3. Determine the dimensions of the cone of maximum volume inscribed in a sphere of radius 2.

4. Find the point on y = ax2+bx+c when the curvature is greatest.

5. What is the area under y(x2 — 1)} = x between x=0 and x =4?

10. Expand sin x in a power series of x by McLaurin's series as far as x?

11. A hemispherical bowl 20 inches in diameter has a hole in the bottom through which the water is flowing at the rate of 16 cu. in. per sec. At what rate is the water level falling when the surface is 8 inches from the bottom. 12. Find the polar equation of a curve whose polar subnormal is 2.

MATHEMATICS.—(MAJOR). ANALYTICAL GEOMETRY.

1. Obtain the equation of the locus of a point equally distant from
3y=15 and 3y=5x+6.

2. By change of axes remove the xy term from the equation 3x3
Draw the figure.

3y=32.

3. Determine the focus of the curve 6x2+y=1.

4. Write down the equation of all parabolas whose axis is parallel to the x-axis and whose latus rectum is equal to the distance from the origin to the

6. Draw figures to illustrate the graphs of (a) y=kx+k (b) ky=x2 — k where k is arbitrary.

7. Discuss the equation 25 x 20 xy+4 y2+5 x -2y-6-0. Draw the figure and determine the coordinates of the vertex.

8. Find the equations of the tangents to x-2y=6x from the point (0, 2).

9. Obtain the equations of the line through (2, 1, 3) perpendicular to -7y+2x=4.

10. Calculate the area of the triangle (0, 0, 6), (0, 2, 0), (3, 0, 0) without finding the lengths of the sides.

11. A line is drawn through the origin with direction cosines proportional to 2, 1, 3. Find the equations of the tangent planes where it meets the sphere whose centre is (1, 2, 1) and whose radius is 6

12. Discuss the loci in space of (a) x2 — 6xy=52': (b) y3+6x=7

MATHEMATICS.—(MINOR).

1. If the vertical angle of a triangle is bisected by a straight line which cuts the base, the segments of the base are proprotional to the other sides of the triangle.

2. Construct a figure equal to a given triangle and similar to a give quadrilateral.

3. Obtain a formula for the surface of a right circular cone in terms of its s lant hight and the radius of the base.

4. If one of two parallel straight lines is perpendicular to a plane so is the other

5. By the binomial theorem calculate (.4996) correct to nine significant digits.

6. Sum to infinity the series

7. Solve x2

3xy+2y2 -2x-3y-350 for x in terms of y and show that x is real if y is real.

8. If the number of permutations of 56 things taken r+6 at a time is 30800 times the number of 54 taken r+3 at a time, find r.

9. Prove cot A+cot (A+60°)+cot (A+120°) =3 cot 3A.

11. Solve for y completely sin y+sin 2y+sin 3y+sin 4y=0.

12. Write down the relation between a, b, A in the spherical triangle in which C90° and prove it from a figure.

BIOLOGY.—(BOTANY, MAJOR AND MINOR)

Note.-Candidates writing this paper as a "Minor" will answer A and B, those writing it as a "Major" will answer B and C

A.

1. Discuss the food constituents of seeds and their transformation in germination

2. Describe the structure and operation of stomata.

3. Describe the internal structure of the stem in monocotyledonous plants.

B.

4. Compare the two main divisions of the Bryophytes with each other illustrating by comparison of a species of each.

5. Describe the vegetative structure and reproduction in Vaucheria.

6. Write an illustrated life history of a Horsetail.

7. Trace the development of Heterospory and the reduction of the Gametophyte in the plant world to a culmination in the flowering plants. Make clear your understanding of homologies in the different groups referred to.

8. Name and describe (a) carnivorous plants of Nova Scotia (b) any native semi-parasitic plant.

9. Tell what you know of the organisms responsible for any two of the following plant diseases: Club Root of turnips, smut of oats, potato blight, plum pocket, blister blight of shepherd's purse, ergot of rye, apple scab, black knot of plum, leaf rust of oats..

10. Write an account of any one of the Brown Algae under the following heads: (a) Habitat, (b) gross morphology, (c) Histology, (d) repro

duction.

C.

11. Give the systematic position, characters, means of propagation and methods of eradication of any three troublesome farm weeds of Nova Scotia.

12. What do you know of the observations, experiments and conclusions of Mendel on Inheritance.

13. Write a summary account of any special study which you have made in plant histology, Physiology or in systematic botany.

GEOLOGY.-(MINOR).

1. Show the relation between denudation and deposition.

2. What is matamorphism? Show how rocks are metamorphosed and in what ways their character is affected.

3. Discuss methods of formation, and the structure of ore deposits.

4. (a) Describe geological features of interest that you have noticed in your study during the present summer.

(b) Describe the terms, color, etc., of geological maps.

