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6. Solve the equations, xya, and x2 + y2 = b.

5. Solve the equation I

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JUNE 1891.

1. If x y + z is one factor of x2 — y3 — z2 + 2yz, find the other factor.

2. Reduce the following expression to its simplest form:

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3. Find all possible values of x in the following equa

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4. Solve the simultaneous equations

3x2 — 11y2 = 1, x − y = 3.

5. Reduce to a simple fraction

I

I + I
2+1

3+1

4 + I

5

6. Find the sum of all the numbers which are less than

500 and are divisible by II without remainder.

7. Write the 6th term of the series (2a — 3b)→.

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2. Solve the equations (a) 2x

--

5y=- 19, 3y+4z 7, 2z 5X 2. (b) 2x + 10 + 2√x + 6 = 2.

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5. Extract the square root of 22 + 101-3.

6. Find the sum total of all the odd numbers between 74 and 692, als find the sum of an infinite number of terms in the geometric series 16, 2, 4, etc.

7. Write the 6th term of (a + b).

8. Write the values of the following expressions:

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JUNE 1893.

1. Write the factors of the following expressions: xʻ — (x — 6)2, and mo — 6411o.

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3. A and B can do a piece of work in m days; B and C can do it in n days; C and D in p days; and D and A in r days. In how many days can all working together do it? 4. Multiply x + yv-z by yzy-x.

5. Solve the equation y2+ 2(a + 6)y — 18a.

6. Extract the square root of

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JUNE 1894.

(a)

1. Remove the parentheses from [a (b+c+ 2x

y — z)].

2. Resolve into factors the following: (a) ao — xo; (b) I a'x' b'y2+2abxy; (c) 4x2 + 23x + 15.

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4. A and B together possess only 2/3 as much money as C; B and C together have 6 times as much as A; and B has $680 less than A and C together; how much has each?

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(b) 84ab2+ by/75a + 1/3a(a — 9b)'.

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