6. (a) Compare the mode of growth in the stems of the Strawberry; Morning Glory, Pea.

(b) How do the stem and branches of a plant contribute to its life purpose?

7. Outline the structure of a leaf. Distinguish between foliage and storage leaves. Give examples of anomalous leaves. State their uses.

8. (a) Distinguish sterile and fertile flowers.

(b) Name and tell the uses of the different divisions of the stamen and the pistil.

(c) How does nature provide for the reproduction of plants having sterile flowers?

9. What is a fruit? Show how the fruit of the plum, maple and raspberry conform to your definition.

10. Compare specimens A and B as to margin, outline, base, shape, venation, surface and arrangement.

11. Identify specimen C. Name other plants of the same order and give the characteristics of the order.

THIRD CLASS.

PHYSICS.

Time-Two and one-half hours.

1. (a) What common properties have all kinds of matter?

(b) Under what conditions will two trains be in a state of (1) relative motion, (2) relative rest?

2. (a) Draw a diagram of an air-pump and explain its action. (b) Why is it impossible to obtain a complete vacuum by means of an air pump?

(c) Does the completeness of the vacuum depend in any way upon the capacity of the barrel of the pump? Explain.

(d) If the direction in which the valves open were reversed show what would take place when the pump is worked.

3. Explain,

4.

(a) Why a balloon rises in the air, while iron sinks in water.

(b) Why the velocity of a falling body is independent of its mass. (c) Why bullets are made of lead instead of wood.

(d) Why the course of a cannon ball projecte in a horizontal direction is not straight.

A syphon is an instrument used for transferring a liquid from one vessel to another through the agency of atmosphere pressure.”

(a) Explain this statement making use of a diagram. (b) Will a syphon work in a vacuum? Why?

5. (a) Describe the construction of a mercurial barometer.
(b) Why must one of the ends of the tube used be closed?

(c) If there is some air in the tube above the mercury how will it
affect the reading of the barometer?

(d) Will the barometer rise or fall when taken down into a mine? Why?

6. (a) The utmost force a man can exert is a little more than 200 lbs. If he wishes to raise a block of stone weighing 400 lbs., show how he may do so by using (1) a fixed and a moveable pulley combined, (2) a lever,

(b) Explain the meaning of the terms force, energy, and work, by referring to what takes place while the stone is being raised by the use of either contrivance.

7. (a) Show how to find the specific gravity of a solid body heavier than water.

(b) Find the specific gravity of a goblet composed of 15 ounces of silver and 4 ounces of gold. Sp. G. of gold=19.36, Sp. G. of silver 10.5.

=

8. State the three laws of motion and describe simple experiments in verification of any two of them.

9. An open U-shaped tube connects two bottles A and B in such a way that the ends of its arins are but a short distance from the bottom of each. Bottle A is half full of water and is so corked that air can enter only through the end of the tube in B. The mouth of bottle B is open. If the bottles are placed under the receiver of an air-pump explain, making use of a figure showing the apparatus, the action that takes place,— (a) When the air is being exhausted.

(b) When it is being admitted.

(c) When the connecting tubes break in the centre during the second experiment.

1. (a) Show clearly how to change a vulgar fraction into the form of a decimal.

(b) Multiply 4 x 004 without reducing to vulgar fractions.

(c) State and prove the general rule governing the multiplication of decimals.

2. Edmonton coal is 163% heavier than water, and a cubic foot of water weighs 1000 ounces. If a cubic foot of coal when broken occupies 1 cubic feet of space show how to find the height of a bin 6 ft long and 3 ft. 6 in. broad so that it may contain exactly 13 tons.

3. An agent remitted to a shipper, in settlement of a sale of 4000 bus. of potatoes, $2829.65, after deducting his commission of 5 and $286.35 for freight charges. Find (a) the selling price of a bushel of potatoes, (b) the agent's commission.

4. A bankrupt merchant has liabilities amounting to $10,000. One of the creditors, after the business is wound up at an expense of 10% of the assets, receives $2520 as his share. If he received 63c. on the dollar, find (a) the amount of his account, (b) the amount the merchant required to become solvent, (c) the amount of the expenses.

5. If one thousand laths cover 70 yards of surface and 12 lbs of nails nail them on, what will it cost to lath the ceiling of a church having the following inside dimensions: length 40 ft.; breadth 24 ft.; height of side walls 12 ft; height from the floor to the middle point of the ceiling 28 ft.; (the laths are nailed to the rafters.) Labor costs 4c. per yard, nails 6c. per tb., and lath $3 per M.

