MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Reading edition
ALGEBRA B
Time: One Hour and Three Quarters
1. How many terms must be taken in the series 2, 5, 8, 11, ··· so that the sum shall be 345?
2. Prove the formula for solving the quadratic equation
3. Find all values of a for which is a root of and check your results.
4. Solve and sketch the graphs.
5. The sum of two numbers x and y is 5, and the sum of the two middle terms in the expansion of is equal to the sum of the first and last terms. Find the numbers.
6. Solve
6. (Hint: Divide by and substitute )
7. In anticipation of a holiday a merchant makes an outlay of $50, which will be a total loss in case of rain, but which will bring him a clear profit of $150 above the outlay if the day is pleasant. To insure against loss he takes out an insurance policy against rain for a certain sum of money for which he has to pay a certain percentage. He then finds that whether the day be rainy or pleasant he will make $80 clear. What is the amount of the policy, and what rate did the company charge him?