The diagonals of an isosceles trapezoid are represented by 6 29 and 4 15 what is the value of x

Check out the new look and enjoy easier access to your favorite features

Page 2

Question i. (a) Point out the dependent clauses in the following sentence, and tell

whether they are adverbial, adjective, or noun clauses, and (b) explain the syntax of the italicized words and phrases:

“It is this haziness of intellectual vision which is the malady of all classes of men by nature, of those who read and write and compose quite as well as of those who can not-of all who have

not had a really good education." Question 2. (a) Write sentences containing (1) indirect object, (2) noun clause as

object, (3) past participle of swim, (4) infinitive modifying the

subject. (6) Write sentences illustrating the meaning of the following words:

Effect (verb); affect; principal; counsel. Question 3. Correct the following sentences, if necessary, and give reasons for each

correction:

(a) There isn't hardly any ink in my pen.
(6) The strength of Stephen's features were in hers.
(c) Take the college Commons, which in its corps of waiters three-

fourths of them are athletes.
(d) If I was him I'd refuse to stand it.
(e) If anybody will pay their own expenses they can go to Platts-

burg. (1) He staggered just like a drunken man would. (9) Tom says he don't see why Englishmen should blame the

Irish. (h) The sources of the oil are most always found at the foot of a

mountain. Question 4. Write a theme of at least one page (about 300 words) on one of the fol

lowing subjects:

(a) The campaign of Verdun.
(b) The importance of sea power in the present war.
(c) How candidates for the Naval Academy should prepare.
(d) Whom I would vote for in the next presidential campaign,
and why.

GEOGRAPHY.
Question 1. (a) Identify the following names and give the exact location of each:

(1) Hobart; (2) Wake; (3) Tegucigalpa; (4) Grand Cayman; (5)

Rhodesia; (6) Brazos; (7) Lena; (8) Katahdin. (b) Name the capitals of the following States and countries: (1) Vermont;

(2) Tennessee; (3) New Mexico; (4) Oregon; (5) Arkansas; (6) Switzerland; (7) Korea; (8) Roumania; (9) Uruguay; (10)

Colombia. Question 2. (a) In what respect has the geography of Europe been temporarily

altered by the present war? (6) Where are (1) Libau, (2) Verdun, (3) Gallipoli, (4) Erzerum, (5)

Hartlepool? Question 3. (a) Explain the terms (1) relief map, (2) international date line, (3) bore,

(4) pampas, (5) Tropic of Capricorn. (6) Draw a map of your State, showing its principal mountain ranges,

cities, lakes, and rivers. Question 4. (a) In a voyage from Bombay to New York, name five bodies of water

to be crossed and five ports of call. (b) What islands and continental states are crossed by the equator?

Page 3

Question 3. (a) Find the value of x3+x2 - 4x+5 when x=2+v5.

Find the square root of 28—57/12, and of 117+36V/10. (6) Simplify (15+3/3)+(215-13).

Find the fourth power of (1+1=1). Question 4. (a) Find the values of x, y, and z from the simultaneons equations

X-y+z=34

2y=5c+8 32-12=133

4x -17 10x -13 8x - 30 , 5x -4 (6) Solve (1) ti

+ and (2) Va+x+va-x= X-4 2x - 3 2x -7

X-1' 12a

5γα--α Question 5. (a) Solve the equation x2 +px+q=0. (This is to be completely worked

out, not merely written down from memory.) Find the sum and the product of the roots. Denoting the roots by a and b, find the value of a2 +ab+62, and of a3+63, in terms of р

and

9. (6) Solve the equation 12x2 — 103x+221=0.

Solve the equation bx2 — ax(1+62)+a?b=0, and then find the equa

tion whose roots are the reciprocals of the roots of the given equation.

ARITHMETIC. Question 1. (a) Divide 2.99573 by 2.302585, contracting the operation to give the

result correct to five decimal places only. Multiply the quotient obtained by the divisor given, contracting the operation to

give the result correct to three decimal places only. (b) Express as common fractions reduced to their lowest terms: .109375; .03125; .0086375: .000125.

