University of the State of New York 105th examination ALGEBRA Wednesday, November 23, 1892—9: 15 a. m. to 12:15 p. m., 40 credits, necessary to pass, 30 onl NOTE. Give each step of solution. Reduce fractions to lowest terms Express final result in its simplest form and mark it Ans. I Write (a) a homogeneous polynomial; (b) a binomial surd; (c) a complete equation. State in each case why the thing written is wha is required. 2 Indicate the following operations in one connected expression from times the sum of a and b subtract times the difference of a and b; add a2 to the result and multiply the sum by b; divide this product by the square of the sum of a and b. 5 3 Reduce the following expression to its simplest form and then find the value of the result when m=3 and n = 2: n3 + m 4 Resolve each of the following polynomials into its prime factors and then indicate by signs which of these factors must be combined to form the greatest common divisor and which to form the least common multiple a3ba2b2 — 6ab3, a3 + 2a2b— 3ab2, a2b+4ab2 + 363. 5 Solve the following equations: (a) 2ax2+4bx = = 6c. - 4xy: 16 5 3 4. 3 4 and 3; form the 8 The sum of two numbers is to their difference as 5 to 1, product is to the quotient of the greater divided by the less as find the numbers 9 Find the sum of 12a3 and /27ab2. 3 and their 16 to 1; 2 University of the State of New York Examinations Department 107th examination ALGEBRA Wednesday, January 25, 1893-9: 15 a. m. to 12:15 p. m., only 100 credits, necessary to pass, 75 NOTE.-Give each step of solution. Reduce fractions to lowest terms. Express final result in its simplest form and mark it Ans. 1 Define elimination, surd, imaginary quantity, literal equation, identic equation. 2 Simplify 3x-2y—(x−y)—(x+y—(−x—y)). ΙΟ 5 ΙΟ 6 Resolve the following quantities into their prime factors: 9 7 12 7 Solve 2x2+312=35 2x+3y=13. I 2 8 The difference of two numbers is I and the difference of their University of the State of New York 108th examination ALGEBRA Wednesday, March 15, 1893--9:15 a. m. to 12:15 p. m., only 100 credits, necessary to pass, 75 NOTE- Give each step of solution. Reduce fractions to lowest terms. Express final result in its simplest form and mark it Ans. I Define exponent, coefficient, numeric equation, pure quadratic equation, radical quantity. 2 Simplify a-2 [−a+{b−(c+2b)—2a}+3c—6]. 3 Factor abx2+(a2+b2)xy+aby2; ΙΟ 8 6 6 6 ΙΟ 8 Find the value of the following expression when x=4, y=8, a=3, 6 Sold an article for a dollars gaining thereby b per cent on the cost; what was the cost? ΙΟ 7 One half the sum of two numbers is equal to one and one half times their difference; twice the larger number exceeds three times the smaller by 12; find the numbers. 8 Expand by the binomial formula, giving all the operations for find University of the State of New York 111th examination ALGEBRA Wednesday, June 14, 1893-9:15 a. m. to 12:15 p. m., only 100 credits, necessary to pass, 75 NOTE- Give each step of solution. Reduce fractions to lowest terms. Express final result in its simplest form and mark it Ans. 1 Define elimination, exponent, equation, root of equation, polynomial. ΙΟ 5 The difference between two numbers is 2, and the sum of their squares is 10; find the numbers. I 2 6 Write the fifth power of a2 + 2b, and give all the operations for finding the coefficients. 7 Simplify√/56, √3 × √1. I 2 I 2 University of the State of New York Examinations Department 111th examination ADVANCED ALGEBRA Monday June 12, 1893—9: 15 a. m. to 12:15 p. m., only 100 credits, necessary to pass, 75 NOTE - Give each step of solution. Reduce fractions to lowest terms. Express final result in its simplest form and mark it Ans. I Prove that a quadratic equation of one unknown quantity can not have more than two roots. 2 Find the meaning of a1, p being integral or fractional. 3 15 15 Derive the formula for finding the sum of an infinite series whose ratio is less than 1. Illustrate its use by finding the value of the repetend .3. 4 Expand √1 20 3x into a series to three terms by the method of undetermined coefficients. 15 5 Find by the differential method the 12th term of the series 4, 11, 28, 55, 92. 6 Find all the roots of the equation x4-9x329x2-39x+18=0. 20 15 |