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1. Questions prepared by the State Board of Education for the State examination held at Lansing and Marquette,
March 25-29, 1907.
1. Discuss algebra under the following heads:
(a) Its relation to mathematics.
(c) Its practical utility.
(a) a ? + 2 ab + b? as the square of (a + b).
(b) a? – b? as equal to (a + b)(a - b). 4. Show that in a series of equal ratios the sum of the antecedents is to the sum of
the consequents as any one antecedent is to its consequent. 5. (a) Prove that (ab)n ar bn
(b) Discuss the Binomial Theorem. 6. Solve for value of x:
x' + y - 82.
X- у 2. 7. If the product of two numbers be added to their difference, the result is 26; and the
sum of their squares exceeds their difference by 50. What are the numbers? 8. What is the length of that rectangular field of 24 acres whose area would be diminished
one acre by decreasing its length 10 rods and its width 2 rods? 9. Two cubical vessels have together a capacity of 1,072 cubic inches and the sum of
their heights is 16 inches. What is the capacity of each? 10. A man rents a farm for $200. He retains 5 acres for his own use and sublets the rest
at $1 an acre more than he gave, gaining thereby $10 on his entire rental. How · many acres does he rent?
1. Discuss the educational value of arithmetic with reference to its effect upon (a)
reason, (b) memory, (c) imagination, (d) judgment. 2. (a) Show why the difference between 1234 and 6725 may be found by adding the
complement of 1234 to 6725 and then subtracting 10,000. (b) 252 - 20 X 30 + 5?.
Explain why this is true. 3. (a) Prove that the product of any three consecutive numbers is divisible by 6. (b) Show that the product of the L. C. M. and H. C. D. of two numbers is always
the product of the numbers. 4. How much pure alcohol must be added to a mixture of 4 alcohol and } water, so that
10 of the mixture shall be pure alcohol? Solve by analysis. 5. (a) Express on a Fahrenheit scale the following temperatures:
+ 40° C., — 5° R. Explain. (b) The surface of a pyramid one foot high is made up of equilateral triangles. Find
the surface of its sides. 6. Explain standard time, illustrating by examples. 7. A sphere and a cube have the same volume; find the ratio of their surfaces.
8. (a) Which is better for the purchaser and how much? 30%, 15%, 10% off or one
discount of 47%? (b) At what price above cost must goods be marked that r% may be deducted and
still s% profit be made?
1. State and describe the several stages or epochs in the life history of a plant. 2. Name the chemical elements of plants which may be discovered by the use of reagents.
Name several of the reagents you would use in such work. 3. Name the essential material and apparatus for a well-equipped botanical laboratory
for a high school. 4. What subjects should be introduced in a course in elementary agriculture? Why? 5. Name five kinds of roots and describe each. 6. (a) Describe dormant bud, accessory bud, terminal bud.
(b) Describe several kinds of estivation. 7. (a) Describe osmosis in roots and root hairs.
(b) What is meant by root pressure? 8. Explain how plants obtain food from the air and from the soil. What foods are se
cured from each source? 9. Describe three types of bundles found in fibro vascular tissue. 10. (a) Name and describe five flower clusters.
(b) Describe the process of pollination.
1. Define and illustrate acid, salt, base, alkali, neutralization. 2. Write the formulæ and give brief description of each: glycerin, chloroform, meth, 1,
alcohol, glucose, phenol. 3. (a) Where and in what forms is nitrogen found in nature?
(n) Name several compounds with nitrogen. 4. (a) Describe the preparation of hydrochloric acid. O Name and give formulæ for the several compounds of chlorine, hydrogen, and
oxygen. 5. Outline a method for the sanitary analysis of water; of vinegar. 6. Give a few simple tests to detect the presence of iodine, silver, and sulphuric acid in a
solution. 7. (a) What are hydro carbons? Name several.
(b) Give a test for carbon dioxide in the air. 8. Give the chemical significance of the terminations ate, ic, and ite. 9. Describe gunpowder chemically. Write the reaction caused by the explosion. 10. (a) Name and describe four compounds of iron.
(b) Give Avogadro's law.
1. How can civil government be correlated with United States history? 2. What are the sources of revenue for the national government? How may such reve
nues be increased? State the reasons for and against your answer. 3. Explain fully, using concrete illustrations, what is meant by the 59th Congress. 4. What steps have been taken to revise the constitution of Michigan? What remains to
be done? What are some of the weaknesses of the present document? 5. What are the Michigan methods of controlling the sale of liquor? Are they effective?
