MENTAL EXAMINATION
The examination takes place as follows, viz.:
| 1st Day.— | Blank for personal and school history to be filled out by all who report for examination, 11 a.m. to 12, noon, 1 hour. |
| History, 1 to 5 p.m., 4 hours. | |
| 2d Day.— | Algebra, 9 a.m. to 1 p.m., 4 hours. |
| Geography, 2 to 5 p.m., 3 hours. | |
| 3d Day.— | Geometry, 9 a.m. to 1 p.m., 4 hours. |
| English Grammar, Composition, and Literature, 1:30 to 5:30 p.m., 4 hours. |
Every candidate who reports is required to fill out, in the most careful manner, the personal and school history sheet and the autograph and official notification address blanks. The fact that a candidate may be reporting for the physical examination only, does not by any means exempt him from accomplishing these blanks, as the information they contain is vitally necessary for the permanent and statistical records of the Military Academy.
The candidate is given all assistance needed to insure the proper filling out of these papers.
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; graphical representation and solution of linear equations with two unknowns; 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:
1. (a) Simplify [(x - y)2 + 6xy] - [(x2 + 2xy) - {x2 - [2xy - (4xy - y2)]} - (-x2 - 2xy)].
(b) Factor (1) a9b9 + 64c6 (2) x2 - y2 - 2y - 1 (3) x3 - 3x2 + 4.
2. Solve √((4/x2) + 5) - √((4/x2) - 5) = 2. Prove that your answers are correct.
3. How many terms will there be in the expansion of (a⅒ + b⅕×15) by the binomial formula?
Write the 6th term in the simplest form.
What other term will have the same coefficient?
Write down this term and simplify it.
4. A number of workmen, who receive the same wages, earn together a certain sum. Had there been 7 more workmen, and had each one received 25 cents more, their joint earnings would have increased by $18.65. Had there been 4 fewer workmen, and had each one received 15 cents less, their joint earnings would have decreased by $9.20. How many workmen are there, and how much does each one receive?
5. (a) Find the value of 5x3 + 2x2 - 3x - 1 when x = 1 - √(-4)
(b) Simplify (5×√(x4/3)-3/2
6. Two trains run toward each other from A and B, respectively, and meet at a point which is 15 miles farther from A than it is from B. After the trains meet, it takes the first train 2⅔ hours to run to B, and the second 3⅜ hours to run to A. How far is it from A to B?
| 7. Solve | { (1/a + 1/b)x + (1/a - 1/b)y = 4 |
| { | |
| { x/(a + b) + y/(a - b) = 2 |
8. (a) Deduce a test for finding when the roots of the equation ax2 + bx + c = 0 are: 1º real and unequal; 2º real and equal; 3º imaginary; 4º numerically equal with contrary signs.
(b) Apply the tests to find the nature of the roots of the equations
| 1º 3x2 + 4x - 10 = 0 |
| 2º 5x2 + 6 = 0 |
9. Given a square whose side is 2. The middle points of its adjacent sides are joined by straight lines forming a second square inscribed in the first. In the same manner, a third square is inscribed in the second, a fourth in the third, and so on indefinitely. Find the sum of the perimeters of all the squares.
Substitute for any of the above.—A person has $6,500, which he divides into two portions and lends at different rates of interest, so that the two portions produce equal returns. If the first portion had been lent at the second rate of interest, it would have produced $180; and if the second portion had been lent at the first rate of interest, it would have produced $245. Find the rates of interest.
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. Theorem: The three medians of any triangle intersect in a common point which is at two-thirds of the distance from each vertex to the middle of the opposite side.
2. Theorem: If two triangles have their three sides respectively equal, the triangles are equal in all respects.
3. (a) How many circles can be drawn tangent to three given straight lines? (b) Problem: To draw a circle through a given point and tangent to two given straight lines.
4. Theorem: If two parallel right lines be divided into corresponding parts, proportional each to each, and straight lines be drawn through the corresponding points of division, these straight lines will pass through a common point.
5. Exercise: Find the locus of all points, the sum of the squares of the distances of any one of which from two fixed points is equal to a given square.
