4. A and B have the same annual income. A saves of his income each year, and B spends $50 each year more than A. At the end of four years B finds himself $100 in debt. Find their annual income.

Take either 5 or 6.

5. Give the formula or equation for the amount a when a sum of money p is put at simple interest for t years at a rate per cent. represented by r. From this formula for a obtain the value of p. Translate the formula for p thus obtained into a rule.

With the aid of this formula for p, find what principal will yield an amount of $570 in 4 years at 5 per cent.

1. Prove that the bisectors of the adjacent angles of a parallelogram are perpendicular to each other.

2. ABCD is a parallelogram; E and F are middle points in the parallel sides AD and BC respectively. Show that BE and DF, cutting the diagonal AC at the points G and H respectively, will trisect it.

Take either 3 or 4.

3. Prove that the non-parallel sides of an inscribed trapezoid are equal.

4. Prove that the angle formed by a tangent and a chord is measured by one half of the intercepted arc.

6. The side of a square is m. Express in terms of m

(b)

The area of a circle circumscribed about the square.

(g)

STATE NORMAL SCHOOLS.

SEPTEMBER 12 AND 13, 1899.

III.-HISTORY AND GEOGRAPHY.

Time allowed for this paper, one hour.

1. If you have done any collateral reading in connection with your study of United States history, or have studied the history of any other country, make a statement to that effect, mentioning the books used, the extent of your work, and so on.

2.

Take one number only.

The Critical Period between 1783 and 1789.

(a) Two or three sources of weakness in the government of the United States during this period.

(6) Two or three causes of State jealousies and antagonisms during this period.

(c) The money of this period.

(d) The movement for a better government and some of its leaders.

(e) The outcome of the movement and the wisdom of that outcome.

3. Slavery.

(a) Slavery before the Revolution, — its prevalence, the attitude of the people towards it, and how it came to die out in the North while surviving in the South.

(b) Circumstances after the Revolution that increased the demand for slave labor in the South.

(c) Why the South had occasion to fear for the welfare and existence of the institution.

(d) The balance of power between the free States and the slave, — what it was, why it was deemed important, and one or two illustrations of compromises made to preserve it.

(e) The final destruction of this balance of power.

4. Andrew Jackson.

(a) How Jackson came to be president.

(b) The spoils system, what it is, Jackson's relation to it, its evils and recent efforts to overcome them.

(c) Nullification, the significance of the doctrine, circumstances that led to its advocacy by one of the States, a memorable discussion of it in the United States Senate, Jackson's attitude towards it and the service rendered by him to the country in taking that attitude.

(d) Two or three prominent traits in Jackson's character.

5. The Great Lakes.

(a) A sketch or diagram to show the relative positions of the Great Lakes and the locations of at least five important cities on or near their borders (the accuracy of a map is not called for).

(b) Their communication with the sea, certain limitations that impair it and measures adopted to overcome them.

(c) Their commercial importance.

(d) One or two historical events associated with them.

(c) The ownership of the Great Lakes and the policy adopted with reference to war vessels thereon.

(a) Their location, magnitude, people, industries, etc.

(b) The nature of the title on which the United States bases its claim to govern the islands.

(c) The nature of the title on which the Philippine insurgents base their claim to govern the islands.

(d) The Monroe doctrine,

what it is and why it figures in the discus

sions that concern our attitude towards the Philippines.

(h)

At the beginning of your paper tell briefly in what sciences you have done laboratory work, kept notebooks, etc., and to what extent. Under each science take one number or topic only, with its subdivisions. Time for the entire paper, two hours; for each topic, twenty-four minutes.

PHYSICAL GEOGRAPHY.

1. Study of a Weather Map.

(a) The significance of the words "high" and "low as applied to the regions so marked on the accompanying weather map.

(b) The directions of the winds about the high area as compared with their directions about the low, and the causes that determine these directions.

(c) Why clouds and rain are more likely to be present in the low area than in the high.

(d) A weather map based on observations a day later than those of the map here given indicates that the low area is central over Lake Erie, the high area having moved parallel with it. The weather bureau, anticipating on the first day the conditions revealed by the map on the second, was able to make what weather predictions for the second day at Buffalo ?

(e) What predictions was it able to make for the second day at St. Louis?

2. Changes which Lands undergo.

(a) The weathering of the lands.

(b) The wearing away of the lands.

(c) The formation of soil.

(d) Other land changes than the foregoing.

(e) Two or three illustrations to show the relation of some of these changes to life and history, whether plant, animal or human.

(a) The various kinds of service rendered by them, with illustrations.

(b) Joints, their general structure, with some account of those at the knee, the hip and the neck, respectively.

(c) The bones of childhood and the special dangers to which they are exposed.

(d) The bones of old age and the special dangers to which they are exposed.

(e) The sprain, the dislocation and the fracture, — what they are.

2. Why we need Food.

(a) Energy in the body, various ways in which it is exhibited.

(b) Animal heat, its source, constancy, distribution, regulation, etc. (c) Waste material of the body, — its origin, the ways in which it is eliminated from the system, and what the consequences are when the loss is not made good.

(d) The four classes into which foods may be conveniently divided.

(c) The service rendered by each class to the needs of the body.