12 multiple-choice questions, progressively harder.
A flat skating area has a straight-sided rectangular section and a rounded end that is close to half a circle. Which pieces give a simple model of its surface area?
Solution
Correct answer: B
The rectangular section and the rounded half-circle section cover the two parts of the surface in the model.
A carpenter reads 93 cm on a tape held across a shelf. The plan sets the depth to exactly 31 cm for the model. Which is the measured dimension?
Correct answer: D
The tape reading is measured. The plan fixes the depth for this calculation.
A sign is modeled as a circle to estimate how much paint its face takes. Which detail can be left out of this area calculation if it leaves the outline and surface unchanged?
Correct answer: A
Lettering color changes neither the region to be painted nor its dimensions.
A rectangular ramp footprint is reported as 180 cm long by 0.9 m wide. Which length in meters can be used with the width?
Correct answer: C
Use 100 centimeters per meter to express the length in meters.
A rectangular shade panel measures about 495 cm by 2.9 m. Which is the closest rough estimate of its area?
Convert 495 cm to 4.95 m. Round the dimensions to about 5 m and 3 m.
A length is reported as 17 cm to the nearest centimeter, with ties going to the larger report. What is the half-step from the reported value to either endpoint of the measurement interval?
Consecutive reports are one centimeter apart. Each endpoint is half that distance from the report.
A meter reading of 2.65 is exactly halfway between two tenths. The rule sends a tie to the larger report. What will be reported?
The neighboring reports are 2.6 m and 2.7 m. The rule chooses 2.7 m.
A floor model has a fixed outer area. A rectangular opening of fixed length gets wider. What happens to the modeled floor area outside the opening?
The wider opening takes a larger area away from the same outer area.
A pond model uses a tape-measured length and width to predict the water surface area. Which is an independent check of that prediction?
A grid survey can estimate the area from different data. The other steps use the original inputs or their result.
A sidewalk model predicts an area from 58 to 61 square meters. A separate measurement of the same area gives 55 square meters. Which is justified?
The observation is outside the prediction interval. The difference gives a reason to investigate the inputs, assumptions, and observation.
A straight-sided model extends beyond a real edge in one place. That extra patch is the only difference between the two shapes. What effect does the extra patch have on the modeled area?
The model counts all of the real region and also counts the extra patch.
A positive width can take any value less than 3.2 cm but at least 3.1 cm. Which describes 3.2 cm?
Widths can approach 3.2 cm from below, and the inequality excludes 3.2 cm.
Reset this practice set?
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