# The University of New Zealnad. — Entrance Examination, 1885.—Junior Scholarships. — Arithmetic and Algebra

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## 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.

Find the Highest Common Divisor of
• 11x4−9ax3a2x2a4
• 13x4−10ax3−2a2x2a4

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 (xa) (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