6. Problem: Given two circles, to construct a third circle equivalent to their difference.
7. Exercise: If the radius of a circle is 5, find the area of the segment subtended by the side of a regular hexagon.
8. Theorem: The areas of two triangles which have an angle of the one equal to an angle of the other, are to each other as the products of the sides including those angles.
9. Problem: Through a given point on one side of a triangle to draw a right line which shall divide the triangle into two equivalent areas.
Substitute for any one of the above.—(a) Define commensurable quantities; incommensurable quantities. Give example of each. (b) Theorem: In the same circle or equal circles, two angles at the centre have the same ratio as their intercepted arcs (whether commensurable or incommensurable).
English Grammar.—Candidates must have a good knowledge of English grammar; they must be able to define the terms used therein; to define the parts of speech; to give inflections, including declension, conjugation, and comparison; to give the corresponding masculine and feminine gender nouns; to give and apply the ordinary rules of syntax.
They must be able to parse correctly any ordinary sentence; giving the subject of each verb, the governing of each objective case, the word for which each pronoun stands or to which it refers, the words between which each preposition shows the relation, precisely what each conjunction and each relative pronoun connects, what each adjective and adverb qualifies or limits, the construction of each infinitive, and generally to show a good knowledge of the function of each word in the sentence.
They must be able to correct in sentences or extracts any ordinary grammatical errors.
It is not required that any particular textbook shall be followed; but the definitions, parsing, and corrections must be in accordance with good usage and common sense.
The following questions indicate the character of the examination:
1. (a) He comes, the herald of a noisy world. (b) Next anger rushed, his eyes on fire. (c) Get on your nightgown, lest occasion call us and show us to be watchers. (d) Hark! Hark! the lark at heaven’s gate sings. (e) Why do you stay so long, my lords of France? (f) Go you before to Gloucester with these letters. (g) Society has been called the happiness of life. (h) The guardsman defended himself bravely. (i) They that reverence too much old times are but a scorn to the new. (j) I will bring you certain news from Shrewsbury.
In the above sentences pick out the following grammatical constructions. (Indicate the number of the sentence and write the word or words which answer the question.)
Imperative mood. Abstract noun. Transitive verb. Two relative pronouns. Noun in apposition. Verb in subjunctive mood. Adverb of manner. Relative pronoun. Indirect object. Interjection.
2. Write a simple sentence containing a compound subject. Write a simple sentence containing a compound predicate. Write a complex sentence containing an adjective clause. Write a complex sentence containing an adverbial clause of manner. Write a sentence containing a preposition with a compound object. Write a sentence containing an adverb clause of time. Write a sentence containing a noun (or substitute) clause used as the subject of the sentence. Write a complex sentence containing an adverb clause of place. Write a sentence containing an adjective phrase, and an adverb phrase. Write a sentence containing a verb in the passive voice.
3. Write sentences containing the following: The preterite (or past) tense (active voice) of the verb “choose.” The perfect tense (active voice) of the verb “swim.” The pluperfect (or past perfect) tense (active voice) of the verb “burst.” The future perfect tense (active voice) of the verb “eat.” The perfect tense (active voice) of the verb “know.” The present participle of the verb “lie.” The perfect infinite of the verb “study.” The perfect participle of the verb “knock.” The future tense, passive voice, of the verb “defeat.” The future perfect tense, passive voice, of the verb “pay.”
4. In the passage below, indicate the gender of all the nouns and pronouns by the following device: Underscore once those that are masculine; twice those that are feminine; thrice all those that are neither.
“The bride kissed the goblet, the knight took it up.
He quaffed off the wine, and he threw down the cup,
She looked down to blush, and she looked up to sigh,
With a smile on her lips and a tear in her eye.
He took her soft hand ere her mother could bar,—
‘Now tread we a measure!’ said young Lochinvar.
So stately her form and so lovely her face,
That never a hall such a galliard did grace;
While her mother did fret, and her father did fume,
And the bridegroom stood dangling his bonnet and plume;
And the bride-maidens whispered, ‘‘Twere better by far,
To have matched our fair cousin with young Lochinvar.’”
5. Write sentences containing the following: An auxiliary verb. The comparative of “recent.” The superlative of “bad.” The plural of “lily.” The masculine of “witch.” An intransitive verb. A collective noun. The comparative of “lazy.” The plural of “shelf.” The plural of “ruby.”
