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NSWMaths Standard 2Year 12: Measurement

Quick questions on Rates, unit conversions and the unitary method for HSC Maths Standard 2

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is treating units as algebra?
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The reliable way through every rate problem is to carry the units along with the numbers and cancel them like the letters in algebra (a "symbol" you cancel from top and bottom). Set up each calculation so the unwanted units cancel and the unit you want is left. This turns a wordy problem into a single line of arithmetic. It also shows up at once if you have multiplied when you should have divided.
What is wrong unit conversion direction?
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11 km = 10001000 m, so converting 55 km to m gives 50005000, not 0.0050.005. From larger to smaller the number grows; from smaller to larger it shrinks.
What are area and volume factors?
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11 m2^2 = 1000010000 cm2^2 (not 100100) and 11 m3^3 = 10000001\,000\,000 cm3^3. Squared units need squared factors; cubed units need cubed factors.
What is mismatched units in a rate?
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A speed in km/h needs the time in hours, not minutes. Convert first.
What are not sanity-checking dosages?
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An answer of dozens of tablets a day signals a unit error. Flag it.

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