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.
- 11 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.
9. Solve the equations
10. 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