Measurement and units — ISEE Upper practice questions

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Practice 87 Measurement and units questions in the app

What this topic is

Measurement and units questions test conversions, scale drawings and the choice of sensible tools and scales.

Converting a rate takes care: kilometers per hour becomes meters per second by multiplying by a thousand and dividing by the number of seconds in an hour, and the choices often ask for the expression rather than the final number. Scale drawings use a proportion between drawing length and real length.

Some questions describe a measuring task and ask which tool and level of precision fit, such as measuring to the nearest centimeter rather than the nearest meter. Setting up units in a chain, so unwanted units cancel, prevents upside-down conversions.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

On a scale drawing, every 3 inches represents 2 feet. If a line on the drawing is 12 inches long, how many feet does it represent?

6✗ Not this one8✓ Correct10✗ Not this one18✗ Not this one

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Answer: B — 8

The drawing length is multiplied by 4 because $3 \times 4 = 12$ . The represented distance is also multiplied by 4, so $2 \times 4 = 8$ feet.

Question 2Mid

A train travels at a rate of 90 kilometers per hour. There are 1,000 meters in a kilometer. Which numerical expression gives the train’s speed in meters per second?

\frac{90 \times 1, 000}{60 \times 60}

✓ Correct

\frac{90 \times 60 \times 60}{1, 000}

✗ Not this one

\frac{60 \times 60}{90 \times 1, 000}

✗ Not this one

\frac{90 \times 60}{1, 000 \times 60}

✗ Not this one

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Answer: A — $\frac{90 \times 1, 000}{60 \times 60}$

Converting 90 km/h to m/s requires multiplying by 1,000 m/km (to get meters per hour) and dividing by 60 × 60 s/h (to get meters per second): $\frac{90 \times 1, 000}{60 \times 60}$ . (B) multiplies by seconds-per-hour instead of dividing, (C) inverts the whole expression, and (D) divides by only one factor of 60 instead of both.

Question 3Mid

An athletics coach expects jump distances from 3.6 meters to 5.9 meters and must measure each jump to the nearest centimeter. A graph will have 10 equal vertical intervals beginning at 3.5 meters; its scale should include every jump while showing as much detail as possible. Which measuring tool and graph interval are most appropriate?

A tape marked every 10 centimeters and graph intervals of 0.25 meter✗ Not this oneA tape marked every 1 centimeter and graph intervals of 0.2 meter✗ Not this oneA tape marked every 1 millimeter and graph intervals of 1 meter✗ Not this oneA tape marked every 1 centimeter and graph intervals of 0.25 meter✓ Correct

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Answer: D — A tape marked every 1 centimeter and graph intervals of 0.25 meter

Centimeter markings provide the required measuring precision, and the graph reaches $3.5 + 10 \times 0.25 = 6.0$ meters. Intervals of 0.2 meter stop at 5.5 meters, while 1-meter intervals are unnecessarily coarse.

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Practice 87 Measurement and units questions in the app

Measurement and units — ISEE Upper practice questions

What this topic is

Sample questions

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