Find all the values of a for which the roots of ax² + 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 x² - 4y² = 9, xy + 2y² = 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:
Define the following: