Negative numbers and number lines：練習問題

Which of the following points on the number line represents the number \(-3\)?

On a number line, point \( X \) is at \( -18 \). Point \( Y \) is 25 units to the right of \( X \). Point \( Z \) is 14 units to the left of \( Y \). What is the position of point \( Z \)?

Calculate the value of \( 12 - (-5) + (-8) - 3 \) and plot the result on a mental number line. What is the final value?

Which of the following numbers has the smallest value?

Point \( P \) on a number line is at \( -15 \). It moves 8 units to the right to point \( Q \), and then moves 12 units to the left to point \( R \). Finally, it moves 5 units to the right to point \( S \). What number does point \( S \) represent?

On a horizontal number line, point P represents the number \(-14\) and point Q represents the number \(6\). What is the distance, in units, between point P and point Q?

A submarine is at a depth of \(-150\) metres relative to sea level. It descends a further \(85\) metres and then ascends \(112\) metres. What is the final depth of the submarine? Represent your answer as a negative number.

On a vertical number line, the temperature at the top of a mountain is \(-8^{\circ}\text{C}\) and the temperature at the base is \(14^{\circ}\text{C}\). If the temperature drops by \(2.2^{\circ}\text{C}\) for every \(300\text{ m}\) increase in altitude, what is the height of the mountain in metres?

On a horizontal number line, the distance between two points representing integers \(x\) and \(y\) is 15 units. Point \(x\) represents \(-7\).
(a) Find the two possible values of \(y\).
(b) If point \(z\) is exactly halfway between \(x\) and the larger value of \(y\), what integer does \(z\) represent?
(c) If a point \(w\) starts at \(z\) and moves 4 units to the left and then 9 units to the right, what is its final position?

A temperature sensor records the following changes in a laboratory freezer over three hours:
Hour 1: The temperature starts at \( -12^{\circ}\text{C} \) and rises by \( 5.5^{\circ}\text{C} \).
Hour 2: The temperature drops by \( 8.25^{\circ}\text{C} \).
Hour 3: The temperature rises by \( 3\frac{3}{4}^{\circ}\text{C} \).
(a) Calculate the temperature at the end of Hour 2.
(b) What is the final temperature at the end of Hour 3?
(c) If the safety limit is \( -10^{\circ}\text{C} \), is the final temperature above or below this limit, and by how many degrees?