9. The sum of two numbers is 16 and the difference of their squares is 128. What are the numbers?

10. Divide 20 into two parts whose product is 96.

ARITHMETIC.

FIRST AND SECOND GRADES.

NOTE: Algebraic solutions of problems should not be accepted. Second grade applicants answer first ten; first grade applicants, last ten.

1. A man sold two farms at the same price, gaining 25% on one and losing 10% on the other. The gain on the entire transaction was $200. What did each farm cost him?

2.

3.

4.

A fast train running 40 miles an hour is 15 miles behind a train running 25 miles an hour. How many miles must the former run to overtake the latter?

A owns 2 the capital stock of a company and B the remainder. They gain $400. What is each man's share of the gain?

A's age is to B's as 3 to 4 and the sum of their ages equals their father's age. What is the ratio of A's age to the father's age?

5. A man buys milk at 4 cents a quart. He dilutes it with water and sells at the same price, gaining 25%. What proportion of the mixture is water?

6.

7.

8.

A man buys an article listed at $1.25 at 10% and 11 1-9% off. At what per cent advance on cost must he sell it that he may receive $1.50 for it? A merchant buys 20 lbs. of butter at 18 cents a pound; 24 dozen eggs at 15 cents a dozen; 36 lbs. of poultry at 8 cents a pound, giving in exchange 16 yds. of dress goods, at 36 cents a yard, and the balance in fruit jars at 6 cents each. Indicate by symbols the complete operations necessary to solve the above to find the number of fruit jars.

NOTE: Examiners mark on the symbolic solution only.

Prove that the ordinary interest for any time less than one year is 73 of the exact interest.

9. Find the difference between the common interest on $360 for 1 yr. 7 mo., 15 da. at 6% and the compound interest for the same time compounded quarterly.

10. What is the side of the largest square board that can be cut from a circle whose area is 4 sq. ft.?

11.

Discuss circulating decimals.

12. Three men, A, B, and C, can walk around an island in 14, 18, and 14 days respectively. If they start together when will they be together again? 13. Goods marked to gain 20% were changed for eggs, 3 out of every dozen prov

14.

ing to be bad. What was the true gain or loss per cent on the goods?

I sold a farm of 160 acres at $75 per acre, which annually yielded a net income of $6 an acre, and invested the proceeds in 8% stock at 80 including brokerage. What was the change in my income?

15. The specific gravity of milk is ordinarily 1.032. If a sample of milk shows a specific gravity of 1.0256 what per cent of water has been added?

2.

How much oil must be mixed with a gallon of paint containing 2% of oil so that 25% of the mixture will be oil?

3. A jobber gains 20% at retail and his wholesale price is 10% below his retail price. What is his gain at wholesale?

4. A man consigned to a commission merchant 50 tons of hay at $13 a ton. Storage was $1 a ton and the commission 3%. Find the commission and the net proceeds of the sale.

5. Draw a note dated June 1, 1907, for $400 at the legal rate in Michigan upon which payments are indorsed on December 1, 1907, and April 1, 1908, and compute the amount due July 1, 1908.

NOTE: Five credits for correct form of note with endorsements.

6.

7.

8.

(a) Draw a receipt for money.

(b) Draw a due bill for 3 months' tuition at 75 cents per month. Find the size of a cube the surface of whose faces is 3 3-8 sq. yd. The expense of building a schoolhouse was $9,166.50, which was paid by a tax on property at 24 mills on the dollar, with a commission of 3% charged for collecting. What was the assessed property taxed? 9. What is the radius of a wheel that makes 420 revolutions in traveling a mile?

10. How much land in a square field one mile square containing a circular lake 80 rods across?

MENTAL ARITHMETIC.

NOTE (1) Distribute these lists among all the applicants, placing them face down upon the desks. (2) Each applicant write his number or name across the back of the list.

(3) At a signal from the commissioner, all reverse the papers and ir. the right hand margin write as many answers to the questions as possible in 20 minutes.

(4) At the second signal, all again reverse the papers when they will at once be collected by the examiners.

Give one credit for each correct answer written, making 20 credits for this part of the examination.

