12 1/1081/72; (2 + 31/5) (31/5 — 2); pax12 ; 1 Xa-b. 6. Rebuce nominator. a+b a 6 to a fraction having a rational de a +6 271 2. Form a quadratic whose roots shall be 3 and 3. Given x2 + y2 of x and y. = 436 and x y= 14 to find the values 4. Given the first term a, the ratio r, and the number of terms n, of a geometric progression, to deduce a formula for the sum of the progression. 5. How many different products of 2 factors can be formed from n different numbers? 6. Expand 3 + 2x into a series of ascending powers of x by the method of indeterminate coefficients. 3. Write four terms of the development of I + 3 4. (1) Write equivalent expressions for a°b-m; pa2; až (2) Simplify 1/12 × 72; 49; 18xo; †3 ́54+ ß3 ́128. 4 V 5. Given 3 V x2 I 2x to find the values of x. 6. Resolve 3x2 6x10 into factors. 7. Given x2 + xy = 15 and xy- y = 2 to find the values of x and y. 8, If each of n straight lines intersects all the others, not more than two lines intersecting in the same point, how many points of intersection will there be? 9. Find the value of the repeating decimal 0.72525 +. 10. Develop I + x terminate coefficients (four terms of the series will suffice). JUNE 1886. TO QUADRATICS. 1. Resolve the following expressions into factors as far as possible: I 1⁄4 ; x3 + y3. x'; x'y' + 2x'y'z' + y2z'; x21 — x2+ 2m I 2 m 3 + m 2. Get as simple an expression as you can for the limits between which x lies. 6. (a) Expand (1 + x)" by the binomial formula. JUNE 1886. FROM QUADRATICS. 1. Solve the quadratic ax + bx + c = o, and point out when the roots are real and unequal, when real and equal, and when imaginary, if numerical values be assigned to a, b and c. 2. Form a quadratic equation whose roots shall be 3 and . 4. Knowing that y varies as x and that when x = 1, y =a, to express the relation between y and x by an equation 5. Find the value of the repeating decimal 0.23232 +. 6. How many different quantities of anything ponderable can be weighed with n different weights? 7. How many changes can be rung with 3 bells out of 6; and how many with the whole peal? |