6. Parse the words in italics in the following sentences: “Some soils, like the rocky tract called the Estabrooke Country in my neighbourhood, is so suited to the apple, that it will grow faster in them without any care, than it will in many places with any amount of care.”—Henry D. Thoreau.
7. Correct all errors in the following: The man who committed the murder was hung. Who can this letter be from? It is me that he fears. The red rose smells sweetly, but the yellow one does not smell so good. He asked if either of the men could identify their own clothing.
8. Punctuate and capitalize the following: it was old dr parr who said or sighed in his last illness oh if i can only live till strawberries come the old scholar imagined that if he could weather it till then the berries would carry him through no doubt he had turned from the drugs and the nostrums or from the hateful food to the memory of the pungent penetrating and unspeakably fresh quality of the strawberry with the deepest longing the strawberry is always the hope of the invalid and sometimes no doubt his salvation it is the first and finest relish among the fruits and well merits dr botelers memorable saying that doubtless god could have made a better berry but doubtless god never did john burroughs.
English Composition and English Literature.—Candidate will be required:
1. By the writing of short themes on subjects chosen by themselves within limits set by the examination paper, to prove (a) their ability to spell, capitalize, and punctuate, and (b) their mastery of the elementary principles of composition, including paragraphing and sentence structure.
2. To give evidence of intelligent acquaintance with three plays of Shakespeare—one comedy, one history, and one tragedy—The Merchant of Venice, Henry V, and Macbeth being especially recommended.
3. To exhibit a fair knowledge of the history of English literature and of the names of the most prominent authors, and of the names of their principal works.
The general character and scope of the examination are indicated by the following:
1. In a few paragraphs (about 250 words) tell the most important facts about the life and works of any one of the following authors: Robert Burns, John Milton, John Keats, Edgar Allan Poe, Alfred Tennyson, Charles Dickens.
2. In a paragraph (about 250 words) discuss the Victorian period in English literature, paying attention to the following points: (a) the characteristics of the literature, (b) the chief writers, both in prose and poetry.
3. In a few paragraphs (about 250 words) discuss the Puritan period in English literature, telling what is meant by the term, the object and results of the Puritan movement, the chief writers with their works, and the main characteristics of the literature.
4. Elective question (may be chosen in place of either 2 or 3). Write a few paragraphs (250 words) on the characteristics and importance of the works of the Concord writers, Emerson, Hawthorne, and Thoreau, mentioning the chief works of each.
5. Write two compositions of about 200 words each selecting your subjects from the following list: (a) The story of the chase. (Lady of the Lake—Scott.) (b) Silas Marner’s Early Life. (Silas Marner—George Eliot.) (c) The Story of Jessica. (Merchant of Venice—Shakespeare.) (d) The Character of Brutus. (Julius Caesar—Shakespeare.) (e) The Story of Ida and the Prince. (The Princess—Tennyson.) (f) The Trial of Rebecca. (Ivanhoe—Scott.) (g) The Murder of Duncan. (Macbeth—Shakespeare.) (h) Character Sketch of the Ancient Mariner. (The Ancient Mariner—Coleridge.) (i) Threshing Day on a Western Farm. (j) The Village Drug Store. (k) Along the Wharves in a Seaport Town. (l) An Irrigated Farm. (m) A Cotton Mill. (n) An Accident.
Geography.—Candidates will be required to pass a satisfactory examination in descriptive geography and the elements of physical geography. A preponderance of weight is attached to a knowledge of the geography of the United States.
In descriptive geography of the United States, candidates should be thoroughly informed as to its general features and boundaries; adjacent oceans, seas, bays, gulfs, sounds, straits, and islands; lakes, the location and extent of mountain ranges; the sources, directions, and terminations of the important rivers, the names of their principal tributaries, and at what points, if any, these rivers break through highlands on their way to the ocean; the water routes of communication from one part of the country to another; the location and termination of important railroad lines; the boundaries of the several States and Territories and their order along the coasts, frontiers, and principal rivers; the location and boundaries of the island possessions; and the names and locations of the capitals and other important cities of the several States, Territories, and island possessions.
In short, the knowledge should be so complete that a clear mental picture of the whole of the United States is impressed on the mind of the candidate.
