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JUNE 1897.

(b)

1. A tree 90 feet high stands on the bank of a stream. At a certain hour it casts a shadow directly across the stream and just reaching the opposite bank. If at the same time a telegraph pole 40 feet high casts a shadow 30 feet in length, what is the width of the stream?

2. Find by logarithms the value of

3/34875 X .087624 V(6.323) × 73.47

3. The area of a regular hexagon is equal to 961/3 sq. inches. Find the perimeter of the hexagon.

4. Find in square yards the area of a circle of which the radius is 39.87 meters. (Use logarithms.)

5. Define a logarithm, and explain why the multiplication of numbers is performed by the addition of their logarithms.

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pute the value of the expression to three decimal places.

5. Given a + x = √/a2 + x√/b2 + x2, to find x.

6. Solve the equations x + y = 12, x2 + y2 = 74.

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7. If A B C : D, prove by the principles of proportion that A2 B2: B2 C2 — D2 : D2.

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JUNE 1887.

1. Resolve the following expressions intò three factors: a1b + 8ac3bm, 4c3x2 + 4c2xy + cya.

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5. Solve mx' + mn = 2mV/nx + nx.

6. Given (15x): (21 y) = 3: 7, and x'y' = 9,

to find x and y.

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37,

7. Expand by the binomial theorem 3by/2x — y.

JUNE 1888.

1. Remove the parenthesis from the following expression and reduce it to its simplest form.

5x — (3x 4) [7x (29x)].

2. Resolve each of the following expressions into as many factors as possible: (a) x' — 1; (b) (x2 + — y2 z3)2 - 4x3y'.

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5. Solve the equation √x — 3 — √2x + 8 = — 3.

6. Solve the equation x3 -x=256.

7. Multiply x + 3 — 27—1 by x + 3 + 21—1.

8. Expand (x2 + b) to four terms.

9. Given the series, y = x — 1⁄2 x2 + 4x3-%x' + etc.,

to find the value of x in terms of y.

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4. Give the four factors of the first degree in x and y of the expression 9x - 40x'y' + 16y*.

5. Solve 6x2

5x = 6; solve also x(1 x) = ax + b.

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8. State and prove the formula expressing (s) the sum of n terms of a geometric progression having the first term a and the ratio r.

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