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The Pamphlet Collection of Sir Robert Stout: Volume 50

University of New Zealand. — Mathematics. — Paper b. Algebra

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University of New Zealand.


Paper b. Algebra.

1. Show that formula/equation is exactly divisible by a2+b2+c2abacbc; and show that if x+y+z=0, then yzx2=zxy2=xyz2.

2. Find the Greatest Common Measure of 2x3x2−4x+3 and 4x4−5x3x+2, and the Least Common Multiple of (2x2−2, 3x3+3, 2x2−2x−4, x2x+1.

3. Find whether formula/equation greater or less than a/b, and whether formula/equation is greater or less than formula/equation it being given that c/d is a/b reduced to its lowest terms.

Simplify the following:—


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4. Solve these equations:—formula/equation

5. You can buy from a wine-merchant 10 dozen sherry and 12 dozen claret for £48, and 5 dozen more of sherry can be had for £45 than of claret for £50: required the price of each per dozen.

6. Define ratio, and explain why the equality of two ratios may be expressed by equating two fractions.

If a+b+c: −a+b+c:: ab+c: a+bc, show that a is a mean proportional between b+c and bc.

7. Define a Geometrical Series, and find the sum of n terms of the series.

The 2nd and 5th terms of a Geometric Series are—1/3 and 8/81; write down the intermediate terms, and sum the series to n terms and to infinity.

8. Write down the Binomial Theorem, and find the middle term, when there is one, and the sum of the alternate coefficients.

Find the coefficient of x4 in the expansion of formula/equation