2} Question 2. (a) Simplify 2 +14 yf of 3+3+3 of 4

831--34 1 +of+ (6) Find the capacity in gallons of a cylindrical tank 10 feet deep and

10 feet in diameter. Question 3. (a) Find, to six places of decimals, the value of

5-15

5+75 (6) Ice weighs .909 as much as water. If water weighs 62.4 pounds a

cubic foot, find in feet, to two decimals, the edge of a cube of

ice weighing 500 pounds. Question 4. (a) A year and three months after the date of a note the interest and

principal amounted to $272. If the interest is at 5 per cent per

annum, what was the face of the note? (b) A man earned 41% per cent more in February than he did in January.

If his earnings for January and February together were $1,812.50,

what did he earn each month? Question 5. (a) 32° Fahrenheit is the same temperature as 0° centigrade, and 100°

centigrade is the same as 212° Fahrenheit. What would be the readings on a centigrade thermometer corresponding to -18° F., 5° F., 72° F.? What would be the readings on a Fahrenheit

thermometer corresponding to -12° C., 25° C., 75° C.? (6) The longitude of St. Louis is 90° 15' W., and the longitude of Wash

ington is 77° 01' W. When it is 6.30 a. m., local time, at Washington, what is the local time at St. Louis?

Page 4

1. vulgarism. 10. successful. 19. advisable. 30. mortgage. 2. satellite. 11. liquefaction. 20. recipient. 31. procedure. 3. sanitary. 12. salable.

21. persistence. 32. apparent. 4. esophagus 13. besiege. 22. all right. 33. separate. (e-sof'a-gus). 14. massacre (mas' 23. seize.

34. diffusion. 5. interference.

a-ker). 24. development. 35. luscious. 6. epidermis (ep-i- 15. gesture.

36. hypocrite. der' mis).

16. rescind (re- 26. villain (vil'en). 37. demurrage. 7. infinitive.

sind').

27. supersede. 38. intricate. 8. description. 17. concurrent. 28. calendar. 39. futile (fu'li;. 9. disinfectant. 18. oracle.

29. embarrass. 40. opulence.

GRAMMAR.
Question 1. (a) Give the principal parts of swing, fly, awake, throw.

(6) Compare ill, much, southern, far.
(c) Give the singular and plural of ally, genus, errata, Murphy.
(d) Conjugate the verb to trust in the present perfect tense, indicative

mood, active voice; and in the past tense, subjunctive mood,

passive voice.
Question 2. (a) Give the syntax of the words italicized:

Each speaker was allowed an hour.
Walk two miles farther and you will come to the road.

Unwilling to accept aid, the widow suffered many privations.
(6) Give an example of each of the following: Compound complex

sentence; noun clause; temporal clause; interrogative adverb. Question 3. Correct, if necessary, the following, and give your reasons:

(a) Mebbe that's right, but it is some different than the story I

heard.
(6) I would think that this data were sufficient.
(c) His face bore the look of the most absolute astonishment.

(d) Give it to whoever you think is worthy of such an honor. Qustion 4. Name two uses of the colon and two of the semicolon, and give examples

of each..
Question 5. Write a theme of one page on one of the following subjects:

My favorite author.
The future of Mexico.
The importance of the Balkan States in the European War.

GEOGRAPHY. Question 1. Write a one-page theme on the island possessions of the United States, discussiong their location, products, and population. . Question 2. Draw an outline map of Europe, and indicate the Russian trade routes during the war. Question 3. (a) In going by steamer from Duluth, Minn., to Valparaiso, Chile, what

waters would you traverse and what large cities would you pass? (6) Name the most populous State in the Union, and give in order the

States that touch it. Question 4. Give the location of the following and tell what each is: (a) Oahu; (6) Parana; (c) Bug; (d) Delft; (e) Bukowina; Mendocino; (9) Sakhalin; (h) Jungfrau; (0) Kola; 6) Helsingfors.

