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.
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_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?
PLANE GEOMETRY.—Candidates will be required to give accurate definitions of the terms used in _plane geometry_, to demonstrate any proposition of plane geometry as given in the ordinary text-books and to solve simple geometrical problems either by a construction or by an application of algebra.
The following questions were used at a recent examination:
1°. Rhombus. 2°. A mean proportional. 3°. Similar triangles. 4°. A segment of a circle. 5°. The apothem of a regular polygon.
Theorem: The perpendicular is the shortest line between a point and a straight line.
Theorem: In the same circle or equal circles, the less of two chords is at the greater distance from the centre; conversely, the chord at the greater distance from the centre is the less.