MENSURATION.

1. If the cost of carpeting a room 11 yards long and 8 yards wide, @ 3s. a yard, be £19 16s., find the width of the carpet.

2. (a.) If the mean diameter of the earth be 7,912 miles, find the mean circumference. (b.) How many acres are contained in a farm of the form of a parallelogram, the length and breadth of which are 48 and 28 chains respectively.

3. The sides of a triangle are 68, 75, and 77; a straight line is drawn across the triangle, parallel to the longest side, dividing each of the other sides into two equal parts: find the area of the two parts into which the triangle is divided.

4. A moat, of the uniform width of 15 yards, and depth of 7 plot of land containing 2 acres, is quite full of water. contain? (1 gall. = 277.274 cu. in.)

feet, surrounding a square How many gallons does it

5. A conical stack of hay is 20 feet high, and its base 15 feet in diameter: what is its weight, allowing 5 lbs. to a cubic foot?

6. If thirty cubic inches of gunpowder weigh 1 b., find the diameter of a hollow sphere that will hold 11 lbs.

ALGEBRA.

1. (a.) Simplify 2x - [3x-9y - {2x-3y – (x+5y)}].

(b.) From 1 take x-1. Explain the work.

2. (a.) Prove the Rule of Signs in Multiplication.

(b.) Divide 9a2b3 – 12a4b+3b5 + 2a3b2 + 4a5 - 11ab4 by 3b3 + 4a3 – 2ab2.

3. (a.) Factor x4 7x2 - 18.

4x2 - 28xy+48y2.
x + 12− x2.

(b.) Simplify

-

4. Find the L. C. M. of x2-7x+12, 3x2-6x - 9, and 2x3 – 6x2 – 8x.

5. Solve the equations

6. A farmer bought 100 acres of land for $4,220, part at $37 an acre, and part at $45 an acre. How many acres had he of each kind?

7. The sum of a certain number and its square root is 90. What is the number?

GEOMETRY.

1. (a.) If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines must be in one and the same straight line.

(b.) Give the enunciations of propositions that prove the equality of two triangles. (c.) Any two exterior angles of a triangle are together greater than two right angles.

2. (a.) To describe a parallelogram equal to any given rectilinear figure, and having an angle equal to a given angle.

(b.) The straight line joining the middle points of two sides of a triangle is equal to half the base, and cuts off a quarter of the triangle.

3. Describe a square that shall be equal to a given rectilinear figure.

4. The angle at the centre of a circle is double of the angle at the circumference, subtended by the same arc.

5. (a.) Describe a circle which shall touch three given straight lines.

(b.) Required the locus of all points equally distant from two fixed lines which intersect. 6. (a) Describe the four parts of which every problem consists. What two parts make up the enunciation of a theorem?

(b.) Give Euclid's construction for bisecting a right angle; for finding the centre of a circle.

TRIGONOMETRY.

1. (a.) The sum of two angles is 30 grades, and their difference is 9 degrees: find each angle.

(b.) Given cos A = 3, find the other trigonometrical ratios.

2. Find A from each of the following equations:

(a.) Sec A tan A = 2√3.

(b.) Tan 2A-4 tan A+ 1 = 0.

3. (a.) Show how to find the area of a triangle when the two sides and the included angle are given.

(b.) How many seconds in an angle which at the centre of a circle stands on an arc equal in length to the radius of the circle?

4. (a.) Solve the triangle

a = 1, b=1+ √3, A = 15°.

(b.) A man 6 ft. high stands at a distance of 4 ft. 9 in. from a lamp-post, and it is observed that his shadow is 19 ft. long: Find the height of the post.

5. A tower is situated on the top of a hill whose angle of inclination to the horizon is 30°; the angle subtended by the tower at the foot of the hill is found by an observer to be 15°; and on ascending 485 feet up the hill the tower is found to subtend an angle of 30°; determine the height of the tower and the distance of its base from the foot of the hill.

log 3.4771213,

log 4852.6857417, log 280.0152.4471813.

