Question 1
1 markIn the formula \( y = 3x + \frac{z}{2} \), express \( z \) as the subject of the formula.
Junior Secondary · Mathematics
Formula: Practice Questions
5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Formula.
10 questions27 marksFree, no account
Question 2
1 markMake $$x$$ the subject of the formula $$y = \frac{3x+1}{x-2}$$.
Question 3
1 markA 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.
Question 4
1 markMake $$b$$ the subject of the formula $$c = \frac{ab}{2}$$.
Question 5
1 markGiven the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \), express \( y_1 \) in terms of \( m \), \( x_1 \), \( x_2 \), and \( y_2 \).
Question 6
3 marksThe 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, \( n \).
Write your answer out first, then check it against the worked solution.
Question 7
3 marksThe 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, $$n$$.
Write your answer out first, then check it against the worked solution.
Question 8
5 marksMake $$x$$ the subject of the formula $$y = \frac{x+a}{bx-c}$$.
Write your answer out first, then check it against the worked solution.
Question 9
4 marksThe 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 \(77^\circ\text{F}\).
Write your answer out first, then check it against the worked solution.
Question 10
7 marksIn 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.
Write your answer out first, then check it against the worked solution.
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