Page 5

5,8 Question 4. (a) Solve + =3.

(6) A crew can row 16 miles downstream and back in 6 hours. Their

rate upstream is twice the rate of the stream. Find the rate of

the stream and the crew's rate of rowing in still water. Question 5. (a) In the equation mx2+2x2 +2m-3mx+9x— 10=0, for what values of

m are the roots real? For what values of m are the roots

imaginary? (6) A can do a piece of work in 3 hours less time than B, and together

they can do the work in 2 hours less time than A alone. How long would each take to do the work if each worked alone?

Question 1. (a) Find the values, correct to five decimal places, of (1) 8.71835 mul

tiplied by 31.0098, and (2) 47.2089 divided by 7.32097. (b) A cubic foot of water weighs 999 ounces avoirdupois. Find the

weight in grains of a gill of water, to the nearest tenth of a grain. Question 2. (a) Find the G. C. D. of 44067 and 56721.

227 (6) Reduce to decimal form, to the nearest hundred thousandth,

23 Express 0.77875 as a common fraction in its lowest terms. Question 3. (a) A train goes a certain distance in a certain time. Its speed is then

changed so that it goes of the former distance in 40 of the for

mer time. Find the ratio of its first speed to its last speed. (5) When it is 3.30 a. m. Tuesday in longitude 5° 17' E., what time

and day is it in longitude 115° 8' W.? Question 4. (a) The engine of an automobile makes 3.5 revolutions while a wheel

makes one.

The wheel is 30 inches in diameter. How many revolutions

per minute will the engine make when the speed of the automobile is 30 miles per hour? (Use 7=27). (b) A square field contains 30 acres. Find the length of one side, in

feet, to the nearest hundredth of a foot. Question 5. (a) Find the simple interest on $5,265 for 3 years 5 months 17 days at

5 per cent. Find the interest on the same principal for the same
time when compounded semiannually at 4 per cent.

43
(6) Simplify X - 11

X
11 X 12 - 19 of 36

1. acquaintance. 2. aggravating 3. agreeable. 4. ammunition. 5. auxiliary. 6. believe. 7. boundary. 8. candidate. 9. cartridge. 10. changeable.

11. commander. 12. competent. 13. controlling 14. deficiency.

15. development.

16. expel. 17. governor. 18. hateful. 19. immediately. 20. indelible.

21. miniature. 31. receive. 22. navigable. 32. recommend. 23. occurred. 33. sensible. 24. personnel. 34. shamefully. 25. persuade. 35. siege. 26. preceding. 36. strategy. 27. preparation. 37. superintendent.

28. privilege. 38. torpedo.

29. profiting. 39. undoubtedly. 30. pronunciation. 40. until.

Page 6

Question 1. (a) Define (1) diagonal, (2) chord, (3) similar polygons, (4) equivalent

triangles, (5) apothem. What is the locus of points equidistant from two intersecting straight

lines? (1) Prove: Two triangles are equal if the three sides of one are equal,

l'espectively, to the three sides of the other. Question 2. (a) Construct a triangle, given two sides and the angle opposite one of

them. Discuss the several cases. (b) The perimeter of a rhombus is 48 inches and one of its angles is 60

degrees. Find the area of the quadrilateral whose vertices are

the middle points of the sides of the rhombus. Question 3. (a) Prove that if two circles are tangent to each other and two straight

lines drawn through the point of contact are terminated by their circumferences, the chords joining the ends of these lines are

parallel

( Show how to draw a tangent to a circle from an exterior point. Question 4. (a Prove: The areas of two similar triangles are to each other as the

squares of any two homologous sides. (b) A regular hexagon is inscribed in a circle, and another is circum

scribed. Find the ratio of the areas of the two hexagons. Question 5. If the side of a regular polygon inscribed in a circle of radius r is a, find the side of the inscribed regular polygon of double the number of sides.

