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Measurement and units — ISEE Upper practice questions

Measurement and units on the ISEE Upper Mathematics Achievement section covers converting lengths and rates, reading scale drawings, and choosing a tool or graph scale that matches a needed precision. A student must set up a scale ratio, convert a speed from kilometers per hour into meters per second, and pick an interval that shows every measured jump with as much detail as possible. Items are short multiple-choice word problems; some ask for a numerical expression rather than a finished value. Traps include converting only one part of a rate, mixing inches with feet, and picking a scale that clips the data or is too coarse.

  • Section: Mathematics Achievement 47 questions on the paper
  • 87 practice questions in the app

Sample questions

Question 1

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?

  1. A6
  2. B8
  3. C10
  4. D18
Show answer

Answer: B — 8

The drawing length is multiplied by 4 because 3×4=123\times4=12. The represented distance is also multiplied by 4, so 2×4=82\times4=8 feet.

Question 2

A train travels at a rate of 90 kilometers per hour. There are 1,0001{,}000 meters in a kilometer. Which numerical expression gives the train's speed in meters per second?

  1. A90×1,00060×60\dfrac{90 \times 1{,}000}{60 \times 60}
  2. B90×60×601,000\dfrac{90 \times 60 \times 60}{1{,}000}
  3. C60×6090×1,000\dfrac{60 \times 60}{90 \times 1{,}000}
  4. D90×601,000×60\dfrac{90 \times 60}{1{,}000 \times 60}
Show answer

Answer: A — 90×1,00060×60\dfrac{90 \times 1{,}000}{60 \times 60}

Converting 90 km/h to m/s requires multiplying by 1,0001{,}000 m/km (to get meters per hour) and dividing by 60 × 60 s/h (to get meters per second): 90×1,00060×60\dfrac{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 3

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?

  1. AA tape marked every 10 centimeters and graph intervals of 0.25 meter
  2. BA tape marked every 1 centimeter and graph intervals of 0.2 meter
  3. CA tape marked every 1 millimeter and graph intervals of 1 meter
  4. DA tape marked every 1 centimeter and graph intervals of 0.25 meter
Show answer

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+10×0.25=6.03.5+10\times0.25=6.0 meters. Intervals of 0.2 meter stop at 5.5 meters, while 1-meter intervals are unnecessarily coarse.

Practice 87 Measurement and units questions in the app

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