In descriptive geography of other countries, candidates should be familiar with the continental areas and grand divisions of water; the earth’s surface; the large bodies of water which in part or wholly surround the grand divisions of the land; the capes, from what part they project and into what waters; the principal peninsulas, location, and by what waters embraced; the parts connected by an isthmus; the principal islands, locations, and surrounding waters; the seas, gulfs, and bays, the coasts they indent, and the waters to which they are subordinate; the straits, the lands they separate, and the waters they connect; the locations of the principal lakes, the locations, boundaries, capitals and principal cities of the political divisions of the world.
In physical geography, candidates should be familiar with the relief of the earth’s surface; the principal mountain systems, the river systems and watersheds; the coastal and lake plains; and the influence of climate, soil, mineral deposits, and other physical features on the resources, industries, commercial relations, and development of a country and its people, especially of the United States.
The following questions indicate the character of the examination:
1. Define. (a) Geography, (b) Physical Geography, (c) strait, (d) isthmus, (e) isotherm.
2. In respect of climate, into what zones is the earth’s surface divided? Name the circles separating these zones from one another. In what zone are the Philippines?
3. (a) What and where is the International Date Line? (b) In going from San Francisco to Manila is a day lost or gained? Give reasons for answer.
4. How many “times” has the United States! What are they?
5. What waters surround the United States?
6. Is it possible to go from Duluth to Detroit by water? If so, what bodies of water would be passed through?
7. Name the larger islands of the Philippines, and of the Hawaiian Group, respectively. On what island is Manila? Honolulu? Iloilo?
8. Name two great coal regions of the United States.
9. What is (a) the most northern State of the United States? (b) the most southern? (c) the most eastern? (d) the most western?
10. Which of the United States has the longest coast line?
11. Where is the Mohawk Valley?
12. Bound—Michigan, Kentucky, Connecticut.
13. Locate accurately the following cities—El Paso, Albany, Zamboanga, Panama, San Antonio, Kalamazoo.
14. Name the transcontinental railways west of the Mississippi in order from north to south.
15. Name the countries of Central America. Which one of these borders on Mexico?
16. Name in order, beginning at the Isthmus of Panama, the countries of South America that touch on the Caribbean Sea and the Atlantic Ocean.
17. The meridian through Atlanta, Georgia, intersects what South American Republics? Is the continent of South America, as a whole, east or west of the United States?
18. What two countries of South America have no sea coast?
19. A vessel goes from London, England, to San Francisco by the Suez Canal. Through what waters does it pass?
20. What waters connect the Black Sea with the Mediterranean? The Gulf of Aden with the Red Sea?
21. Where does the Danube rise? through what countries does it flow? and where does it empty?
22. What three rivers flow north into the Arctic from Siberia?
23. What mountains lie between France and Spain? Between Tibet and India?
24. Name in order in a clockwise direction the countries bordering on the Mediterranean.
25. Where is—Mount Shasta, Popocatepetl, Chimborazo, Everest, Apo, Fujiyama, Blanc, Mayon.
26. Where and what is—Mukden, Valdivostok, Liberia, Melilla, The Celebes.
27.—Locate—Elba, Saint Thomas, Cape Race, Hankow, Formosa, Bonin Islands, Juraez, Zanzibar, Colon, Volga River, Elbe River, Cebu, Seville, Andalusia, Zaragoza, Macedonia, Nepaul, Bogota, Beirut, Malta, Macao, Dublin.
28. Name the capitals respectively of—Afghanistan, Portugal, Nebraska, Vermont, French Indo-China, Philippine Islands, Montenegro, Georgia, Oregon, Roumania, Persia, Florida, Java.
History.—Candidates must be thoroughly familiar with such material as is contained in good high school textbooks on the subject (a) of the History of the United States, and (b) of the History of Europe from the Fall of Constantinople (1453) to the outbreak of the French Revolution (1789).
In history of the United States, the examination will include questions concerning early discoveries and settlements; the forms of government in the Colonies; the causes, leading events, and results of wars; important events in the political and economic history of the Nation since its foundation.
In history of Europe from 1453 to 1789, special emphasis will be laid upon the political and social development in France, Prussia, and England.