ALGEBRA.
Question 1. (a) Simplify 9m -- [3n+{4m-(n-6m)}-(m+7n)].

(b) Multiply 3x-(5y+2z) by 32-(y-22).
(c) Multiply out (a−b)(au+b3)[a(a+b)+62].

(d) Divide 6.26 +228 — 9x+ +5x2 +18x—30 by 3x3+x2–6. Question 2. (a) Factor (1) 2+5x — 3x2, and (2) ao — 63.

(6) Factor 1+4y*.

(6) Find the L. C. M. of 2x3 +13x2 +5% -6,6x3 - 22 — 5x+2 and 6x3+29x2 –

40x+12. Question 4. (a) Simplify by reducing to a common denominator.

1 1 1 1 a-1

+ (6) The first digit of a number of three figures is three-fourths of the

second digit and exceeds the third digit by 2. If the number is divided by the sum of its digits the quotient is 38. Find the

number. Question 5. (a) A regiment in solid square has 24 fewer men in the front rank than

when in a hollow square 6 deep. How many men are in the

regiment? (6) A cistern can be filled by two pipes. One of them can fill it in

two hours less time than the other. Both together can fill it in 13 hours. Find the time required for each pipe alone to fill the cistern.

62881-21 -4

Page 7

Question 3. (a) At what time between 7 and 7.30 o'clock are the hands of a watch at right angles to each other?

-4.
(b) Divide 4–52-%;+x-*yby 2x+x-4-2-y!.
) +

yo Question 4. (a) Solve væ+o+Vx+13= 4x+37.

(6) Cloth being wetted, shrinks one-eighth in its length and one-sixteent

in its width. If the surface of a piece of cloth is diminished by 54 square yards, and the length of the four sides by 41 yards, what

was the length and width originally? Question 5. (a) Given x2 — 8x+K=0, find the value of K which makes one root

three times the other; also, find the value of K which will make the roots differ by two units.

distributing a sum of money to his children, found that, in order to give them a dollars each, he should want b dollars more; he therefore gave them c dollars each, and had d dollars left. Find the number of children, and the amount of money the man had before distribution.

ARITHMETIC. Question 1. (a) Multiply 79,632 by 2.875; also 37.2836 by .049867, the second result

to be correct to six decimal places. (6) Divide 244,118 by 742; find correct to five decimals the value of

29.3786

.05783 Question 2. (a) A square field contains 2 acres, 13 square rods, 15 square yards.

Find the length in feet of the fence required to inclose it, the result to be correct to the nearest tenth of a foot.

a of 11

6 (6) Simplify:

33 +5

+4=-(5+:

111 Question 3. (a) What per cent of £19 138. 6d. is £3 78. 4d.?

(6) Find the simple interest at 41 per cent on $2,350 from September

19, 1917, to March 10, 1920. (c) Find the interest on $2,350 between the dates as given in (b) if compounded semiannually at 4 per cent.

4 Question 4. (a) Find the greatest common divisor of 3,683 and 38,227; also the least

common multiple of 126, 154, and 560. (6) If the driving wheel of a locomotive makes 227 revolutions in going

206 rods 6 feet, how many revolutions will it make in going 18

miles 240 rods? Question 5. (a) A grocer mixed 5 gallons molasses costing 80 cents a gallon and 13

gallons of water with 30 gallons of cider costing 20 cents a gallon.

What was the cost per gallon of the mixture? (b) A piece of cloth costs $4.50 per yard. What price must be set on it

so that when sold with a discount of 10 per cent the profit will be 15 per cent?

Page 8

SERIES No. 44.- FEBRUARY, 1920.

GEOMETRY. Question 1. (a) Define (1) isosceles triangle, (2) parallelogram, (3) sector, (4) ratio of

similitude, (5) regular polygon. Prove that two triangles are equal when the three sides of the one are respectively equal to

the three sides of the other.

