The Pamphlet Collection of Sir Robert Stout: Volume 50
The University of New Zealnad. — Entrance Examination, 1885.—Junior Scholarships. — Arithmetic and Algebra
The University of New Zealnad.
Entrance Examination, 1885.—Junior Scholarships.
Arithmetic and Algebra.
2. Land is sold for £30 an acre, cakculate its price in france per hectrarem having given that a hectare os 100 square décamètres, that a decameter = 393·7 inches, and that a pound contains 25·2 francs.
3. If the discount on £461 4s 7½d. at 8 per cent. Be £11 7s 9 2/9d., when is the bill due?
4. The birth rate and the death rate of a population in my year ar respectively 7 per cent. And 2 per cent of the population at the beginning of that year. If the present population be 20,000, what will it be five year hence?
5. A person who has £3645 can make £6 a year more by investing it in the 4 per cents at 102½ than in the 3½ per cents. What is the price of the latter stock?
6. Prove the rule for finding the Highest Common Divisor of two algebraical expression.
7. In what sence can you be said to multiple by a fraction or by a negative quantity?page break
10. In the product (x+a)(x+b)(x+c), the coefficient x2 vanishes, and in the product (x−a) (x+b) (x+c) the coefficient of x vanishes, and the coefficient of x in the former is the same as that of x2 in the latter, find a.
11. Find the relations between the roots of the equation x2+ax+b=0 and its coefficients.