5. Discuss earthquakes or volcanoes.

6. Give what you know of the geology of the Malagash deposits; Or, discuss how fiords have been made.

7. (a)

How does the geology of a country influence its scenery?

(b) Draw a section of the geological strata of any part of the Province. 8. Describe Six minerals found in Nova Scotia; giving, if you can, one or two which are probably found to a greater extent in Nova Scotia than anywhere else.

9. One set of rocks is found lying upon a different set. How could it be determined whether they were nearly or quite contemporaneous or separated by a great interval of time?

10.

Discuss the relation of geology to mining. Or, Discuss the bearing of any other science upon geology.

CHEMISTRY.-(MINOR).

1. The text book says that the speed of chemical action gives a means of measuring activity, but it tells of a number of precautions that must be taken in carrying out experiments. Discuss this subject.

2. Discuss crystalline forms; Or, the influence of temperature on solubility.

3. Why do we consider that the molecule of argon contains one atom, the molecule of hydrogen two atoms, and the molecule of phosphorus four atoms?

4. Describe experiments to show migration of ions or to illustrate chemical equilibrium.

5. Potassium bromate K Br 0: oxidises arsenic trioxide to arsenic pentoxide, becoming itself potassium bromide. How many grams of potassium bromate are there in a tenth-normal solution? How many grams of arsenic trioxide? (K=39; Br=80; As=75).

6. A gas is produced by heating together sodium acetate and caustic soda. What is the gas? Give any other method of preparation. Give properties of the gas and some of the substances which may be derived from it.

7. What is obtained by heating sodium nitrate, copper nitrate, mercuric nitrate and ammonium nitrate?

8. What facts regarding the group of the alkali metals, and of the halogens lead to the conclusion that caesium fluoride should be a very stable compound? Or, Give a short account of the platinum group of metals.

9. What do you know about post-war problems in industrial chemistry? Or, Give a list of the oxygen acids of sulphur with the characteristics of the less

common ones.

10. Discuss any chemical matter which has interested you, in a manner suitable to the grade of this examination.

PHYSICS (MINOR).

1. A metal sphere loses one-eighth of its weight when put into water. Another sphere of the same mass, but double the diameter floats in a liquid whose density is twice that of water; what fraction of the volume of the larger sphere will be above the liquid?

2. Explain the action of the syphon.

3. If a certain quantity of work is represented by the number 600 in the foot, pound, second units; what number would represent it if the unit of length were a yard, the unit of mass a hundredweight, and the unit of time a minute?

4. If in Joule's experiment for determining the mechanical equivalent of heat, the weight moving the paddles reaches the ground, at one time with a velocity of ten feet a second, and at another time with a velocity of five feet a second; what will be the difference in temperature of the water, assuming that the weight moving the paddles is one hundred pounds and the weight of the water five pounds? In which case will the temperature be greater? Why?

5. Explain, as far as you can, the phenomena of capillarity; Or, describe some form of hygrometer.

6. Write a short description of spectrum analysis, including the dark lines of the solar spectrum.

7. Describe the tangent galvanometer; Or, discuss hysteresis in magnetism.

8. If an object placed eight feet in front of a concave mirror gives an image twenty feet from the mirror, what is the focal distance of the mirror? In addition to the calculation, draw a diagram approximately to scale.

9. Describe some form of induction machine in statical electricity, such as the Holtz; Or, tell what you can in the time of theory of color including complementary colors.

10. Discuss any subject in physics, not already referred to, in such a way as to show your knowledge of some particular question in which you have been interested.

Greek, French and German Papers not in Type.

TEACHERS' MINIMUM PROFESSIONAL QUALIFICATION EXAMINATION.

For Syllabus, See Pages 126-127 of the April, 1921, Journal of Education.

M. P. Q.

SCHOOL LAW AND FORMS.

9 to 10 a. m., Thursday, 30 June, 1921.

1. For what do the letters M. P. Q. stand, and what does the phrase mean? What is the purpose of this examination and why do not all High School candidates write it?

2. What is the purpose of the Journal of Education? tents of the April and the October Journal.

Give briefly the con

3. When is the Annual School Meeting held? What business must be transacted at such a meeting?

4. What are the legal requirements for outhouses in rural sections? What improvement was suggested in the last October Journal of Education?

(Answer any one of the following).

5. Write notes on (a) Prescribed Minimum Salary, (b) Special Statistics for columns 150 (a, b and c) of the School Register for 1920-21.

6. What constitutes the Council of Public Instruction? Name as many as you can of the present Council.

THEORY AND PRACTISE OF TEACHING.

10.10 to 11.10 a. m., Thursday, 30 June, 1921.

1. In the general prescriptions for the teaching of Hygiene and Temperance It is laid down as fundamental that the teacher should do seven things. State them.