(6) Prove that the three medial lines of a tri agle meet in a point. Question 2. (a) Prove that if E and F are the middle points of the opposite sides,

AD, BC, of a parallelogram ABCD, the straight lines BE and DF

trisect the diagonal AC. (b) Find the locus of centers of chords drawn through a point on the

circumference of a circle. Question 3. (a) The sides of a triangular are a, b, and c. Find, in terms of a, b, and

C, the segments of the side c made by the bisector of the opposite angle. What are the segments made by the bisector of an exte

rior angle opposite the side c? (b) A straight line of length a is divided internally and externally in

extreme and mean ratio. What are the lengths of the four seg

ments? Question 4. (a) Prove that the area of a triangle is equal to half the product of its

base and altitude. Prove that the areas of two triangles having an angle of the one equal

to an angle of the other are in the ratio of the products of the sides

including the equal angle. (6) Find the perimeter and the area of a regular octagon inscribed in a

circle of radius a. Question 5. (a) Find the length of a diagonal of a regular pentagon inscribed in a

circle of radius a. (6) The areas of two similar pentagons are 576 square inches and 529

square inches, respectively. If the perimeter of the larger is 16 feet 6 inches, what is the perimeter of the smaller?

Question 1. (a) Factor (1) 24 — y4, (2) x4 +4y4, (3) X5+y", (4) 14x2 — 25x+6, (5) a---20a

–69. Divide x+vay+y by V&+Vry+vy.

pa 6

and 3/a-6-1ci al ci di

V -2 e5 V7-1e
Question 2. (a) Extract the cube root of X6 — 3x5 +5x3 — 3x-1.

24 — 6x3 +13x2 – 12x+4
(b) Simplify: x*-423 +8x2 – 16x+16

Page 9

Question 1. (a) Define (1) parallel lines, (2) scalene triangle, (3) trapezoid, (4) ex

treme and mean ratio, (5) similar polygons. Prove that the sum of the angles of any triangle is equal to two right

angles. (6) Prove that the three perpendiculars from the vertices of a triangle

to the opposite sides meet in a point. Question 2. (a) Prove that the sum of the lengths of the three medial lines of a

triangle is less than its perimeter and greater than half its perim

eter. (6) Through a point, P, two straight lines are drawn intersecting a

circle. How is the angle between the lines measured (1) when P is within the circle, (2) when P is outside the circle? Prove

your statements. Question 3. (a) Prove that any chord drawn through P, a point within the circle,

is divided by P into segments of which the product is constant. Prove that if a secant is drawn to a circle through an exterior point,

P, the product of the whole secant and its external segment is

constant. (6) Prove that the squares of the legs of a right triangle are proportional

to the segments of the hypotenuse made by the perpendicular

let fall upon it from the vertex of the right angle. Show how to construct a square having five times the area of a

given square. Question 4. (a) Prove that the ratio of the areas of two similar triangles equals the

ratio of the squares of two homologous sides. How should a line be drawn parallel to the base of a triangle so as to

bisect the area? (6) Find the perimeter and the area of a regular dodecagon inscribed

in a circle of radius a. Question 5. (a) Find the length of a side of a regular pentagon inscribed in a circle

of radius a. (6) Prove that the area of the regular hexagon inscribed in a circle

is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.

Question 1. (a) Reduce by removing parentheses: 2x - 4x— (5x-(-6x-6)}+

[- {} {32–(80 – 9)}]

Divide x3m+2+8x3m-1 by x2m+1 — 2x2m+4x2m-1.

(6) Factor: (1) a2 +62+c2—2ab-2bc+2ac.

(2) m6 -n6. (3) 9x4+ 6x2y2+49y4.

(4) 84+5a-aa.

