Investigating Earth — Chapter quiz · Earth & Space Science, Grade 9

Use measurements, models, maps, and reference tools to build explanations from evidence.

Problem 1

Rain readings are 16, 18, and 20 mm. Find the mean.
Answer and explanation

18 mm

54 ÷ 3 = 18.

Problem 2

A simulation predicts 30 mm of rain; 25 mm is observed. Give two things to examine before rejecting the model.
Answer and explanation

Check uncertainty and spatial/time scales, input data, instrument accuracy, and whether the model represents the conditions. One mismatch alone does not determine its overall usefulness.

Problem 3

Independent chapter check: A balance repeatedly reads 19.7 g for a 20.0 g reference. A student reports their average as accurate because the readings agree. Explain the error and propose a correction check.
Answer and explanation

The readings are precise but 0.3 g below the reference. Their average is still 19.7 g. Check calibration with suitable reference masses over the working range and repeat the measurement; do not assume repeatability proves accuracy.

Compare the repeated values with the independent 20.0 g reference.

Find the bias: 19.7−20.0 = −0.3 g.

Use calibration checks to distinguish a systematic offset from random spread.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 4

A slope rises from 80 m to 140 m over 1.5 km horizontally. Find its average gradient.
Answer and explanation

40 m/km

(140 − 80) ÷ 1.5 = 40.

Problem 5

Two routes rise the same height. One is twice as long horizontally. Compare average gradients.
Answer and explanation

The longer route has half the average gradient because the same rise is divided by twice the distance.

Problem 6

Independent chapter check: A map scale is 1 cm = 0.4 km. Two points 3 cm apart along a stated map line rise from 220 to 280 m. Calculate average gradient and explain why it does not establish every local slope.
Answer and explanation

Ground distance is 1.2 km and rise is 60 m, so average gradient is 50 m/km. Local segments can be steeper or flatter; additional contour crossings or survey points are needed.

Convert 3×0.4 = 1.2 km.

Subtract 280−220 = 60 m.

Divide 60/1.2 = 50 m/km and distinguish the average from local values.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

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