1. Formulae and expressions
[ A3.3 Extension Starter]
1) According to sports’ doctors the maximum heart beat rate (beats per minute) during exercise is given as a person’s age in years subtracted from 200. Another formula used for a maximum safe heart beat rate (H) of a person of age a years is H = 208 – 0.7a.
Is Amy correct?
2) The height of a standing jump can be used to give a rough measure of a person’s power in horse power! The formula is
P horse power for a person of weight w kg jumping h cm.
Tom, who is an average 14-year old, says he can generate 10 horse power. Investigate his claim using the formula.
Preamble
Two activities involving substituting and using real-life equations. The second may well prove challenging, but within a small group situation children should be able to access it.
Possible content
Using and interpreting formulae, re-calling weight of average teenager.
Resources
Calculator, possibly use of a spreadsheet to reduce the “number crunching”.
Solution/Notes
Amy is correct – children need to show a few results – perhaps even a chart from a spreadsheet.
(2) A reasonable estimation of a 14-year olds weight would be 40 to 70 kg. Substituting these values into the equation gives √h in the range 110 to 193, so predicting a standing height of to 37249cm – about 100 to 300metres – certainly not reasonable, therefore Tom must be wrong.
Original Material © Cambridge University Press 2010
Original Material © Cambridge University Press 2010