DIMENSIONAL ANALYSIS
Convert 4.50 km to centimeters. Your response must include the correct conversion chain and final answer.
A. 4.50 × 10² cm
B. 4.50 × 10³ cm
C. 4.50 × 10⁵ cm
D. 4.50 × 10⁶ cm
C. 4.50 × 10⁵ cm
Which setup correctly converts 350 cm to km AND correctly cancels the units?
A. 350 cm × (100 cm/1 m) × (1000 m/1 km)
B. 350 cm × (1 m/100 cm) × (1 km/1000 m)
C. 350 cm × (1 km/1000 m) × (1 m/100 cm)
D. Both B and C
D. Both B and C
Identify the graph type AND state what kind of data it is best suited to display.
A. Bar graph; categorical/discrete comparisons
B. Line graph; parts of a whole
C. Pie chart; continuous change over time
D. Scatter plot; percentages only
A. Bar graph; categorical/discrete comparisons
Using the points (2, 6) and (6, 18), calculate the slope.
A. 2
B. 3
C. 4
D. 6
B. 3
A scientist changes light intensity and measures plant growth. Identify BOTH the manipulated variable and the responding variable.
A. Plant growth; time
B. Plant growth; light intensity
C. Time; light intensity
D. Light intensity; plant growth
D. Light intensity; plant growth
Convert 7.25 g to micrograms. Which answer AND setup is correct?
A. 7.25 g × (1 mg/1000 g) × (1 μg/1000 mg) = 7.25 × 10⁻⁶ μg
B. 7.25 g × (1000 mg/1 g) × (1000 μg/1 mg) = 7.25 × 10⁶ μg
C. 7.25 g × (1000 g/1 mg) × (1000 mg/1 μg) = 7.25 × 10⁶ μg
D. 7.25 g × (1 g/1000 mg) × (1 mg/1000 μg) = 7.25 × 10⁶ μg
B. 7.25 g × (1000 mg/1 g) × (1000 μg/1 mg) = 7.25 × 10⁶ μg
Convert 2.40 kg/L to g/mL. Which sequence is correct?
A. 2.40 kg/L × (1000 g/1 kg) × (1 L/1000 mL) = 2.40 g/mL
B. 2.40 kg/L × (1 kg/1000 g) × (1000 mL/1 L) = 2.40 g/mL
C. 2.40 kg/L × (1000 g/1 kg) × (1000 mL/1 L) = 2.40 × 10⁶ g/mL
D. 2.40 kg/L × (1 kg/1000 g) × (1 L/1000 mL) = 2.40 × 10⁻⁶ g/mL
A. 2.40 kg/L × (1000 g/1 kg) × (1 L/1000 mL) = 2.40 g/mL
Look at the scatter plot. Identify the correlation AND describe what happens to Y as X increases.
A. Positive; Y generally increases
B. Negative; Y generally increases
C. Positive; Y generally decreases
D. No correlation; Y stays constant
A. Positive; Y generally increases
Using points (2, 6) and (6, 18), calculate the slope AND classify the relationship.
A. 2; negative
B. 3; positive
C. 4; positive
D. 6; negative
B. 3; positive
A graph has X-axis values of 0, 5, 10, 15, 20 and Y-axis values of 0, 10, 20, 30, 40. What are the intervals for X and Y?
A. X = 5; Y = 10
B. X = 10; Y = 5
C. X = 5; Y = 5
D. X = 10; Y = 10
A. X = 5; Y = 10
A cyclist travels 18.0 km in 45.0 min. What is the cyclist's average speed in m/s?
A. 0.400 m/s
B. 6.67 m/s
C. 8.00 m/s
D. 24.0 m/s
B. 6.67 m/s
A student converts 4.50 m/s to km/h and writes: 4.50 m/s × (1000 m/1 km) × (1 h/3600 s). What is the error and what should the correct setup use?
A. The m factor is correct; only the hour factor is wrong.
B. Both conversion factors are backwards; use (1 km/1000 m) × (3600 s/1 h).
C. Only the m factor is backwards; use (1 km/1000 m).
D. The setup is correct and gives 0.00125 km/h.
B. Both conversion factors are backwards; use (1 km/1000 m) × (3600 s/1 h).
Using the bar graph, identify the greatest value AND calculate the difference between the greatest and smallest values.
A. 40°C; 18 mL
B. 40°C; 20 mL
C. 30°C; 12 mL
D. 10°C; 18 mL
A. 40°C; 18 mL
The Mass vs. Volume graph passes through (10 mL, 10 g) and (40 mL, 40 g). Calculate the slope AND include the correct unit.
