We have now completed the work on Rates of Change. The complete solutions to all problems from exercises 6.1 to 6.4 have now been posted on the Maths Methods Wiki.
You will have noticed by now that Rates of Change involves many of the skills that you have already learned; gradients in particular. When finding an average velocity you really are only finding the gradient between two points. When you are finding the instantaneous velocity, you fit a tangent to the curve and find the gradient of that tangent which, once again, involves finding two points on the tangent line and then using these to calculate the gradient between these two points. Same old skills you have been using all year only in a different context.
You also learned that a rate is a measure of how one variable changes with respect to another variable. In the case of distance time graphs this change of distance with respect to a change in time is called … wait for it … speed (velocity for displacement verses time). So the “new” skills learned in this unit are just previously learned skills within a new context.
This Rates of Change unit we have just completed is actually an introduction to two topics; one from maths and one from physics. The Physics topic is called Kinematics, which is the study of motion. The mathematics topic is Calculus. This is a significant area of study which dominates much of the remainder of your mathematics studies in Year 11 and 12, particularly in Maths Methods and Specialist Maths. More on that in term 3!
Please make sure that you have completed all of Ex 6.1 to 6.4 by the need of the school holidays so you will be ready for the assessment task in week one of term three. See you all then. 🙂