If not, why not? 6. Describe a trial in a justice court in detail? What is the jurisdiction of the justice
court? 7. Give and explain several new ideas in methods of government-national, state, or
local. 8-10. Give a full account of the Michigan system of taxation.
1. (a) Mention three elements of civilization transmitted by the ancients. Trace the
transmission. (b) Characterize the first century A. D. as to politics and religion.
2-3. (a) What reference works (not regular text-books) do you use for the study of
English history? What books on general history has your school library?. Name a short, comprehensive list of histories (not less than ten) which should be used
for studying the history of France, Greece, Rome, Germany. (b) How should reference work in general history be assigned? What is its purpose? 4. What is the condition of Germany (a) politically, (b) commercially? Account for each. 5. (a) What is a concordat? (b) What was the famous concordat of Bonaparte in 1801, and how is it affecting
the history of France at the present time? (c) What seems to be the social spirit of the French people and what is your
opinion of this? 6. Discuss the present relations between the United States and Japan. 7. Trace in outline the struggle between France and England. What are their rela
tions at the present time? 8. Mention some of the great problems which the English people are facing. Name some
of her statesmen and state what solutions of these problems they advocate. 9. When and how were England and Scotland united? 10. What was the Holy Alliance, its purpose, and its effects?
1. What mathematical geography should be taught in the grades? 2. What nations of Europe have interests in Africa and where? Which one has re
cently come into unpleasant notoriety over the rubber industry? How and why? 3. Name some geographical material and state what use you have made of the same. 4. Describe the physical features of Michigan (both peninsulas). 5. What would you aim to bring out and enforce in the study of a single foreign country,
say Italy? 6. Name ten products of any kind and the state or country that stands pre-eminent in
the production of each.
(a) Countries: Capitals; government.
tea, (e) nitrates, (f) wool, (g) vegetable ivory, (h) frozen mutton, (i) coca, ()
1. (a) Give proofs of the theory of the origin of soils.
(b) Define disintegration and give factors of same. 2. Describe the formation of water falls, ravines, gorges, and give examples. 3. Describe glaciers. Name several noted glaciers. What is drift? 4. (a) Name organic agencies which have operated to change geographic and geologic
conditions. (b) Give notable examples. 5. What is the theory of the internal condition of the earth. Give proofs. 6. Describe the formation of coal beds, pet roleum beds, salt beds and lakes. 7. Name and describe the stratified rocks. 8. Explain the terms fault, dip, strike, syncline, cleavage. 9. (a) Describe igneous rocks.
(b) Describe and name the granitic group or forms.
(c) Describe and name the volcanic group or forms. 10. (a) Explain the origin of mineral and metal veins.
(h) Explain the formation of mountain ranges and systems.
1. (a) Give your method of distinguishing and illustrating the following geometrical
terms: axiom, corollary, scholium. (b) Give what you consider the three most important axioms of geometry. 2. Discuss
(b) Theory of limits, giving such illustrations as you would use before a class. 3. (a) In how many cases are two triangles identically equal?
(b) Give four cases. 4. Discuss concurrency of lines as related to triangles, illustrating one case by a theorem
with proof. 5. (a) Draw a figure to prove the square upon the hypotenuse equal to the sum of the
squares on the other two sides of a right triangle. (b) Mention in their logical order the points to prove in making the demonstration
of the above from the figure. 6. Prove that if two line segments intersect so as to make the product of the segments
of one equal to the product of the segments of the other, their four extremities
are concyclic, i. e., in a circumference. 7. Compute the area of a triangle in terms of its sides. Demonstrate. 8. (a) What is the volume of a truncated triangular prism? Demonstrate. (b) A cistern is 8 ft. square at the top, 6 ft. square at the bottom, and 8 ft. deep.
How many gallons of water will it hold? 9. The area of a regular tetrahedron is 16 inches. Find the edge of a similar tetrahe
dron having twice the volume. 10. The area of a zone is equal to the product of its altitude and the circumference of a
great circle. Demonstrate.
