Absolute value Transitional Reasoning Practice

Questions

1. 1.

   In an energy storage system, the operating voltage variations of two battery modules, Module P and Module Q, are monitored relative to a balanced baseline of 0 volts. Module P operates above the baseline with an absolute voltage variation of 3.6 volts such that $|p| = 3.6$ with $p > 0$, while Module Q operates below the baseline with an absolute voltage variation of 5.4 volts such that $|q| = 5.4$ with $q < 0$. The system controller evaluates the difference between the voltage spread separating the two modules, $|p - q|$, and the magnitude of their combined net variation, $|p + q|$. What is the value of $|p - q| - |p + q|$, in volts?

   • A) 0.0 volts
   • B) 3.6 volts
   • C) 10.8 volts
   • D) 7.2 volts
2. 2.

   In an oceanographic survey, vertical positions are measured relative to the ocean surface at 0 meters, with depths below the surface represented by negative rational numbers. An acoustic beacon is anchored at an elevation of $-34.5$ meters, and a seabed monitoring station is fixed at an elevation of $-80.4$ meters. A research submersible operates at an elevation $d$ such that its vertical distance from the beacon satisfies $|d - (-34.5)| = 18.2$ meters. If the submersible chooses the operational elevation that is closer to the seabed monitoring station, what is the distance between the submersible and the ocean surface, in meters?

   • A) 52.7 meters
   • B) 16.3 meters
   • C) 27.7 meters
   • D) 45.9 meters
3. 3.

   A hydrological station monitors the water level of a mountain reservoir relative to a standard flood-control baseline. During a four-week observation period, the weekly water levels are recorded as Week 1 at $-4.8$ meters, Week 2 at $+2.6$ meters, Week 3 at $-5.3$ meters, and Week 4 at $+3.9$ meters. The station evaluates each reading's deviation from an alert threshold of $-1.5$ meters using the formula $|w - (-1.5)|$, where $w$ represents the recorded water level. What is the sum of the greatest and least deviation values among the four weeks, in meters?

   • A) 8.7
   • B) 9.2
   • C) 7.1
   • D) 2.1
4. 4.

   In a materials science laboratory, the temperature of an alloy sample is monitored across three consecutive stages. The temperature is initially set to -12.4°C in Stage 1, adjusted to +8.6°C in Stage 2, and finally brought to -5.5°C in Stage 3. If the total thermal adjustment magnitude is defined as the sum of the absolute values of the temperature changes between consecutive stages, what is this total magnitude in degrees Celsius?

   • A) 24.1°C
   • B) 35.1°C
   • C) 26.5°C
   • D) 6.9°C
5. 5.

   A robotic arm moves along a vertical calibration track where the reference mark represents 0 cm. During a precision test, the arm records three stop positions: Point K at $-\frac{15}{2}$ cm, Point L at $+\frac{29}{4}$ cm, and Point M at $-\frac{31}{4}$ cm. The system evaluates the distance of each stop from the reference mark using absolute value. What is the difference between the greatest and smallest distances from the reference mark, in centimeters?

   • A) 0.25 cm
   • B) 0.75 cm
   • C) 15.00 cm
   • D) 0.50 cm

Answers and step-by-step solutions appear after you finish the test.