8. Explain the principle upon which vulgar fractions are reduced to equivalent fractions having a common denominator.

Express in its lowest terms the sum of the

fractions

9. What fraction of 61. is

the value of of 11. +7 of 5s.

231.

of one guinea: find

of 1s. 4d.

10. Express 0025 as a vulgar fraction in its lowest terms, and 13 as a finite decimal.

11. Multiply 6667. 13s. 4d. by 015, and divide 141. 16s. 8d. by '02.

12. Find the value of (1.2)2 + (002)3. Extract the square root of 7922-602081.

MATHEMATICS.

Voluntary Paper, No. I.

REV. CANON HEAVISIDE, M.A.

1. The interest on Indian railway shares is 5 per cent., 1007. is paid up, the shares are quoted at 105: find the difference of income from transferring 3500l. from the 3 per cent. Consols at 87, to Indian railway shares at the above price.

2. A gunsmith sells 40 guns, 10 are sold at a profit of 10 per cent., and the remainder at a profit of 12 per cent.: what is the gain per cent. on the whole ?

3. What is a folio in the language of bookkeeping; how is it prepared for opening a cash account; what is a balance; when is it entered To'

and when By'; what are personal accounts; what is meant by 'taking stock'?

Enter and balance the following entries from a waste-book, in a cash account:

45 0 0

Jan. 6. Debt, part repaid, by Thos. Friend

Jan. 7. John Browne's Draft on me, paid

by Banker

Jan. 9. Paid into my banker's by Cox and Co...

Jan. 10. Donation to a hospital

321 17 9

50 0 0

Bills paid for repair of premises.. 129 17 0

4. If the price of wheat in France be 33 francs per hectolitre, calculate the price per imperial quarter, the course of exchange being 25 francs 50 centimes, it being given that an hectolitre is 22 imperial gallons, and that 8 gallons make an imperial bushel.

5. If log10 2 = ·301030, find, without the tables, the logarithm of 125000, and of '0000625. Find, by the aid of the tables :

(1) (·00002879).

(2) The amount of 2500l. in ten years at 4 per cent. per aunum, compound interest.

(2) √x2-2x+3x-2x+1.

7. Solve the following equations :

8. Write down the (p)th term of the expansion of (1+x)". If (n) be a positive integer, show that the number of terms is (n+1), and if (n) be even, show that the middle term has the greatest coefficient.

MATHEMATICS.

Voluntary Paper, No. II.

REV. CANON HEAVISIDE, M.A.

1. State Euclid's 12th axiom. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite angle on the same side, and likewise the two interior angles upon the same side together equal to two right angles.

2. Draw a straight line from a given point without the circumference which shall touch a given circle.

Show that two tangents can be drawn to the circle from the same point, and that they are equal to each other.

3. In a given circle inscribe an equilateral and equiangular pentagon.

4. If an angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square of the straight line which bisects the angle.

5. If a solid angle be contained by three plane angles, any two of them are greater than the third.

6. For what angle is the sine equal to the cosine : find the value of the sine or cosine, and also the value of the tangent, in this case.

=

7. ABC is a triangle. If the data for solving it be AC 690, BC= 464, A = 37° 20', show that there are two triangles that satisfy the conditions.

Find the third side of the greater of these triangles.

8. A person wishing to ascertain the height of a tower standing on an inclined plane, ascends 240 feet from its base, the tower then subtends an angle of 30°, the inclination of the inclined plane being 15°, find the height of the tower.

9. If the radius of a circle be 10 inches, find the side of a regular pentagon inscribed in the circle.

Express also the side of a regular hexagon, inscribed in this circle.

10. Show how to find the angle at which a given force must act so as just to prevent a given weight from sliding down a given inclined plane

(1) when the plane is smooth;

(2) when it is rough, and the limiting angle of resistance is given.

11. If a ball of given elasticity strike a plane obliquely with a given velocity, determine the motion of the ball after impact.

If a ball be projected from one extremity of the diameter of a circle in a direction making an angle (0) with the diameter, and if, after one reflection at the curve, the ball passes through the other extremity of

Colbert veille sur tout ce qui touche au négoce. Comme il a soin d'écrire aux intendants d'être plutôt un peu dupes des marchands que de gêner le commerce! Comme il tient à la liberté des grandes foiresquand il recommande une adresse, une vigilance exces, cives pour ne pas éloigner les vendeurs et acheteurs! L'ordonnance sur le commerce est un monument de cette austère et féconde inquiétude. Education des