ALGEBRA.—Candidates will be required to pass a satisfactory examination in that portion of _algebra_ which includes the following range of subjects: definitions and notation; the fundamental laws; the fundamental operations, viz.: addition, subtraction, multiplication and division; factoring; highest common factor; lowest common multiple; fractions, simple and complex; simple, or linear, equations with one unknown quantity; simultaneous simple, or linear, equations with two or more unknown quantities; involution, including the formation of the squares and cubes of polynomials; binomial theorem with positive integral exponents; evolution, including the extraction of the square and cube roots of polynomials and of numbers: theory of exponents; radicals, including reduction and fundamental operations, rationalization, equations involving radicals, operations with imaginary numbers, quadratic equations; equations of quadratic form; simultaneous quadratic equations; ratio and proportion; arithmetical and geometrical progressions. Candidates will be required to solve problems involving any of the principles or methods contained in the foregoing subjects. The following questions were used at a recent examination: Substitute _y_ + 3 for _x_ in _x_⁴-_x_³ + 2x²-3 and arrange the result in descending powers of _y_. On the eve of a battle one army had 5 men to every 6 men in the other. The first army lost 14,000 men and the second 6,000 men. The first army then had 2 men to every 3 men in the other. How many men were there originally in each army? Solve 1.2_x_ - (.18_x_ - .05)/.5 = .4_w_ + 8.9 Find the lowest common multiple of 1-_x_, _x_²-1, _x_-2, and _x_²-4. Solve √_x_ + 9 = 2 √_x_ - 3. Solve (2_x_ - 3)² = 8_x_. Expand (_m_-3/4-_m_(4/3))⁴ by the Binominal Theorem. Find all the values of _a_ for which the roots of _ax_² + 2(_a_ + 3)_x_ + 16 = 0 are equal. Solve ((_x_ + _y_)/2) - ((_x_ - _y_)/3) = 8 and ((_x_ + _y_)/3) + ((_x_ - _y_)/4) = 11. Solve _x_² - 4_y_² = 9, _xy_ + 2_y_² = 3. A certain article of consumption is subject to a duty of $1.50 per cwt. In consequence of a reduction in duty the consumption increases one half, but the revenue falls off one third. Find the duty per cwt. after the reduction. A and B run a mile. First A gives B a start of 44 yards and beats him by 51 seconds; at the second heat A gives B a start of 1 minute and 15 seconds and is beaten by 88 yards. Find the time in which A and B can run a mile separately. Sum to infinity the progression 3 + 2 + 4/3.... A servant agrees for certain wages the first month, on the understanding that they are to be raised a dollar every subsequent month until they reach $60 a month. At the end of the first of the months for which he receives $60 he finds that his wages during his time of service have averaged $48 per month. How long has he served?