(5) 24ab-18ay-20bx+15xy. 62881°—21-5

(65)

Page 10

Question 1. (a) Give the past tense and the past participle of the following verbs:

(1) Lie, (2) drag, (3) attack, (4) shun, (5) put, (6) go, (7) slay,

(8) deny. (6) Give the plural of the following nouns: (1) Commander-in-chief,

(2) potato, (3) piano, (4) phenomenon, (5) church, (6) mouse,

(7) enemy, (8) memorandum. Question 2. (a) Write a sentence to illustrate each of the following (1) Restrictive

relative clause; (2) Conditional clause, contrary to fact; (3)

Object clause; (4) Participal phrase. (6) Punctuate the following sentences:

(1) Impossible exclaimed Smith when where and how could

he have escaped (2) Although in spite of all his faults I like him I should not

wish him for a companion (3) The large ship which you saw is the Leviathan which during

the war was used as a transport (4) Germanys allies and dangerous allies they turned out to be

were the following countries Austria Hungary Bulgaria

and Turkey Question 3. Correct whatever is wrong or undesirable in the following sentences:

(a) It looks like it was going to rain.
(6) After shaking hands with John and I the train carried him

from our sight.
(c) The boy who tries his best, not the boys who are slowest to

work and quickest to play, win out. (d) Everybody on board were doing their best to get the ship in

action. (e) I will not hear from this examination for some days. (f) He is a man who I know to be trustworthy, but his brother is a

man who I feel is not to be depended on. (9) We knew we were a long ways from home, but couldn't hardly

tell just where.

(h) We would have been forced to have abandoned our plans. Question 4. Write a theme of about three hundred words on one of the following

subjects:

(a) An interesting friend of mine.
(6) My favorite character in fiction.
(c) An experience in wage-earning.

Question 1. Tell what and where the following are: (a) Armenia; (6) Sonora; (c) Scapa Flow; (d) Luzon; (e) Solway Firth; (f) Tientsin; (g) Schleswig; (h) Prague; (2) Dardanelles; (j) Azores.

Question 2. In a page or so, describe Ireland, giving its physical features, principal cities, products, climate, and other geographical characteristics. Draw an outline map showing its situation relative to England.

Question 3. What bodies of water, including seas, straits, gulfs, canals, etc., would one traverse in a voyage from Petrograd to Vladivostok? Describe briefly two other possible routes.

Question 4. Mention six of the most important river systems in the world, and give reasons for your choice in each case.

Page 11

Question 1. (a) Find, correct to five decimal places, the value of

2.17064X34X0.48+3.29431:-0.72303. (b) Find the value of

(18.6X79+14X3.6)2 – (7.2X13+22X1.6)2.
Question 2. (a) A flywheel is 11 feet in diameter and is making 76 revolutions per

minute. Taking =3.1416, find, to three decimal places, the
number of miles traveled by a point on the rim in 1 hour 22 minutes

and 18 seconds.
(b) Find the L. C. M. of 7,140 and 25,025.

5-16 Question 3. (a) Find, correct to five decimal places, the value of

1+16
(6) Find the amount of $1,000 for two years and six months if compounded

semi-annually at the rate of 6 per cent per annum. Also find the
rate of interest that would yield same amount if computed as

simple interest for the same period.
Question 4. (a) If it costs $16,200 to feed 870 men for 2 weeks and 4 days, what will

it cost to feed 19,600 men for 12 weeks and 2 days?
(6) Two miles of copper wire, { of an inch in diameter, is melted and cast

into a rectangular block whose base is 20 inches by 16 inches. Find

the height of the block.
Question 5. (a) A and B are 2 miles apart on a stream in which the current runs 3

miles per hour. A is downstream from B, and they start to row
towards each other at the same instant. If A rows at the rate of
5 miles per hour in still water, and B at the rate of 4 miles per hour,

how far from A's original position will they be when they meet?
(6) A rectangular field contains 324 acres, and its length is thirteen times

its width. How many rods of fence are required to inclose the field ?

