問 1
1 点Evaluate the following expression:
\( -9 - (-15) \)
Junior Secondary · Mathematics
Directed Numbers：練習問題
その場で採点される選択問題 5 問と、解説つきの記述問題 4 問。すべて「Directed Numbers」からの出題です。
9 問21 点無料・登録不要
問 2
1 点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?
問 3
1 点Evaluate the expression:
\( \frac{|-4^2 + (-2)^3 \times (-1)| - (-3)^2}{(-1)^{2024} + (-22) \div 11} \)
問 4
1 点Which of the following statements is correct?
問 5
1 点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?
問 6
2 点A point on a number line starts at position \(3\). If it moves \(8\) units to the left, what is its final position?
まず自分で答えを書いてから、解説と照らし合わせましょう。
問 7
5 点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 \( \frac{A + B}{C} \).
まず自分で答えを書いてから、解説と照らし合わせましょう。
問 8
4 点Find the results of the following.
(a) 7 times 22.
(b) 44 minus 26.
(c) 12 plus 13.
(d) Divide 48 by 8.
まず自分で答えを書いてから、解説と照らし合わせましょう。
問 9
5 点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).
まず自分で答えを書いてから、解説と照らし合わせましょう。
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