10x2-5x+3

18. Reduce

to a mixed quantity. Ex. 6. P. 59.

3

19. Reduce

5x

x3—y3
x-y

to an entire quantity. Ex. 5. P. 59.

20. How do you reduce fractions having different denominators to equivalent fractions having a common denominator? R. P.

62.

C

Ex. 6. P. 60.

22. How do you Add fractions? R. P. 61.

23. What is the sum ofa

a-x

с

d -ba+b a+x

and ? Ex. 10. P.62.

24. Give the process for the subtraction of fractions. R. P.

25. From 3x+ take x

X
b

X-a

Ex. 7. P. 63.

с

26. How do you multiply one fractional quantity by another? R. P. 62.

a2. -x2
a-x x+x3°

27. Multiply a+ ax
at by

Ex. 8. P. 64.

28. How do you divide one fraction by another? R. P. 65.

31. What effect will it have on the quotient to change the signs either of the numerator or denominator? Art. 69.

32. How will the value of the fraction be affected by adding the same quantity to both terms of a proper fraction? Art. 70. 33. By adding the same quantity to both terms of an improper fraction?

Art. 70.

34. Demonstrate the principle in the last two questions.

35. If the same quantity be subtracted from each term of a proper fraction, how will the value of the fraction be affected? Art. 70.

36. By subtracting the same quantity from each term of an

improper fraction, what effect on the value of the fraction? Art.

70.

37. Explain the principle in the last two questions.

41. What does the sign Zero signify? Art. 71.

42. What is the sign of infinity? Art. 71.

EQUATIONS OF THE FIRST DEGREE.

1. What is an Equation? Art. 72.

2. What are members of an Equation? Art. 72.

3. What is the First Member? Which the Second?

Art. 72,

4. How many unknown quantities may an equation have?

Art. 73.

5. How are equations classified? Art. 73.

6. How can you tell what degree an Equation is? Art. 73.

7. What are Numerical Equations? Art. 74.

8. Define Literal equations. Art. 74.

9. What is an Identical equation? Art. 75.

10. State the properties of an equation. Art. 76.

AXIOM.

1. Define an Axiom. Art. 76.

2. How many axioms are used in Algebra? Art. 76.

3. Give the six axioms. Art. 76.

SOLUTION OF EQUATIONS.

1. What do you understand by the Solution of an equation? Art. 77.

2. What do you understand by the Transformation of an Equation? Art. 78.

3. Of what does the First Transformation consist? Art. 78. 4. How do you transform an equation involving fractional terms to one involving only entire terms? R. P. 76.

tion involving only entire terms. Ex. 4. P. 77.

6. Of what does the second transposition consist? Art. 79. 7. How do you transpose a term of an equation from one member to the other? R. P. 77.

8. Upon what principle is the Rule founded for the last question?

9. Give the Rule for Solving an equation of the first degree.

R. P. 78.

10. Find the value of x in the following: 2x

Ex. 16. P. 80.

4x-2 3x-1

a+b

11. Solve the following:

(a+b)(x-b)-3a= 4ab-b3

-2x+

a-b

12. Of how many parts does the solution of a problem consist? Name them.

Art. 81.

13. Of what does the statement consist? Solution? Art. 81. 14. What is the Rule for "Stating" problems? R. P. 81. 15. Solve the following: A capitalist receives a yearly income of $2940; four-fifths of his money bears an interest of 4 per cent., and the remainder of five per cent.; how much has he at interest? Ex. 18. P. 87.

16. In a certain orchard one-half are apple trees, one-fourth peach trees, one-sixth plumb trees, 120 cherry trees, and 80 pear trees; how many trees in the orchard? Ex. 20. P. 87.

17. A person in play lost one-fourth of his money, and then won 3 shillings; after which he lost one-third of what he then had; and this done, found that he had but 12 shillings remaining: what had he at first? Ex. 28. P. 88.

ELIMINATION.

1. Define Elimination. Art. 83.

2. How many methods of Elimination are there? Art. 80. 3. Give the method by Addition and Subtraction. R. P.

5

4. Explain the method by Substitution. Art. 85.

5. Illustrate by an example the method of Elimination by comparison. Art. 86.

6. How do you solve a problem involving three equations and three unknown quantities? Art. 87:

7. What is a Simultaneous equation? Art. 82.

8. Give the general Rule for solving a problem containing any number of equations and unknown quantities. R. P. 94.

9. Given 2x+3y=16 and 3x-2y=11, to find the values of x and y. Ex. 1. P. 95.

X

10. +7y=99, and +7x=51, to find the values of x and y.

Ex. 3. P. 95.

Ꭹ
7

11. Given 7x-2z+3u=17. 4y-2z+t=11. 5y-3x-2u-8. 4y-3u+2t-9, and 3z+8u=33, to find the values of x, y, z, u, and t. Ex. 8. P. 95.

12. Solve the following: A's age is double B's, and B's is triple C's, and the sum of their ages is 140; what is the age of each? Ex. 11. P. 99.

13. A footman agreed to serve his master for £8 a year and a livery, but was turned away at the end of 7 months, and received only £2 13s 4d and his livery; what was its value? Ex. 16. P. 100.

14. If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days, how many days would it take each person to perform the same work alone? Ex. 20. P. 100.

15. A banker has two kinds of money; it takes a pieces of the first to make a crown, and b pieces of the second to make the same sum. Some one offers him a crown for c pieces. How many of each kind must the banker give him? Ex. 28. P. 102.

INDETERMINATE EQUATIONS AND PROBLEMS.

1. Define an Indeterminate Equation. Art. 88.

2. What is an Indeterminate Problem? Art. 88.*

3. How many equations must there be for a given number of unknown quantities?

4. What do you understand by the Interpretation of Negative. Results? Art. 89.

5. Solve and explain the following: A Father has lived a number of years expressed by a; his son a number of years expressed by b. Find in how many years the age of the son will be one-fourth the age of the father. Ex. 2. P. 107.

6. State the four principles in regard to negative results. P. 108, 109.

7. What do you understand by the Discussion of Problems? Art. 91.

8. What is an Arbitrary quantity? Art. 91.

9. Give and solve the problem of the Couriers. Art. 91. 10. Explain all the conditions of the last question. Art. 91.

INEQUALITIES.

1. What is an Inequality? A. 92.

2. State the six distinct principles belonging to inequalities. P. 114, 115, 116.

3. Find x in the following: bx—ax+ab<2,

7

POWERS AND ROOTS.

1. What is the square of a quantity? Art. 93.

Ex. 5. P. 116.

2. Define the Square Root of a quantity. Art. 93.

3. The square of a Number composed of tens and units is equal to what? Art. 94.

4. Illustrate the last question by squaring 64.

5. Also by squaring 365.

6. Extract the square Root of 96785436.

7. How do you extract the square root of a number? Art. 95. 8. Demonstrate the Rule for square root. Art. 95.

9. When can you increase the entire part of the root by 1? Art. 95. P. 122.

10. To what is the number of places in the root always equal? Rem. II. P. 123.

11. Is the square root of an imperfect square commensurable with 1. Rem. 3. P. 123.