Sessional_Paper_1905 — Page 810

No. 18.

732

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ALGEBRA.

CLASS III.

1. When a negative bracket is removed, what must be done to the

Give an example.

terms in it ?

What is a coefficient? Give an example.

What is the law of signs in multiplication?

2. Add together

Tank

5a2 + 2ab2 + 3ab −762; 6a2b + Tab; 3a2 4æb + b2 and subtract 5øb2 + Tab 662 from the total.

3. Divide (æ3 + a3) + ax (x2

a2) + n3 (x + a) by (a + b)

(x + α).

4. To aa + bo add (2 b) (a + b) (a2 + b2) (a2 + B*).

5. Using the letters x and y as variables, and the letters a b c d as coefficients, construct the most general integral expression of the second degree which shall be

(1) homogeneous;

(2) symmetrical;

(3) homogeneous and symmetrical.

No. 19.

ARITHMETIC.

CLASS I.

1. Find, to the nearest penny, the difference between the compound interest on £1,200 for 5 years at 5 per cent. per annum, according as the interest is paid yearly or half yearly.

2. A cistern is filled by 3 taps A, B, and C, such that A and B run- ning together can fill the cistern in 6 minutes, B and C in 84 minutes, and C and A in 64 minutes. If A alone be turned on for 3 minutes and B alone for 5 minutes, how long will it take C alone to complete the filling of the cistern ?

3. How many revolutions does a wheel of radius 2 feet make in 2 miles ?

4. If 2 turkeys and 9 fowls cost £2. 18s. 6d., and 7 turkeys and 3 fowls cost £6. 13s. 6d. ; find the cost of 1 turkey and 1 fowl,

5. Find the volume in cubic feet of a cylindrical gas holder 12 feet high and 100 feet in diameter.

No. 20.

ARITHMETIC.

CLASS II.

1. Find the value of ✓ 13 to 6 places of decimals.

2. Find the cube root of :--

-000000004913.

3. A room is twice as wide as it is high and twice as long as it is wide and contains 48627′125 cubic feet; what would it cost to cover it with carpet 27 inches wide at 2/6 per yard?

4. If the cost of provisioning a ship carrying 64 men be £350. 8s. 0. when the ship is at sea 78 days, what will it cost to provision for 33 days a ship carrying a crew of 110 men ?

5. By ordering coal direct from the pit owner, I obtain 22 cwt. for each ton; what quantity must I order to effect a saving of 30s. when the price of coal is 25s. per ton ?

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