Finding Rates of Change – Part 1 Slideshow 29, Mathematics Mr. Richard Sasaki, Room 307

Objectives Recall the meaning of rate of change Be able to find the rate of change for linear and simple quadratic (square) relationships Be able to find ranges for such relationships with differing rates of change

Meaning What does rate of change mean? The rate of change is the amount a variable changes over time (or in relation to another variable). We looked at rate of change in Grade 8 so we’ll have a review first of a similar example. Example Number of seconds Amount of petrol

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The rate of change…changes? For linear relationships, as we were able to see, the rate of change is constant The rate of change would change for a relationship. non-linear The gradient triangles would all differ.

Dropping Things We’re going to look at mechanics a little. If an object is dropped, what is the formula you use (if we ignore air resistance)? Time (seconds) Distance (metres) (2 s.f) Example Mao dives off of a platform and it takes her 5 seconds to reach the water. How far did she dive?

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Slopes and Rolling Things Again, for estimation, we will ignore air resistance and friction to simplify the examples. These will be similar to square proportion examples at the start of Chapter 4. Example A ball rolls down a slope for 7 seconds and is 98 metres in length. If the distance travelled is directly proportional to the square of the time, write an equation for the distance it has fallen and hence, write down how far it travels rolling for a total of 10 seconds.

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Ranges of Distance As you know, the speed of something moving changes if its distance travelled is directly proportional to the square of time taken. Time & Distance increasing evenly… How is the distance increasing? The distance travelled is increasing more quickly as time passes by This is because the speed is increasing (at a constant rate (acceleration)). Like with these gradient triangles, we can find the average speed for ranges of time.

Ranges of Distance As the speed increases, obviously the range of distance will differ depending on the time. Example Write down the distance travelled from 2 to 5 seconds.

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