(c) 416 312 1 1 ; (d) (a2 — 2a1b1 + a); and compare the magnitudes of 81 3 and 617, and of 12 and 3 without actually extracting the roots, 8. Deduce formulas for the amount of P dollars for n years, and the present value of P dollars due n years hence, subject to compound interest, and the interest of one dollar per annum being i. How may both formulas be combined in one? 3+ 2x into a series of ascending powers of x 9. Develop 99. JUNE, 1888. TO QUADRATICS. 1. Simplify ma -- [nb + (pbc) qe ma - pb)]. 2. Resolve the following expressions into factors: x2 + 27; xa — 16; a'b' — 6a b' + 9a2; a‡ -- b3. 3 a1 3 . (nb (x + y) = n, to find x and y. 6. Expand (ab) by the binomial formula. JUNE 1888. FROM QUADRATICS. 1. Solve the equation mqx' mnx + pqx = np. 5. In how many different ways may seven persons be seated at a table. 6. In a system of twenty lines lying in the same plane, no two of which are parallel and no three of which pass through the same point, how many points will there be where two lines intersect. 7. A person puts out p dollars every year to accumulate at compound interest. What will be the amount of the accumulation at the end of n years, the interest being compounded annually and the interest of one dollar for one year being r? SEPTEMBER 1888. 1. Reduce the following expressions to their simplest x2 9x+20 x2 13x + 42 2 equivalents: (a) x2 X 6x 5X (a 2. Given (a + b) x a'x + x a (ab) y 4ab, and = b)x+(a+b) y 2 (a - b), to find x and y. 3. Show that x2 + 1 > x* + x for all values of x > except x ==== I. and - 1, 5. Simplify, (a) (2axy). (b) 1/4a*b*c*. 9 21 4 6. Expand (a* - a-x) and (2x + y)3 2 (c) 1/125. 3 (2) 4. (1) 71 48 31 27 8. Solve the equation [(x-2)2 --- x] (x-2)= 88 (x — 2). 9. Out of m Democrats and n Republicans how many different committees can be formed consisting of 2 Democrats and 3 Republicans? |