4. How many cows at $40 each can be bought for $800?

5. What will an acre of land cost if the N. E. 4 of N E. 4
of a section costs $1,200?

6. Profit is $2, selling price $10. What is the gain per cent?
7. Selling price is $6, cost is $4. What is the gain per cent?
Interest is $12, time 1 year, 6 mos., rate 4%. What is the
principal?

8.

4.

5.

6.

7.

8.

9.

10.

Amount is $1,300, rate 6%, principal $1,000. What is the time?
What will $250 yds. of cloth cost, at $2.50?

9.

10.

11.

What will 42 spoons cost, if 2 dozen cost $3?

11.

12.

How many yards of calico can be bought with $4.50 at 16 cents a yard?

12.

13.

If a bu. of cherries cost $2.25, what is gained by selling 10 bu. at 10 cents a quart?

13.

14.

If it costs $8 to harvest 7% acres of wheat what will it cost to harvest 75 acres?

14.

15.

What per cent of 4 bushels is 14 of 1 bushel?

15.

16.

If 4 of an article is sold for what % of it cost, what is the

In what time will any principal gain 100 per cent at simple interest?

20.

BOTANY.

FIRST GRADE.

1. Describe the process of photosynthesis or carbon assimilation fully.

2. State four differences between dicotoyledons and monocotyledons.

3. Trace the life history of a moss plant explaining alternation of generations.

4. Define pollination. Name and describe the devices by which flowers prevent self pollination.

What are the functions of roots? Where does a root grow?

7. Outline a laboratory study of buds. Define the different kinds of buds.

8.

9.

10.

Give the characters of two families of dicotyledons and one of monocotyledons.
Describe the structure of an open collateral bundle. Where found?
How are insect and wind pollinated flowers distinguished?

SECOND GRADE.

Answer any ten.

1. Name and give examples of all structure which help in seed dispersal. Describe 3 kinds of underground stems. Examples of each.

2.

3. Describe the different devices by which stems climb. Examples.

4. Name and give the use of parts of a complete flower.

Name and give use of parts of a typical leaf.

7.

8.

9.

10.

What is a weed? Name ten common weeds of your neighborhood. Why

are they common?

Name the organs of a plant.

Describe a bean seed.

11. What conditions are necessary for growth of seeds?

12. How are leaves veined?

Illustrate by diagrams.

CIVIL GOVERNMENT.

FIRST AND SECOND GRADES.

Second grade applicants answer the first ten; first grade applicants, the last ten.

1.

(a) When was the United States Constitution adopted?

(b) The Michigan State Constitution?

2. Give three parallels between them.

3. How are treaties made?

4. Give complete explanation of the steps in the naturalization of an alien.

5. Mention five important powers of Congress. Why important? Amendments to the United States Constitution:

6.

(a) How are they made?

(b) How many have been made?

(c) Give substance of the last one.

7. What is the political significance of "To the victors belong the spoils?"

8. Compare the United States Supreme Court and the Michigan State Supreme

(c) Are there any valid objections to its being made applicable to all officials?

10. Give the origin of the town and township.

11. What were some of the defects of the colonial government?

13. What are the advantages and the disadvantages of political parties?

14. Should or should not the money used in political campaigns be a matter of public knowledge? Why?

15. Discuss the "one term only" question of office.

1.

THIRD GRADE, BOTH CLASSES.

Mention the departments of government.

2. (a) When does Congress next convene? (b) When will the session end?

3. What is the right of "eminent domain"?

4. What officials constitute the cabinet?

5. How does a territory become a state?

6. Give the method of the passage of a bill in Congress.

7. What is the doctrine of "states rights"?

8.

(a) When will the Michigan legislature convene?

(b) How many members has it?

(c) How are the presiding officers designated?

1.

2.

What advantages and what disadvantages in using the Course of Study in

a rural school?

(a) In what grades is it most valuable? Why?

(b) To what class of teachers is it most helpful?

3. Give outline of the first grade.

4. What poems in the Course of Study are in your estimation most valuable? 5-6. In what grades are the various text-books introduced?

7-8. What is suggested in nature study in the first four grades?

9. What is advised with reference to penmanship?

10. What points are suggested with reference to problems in lower grades?

GENERAL HISTORY.

