CUBE ROOT.

1 What is the cube root of a number? P. 311. 2 What is a perfect cube?

3 How many perfect cubes between 1 and 1000?

4 Of how many parts is the cube of a number composed? Name them.

5 Give the rule for extracting the cube root of a number?

6 What is the value of 28991029248? Art. 314, Ex. 8.

7 How do you extract the cube root of a decimal fraction?

8 How many decimal places will there be in the root?

9 Will the same rule apply when there is a whole number and a decimal ?

10 What is the cube root of .0066592? Art. 315, Ex. 7.

11 What is the cube root of 81.729? Art. 315, Ex. 8.

12 How do you extract the cube root of a common fraction?

13 What is the value of

19683 262144

? Art. 316,

Ex. 7.

ARITHMETICAL PROGRESSION.

1 What is Arithmetical Progression? P. 317. 66 the number added or subtracted

2 called?

3 When it is added what is the series called?

every arith.

8 How many parts are there in

metical progression ?

9 How many parts must be given before the remaining ones can be found?

10 When you know the first term, the common difference and the number of terms, how do you find the last term?

11 What is the 18th term of an arithmetical progression of which the first term is 4 and the common difference 5? Art. 320, Ex. 1.

12 When you know the extremes and the number of terms, how do you find the common difference?

13. A board is 17 feet long, 2 inches wide at one end, and 14 inches at the other: what is the average increase in width per foot in length? Art. 321, Ex. 3.

14 How do you find the sum of a series?

15 If he travels 30 miles the first day, and a quarter of a mile less each succeeding day, how far will he travel in 30 days? Art. 320, Ex. 3.

16 Having given the first and last terms and the common difference, how do you find the number of terms?

17 I owe a debt of $2,325, and wish to pay it in equal installments, the first payment to be

$575, the second $500, and decreasing by a common difference, until the last payment which is $200 what will be the number of installments? Art. 323, Ex. 3.

GEOMETRICAL PROGRESSION.

1 What is Geometrical Progression? P. 323. the constant multiplier called?

2

66

3 If the ratio is greater than 1, how do the terms compare with each other?

4 What is the series then called?

5 If the ratio is less than 1, how do the terms compare with each other?

6 What is the series then called?

7

8

9

66 "intermediate ones 66

10 How many parts in every geometrical progression?

11 How many parts must be known before the others can be found.

12 Knowing the first, the ratio and the number of terms, how do you find the last term?

13 A merchant engaging in business, trebled his capital once in 4 years; if he commenced with $2000, what will his capital amount to at the end of the 12th year? Art. 327, Ex. 7.

14 Knowing the two extremes and the ratio, how do you find the sum of the terms?

15 What debt can be discharged in one year by monthly payments, the first being $2, the

second $8, and so on to the end of the year, and what will be the last payment. Art. 328, Ex. 3.

the number of small squares con

tained in a large square equal to?

5 What is the base of a triangle?

6

7

8

66

66

66

area of a triangle equal to?

are the contents of a triangle whose base is 75 chains and perpendicular 36 chains? Art. 331, Ex. 4.

11 How do you find the area of a square, rectangle, or parallelogram?

12 What is the area of a square piece of land of which the sides are 54 chains? Art. 334, Ex. 2. 13 What is a trapezoid?

14 How do you find the area of a trapezoid?

15 What is the area of a trapezoid whose parallel sides are 15 chains, and 24.5 chains, and the perpendicular height 30.80 chains? Art. 336, Ex. 5.

16 What is a circle?

66 the centre of a circle?

17

20 What is the radius of a circle?

21 How do you find the circumference when the diameter is known?

22 How do you find the diameter when the circumference is known?

23 The diameter of a circle is 40: what is the circumference? Art. 337, Ex. 3.

24 The circumference of a circle is 13,700: what is the diameter? Art. 338, Ex. 3.

25 How do you find the area of a circle?

26 How many yards in a circle whose diameter is 3 feet?

27 What is a sphere? Art. 339, Ex. 4.

28 How do you find the surface of a sphere? 29 What is the surface of a sphere whose diameter is 14?

30 What is a volume?

31 How do you find the contents of a sphere? 32 What are the contents of a sphere whose diameter is 12 feet? Art. 343, Ex. 5.

33 What is a prism?

34

35

66

66

the perimeter of the base?

the convex surface of a prism? 36 How do you find the convex surface of a prism?

37 What is the convex surface when there are eight equal sides, each 15 feet in length, and the altitude is 12 feet? Art. 345, Ex. 2.

38 How do you find the contents of a prism? 39 What are the contents of a triangular prism whose height is 20 ft. and area of the base 691 ft.?