1. (a) Decline a masculine, a feminine, and a neuter noun of the strong declension to
gether with an article and a qualifying adjective. (b) What nouns are declined in the weak declension? 2. Give the principal parts of brennen, senden, rufen, finden, bitten, sprechen, preisen,
wissen, loben. 3. (a) What prepositions govern either the dative or the accusative case? When the
dative and when the accusative? (b) What is the use of the passive voice in German? How is it formed? Conjugate
finden in the present, past, and perfect subjunctive, passive voice. (c) What idioms are used in German as a substitute for the passive voice? 4. (a) When is von used in place of the genitive?
(b) When do als, wenn, and wie each introduce adverbial clauses?
(c) What adjectives require the dative? Illustrate. 5. Translate:
(a) He is the father of three children.
(e) The gentleman whose house I bought has gone away. 6-7. Translate and give constructions of italicized words:
Drauszen auf der Strasze war es tiefe Dämmerung; er fühlte die frische
Winterlust an seiner heiszen Stirn. Hie und da fiel der helle Schein eines brennenden Tannenbaums aus den Fenstern, dann und wann hörte man von drinnen das Geräusch von kleinen Pfeifen und Blechtrompeten und dazwischen jubelnde Kinderstimmen. Scharen von Bettelkindern gingen von Haus zu Haus, oder stiegen auf die Treppengeländer und suchten durch die Fenster einen Blick in die Versagte Herrlichkeit zu gewinnen. Mitunter wurde auch eine Thür plötzlich aufgerissen, und scheltende Stimmen trieben einen ganzen Schwarm solcher kleinen Gäste aus dem hellen Hause auf die dunkle Gasse hinaus; anderswo wurde auf den Hausflur ein altes Weihnachtslied gesungen; es waren klare Mädchenstimmen darunter. Reinhardt hörte sie nicht, er ging rasch an allem vorüber, aus einer Strasze in die andere. Als er an seine Wohnung gekommen, war es fast völlig dunkel geworden; er stolperte die Treppe hinauf und trat in seine Stube. Ein süszer Duft schlug ihm entgegen; das heimelte ihn an, das roch wie zu Haus der Mutter Weihnachtstube. Mit zitternder Hand züendete er sein Licht an; da lag ein mächtiges Paket auf dem
Tisch, und als er es öffnete, fielen die wohlbekannten braunen Festkuchen heraus; auf einigen waren die Anfangsbuchstaben seines Namens in Zucker ansgestreut; das konnte niemand anders als Elisabeth gethan haben. Dann kam ein Päckchen mit feiner, gestickter Wäsche zum Vorschein, Tücher und
Manschetten, zuletzt Briefe von der Mutter und von Elisabeth.
1. Discuss, under not more than three heads, the educational value of grammar study. 2. Give accurate and complete definitions of the following: verb, infinitive, preposition,
relative pronoun, case, conjugation. 3. Illustrate the various uses of the infinitive. 4. Define and illustrate the factitive, adverbial objective, dative object, objective sub
He who made the mistake you should talk to, not me.
The band have bought their instruments. 7. Discuss mode, giving outline. 8. Give outline of the verb. 9. Show four grammatical uses of the word as; four of the word but; three of the word so;
three of the word that. 10. Analyze the following and parse the italicized words:
He looked as though the speed of thought were in his limbs.
Erant hae difficultates belli gerendi, quas supra ostendimus, sed multa Casarem
tamen ad id bellum incitabant: iniuriae retentorum equitum Romanorum, rebellio facta post deditionem, defectio datis obsidibus, tot civitatum coniuratio, imprimis ne, hac parte neglecta, reliquae nationes sibi idem licere arbitrarentur. Itaque cum intellegeret, omnes fere Gallos novis rebus studere et ad bellum mobiliter celeriterque excitari, omnes autem homines natura libertati studere et condicionem servitutis odisse, priusquam plures civitates conspirarent,
partiendum sibi ac latius distribuendum exercitum putavit. 3. Decline liber, natio, nomen, acer, plus, relative qui. 4. (a) Distinguish between the use of posse and licet. (b) Give the outline for formation of tenses for verbs of the third conjugation, passive
voice, indicative and imperative modes. 5. Give constructions for all verbal forms in 1-2. 6. Name five uses of the dative case, seven of the ablative. 7. How is condition expressed in Latin? 8. What cases are used in relative clauses and when? 9. (a) Name the causal conjunctions.
(b) What verbs take the infinitive construction? 10. Translate:
(a) Even if Cæsar had come, yet we should have been conquered.