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NSWMaths Standard 2Quick questions

Year 12: Measurement

Quick questions on Ratios, scale drawings and the trapezoidal rule for HSC Maths Standard 2

13short 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 ratios and scale?
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A scale of 1:n1:n means 11 unit on the drawing represents nn units in reality.
What is linear scaling?
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Real distance = drawing distance ×\times scale factor.
What is area scaling?
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When you scale linear dimensions by a factor kk, area scales by k2k^2.
What is volume scaling?
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When you scale linear dimensions by kk, volume scales by k3k^3.
What is reading maps?
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Australian topographic maps commonly use 1:250001:25000 or 1:500001:50000. A 44 cm distance on a 1:250001:25000 map is 4×25000=1000004 \times 25000 = 100000 cm = 11 km.
What is when the trapezoidal rule applies?
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Use when the area is bounded by one straight side (where you measure the baseline) and one irregular curve (where the offsets are taken perpendicular to the baseline).
What is multiple-strip?
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A lake shoreline is measured against a 120120 m baseline. Offsets at 0,30,60,90,1200, 30, 60, 90, 120 m are 0,25,32,20,00, 25, 32, 20, 0 m. Estimate the lake area.
What is floor plan (Australian context)?
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A house floor plan at scale 1:1001:100 shows a rectangular kitchen 5.45.4 cm by 4.24.2 cm.
What is map distance to ground distance?
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On a 1:500001:50000 map, two summits are separated by 6.46.4 cm. Ground distance:
What is mixing units mid-calculation?
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Convert cm to m before computing real area in m2^2, or convert at the end.
What is doubling the end offsets in the trapezoidal rule?
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Only the interior offsets are doubled. End offsets are counted once.
What is wrong strip width?
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hh is the distance between consecutive offsets, not the total baseline length.
What is using a closed-form formula for an irregular region?
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The trapezoidal rule is the right tool when the boundary is irregular. Do not try to fit a triangle or rectangle to the whole shape. :::

All Maths Standard 2Q&A pages