1. JUNE 1889. FROM QUADRATICS. I. Solve the equation (a + b)2x2 - (a - b2) x = ab. 2. Find all the roots of the equation 4x3 + 8x2 — 140x O. 5 Having given the first term a, the ratio r, and the number of the terms n, of a geometric progression, to deduce a formula for the sum of the n terms. 6. Determine in how many different ways the letters of the word Cincinnati can be arranged. Find the What sign 7. When is a variable said to have a limit? limit of log. (1 + x) when x approaches o. does the expression have when near its limit, positive, second, if x is negative, log. being supposed to denote the common logarithm. first, if x is JUNE 1889. TO QUADRATICS. 1. Simplify 3a — [b — a — (2a + b — a — b)]. 2. Resolve the following expressions into factors: ca; x2 +64. a“ — bo ; n3 + 2n2 + n; a X 5. Solve the simultaneous equations, bex = cy 6. Show that a2 + 3b2 > 2b (a + b). 7. Simplify the following expressions: JUNE 1889. FROM QUADRATICS. b)2x2 1. Solve the equation (a + b)' x2 - (a2 — b2) x = ab. 2. Find all the roots of the equation 4x8x140x=0. I I = 7, and + = 25, to find x and y. 4. Solve the equation x2 X 3x + 1/4x 3X √4x 5 Having given the first term a, the ratio r, and the number of the terms n, of a geometric progression, to deduce a formula for the sum of the n terms. 6. Determine in how many different ways the letters of the word Cincinnati can be arranged. Find the What sign first, if x is JUNE 1890. FROM QUADRATICS. 1. Solve the equation ax2 + a = (a2 + 1)x. 3. Solve the equation 2 (x-4) = 1 3x — 2. x'xy 15 and xy-y2 = 2; to find all values of x and y which satisfy them. 5. Given the amount of a given principal at compound interest for a given number of years, to find the rate per |