6. A rancher sold two horses, which he considered to be of equal value, as follows:-for the first he got a promissory note for $60 due in 2 mos, for the second, $30 cash and a promissory note for $30 due in 4 mos. and bearing interest at 6%. He immediately had the notes discounted at 1%. per mouth. What did he realize in cash for each horse?

7. A merchant pays $72 to insure a $2400 stock of goods. If the rate of insurance is 4% and a fire, which completely destroys the stock, occurs on the day the policy is taken out, estimate (a) the merchant's loss (b) the insurance company's loss.

8. A locomotive burns a ton of coal while going 75 miles. How many times will the driving wheel, which has a radius of 1 ft. 9 in., revolve for every cwt. of coal used?

9. (a) By means of an example show how you would proceed to find the area of a field having the form of a parallelogram.

(b) Find the dimensions of the top of a circular table whose area is 13 sq. yards.

THIRD CLASS.

ALGEBRA.

Time-Three hours.

Use your result to

1. Find by multiplication the square of a+b. write the square of a-b; of a+b+c; and of 2a+3b.

to four terms. State the observations that will en

able you to write the mth term of this expansion.

3. Find the product of a+ab+b into a-ab+b2. Use your result to determine;

(1) The product of a +ab+b into a ab2+b1.

(2) The quotient of (a+b)+(a+b)2 (a−b)2(a−b)1 by (a+b)2+ (a+b) (a−b)+(a−b)2. Simplify this quotient.

5

4. Divide 8y-x+21x3y3-24xy by 3xy — x2-y2.

State in the form of an equation the relation between the terms of division; hence find by division the numerical value of x3 — 18x1 − 20x3 +16x2+58x+63 when x= 19.

x+2y+32-14=2x+3y+2-11=3x+y+2x-11=0

then will x-1=y-2=-3=0.

7. A and B are equal owners of a flock of sheep. They agree to divide it. A took 72; B took 92, and paid A $35. Find the value of the flock of sheep.

8. A pony and a saddle are worth $65. Three-fourths of the value of the saddle is equal to one-third of the value of the pony. Find the value of the saddle.

9. A number of boys join to purchase a ball. Before payment 5 boys withdrew. The share of each was then half as much again. Find the number of boys. Why cannot the price of the ball be found?

1. (a) Prove that if two sides and the contained angle of one triangle be equal to two sides and the contained angle of another triangle the two triangles shall be equal in every respect. I. 4.

(b) Enunciate the axiom on which the proof depends.

(c) Distinguish between a theorem and a problem; and between an axiom and a postulate.

(d) Show how the distance across an impassable morass may

sured.

be mea

2. (a) Show how to draw a straight line perpendicular to a given straight line from a given point without it. I. 12.

(b) What property of a circle is used in the construction?

(c) Two weights are suspended from a ceiling. Are they parallel? (d) Perpendiculars are dropped from the angular points of an equilateral triangle. Determine the size of the angles at their intersection. (Assume the perpendiculars pass through the same point.)

3. (a) Prove that any two sides of a triangle are greater than the third side. I. 20.

(b) Show how this is acted upon in every day life.

(c) Prove proposition (a) by bisecting one of its angles.

(d) Prove that in a figure of n sides the sum of n-1 sides is greater than the nth side.

4. (a) Prove that if a straight line cutting two other straight lines makes the alternate angles equal to one another the two straight lines shall be parallel. I. 27.

(b) What is the essential quality of parallelism?

show that a pair of parallel lines may exist?

How does Euclid

(c) Are two lines which will not meet in either direction necessarily parallel?

(d) Prove that if the diagonals of a quadrilateral bisect each other the quadrilateral is a parallelogram.

5. (a) Show how to draw through a given point a straight line parallel to a given straight line. I. 31.

(b) Prove that only one such line can be drawn.

(c) Through the angular points of a triangle straight lines are drawn parallel to the opposite sides, and produced till they meet. Compare the area of the triangle thus formed with the original one.

6. (a) Show how to describe a parallelogram that shall be equal to a given triangle and have one of its angles equal to a given angle. I. 42.

(b) If the angle be 90° what kind of parallelogram would be described?

(c) Describe a triangle equal to a given parallelogram and having a base angle of given dimension.

(d) Describe a parallelogram one-half as large again as a given triangle and having one angle equal to a given angle.

7. (a) Show how to describe a square of given dimensions.

(b) Point out six properties of a square.

(c) Determine the size of the angles at the intersections of the diagonals of a square.

(d) Describe a square having given the diagonal. The diagonal is 20/2 feet long; find the area.