VASSAR COLLEGE
ELEMENTARY AND INTERMEDIATE ALGEBRA
Answer any six questions.
1. Find the product of
and
2. Resolve into linear factors:
2. (a)
2. (b)
2. (c)
2. (d)
3. Reduce to simplest form:
3. (a)
3. (b)
4. (a) Divide by
4. (b) Find correct to one place of decimals the value of
5. (a) If show that
5. (b) Two numbers are in the ratio and if 7 be subtracted from each the remainders are in the ratio Find the numbers.
6. Solve the equations:
6. (a)
6. (b)
6. (c)
7. A field could be made into a square by diminishing the length by 10 feet and increasing the breadth by 5 feet, but its area would then be diminished by 210 square feet. Find the length and the breadth of the field.
VASSAR COLLEGE
ELEMENTARY AND INTERMEDIATE ALGEBRA
Answer six questions, including No. 5 and No. 7 or 8. Candidates in Intermediate Algebra will answer Nos. 5-9.
1. Find two numbers whose ratio is 3 and such that two sevenths of the larger is 15 more than one half the smaller.
2. Determine the factors of the lowest common multiple of and
3. Find to two decimal places the value of
when and
4. Solve the equations:
5. Solve any 3 of these equations:
5. (a)
5. (b)
5. (c)
5. (d)
6. The sum of two numbers is 13, and the sum of their cubes is 910. Find the smaller number, correct to the second decimal place.
7. The sum of 9 terms of an arithmetical progression is 46; the sum of the first 5 terms is 25. Find the common difference.
8. Explain the terms, and prove that if four numbers are in proportion, they are in proportion by alternation, by inversion, and by composition. Find x when
9. Find the value of x in each of these equations:
9. (a)
9. (b)
YALE UNIVERSITY
ALGEBRA A
Time: One Hour
Omit one question in Group II and one in Group III. Credit will be given for six questions only.
Group I
1. Resolve into prime factors: (a) (b) (c)
2. Simplify
3. Solve
Group II
4. Simplify and compute the value of the fraction to two decimal places.
5. Solve the simultaneous equations
Group III
6. Two numbers are in the ratio of If a be added to the first and subtracted from the second, the results will be in the ratio of Find the numbers.
7. A dealer has two kinds of coffee, worth 30 and 40 cents per pound. How many pounds of each must be taken to make a mixture of 70 pounds, worth 36 cents per pound?
8. A, B, and C can do a piece of work in 30 hours. A can do half as much again as B, and B two thirds as much again as C. How long would each require to do the work alone?
YALE UNIVERSITY
ALGEBRA B
Time: One Hour
Omit one question in Group I and one in Group II. Credit will be given for five questions only.
Group I
1. Solve
2. Solve the simultaneous equations
2. Arrange the roots in corresponding pairs.
3. Solve
Group II
4. In going 7500 yd. a front wheel of a wagon makes 1000 more revolutions than a rear one. If the wheels were each 1 yd. greater in circumference, a front wheel would make 625 more revolutions than a rear one. Find the circumference of each.
5. Two cars of equal speed leave A and B, 20 mi. apart, at different times. Just as the cars pass each other an accident reduces the power and their speed is decreased 10 mi. per hour. One car makes the journey from A to B in 56 min., and the other from B to A in 72 min. What is their common speed?
Group III
6. Write in the simplest form the last three terms of the expansion of
7. (a) Derive the formula for the sum of an A. P.
7. (b) Find the sum to infinity of the series 1, ···. Also find the sum of the positive terms.