GEOMETRY.
Question 1. (a) Define (1) segment (2) secant, (3) axiom, (4) theorem, (5) geometric

locus, (6) rhomboid, (7) trapezium, (8) right angle.
(6) State and prove the proposition relating to the measure of an angle

inscribed in a circle.
Question 2. (a) Prove that if from a point outside a circle a tangent and a secant are

drawn, the tangent is a mean proportional between the whole

secant and its external segment.
(6) Two chords intersect at a point 0 within a circle. If the segments of

one chord are 5 and 9 inches, and one segment of the other chord is
8 inches, find the other segment of the latter chord. If the diameter
of the given circle is 15 inches, find the distance of O from its center,

to hundredths of an inch.
Question 3. (a) In a right triangle ABC, right-angled at C, the line CD is drawn,

perpendicular to AB. If AC equals 8 inches, and DB equals 12

inches, find AB and CD to hundredths of an inch.
(6) Three equal circles, radius a, touch each other, and another circle is

circumscribed about them. Find the radius and area of the cir

cumscribing circle.
Question 4. (a) Prove that the sum of the three angles of a triangle is equal to 180

degrees.
(b) The parallel sides of a trapezoid are 18 inches and 32 inches, and its

nonparallel sides are 13 inches and 15 inches. Find the area of the
trapezoid.

Page 12

Question 3. (a) A man travels from Halifax to St. Louis. On arriving his watch

shows 9 a. m. Halifax time. The time in St. Louis being 13 minutes and 32 seconds after 7 o'clock a. m., find the longitude of Halifax, given that the longitude of St. Louis is 90° 12' 14west of Green

wich. (6) Water runs steadily at the rate of 300 cubic inches per minute into a

tank 64 feet long, 4 feet wide, and 3 feet deep, while it leaks away at the rate of 5 cubic feet per hour. In what time will the tank be

filled? Question 4. (a) At what time between 5 p. m. and 5.30 p. m. are the hands of a watch

5 at right angles to each other? (6) A boat goes 161 miles per hour downstream and 10 miles per hour

upstream. Ifit is 224 hours longer in coming up than in going down,

how far does the boat travel on the round trip? Question 5. (a) A railway curve of radius 840 yards joins two lines at right angles to

each other. Find its cost at the rate of $8,000 per mile. (6) A solid metal block consists of a rectangular base 2 feet by 24 feet by 8

inches, surmounted by a cylinder 10 inches in diameter and 19
inches high. It is melted and recast into a solid cubical block.
Find the length of the edge of this cube to the nearest tenth of an inch.

GEOMETRY.
Question 1. (a) Write, in terms of a, the values of the following:

(1) Area of a triangle, base 5a, altitude a.
(2) Area of a triangle, sides 3a, 4a, and 5a.
(3) Area of a circle, diameter 3a.
(4) Area of a trapezoid, parallel sides 5a and 4a and altitude 2a.

(5) Area of a sector of a circle, radius a, length of arc 2a.
(6) Prove that, if two chords of a circle intersect at a point within the

circle, the product of the segments of one chord is equal to the

product of the segments of the other chord. Question 2. (a) The circumference of a circle is divided by four points on the circle,

A, B, C, D, taken in the order named, so that the lengths of the arcs AB, BC, CD, and D A are in proportion as 5 : 4:6:9. If the chords AB and DC are produced to meet at 0, and the chord AD be

drawn, find all the angles of the triangle AOD in degrees. (6) In a triangle, ABC, right angled at C, the side AC is 105, and the per

pendicular from C upon AB is 84. Find the area of the triangle. Question 3. (a) Prove that 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 the equal angles. (6) A square is inscribed in a given semicircle, radius a. Find the ratio

of the area of this square to the area of the given semicircle. Question 4. (a) Show how to divide a given line into extreme and mean ratio, and give

the proof. If a line 10 inches long is so divided, what is the length

of the shorter segment?

(6) Determine the area of a regular octagon whose side is a. Question 5. (a) The chord of an arc is 80 inches; the chord of one-half the arc is 41

inches. What is the diameter of the circle? (b) The sides of an isosceles triangle are a, a, and 2b; show that the area of the inscribed circle is equal to