Afternoon Sample Questions

1. Towns A and B are d miles apart. A traveler goes from A to B and back to A. From A to B the average speed is 60 miles per hour. Returning from B to A, the average speed is 40 miles per hour. What is the average speed for the entire trip?

2. If x and y are real numbers such that

find the maximum value of y-x.

3. A certain species has a female-male ratio of 2 to 1. The species is classified by age into pups (less than 1 year old) and adults (at least 1 year old). All adult females, including those born the prior June have a litter each June with an average litter size of 4 pups. The July population of the species in a certain area is estimated to be 22,000. Estimate the number of adults and pups in the population.

4. An object dropped near the surface of a small planet falls 7 feet in the 1^st second, 21 feet in the 2^nd second, 35 feet in the 3 ^rd, 49 feet in the 4 ^th second, and so on 14 more feet each second. What is the total distance it falls in n seconds?

5. How many different messages can be represented by sequences of length 5 that use three dashes and two dots?

Solutions

1. 48 miles per hour

2.

3. 6000 adults and 16000 pups

4. 7 n²

5. 10