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1.

JUNE 1889. FROM QUADRATICS.

I. Solve the equation (a + b)2x2 - (a - b2) x = ab.

2. Find all the roots of the equation 4x3 + 8x2 — 140x O.

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5 Having given the first term a, the ratio r, and the number of the terms n, of a geometric progression, to deduce a formula for the sum of the n terms.

6. Determine in how many different ways the letters of the word Cincinnati can be arranged.

Find the What sign

7. When is a variable said to have a limit? limit of log. (1 + x) when x approaches o. does the expression have when near its limit, positive, second, if x is negative, log. being supposed to denote the common logarithm.

first, if x is

JUNE 1889. TO QUADRATICS.

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1. Simplify 3a — [b — a — (2a + b — a — b)].

2. Resolve the following expressions into factors: ca; x2 +64.

a“ — bo ; n3 + 2n2 + n; a

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X

5. Solve the simultaneous equations, bex = cy

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6. Show that a2 + 3b2 > 2b (a + b).

7. Simplify the following expressions:

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JUNE 1889. FROM QUADRATICS.

b)2x2

1. Solve the equation (a + b)' x2 - (a2 — b2) x = ab. 2. Find all the roots of the equation 4x8x140x=0.

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I

I

= 7, and + = 25, to find x and y.

4. Solve the equation

x2

X

3x + 1/4x

3X √4x

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5 Having given the first term a, the ratio r, and the number of the terms n, of a geometric progression, to deduce a formula for the sum of the n terms.

6. Determine in how many different ways the letters of the word Cincinnati can be arranged.

Find the What sign

first, if x is

7. When is a variable said to have a limit? limit of log. (1 + x) when x approaches o. does the expression have when near its limit, positive, second, if x is negative, log. being supposed to denote the common logarithm.

JUNE 1890. FROM QUADRATICS.

1. Solve the equation ax2 + a = (a2 + 1)x.
2. Determine all the the roots of the equation,
x (xa)(x2- b') = o.

3. Solve the equation 2 (x-4) = 1 3x — 2.
4. Given the simultaneous equations,

x'xy 15 and xy-y2 = 2; to find all values of x and y which satisfy them.

5. Given the amount of a given principal at compound interest for a given number of years, to find the rate per

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3ax

3. Solve the simultaneous equations,

2by c, and a'x + b'y 5bc.

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5. Expand (ax- 2b)" by the binomial formula.

6. Simplify the following expressions:

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