問 1
1 点In the formula \( y = 3x + \frac{z}{2} \), express \( z \) as the subject of the formula.
Junior Secondary · Mathematics
Formula：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 5 問。すべて「Formula」からの出題です。
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問 2
1 点Make $$x$$ the subject of the formula $$y = \frac{3x+1}{x-2}$$.
問 3
1 点A total value \( V \) for two items is given by \( V = a x + b y \), where \( a \) and \( b \) are the unit prices for items 1 and 2 respectively, and \( x \) and \( y \) are the quantities of items 1 and 2. Make \( x \) the subject of the formula.
問 4
1 点Make $$b$$ the subject of the formula $$c = \frac{ab}{2}$$.
問 5
1 点Given the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \), express \( y_1 \) in terms of \( m \), \( x_1 \), \( x_2 \), and \( y_2 \).
問 6
3 点The formula for the total cost, \( C \), of producing \( n \) items is given by \( C = 500 + 10n \). If the total cost is \( \$1200 \), find the number of items produced, \( n \).
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
3 点The total cost $$C$$ of producing $$n$$ items is given by the formula $$C = 150 + 2.5n$$. If the total cost is $$ \$400 $$, find the number of items produced, $$n$$.
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
5 点Make $$x$$ the subject of the formula $$y = \frac{x+a}{bx-c}$$.
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 9
4 点The formula for converting a temperature measured in degrees Celsius (\(C\)) to degrees Fahrenheit (\(F\)) is given by:
$$\text{F} = \frac{9}{5}\text{C} + 32$$
a) If the temperature is \(25^\circ\text{C}\), find the temperature in degrees Fahrenheit (\(F\)).
b) Change the subject of the formula to \(C\).
c) Use the result from (b) to find the temperature in degrees Celsius (\(C\)) when the temperature is \(77^\circ\text{F}\).
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 10
7 点In electrical engineering, a formula is used to estimate the total heat energy output \(H\) (in kilojoules, kJ) generated in a complex circuit segment over a specific time \(t\) (in seconds). This heat output depends on the current \(I\) (in Amperes, A) and the resistance \(R\) (in Ohms, \(\Omega\)), according to the formula:
$$ H = \frac{I^2 R t}{k + I R} $$
Where \(k\) is a fixed constant representing internal factors of the circuit.
(a) If the circuit constant \(k\) is 5, rearrange the formula \( H = \frac{I^2 R t}{5 + I R} \) to make \(R\) the subject.
(b) In a standard circuit configuration where \(k=5\), the measured heat energy output is \(H = 45 \text{ kJ}\) over a time period of \(t = 50 \text{ s}\) with a constant current \(I = 3 \text{ A}\). Use your result from part (a) to find the resistance \(R\) of the segment. Give your answer as a fraction in its simplest form.
(c) A researcher designs an upgraded circuit where the constant changes to \(k=2\). If the circuit segment has a resistance of \(R = 5 \ \Omega\) and a current of \(I = 4 \text{ A}\) flows through it, calculate the time \(t\) (in seconds) required to generate \(H = 100 \text{ kJ}\) of heat energy.
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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