Write the contract, purpose, and header for a function that computes the area of a rectangle given its length and width.

Write three examples for the behavior of this program.

Solution

Develop a function that computes the distance a boat travels across a river, given the width of the river, the boat's speed perpendicular to the river, and the river's speed. Speed is distance/time, and the Pythagorean theorem is c² = a² + b².

Solution

Develop a function that computes how long after their deparature two trains will meet. Assume that the trains travel between two points, along a single section of track, going in opposite directions. The function should consume the trains' speeds and the starting distance between the trains. Speed is distance/time.

Solution

Develop a function that when given an initial amount of money (called the principal), a simple annual interest rate, and a number of months will compute the balance at the end of that time. Assume that no additional deposits or withdrawals are made and and that a month is 1/12 of a year. Total interest is the product of the principal, the annual interest rate expressed as a decimal, and the number of years.

Solution

Develop a function that when given the length and width of a rectangular floor and the edge length of a square tile will compute the whole number of tiles needed to cover the floor completely.

Solution

Develop a function that computes the area of a regular polygon given the length of one side and the number of sides. If n is the number of sides and s is the length of a side, the area of a regular polygon is equal to 1/4 * n * s² * 1/(tan PI/n).

Solution

Develop a function to return the mean of 5 exam scores.

Solution

Develop a function that when given the area of a square will calculate its perimeter.

Solution

Drop a rubber ball from a height h. Each time it hits the ground, the ball bounces up to 2/3 of the height it dropped. Develop a function that computes how far the ball travels by the time it hits the ground for the third time? Hint: try 36[in] for the initial height.

Solution

contributed by Professor Stephen Bloch, Adelphi University

Develop the function, total-inches. The function consumes a length represented by two numbers: the first a number of feet, and the second a number of inches. The function produces the total length in inches.

Solution

contributed by Professor Stephen Bloch, Adelphi University

The nation of Progressiva has a simple tax code. The tax you pay is your salary times the tax rate, and the tax rate is 1/2% per thousand dollars of salary. For example, if you make $40,000, your tax rate is 1/2% times 40, which is 20%, so you pay 20% of $40,000, which is $8,000.

Develop a function to compute the net pay (i.e. pay after taxes) of a person with a given salary. HINT: develop one or two auxiliary functions as well as net-pay.

This tax system has the peculiar feature that, beyond a certain income level, it doesn't pay to earn any more: for every additional dollar you earn, you have to pay MORE than a dollar more to the government. Use your net-pay function to find this income level.

[Note to teachers: this question can be solved easily using differential calculus, but encourage students to find the answer by experiment, even if they've studied differential calculus.]

Solution

contributed by Karen O'Loughlin, Ankeny High School

Develop the function, semester-grade. The function consumes two numbers -- the first representing a cumulative homework score and the other representing the final exam socre -- and produces the semester grade weighted 80% homework and 20% final exam.

Solution

contributed by Karen O'Loughlin, Ankeny High School

Develop the function, winning-average. The function consumes two numbers representing the number of wins and losses and produces the winning average where 1000 would be equivalent to 100 percent.

Solution

contributed by Susan Barocas

1. Write a contract for a function that finds the number of inches in a given number of feet.
2. Write a purpose and contract for a function (operation) that finds the gas consumption (miles per gallon) for a particular vehicle.
3. Write a purpose and contract for a function that computes the slope of a line if the change in y-value and the change in x-value are given.
4. Write the purpose, contract and two examples for a function that consumes the length, width, and depth of a tank and produces its volume.
5. Write the purpose, contract, two examples, and header for a function that consumes five quiz grades for a student and produces the quiz average.
6. Write the purpose, contract, two examples, the header and the body for a function that consumes the amount of money a family spends on groceries per week and that computes the yearly cost of groceries for that family.

Note: This kind of exercise is particularly useful for students who have difficulties with their work habits. It progressively walks them through the very basic design recipe.

Solution

Ms. Sis Y. Fuss wants to push a rock up a hill. The distance is d yards. In one minute, she pushes the rock 30 yards, but then it slides down 4 yards. When she has reached d yards, it won't slide down anymore. How many (entire) minutes will it take her?

Solution