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What is meant by averaging payments? The average tinie? The term of credit? The average term of credit? Solve an example illustrating the process of solution when the terms of credit begin at the same time. Solve an example when the terms of credit begin at different dates. Explain the process. Explain the process of averaging accounts, and give the rule.

What is partnership? Who are partners? What is the capital of a firm or company? Give the principle underlying partnership. What is Case I in partnership? What is Case II? Solve and analyze an example in Case II. Give the rule for partnership settlements.

What is ratio? Of how many kinds is it? What are the terms of a ratio? The antecedent? The consequent? What is the sign of ratio? From what may it be regarded as derived? What is a couplet? What are the principles of ratio? Illustrate each principle.

What is proportion? What is the sign of proportion? From what may it be regarded as derived? What are the antecedents of a proportion? The consequents? The extremes? The means? Give the principles of proportion regarding the relation of extremes and means. What is meant by a simple ratio? A simple proportion? A direct proportion? An inverse proportion? Give the rule for solving examples in simple proportion. What is a compound ratio? A conipound proportion? The principle underlying compound proportion? Solve an example in compound proportion, by successive simple proportions and by cause and effect. Give the rule for compound proportion.

What is a power? How are powers named? What is an exponent? What is involution? How is the power of a number obtained? How is the square of a number expressed in terms of its tens and units? How in terms of any two parts? How is the cube of a number expressed in terms of its tens and units? How in terms of any two parts?

What is a root? How are roots named? What is evolution? What is the radical or root sign? Define a perfect power; an imperfect power. Give the rule for finding the root of a number by factoring. Give the principle relating to the number of figures required to express the square of a number; the cube of a number. Give the principle relating to the number of figures in the square root of a number; the cube root of a nuniber. Solve and explain an example in square root. Repeat the rule. What is done when the

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number is not a perfect square? How are decimals pointed off?
How is the square root of a common fraction found? How is the side
of a square found when its area is given?

What relation do the squares described upon the sides of a right-
angled triangle sustain to each other? How is the hypotenuse of a
right-angled triangle found when the other sides are given? How is
either side found when the hypotenuse and the other side are given?
What are similar figures ? What is the relation between similar
surfaces ?

Solve an example in cube root. Deduce from your solution a rule. What is done when there is a remainder after subtracting the last product? How are decimals pointed off? How is the cube root of a common fraction found? Give the principles relating to similar solids.

Define a series; an ascending series; a descending serics; an arithmetical progression; a geometrical progression. How is the sum of an aritmetical series found? Illustrate by an example. How is the sum of a geometrical series found? Illustrate by an example.

Define mensuration; a line; a straight line; a curved line; parallel lines; a plane surface; a curved surface; an angle; a right angle; an acute angle; an obtuse angle; a vertex of an angle; a triangle; a quadrilateral; a parallelogram; a rectangle; a polygon; a circle; the circumference of a circle; a radius of a circle; a diameter of a circle; the base of a figure; the altitude of a figure; a diagonal of a figure; the perimeter of a figure; the area of a surface.

How is the circumference of a circle obtained from its diameter? The diameter from the circumference? How is the area of a parallelogram computed? How is the area of a triangle computed? Give the rule for computing the area of a trapezium; a trapezoid; a regular polygon; a circle.

What is a solid? A prism? A parallelopipedon? A cylinder? A pyramid? A cone? A frustum? A sphere? A diameter? A radius of a sphere? The circumference of a sphere? The altitude of a solid? The convex surface of a solid ?

Give the rule for finding the convex surface of a prism or cylinder; a pyramid or cone; a frustum of a pyramid or cone; a sphere. Give the rule for finding the volume of a prism or cylinder; a pyramid or cone; a frustum of a pyramid or cone; a sphere.

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ANSWERS

Page 31. 34, 42151. 35. 118422. 36, 12149865. 37. $5165000. 38, 5871 period.

20842475 circ.

Page 23. 2. 947. 3. 1298. 4. $12.70. 5. $28.48. 6. 10845. 7. 20839. 8. 6283. 9. 3530. 10. 21974. 11. 20002. 12. $103.485. 13. $1437.845. 14. 933324. 15. 134739. 16. 349950638. 17. $132.94. 18. 1600.

Page 32 39. $1595.85, Albany;

$4807.37, N. Y.;

$6403.22, both. 40. 45764. 41. 47388. 42. 40590. 43. 540356. 44. 8882. 45. 11031. 46. 109546. 47. 86672.

Page 29, 19. $14593, 20. 21502. 21, 9265, 22. 2775. 23. 8692. 24. 934. 25. 25917.

Page 41. 2. 305. 3. 228. 4. 292. 5. 272. 6. 879. 7. 61. 8. 919. 9. 288. 10. 1299. 11. 150. 12. $3.07. 13. $11.26. 14. $16.07. 15. $23.96. 16. $23.67. 17. 289.

Page 30. 26. 997. 27. 645621. 28. 528408. 29. $8484. 30. 7005 lib.;

1999881 vol. 31. 402399. 32. 377805. 33, 642502.

18. 182.
19. 189.
20. 367.
21. 186.
22. 93.
23. 865.
24. 3886.
25. 5828.
26. 2131.
27. 8132.
28. 10570.
29. 20068.
30. 28879.
31. 80091,
32. 8486888.
33. 256 mi.
34. $508.

Page 12
35. 1163.
36. $131.
37. 1955.
38. 609973105.
39. 159 acres.
40. $202.12.
41. 1492.
42. $1697.
43. $9036.
44. 8687.
45. 3502.

