Algebra Examination Papers for Admission to Harvard, Yale, Amherst, Dartmouth, Brown, And to the Mass. Institute of Technology, From June, 1878, to Sept. 1889 Inclusive

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1888. (See Preface.) 1. Eemove the parentheses from 3a — {3a - [3a - (3a - 3a - 3a) - 3a] - 3a} - 3a, and simplify the result.
2. Give the three theorems used in factoring binomials.
3. Factor 4 a? x* - 9 b* c% 8 6 2 c 8 + 48 P c 2 + 72 J 2 c, x* - 3 X s - 14 a; 2 + 48 x - 32.
4. Eesolve 1 — a 8 into six factors.
5. Give two methods of finding the G. C. D. of two quantities.
a* + b* . a 2 1 2 6. Eeduce — = - X -s r. to a simple fraction and 11 a 8 + 6' r a 6 lowest terms.
„ , (2 a- 1 - y- 1 = 2
...2x", 7 - ^Is*-- 3^ = 18,0.' 8. A and B can do \ of a piece of work in 2 days. B can do J of it in 6 days. How long would it take A to do J of it ?
9. Eeduce to simplest form \/^r~> y/e + V^isxy/e-V^m (35-12 V§)*.
10. Eeduce to equivalent fractions having rational denomi- nators ac 1 c % (J + $) ' afl + $ 11. Solve 1 + * = 12.
x + y/x* — 1 * — V 5 " 2 — 1 ALGEBRA.
65 1889.
1. Find the prime factors of d? — W, a s + b% a"+b & + 2a i b s -x 2 -4:y 2 + 4:xy, and a; 8 -8a! 2 + 13a;-6.


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