Negative numbers and the number line Transitional Reasoning Download PDF

Questions

1. 1.

   A geological survey team maps an underground core-sampling trench along a horizontal number line, with the surface reference station positioned at 0. Sampling marker J is fixed at coordinate $-27$, and sampling marker K is fixed at coordinate 9. The team places two intermediate monitoring beacons, $M_1$ and $M_2$, in order from left to right, such that the segment between J and K is divided into three equal intervals. Which option correctly identifies the coordinate of beacon $M_2$ and the distance between beacon $M_1$ and the reference station at 0?

   • A) Beacon $M_2$ is at $-9$, and beacon $M_1$ is 18 units from 0.
   • B) Beacon $M_2$ is at $-6$, and beacon $M_1$ is 21 units from 0.
   • C) Beacon $M_2$ is at $-3$, and beacon $M_1$ is 15 units from 0.
   • D) Beacon $M_2$ is at 3, and beacon $M_1$ is 15 units from 0.
2. 2.

   An environmental research team places three ground sensors along a straight transect modeled on a horizontal number line where the base station is at 0. Sensor A is installed at coordinate $-28$, and Sensor B is placed 12 units to the right of Sensor A. Sensor C is placed to the left of 0 at a distance from 0 equal to half the distance of Sensor B from 0. Which option correctly orders the coordinates of the three sensors from least to greatest and gives the distance between Sensor A and Sensor C?

   • A) $C < B < A$, and the distance between Sensor A and Sensor C is 20 units
   • B) $A < B < C$, and the distance between Sensor A and Sensor C is 20 units
   • C) $A < B < C$, and the distance between Sensor A and Sensor C is 36 units
   • D) $B < A < C$, and the distance between Sensor A and Sensor C is 20 units
3. 3.

   A marine research team monitors water pressure using a vertical measuring line where sea level corresponds to the reference point 0. Sensor P is installed at a depth corresponding to -32 on the number line, while Sensor Q is placed at -8. A relay device is positioned at point M, which is located on the number line exactly halfway between Sensor P and Sensor Q. What is the coordinate of point M, and what is its distance from the reference point 0?

   • A) The coordinate of point M is -24, and its distance from 0 is 24 units.
   • B) The coordinate of point M is -20, and its distance from 0 is 20 units.
   • C) The coordinate of point M is -16, and its distance from 0 is 16 units.
   • D) The coordinate of point M is -12, and its distance from 0 is 12 units.
4. 4.

   A robotic rover explores an underground cavern system mapped along a horizontal number line where 0 meters represents the cave entrance. The rover begins its mission at point A located at -15 meters and travels 22 meters in the positive direction to establish monitoring station B. The research team then designates point C at the integer that is the opposite of point B's coordinate. What is the location of point C on the number line, and what is the distance between point A and point C?

   • A) Point C is at +7 meters, and the distance between point A and point C is 22 meters.
   • B) Point C is at -7 meters, and the distance between point A and point C is 22 meters.
   • C) Point C is at -7 meters, and the distance between point A and point C is 8 meters.
   • D) Point C is at +15 meters, and the distance between point A and point C is 30 meters.
5. 5.

   A scientist records temperature changes inside a climate chamber using a horizontal number line where 0 °C is the reference origin. At the beginning of a test, the chamber temperature is -9 °C. The temperature rises by 14 °C during the heating phase and then drops by 8 °C during the cooling phase. What is the final temperature of the chamber, and where is it positioned on the number line relative to 0?

   • A) +3 °C, located 3 units to the right of 0
   • B) -5 °C, located 5 units to the left of 0
   • C) -3 °C, located 3 units to the left of 0
   • D) -11 °C, located 11 units to the left of 0