Revise topics. Work through revision questions and practice papers. Discuss the data sheet  make up and work through questions based on it. 

Page last updated on 25 January 2012