FIRST GRADE.

1-2. Contribution of the following nations to later civilization:

Hebrews, Phoenicians, Romans.

Egyptians,

3. What two kings gave Persia the leading place among the Iranian Aryans? Under which one was European ground invaded?

4. Using Greece as an example, show how physical and geographical conditions determine the character of the civilization in different sections of a country.

5. Connect the following terms with the struggle for freedom by the Roman plebeians: Tribunes of the people, Decemvirs and Laws of the Twelve Tables, Consuls.

6-7. (a) What are the two periods into which modern history may be subdivided? (b) What events mark the beginning and end of each?

8. Explain how the struggle between Charles V. and Francis I. helped the cause of the Reformation in Europe.

9. Mention the three most important events in the growth of English constitutional freedom.

10. What would be the bearing upon the future political history of Europe of the proposed new alliance between England, France, and Russia?

SECOND GRADE.

1-2. Into what periods is history usually divided? How may these be subdivided? 3. Why is the Battle of Marathon called one of the decisive battles of the world? 4. What, in general, were the causes and results of the three Punic wars? What dramatic incident in connection with one of them can you relate?

5. What were the good and evil effects of feudalism?

6. What effect did the Crusades have upon the intellectual development of

7.

Europe?

What was the conflict in which Joan of Arc was the central figure? What did she do for France?

8. What war decided Prussia's supremacy over Austria in Germany? Name

one great statesman and one general who were chiefly instrumental in securing this victory.

9. What is England's colonial policy toward Ireland, India, Canada?

10. Who is United States ambassador to Germany?

GEOGRAPHY.

FIRST GRADE.

1. Explain one method of finding latitude.

2. What and where is the international date line? How came it to be there? Why is its present location a good place to keep it?

3. Explain fully why summer is warmer than winter.

4. Locate the following physical divisions of the United States, giving at least one leading characteristic of each:

5.

(1) New England plateau, (2) Alleghany plateau, (3) Colorado plateau, (4) Appalachian Mountains.

Describe and explain the rainfall of the Pacific coast of the United States as to (1) amount, (2) season of greatest precipitation.

6. Name and locate the chief coal fields of the United States.

7.

What was the purpose of the three days conference of governors called by President Roosevelt at the White House on May 13?

8. What economic and industrial conditions in the United States are demanding the improvement of our inland waterways?

9.

What geographic conditions make Chicago a larger city than Milwaukee or Michigan City? 10. Explain why equatorial Africa should have heavy rainfall while the Sahara and much of South Africa are so arid.

SECOND AND THIRD GRADES.

Answer any ten.

1. (a) Name and give width and boundaries of the various zones.

(b) What determines the position of the tropics of Cancer and Capricorn and the polar circles?

2. How would you teach seasons and causes of change of seasons to pupils who are beginning the study of geography?

3. What is the length of the day and the night at the equator, Arctic Circle and north pole on the equinoxes at the summer solstice?

4. What difficulties must be overcome before the Mississippi, Ohio, and Missouri rivers can become great commercial highways?

5. What are the advantages and disadvantages of water transportation as compared with railroads or land transportation?

6. What national resources is there a necessity for conserving? Why?

7. Show by concrete cases how the rainfall of the United States influences the occupations of its people?

8.

9.

What geographical conditions favored the growth and development of (1) Buffalo, (2) Pittsburg, (3) New York, (4) Duluth, (5) Cleveland. Name the chief articles of commerce carried by vessels moving eastward on the Great Lakes. Westward.

10. Show how rainfall influences the distribution of life in Africa.

11.

12.

(a) Locate the copper mines of the United States.
(b) Locate the great diamond mines of the world.
Name five countries and state how they are governed.

GEOMETRY.

FIRST GRADE.

NOTE: All theorems must be demonstrated, all constructions of problems explained, and all figures carefully drawn.

1. The diagonals of a trapezoid divide each other into segments which are proportional.

2.

The difference of the squares on two sides of any triangle is equal to the difference of the squares on the projections of those sides on the third side.

3. If through a point in the circumference of a circle two chords are drawn, the chords and the segments cut from them by a line parallel to the tangent are reciprocally proportional.