1. Simplify (ab^(-2)c^2)^(1/2) . (a^3b^2c^(-3))^(1/3) + [(a^6)/(b)]^(1/3). 2. Simplify a/[(a - b)(a - c)] + b/[(b - c)(b - a)] + c/[(c - a)(c - b)]. 3. Factor (_a_) x^4 - 10x^2 + 9. (_b_) x^2 + 2xy - a^2 - 2ay. (_c_) (a + b)^2 + (a + c)^2 - (c + d)^2 - (b + d)^2. 4. Find H. C. F. of x^4 - x^3 + 2x^2 + x + 3 and (x + 2)(x^3 - 1). 5. Solve x/(x - 2) + (x - 9)/(x - 7) = (x + 1)/(x - 1) + (x - 8)/(x - 6). 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? ~SMITH COLLEGE~ ELEMENTARY ALGEBRA 1. Factor e^(2x) - 2 + e^(-2x), x^(12) - 8, x^2 - x - y^2 - y, 18a^2x^2 -24axy - 10y^2. 2. Solve [7 + 4x + 3[2x^2 + 5x + 7]^(1/2)]^(1/2) - 3 = 0. 3. The second term of a geometrical progression is 3[2^(1/2)], and the fifth term is 3/16. Find the first term and the ratio. 4. Solve the following equations and check your results by plotting: { x^2 + y^2 - xy = 7, { x + y = 4. 5. Solve 1/(x^3) + 1/(y^3) = 243/8, 1/x + 1/y = 9/2. 6. In an arithmetical progression d = -11, n = 13, s = 0. Find a and l. 7. Expand by the binomial theorem and simplify: [(2x)/(y^3) - (y^4)/(x^5 [-6]^(1/2))]^5. 8. The diagonal of a rectangle is 13 ft. long. If each side were longer by 2 ft., the area would be increased by 38 sq. ft. Find the lengths of the sides. ~SMITH COLLEGE~ ELEMENTARY ALGEBRA 1. Find the H. C. F. of 8x^3 - 27, 32x^5 - 243, and 6x^3 - 9x^2 + 4x - 6. 2. Solve: (_a_) (2x + 5)^(-5) + 31(2x + 5)^(-5/2) = 32. (_b_) (x - 1)^(1/2) + (3x + 1)^(1/2) = 4. 3. A farmer sold a horse at $75 for which he had paid x dollars. He realized x per cent profit by his sale. Find x. 4. Find the 13th term and the sum of 13 terms of the arithmetical progression (2^(1/2) - 1)/2, (2^(1/2))/2, (1)/[2([2]^(1/2) - 1)], .... 5. The difference between two numbers is 48. Their arithmetical mean exceeds their geometrical mean by 18. Find the numbers. 6. Expand by the binomial theorem and simplify [3a^(-2) - a/[-2]^(1/2)]^5. 7. Solve: 1/x + 1/y = 3/2, 1/(x^2) + 1/(y^2) = 5/4. 8. Solve the following equations and check the results by finding the intersections of the graphs of the two equations: { x^2 = 4y, { x + 2y = 4. ~VASSAR COLLEGE~ ELEMENTARY AND INTERMEDIATE ALGEBRA Answer any six questions. 1. Find the product of [1 + 2a/3 - (5a^2)/(6)] and [2 - 3a/4 + (a^2)/(3)]. 2. Resolve into linear factors: (_a_) 4x^2 - 25; (_b_) 6x^2 - x - 12; (_c_) a^2b^2 + 1 - a^2 - b^2; (_d_) y^3 + (x - 3)y^2 - (3x - 2)y + 2x. 3. Reduce to simplest form: (_a_) z/(1/x - 1/y) + y/(1 - y/x) - x/(1 - x/y).