PRINCETON UNIVERSITY

ALGEBRA A

Time: Two Hours

Candidates who are at this time taking both Algebra A and Algebra B may omit from Algebra A questions 4, 5, and 6, and from Algebra B questions 1 (a), 3, and 4.

1. Simplify

2. (a) Divide by

2. (b) Simplify

3. Factor: (a)

3. Factor: (b)

4. Solve

5. Solve for x and y:

6. The road from A to B is uphill for 5 mi., level for 4 mi., and then downhill for 6 mi. A man walks from B to A in 4 hr.; later he walks halfway from A to B and back again to A in 3 hr. and 55 min.; and later he walks from A to B in 3 hr. and 52 min. What are his rates of walking uphill, downhill, and on the level, if these do not vary?

ALGEBRA B

1. Solve (a)

1. Solve (b)

1. Solve (c)

2. Solve for x and y, checking one solution in each problem:

2. (a)

2. (b)

3. A man arranges to pay a debt of $3600 in 40 monthly payments which form an A. P. After paying 30 of them he still owes of his debt. What was his first payment?

4. If 4 quantities are in proportion and the second is a mean proportional between the third and fourth, prove that the third will be a mean prop. between the first and second.

5. In the expansion of the ratio of the fourth term to the fifth is Find x.

6. Two men A and B can together do a piece of work in 12 days; B would need 10 days more than A to do the whole work. How many days would it take A alone to do the work?

ALGEBRA TO QUADRATICS

1. Simplify

2. Simplify

3. Factor (a)

3. Factor (b)

3. Factor (c)

4. Find H. C. F. of and

5. Solve

6. The sum of three numbers is 51; if the first number be divided by the second, the quotient is 2 and the remainder 5; if the second number be divided by the third, the quotient is 3 and the remainder 2. What are the numbers?