Junior Secondary · Mathematics

Directed Numbers: Practice Questions

5 multiple-choice questions marked as you go, and 4 written questions with worked solutions. All on Directed Numbers.

9 questions21 marksFree, no account

Question 1

1 mark

Evaluate the following expression:
$ -9 - (-15) $

Question 2

1 mark

The altitude of a mountain climber changes over three hours as follows:
Hour 1: Ascends $ 450 $ m from base camp (altitude $ 1200 $ m).
Hour 2: Descends $ 15 \% $ of his current altitude.
Hour 3: Changes altitude by $ -120 $ m.
What is the climber's final altitude relative to sea level?

Question 3

1 mark

Evaluate the expression:
$ \frac{|-4^2 + (-2)^3 \times (-1)| - (-3)^2}{(-1)^{2024} + (-22) \div 11} $

Question 4

1 mark

Which of the following statements is correct?

Question 5

1 mark

In a science experiment, the initial temperature of a liquid is $12^{\circ}\text{C}$. The temperature then decreases at a constant rate of $3^{\circ}\text{C}$ per minute for $7$ minutes. After that, it increases by $5^{\circ}\text{C}$. What is the final temperature of the liquid?

Question 6

2 marks

A point on a number line starts at position $3$. If it moves $8$ units to the left, what is its final position?

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Question 7

5 marks

Given three values A, B, and C:
$ A = -4^2 - (-3) \times 2 $
$ B = |(-2) \times 5 + 4| $
$ C = [10 + (-2) \times 6] \div (-1) $

Evaluate the value of the expression $ \frac{A + B}{C} $.

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Question 8

4 marks

Find the results of the following.

(a) 7 times 22.
(b) 44 minus 26.
(c) 12 plus 13.
(d) Divide 48 by 8.

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Question 9

5 marks

A deep-sea exploration submersible starts its operation at a depth of 50 meters below sea level. We represent depths below sea level using negative directed numbers (e.g., 50 m below sea level is $$ -50\text{ m} $$ ) and movement upwards as positive, and movement downwards as negative.

(a) From its starting position, the submersible first ascends 15 meters, then dives 68 meters, and finally ascends 3 meters. Calculate the final depth of the submersible relative to sea level. Show your calculation.
(b) During a separate deep dive, the submersible traveled from its starting depth of 50 m below sea level to a maximum depth of 150 meters below sea level. The temperature decreased at an average rate of $$ -0.5^\text{o}\text{C} $$ for every 10 meters of depth increase. If the water temperature at the starting depth ( $$ -50\text{ m} $$ ) was $$ 18^\text{o}\text{C} $$ , what was the temperature at the maximum depth of $$ -150\text{ m} $$ ?
(c) Suppose the submersible, currently at the final depth calculated in part (a), must make an emergency ascent back to sea level ( $$ 0\text{ m} $$ ). If this ascent takes exactly 4 minutes, calculate the average vertical speed of the submersible during this ascent, expressed as a directed number in meters per minute (upward movement is positive speed).

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