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The University of New Zealnad.

Entrance Examination, 1885.—Junior Scholarships.

Arithmetic and Algebra.

1. Find the value of 2/37 of of £268 13s 6¼ d.

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?

Multiply and divide the result by

8. Prove that and bence find its value correct to three places of decimals.

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9. Solve the equations

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.

If ⍺ and β be the roots of this equation, find the equation whose roots are a