Formula Practice

Each of these gives you a formula and asks for a program. The work is the translation: naming the symbols, ordering the steps, and deciding what the user has to type. Answer on paper first — the whole difficulty is in the plan, not the typing.

1. Distance travelled

$d=v\times t$

Ask for a speed in kilometres per hour and a time in hours, print the distance to one decimal place.

Answer 1

speed = float(input("Speed, in km/h: "))
time_taken = float(input("Time, in hours: "))
 
distance = speed * time_taken
 
print(f"Distance travelled: {distance:.1f} km")

The units are in the prompts on purpose. A program that accepts a speed in metres per second and calls the answer kilometres is arithmetically perfect and completely wrong.

2. Area of a circle

$A=\pi r^2$

Ask for a radius, print the area to two decimals. Use math.pi, not 3.14.

Answer 2

import math
 
radius = float(input("Radius, in cm: "))
 
area = math.pi * radius ** 2
 
print(f"Area: {area:.2f} square cm")

radius ** 2 is squaring; radius * 2 is a different program that will look fine and be wrong for every input except 2.

3. Celsius to Fahrenheit

$F=\frac{9}{5}C+32$

Answer 3

celsius = float(input("Temperature, in Celsius: "))
 
fahrenheit = 9 / 5 * celsius + 32
 
print(f"{celsius}°C is {fahrenheit:.1f}°F")

Check it against a pair you know: 100 must give 212. That single check catches the version where somebody wrote 9 // 5, which is integer division and quietly gives 1.

4. The cost of running something

$\text{cost}=\frac{\text{watts}\times \text{hours}}{1000}\times \text{rate}$

Ask for watts, hours per day, and the price per kilowatt-hour. Print the daily cost and the cost over a 194-day school year.

Answer 4

watts = float(input("Power, in watts: "))
hours = float(input("Hours per day: "))
rate = float(input("Price per kWh, in dollars: "))
 
kilowatt_hours = watts * hours / 1000
daily_cost = kilowatt_hours * rate
yearly_cost = daily_cost * 194
 
print(f"Per day:  ${daily_cost:.2f}")
print(f"Per year: ${yearly_cost:.2f}")

kilowatt_hours earns its name here: when the yearly figure looks absurd, that is the line you print to find out whether the error is in the conversion or the multiplication.

5. Averaging, with a guard

The mean of a list of readings is the total divided by how many there are. Write a program that reads numbers until the user types done, then prints the mean — and does not crash when the user types done immediately.

Answer 5

readings = []
 
while True:
    entry = input("Reading (or 'done'): ")
    if entry == "done":
        break
    readings.append(float(entry))
 
if len(readings) == 0:
    print("No readings were entered.")
else:
    total = 0
    for reading in readings:
        total = total + reading
    print(f"Mean of {len(readings)} readings: {total / len(readings):.2f}")

The guard is the whole exercise. Dividing by zero is the formula being asked a question it has no answer to, and the program has to answer for it.

Curriculum connection

B3.2

solve common problems (e.g., calculation of hypotenuse, determination of primes, calculation of area and circumference) by applying mathematical equations or formulas in an algorithm;

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A1.3

use assignment statements correctly with both arithmetic and string expressions in computer programs;

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A2.1

write programs that incorporate user input, processing, and screen output;

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