# 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.

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.

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*x*^{4}−9*ax*^{3}−*a*^{2}*x*^{2}−*a*^{4} - 13
*x*^{4}−10*ax*^{3}−2*a*^{2}*x*^{2}−*a*^{4}

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.

page break10. In the product (*x*+*a*)(*x*+*b*)(*x*+*c*), the coefficient x^{2} 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 *x*^{2} in the latter, find *a*.

11. Find the relations between the roots of the equation *x*^{2}+*ax*+*b*=0 and its coefficients.

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