Change and motion

Things move, grow, heat up and slow down. This topic is about measuring how fast something changes: first by comparing, then with speed and slopes, and finally with the two big ideas of calculus, the derivative and the area under a curve.

Step	Page	You will be able to
Play	Fast and slow	Compare speeds fairly, tell speeding up from slowing down, and compare how steep slopes are
Explore	Speed, distance and time	Use speed = distance ÷ time, change units, read distance-time graphs and find a true average speed
Build	Slopes and rates of change	Find the slope of a line, write its equation, and work out an average rate of change on any graph
Master	Speed at an instant: the derivative	Shrink a time interval to find the speed at one moment, and find derivatives of powers of \(x\)
Beyond	Areas under curves	Turn speed into distance as an area, add up thin rectangles, and use the fundamental theorem of calculus