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THE PUPIL TEACHER.

3. In every triangle, the square on the side subtending either of the acute angles is less than the squares on the sides containing that angle by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle.

1.

1

x+3

1

Simplify-1-2(x2+1) ̄2(x+1).

How

2. The diameters of two coins were 1.3 and 1.2 inches respectively, and 160 placed in contact in a straight line measure a pole. many were there of each kind?

3. Solve the equations: 7x-13

(1.)

·

2x-30

x+24

2114(x-1). (2.) 2= 11

969.

1. The diagonal of a field is 303 yards, and it divides the field into two triangles whose sides (in yards) are 100, 217, 303, and 65, 272, find the area in acres, etc.

303;

2. The length of a circular arc is 16 feet, and it contains 11° 15'; find the diameter.

ANSWERS.

1. £259,787. 2. £1,086 13s. 94d. 3. 5s. 4. £14,834 4s.

1. £59 1s. 6d. 2. £3 12s. 9 d. 3. £73 6s. 3d. 4. £60 9s. 41d. FIRST YEAR.-1. £1 0s. 101 d. and 100=77857142.

31. 3. 1893. 4. £4,375.

1862 5045

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1. 30 miles. 2. 18s. 25 d. SECOND YEAR.-1. 21 per cent. £9 48. 7.385d. nearly. 5. £2,000.

3. £32,000. 4.

2. £8 13s. 5d.

3. 10 da. 19 hrs. 24 min.

2. £3,150. 3. B should

1. (a) 5.

(b) 613.

4. 97 pecks.

44 sec.

THIRD YEAR.-1. (a) 5:12. (b) 1:3.

give A £50 3s. 9 d. 4. 13 years.

lac.

1. (a) 1·05. (b) 2-067307692. 2. (a) 15s. (b) 1 ac. 3r. 5 po.

28 yds. 4 ft. 99,9567 in. 3. 6.

7x-2

1. 7x2+y2. 2. (a) G. C. M.=x-3. (b) 52-3x+2.

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FOURTH YEAR.-1. £2 18s. 4d.=utmost gain; £1 5s. 8d.=utmost loss. 2. £30,450. 3. £10 1s. 11d. nearly. 4. 91 787 ft. 5. 3.0117. 6. 29, 13, and 37.

3. 1s. 6d. 4. A £31 5s; B= 1. £256 10s. Od. 2. 12 hours. £41 5s.; C=£52 10s., being 2s. 6d. in the £. x+3 24-1.

1.

2. 60 of the larger and 100 of the smaller.

306 304

or

3. (1.) x=23. (2.) x=; 1938 1938.

1. 3 ac. 8 yds. nearly. 2. 168, ft.

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