ENGLISH LITERATURE.

1. (a.) Describe the Ballad, the Ode, and the Elegy.

(b.) Give an example of each, with name of author.

2. (a.) For what are the writings of Shakespeare specially remarkable? (b.) Name six of his works.

3. (a.) Who was the author of Hudibras?

(b.) With what object was it written?

4. (a.) Give a brief account of the works of Goldsmith.

(b.) Who wrote the following:

5. (a.) Write four quotations, giving the author of each.
(b.) Give a brief account of one of the works of Tennyson.

6. (a.) Name four well-known writers of the present day.
(b.) Give the name of a work written by one of them

BOTANY.

1. (a.) Describe cells and tissues.

(b.) Upon what do plants live?

2. (a.) Describe the difference in mode of growth in root and stem. (b.) What are the functions of the different parts of the leaf?

3. (a.) Distinguish between monocotyledonous and dicotyledonous plants.

(b.) How are cryptogams reproduced?

4. (a.) Describe Labiate corollas.

(b.) Give the botanical names of five plants that you have examined and classified.

5. (a.) What are the characteristics of the Rose Family?

(b.) What are double flowers?

6. (a.) Name five plants valuable for their medicinal qualities.

(b.) What is Sorghum ?

(b.) Give a design for covering a surface, illustrating it by three or more repetitions of

the unit.

3. Draw a pair of scissors, half open, three inches in length.

4. (a.) What is the advantage of drawing from dictation? (b.) What is half-tinting? Give an illustration.

5. Draw any design involving the Maple Leaf and Union Jack.

6. (a.) Fill a circle of two inches diameter with two interlacing triangles.

(b.) Make a free-hand sketch of a window in this room.

GEOLOGY.

1. (a.) What is the aim of this science?

(b.) Name three of its divisions.

2. (a.) Show how to distinguish between igneous and aqueous veins by describing their formation and general character.

(b.) Name some of the most common chemical substances that enter into the composition of rocks.

3. (a.) Describe conglomerate, breccia, and marble.

(b.) In what systems are they found?

4. (a.) What is the origin of soil? Of graphite? Of terraces? Of faults?

(b.) Give some idea of the distribution of granitic rocks.

5. (a.) Briefly describe the oldest fossiliferous system.

(b.) In what system is coal found in this Province ?

6. (a.) Explain stone age, bronze age, iron age. (b.) What are "kitchen-middings"?

ZOOLOGY.

1. (a.) Name the classes of the Vertebrata, giving characteristics of each.

(b.) Give the Orders of the Pachydermata.

2. (a.) Describe the Protozoa.

(b.) How are coral reefs formed?

3. Compare the circulation and the respiration of a frog with those of a cat.

4. What characters has the crab in common with all animals? With all Anthropoda ? With all Crustacea?

5. (a.) What is meant by the fauna of a country?

(b.) Name any species of the following found in this Province:

Diptera, Batrachia, Grallatores, Chiroptera.

6. (a.) Name two Marsupials, stating where each is found.

(b.) State class and order of the Salmon, giving names of its fins and characteristics, &c.

CHEMISTRY.

1. (a.) Distinguish between a physical and a chemical change.

(b.) Name four chemical elements that are solids.

2. Describe the preparation of O. Name the several compounds that result from the union of O with C, or H, and state the properties of each compound.

3. (a.) What is Ozone?

(b.) From what sources do we obtain I, S, P, NaCl, and CaCo,?

4. (a.) Explain the preparation of nitric acid from KNO.

(b.) How many pounds of HCl are required to produce 2 pounds of H?

(b.) How does sulphur become a disinfectant?

6. (a.) What tests would you apply to prove the presence in sea water of Na, and Cl (b.) Explain the chemistry of the reduction of iron ore in a blast furnace.

7. Describe the chemical processes that take place in

(a.) The making of Bread.

(b.) The manufacture of Soap.