A. 1 mL/g
B. 1 g/mL
C. 30 g/mL
D. 30 mL/g
B. 1 g/mL
Using the Mass vs. Volume graph, calculate the slope AND identify which DRY MIX variable is on the X-axis.
A. 1.0 g/mL; independent/manipulated = volume
B. 1.0 mL/g; independent/manipulated = mass
C. 10 g/mL; dependent/responding = volume
D. 0.10 g/mL; dependent/responding = mass
A. 1.0 g/mL; independent/manipulated = volume
A car travels at 55.0 mi/h. Convert its speed to m/s
* 1 mile = 1.609 km
A. 8.90 m/s
B. 24.6 m/s
C. 88.5 m/s
D. 31.8 m/s
B. 24.6 m/s
A liquid has density 0.850 g/mL. A tank contains 3.20 L. What is the mass in kg? Then determine which setup is correct.
A. 2.72 kg; 3.20 L × (1000 mL/1 L) × (0.850 g/1 mL) × (1 kg/1000 g)
B. 2.72 kg; 3.20 L × (1 L/1000 mL) × (0.850 g/1 mL) × (1000 g/1 kg)
C. 2.72 × 10³ kg; 3.20 L × (1000 mL/1 L) × (0.850 mL/1 g)
D. 0.00272 kg; 3.20 L × (1 mL/1000 L) × (0.850 g/1 mL)
A. 2.72 kg; 3.20 L × (1000 mL/1 L) × (0.850 g/1 mL) × (1 kg/1000 g)
Using the Mass vs. Volume graph: (1) identify the independent variable, (2) identify the dependent variable, and (3) determine whether the relationship is positive or negative.
A. Mass; Volume; negative
B. Volume; Mass; positive
C. Volume; Mass; negative
D. Mass; Volume; positive
B. Volume; Mass; positive
A graph shows Distance vs. Time. Calculate the slope AND identify what the slope represents.
A. 7 m/s; speed
B. 7 s/m; time
C. 0.14 m/s; speed
D. 70 m/s; distance
A. 7 m/s; speed
A graph shows Distance vs. Time. A student claims the object is speeding up because the line rises. Which choice correctly evaluates the graph?
A. Correct; any rising line means acceleration.
B. Incorrect; a straight line with constant slope indicates constant speed.
C. Correct; positive slope always means acceleration.
D. Incorrect; a positive slope means the object is not moving.
B. Incorrect; a straight line with constant slope indicates constant speed.
A machine uses 2.75 L of fuel to travel 38.5 km. What is the fuel use in mL per meter?
A. 0.0714 mL/m
B. 0.714 mL/m
C. 7.14 mL/m
D. 71.4 mL/m
A. 0.0714 mL/m
A sample has a mass of 6.40 × 10² mg and a volume of 2.00 cm³. What is its density in kg/m³?
A. 0.320 kg/m³
B. 0.320 × 10³ kg/m³
C. 3.20 × 10⁻¹ kg/m³
D. 3.20 × 10² kg/m³
D. 3.20 × 10² kg/m³
Look at the scatter plot. Determine the correlation, then choose the statement that is supported by the graph.
A. Negative correlation; as time increases, temperature generally decreases.
B. Positive correlation; as time increases, temperature generally increases.
C. No correlation; the points are random.
D. Positive correlation; the graph proves time causes the temperature change.
B. Positive correlation; as time increases, temperature generally increases.
Using the Distance vs. Time graph, determine ALL THREE: (1) slope, (2) relationship, and (3) distance at 12 s if the trend continues at the same rate.
A. 0.14 m/s; positive/increasing; 1.68 m
B. 7 m/s; negative/decreasing; 84 m
C. 7 m/s; positive/increasing; 84 m
D. 70 m/s; positive/increasing; 840 m
C. 7 m/s; positive/increasing; 84 m
A substance has a mass of 45.0 g and occupies 15.0 mL. (1) Calculate density, (2) identify the independent variable if volume is changed and mass is measured, and (3) predict the mass when volume is 20.0 mL if density stays constant.
A. 3.00 g/mL; volume; 60.0 g
B. 3.00 g/mL; mass; 60.0 g
C. 0.333 g/mL; volume; 6.67 g
D. 30.0 g/mL; volume; 600 g
A. 3.00 g/mL; volume; 60.0 g