The following questions indicate the character of the examination:
European History (1453-1789).
1. Describe political conditions during the latter half of the fifteenth century in what is now Germany.
2. What countries were ruled by Charles V of Spain at the height of his power?
3. Why was Luther summoned to the Diet of Worms? What was done at this Diet?
4. Who was Melanchthon? What was the Religious Peace of Augsburg? What was its importance?
5. What was the Council of Trent? Over how long a period did its meetings extend? What were the important acts of this Council?
6. What ruler was instrumental in separating England from Roman Catholic influence? How was this separation accomplished? Describe two acts of Parliament important in this connection.
7. Outline the causes of Elizabeth’s quarrel with Mary Queen of Scots. State its political importance and its results.
8. Under what circumstances during Elizabeth’s reign did England come into conflict with Spain? What event marked the crisis of this conflict?
9. State the nature, causes, dates, and leaders of the Puritan Reformation.
10. Describe the important acts of Parliament passed in the reign of Charles II to regulate the religious situation.
11. Describe the court and court life in France in the time of Louis XIV. Name five prominent men connected with Louis XIV’s court.
12. What part did Gustavus Adolphus and Richelieu play in the Thirty Years’ War? How may we reconcile Richelieu’s political acts with his religious convictions?
13. What nations were engaged in the War of the Spanish Succession? What issues were at stake? What were the important provisions of the Peace of Utrecht (1713)?
14. What was the revolution of 1688 in England? How was it accomplished?
15. What is meant by the cabinet system of government? Account for the advance of cabinet government in the reigns of George I and George II.
16. For what qualities and what acts was the Great Elector (Frederick William of Prussia) noted?
17. State the cause and the result of the first war between Frederick the Great and Maria Theresa. Name two famous battles of the Seven Years’ War in which Frederick the Great was victorious.
18. State the results of the Seven Years’ War for France according to the provisions of the Treaty of Paris (1763).
19. Why were Frederick the Great, Catherine II of Russia, and Joseph II of Austria called “enlightened despots”? Describe the work of any one of these rulers.
20. Outline two of the fundamental causes for the unrest in France during the early years of the reign of Louis XVI.
1. State concisely the achievements of—(a) De Narvaez; (b) De Soto; (c) Hudson; (d) La Salle.
2. (a) Where and when was the first permanent English settlement in America made? (b) What arrangement was made for the government of this settlement?
3. (a) When and where did the first colonial assembly in America meet? (b) What was Bacon’s Rebellion? (c) When and where was the first permanent English settlement in New England established?
4. (a) What brought the first settlers to Maryland? (b) Who was their leader?
5. (a) What was the immediate cause of the Revolutionary War? (b) What were “writs of assistance”? (c) What was the “Mutiny Act”?
6. (a) When and where did the first Continental Congress meet? (b) What was accomplished by this Congress? (c) Name the original thirteen colonies.
7. (a) Who were the principal leaders in the two battles of Saratoga? (b) What were the effects on the American people of these battles? (c) What was the Wyoming Massacre?
8. (a) What European country was the first to acknowledge the American independence? (b) In what ways did this country aid in bringing the Revolutionary War to a successful close?
9. State the significance of the following in United States history: (a) Shays’ Rebellion; (b) Steuben; (c) Alien and sedition laws; (d) Kosciusko.
10. (a) What were the causes of the war with England in 1812? (b) What treaty ended this struggle? (c) Who was President of the United States during this war?
11. By what means, from whom, and during whose Presidency were the following territories obtained for the United States? (a) Louisiana, (b) Florida, (c) Alaska.
12. (a) What was the “Spoils System”? (b) What was the Nullification ordinance passed by South Carolina in 1832?
13. Discuss briefly the nature and importance of the following: (a) The Wilmot Proviso. (b) The Dred Scott Decision. (c) The Fugitive Slave Law.
14. Name the commanders and the results of the following battles: (a) Vicksburg, (b) Fredericksburg, (c) Cold Harbor.
15. Name the Presidents of the United States who have had a second term of office.
16. (a) What various causes underlay the declaration of war against Spain? (b) What important battles on land and sea were fought during the Spanish-American War? (c) What treaty ended this war and what territory was ceded to the United States as a result of it?