Page 48. 2. 942. 3. 2272. 4. 3948. 5. 1725. 6. $4095. 7. $2307.

8. 1570, 9. 2620. 10. 5348. 11. 2490. 12. 4404. 13. $432. 14. $336. 15. $192. 16. $399. 17. $138. 18. $16555. 19. 933.75. 20. $250.16.

26. 47913214. 27. 66319209. 28. 92317008. 29. 76526998. 30. 82613817. 31. 143555004. 32. 291006415. 33. 281072720, 34. 1151707808. 35. 570873555. 36. 1381600350. 37. 1251756036. 38. 1253542212.

4570500. 7. 1215000;

15552000; 20412000;

31590000. 8. 655200;

11856000; 8424000; 14352006.

Page 55. 9. 2640000. 10. 48000. 11. $832. 12. $18256.

Pag. 49, 21, 3825. 22. 1568. 23. $16.02. 24. $43.75. 25. 36960. 26. $300. 27. $127.75. 28. $668.

Page 53. 39. $1358.53. 40. $5211.45. 41. $13309.92. 42. $99253.80. 43. $152323.35. 44. $2332.99. 45. $69520.33. 46. $69577.43. 47. $213469.56. 48. $262816.86. 49, 58650. 50. 11024, 51, 260520. 52, 5022. 53. $48535. 54. $35105. 55. $5108066.

1. $32739.84. 2. $13730.50. 3. 1229. 4. 339904. 5. $4299. 6. $168. 7. 10293. 8. 4776. 9. $35.90.

Page 56. 10. 89232. 11. $247.52. 12. $169.25. 13. 10248. 14, 108 mi. 15. $635.14. 16. $17481.30. 17. $2066.95. 18. $1563.25.

Page 52, 2. 13650. 3. 11826. 4. 17664. 5. $64.63. 6. $114.48. 7, 5472. 8. 8947. 9. 12325. 10. 10098. 11. 101500. 12. 74803. 13. 231903. 14. 3485092. 15. 3942146. 16. 6568848. 17. 1344455. 18. 1332675. 19. 585575. 20. 1570688. 21. 3334932. 22. 2546650. 23. 23748222. 24. 25721944. 25. 62748374.

Page 54. 3. 3750;

37500;
15000;

112500. 4. 25350;

59150;
507000;

760500. 5. 88000;

123200;
70400;

176000. 6. 277000;

2770000;
3047000;

Page 64. 11. 1218. 12. 1366. 13. 496. 14. 597. 15. 1545. 16. 984. 17. 406. 18. 876. 19. 554. 20. 1353. 21. 548.

42. 81987336 43. 77184937).

44. 474536,523 45. 2523843334. 46. 127523 47. 8541043

3118

9 6813 33 732 3 7 25.

Page 68. 48. 162, 49. $258. 50. 130 mi. 51. 18 doz.

52. 10931948

53. 53780. 54. 140 da. 480 left. 55. 494115888 56. $20297. 57. $10086-62

3 65 58, 5280. 59, 100. 60. 2195731

Page 70.

3. 181920

4. 6114. 5. 127426. 6. 39868

1000 8. 3169 9. 75.500 5

7. 2-465

24000

10. 5019370 11. 779387

5 7

12. 118; 4964 bu.rem, 13. 640.

Page 73. 19. 2546}. 20. $421313. 21. 81153 wk. 22. $60. 23. 1920 bu. 24. $2 per bbl. 25. 45 yd. 26. 500 mi. 27. 20 da. 28. 80 bu. 29 60 acres;

$400 loss,

22. 1234.
23. 913}.
24. 14881.
25. 9085
26. 22961.
27. 1205
28. 4855.

30. $3837.50.
31. $92278,121.
32. 18 minutes.
33. 105 head.
34. 10 grandchild'n.
35. 37164606 lb.
36. 212
13500

acres.
Page 79,
2. 7,5.

3. 26.

Page 67. 2. 124. 3. 313. 4. 216. 5. 306. 6. 406. 7. 432. 8. 416. 9. 46. 10. 312. 11, 442. 12. 41. 13. 22. 14. 77. 15. 103. 16. 213. 17. 119. 18. 131. 19. 114. 20. 141. 21. 67. 22. 505. 23. 315. 24. 406. 25. 519. 26. 525. 27. 541. 28. 606. 29. 723. 30. 544. 31. 752. 32. 664. 33. 777. 34. 1802. 35. 1945. 36. 4372. 37. 6203.

1

4. 24, 3, 7.
5. 23, 3, 7.
6. 24, 32.
7. 32, 5, 7.
8. 2, 32, 11.
9. 25, 7.
10. 2, 3, 131.
11, 22, 79.
12. 22, 112.
13. 28, 5.
14, 24, 32,7.
15, 22, 3, 5, 19.
16. 25, 37.
17. 24, 32, 13.
18. 22, 3, 72, 13.
19. 2, 3, 5, 7, 11.
20. 22, 32, 89.
21. 33, 52,7.
22. 7, 13, 43.
23. 22, 953.
24. 72, 11, 13.
25. 22, 5, 199.
26. 23, 5, 11, 61.
27. 22, 3, 11, 172.
28, 22, 34, 5, 7.
29. 23, 3, 7, 11,

13.
30. 22, 53, 37.
31. 29, 35.

Pagr 80.
6. 13600;

15300;
20400;

30600.
7. 102144;

49248; 82080; 196992.

38. 92163 1%

35 0
5 67

39. 56793
40. 12474401
41. 211757

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