Examinations Are Based.
The following lessons are based on previous examinations. The subjects are somewhat broad in scope in order to carry the student over every possible contingency1. Careful study will enable the competitor to meet all the requirements.
Spelling.
Chirography, Pippin,
[53]
Ere, Inaugurate,
Intuition, Freight,
Granary, Quadrille,
Copartner, Lullaby,
Inconstancy, Audacious,
Officiate, Though,
Ninetieth, Bivouac,
Wigwam, Dissolve,
Eyelet, Admittance,
Tyranny, Occupy,
Undulate, Constituency,
Literary, Halibut,
Legislature, Strength,
Desirous, Wheelbarrow,
Radiant, Curtain,
Jamb, Senate,
Chilblain, Superscribe,
[54]
Circuit, Motor,
Claret, Alcohol,
Ludicrous, Charity,
Idea, Plantain,
ARITHMETIC.
Lessons in Decimals.
The paper on arithmetic in second grade examinations usually contains one, sometimes two, problems in common or decimal fractions. These are no more difficult to solve when one understands the rules governing them, than any simple test in addition, division, etc. In whole numbers, as 57, 563, 4278, the various units increase on a scale of ten to the left (or decrease on the same scale of ten to the right). Thus in the last number we say 8 units, 7 tens, 2 hundreds,[55] and 4 thousands or four thousand two hundred seventy-eight.
Decimals also decrease on a scale of ten to the right (or increase on the same scale of ten to the left). In writing decimals, we first write the decimal point, which is the same mark we use at the close of a sentence and is called a period. Then the first figure to the right is called “tenths” and is written thus .6, meaning six tenths. The second figure stands for hundredths as .06, six hundredths; .006 for six thousandths; .0006 for six ten-thousandths; .00006 for six hundred-thousandths; .000006 for six millionths, etc. When a whole number, previously39 mentioned, and decimals are written together as 47.328, it is called a mixed number.
The only distinction between reading whole numbers and decimals is made by adding this to the ending of decimals, and the denomination40 of the right-hand figure must be expressed to give the proper value to decimal parts. For instance, .12, is twelve hundredths; .007, is seven thousandths; .062, is sixty-two thousandths; .201, is two hundred one thousandths; .5562, is five thousand five hundred sixty-two ten-thousandths; .24371, is twenty-four thousand three hundred seventy-one hundred-thousandths; .893254, is eight hundred ninety-three thousand two hundred fifty-four millionths, etc. Remember that in decimals the[56] first figure stands for, tenths; the second, hundredths; the third, thousandths; the fourth, ten-thousandths; the fifth, hundred-thousandths; the sixth, millionths, and that in reading decimals we add the denomination of the right-hand figure. When reading a mixed number the word “and” is used, and then only, to indicate the decimal point. Thus 45.304 should be read forty-five AND three hundred four thousandths.
Addition and subtraction41 of decimals differ from similar operations of whole numbers only in the placing of the figures. In whole numbers units come under units, tens under tens, etc. To illustrate42:
What is the sum of 260, 4398, 305, 2, 29?
The figures are placed thus:
260
4,398
305
2
29
———
4,994
[57]
Now let us take the same figures expressed decimally: .260, .4398, .305, .2, .29.
.260
.4398
.305
.2
.29
———
1.4948
In subtraction of whole numbers or decimals the figures are placed as in addition.
Examples—Subtract .204 from .4723.
.4723
.204
——–
.2683
Subtract 5.346 from .937.
5.346
.937
——–
4.409
Subtract .753 from 18. (Note that the point or period is placed to the left of “753” indicating decimals, but in connection with the number “18,” a dot is placed to the right as a mark of punctuation43 merely, thus showing that “18” is a whole number.)
[58]
Now from the whole number “18,” which is the minuend because it is the number to be subtracted from, we are to subtract .753, and it is done in this way:
Minuend 18.000
Subtrahend .753
———
17.247
The three ciphers45 are added to the minuend to correspond to the decimal places in the subtrahend. It is not necessary to put the ciphers down, but beginners are apt to get confused if there is nothing there to correspond to the decimals below. Annex46 as many ciphers to the minuend as there are decimals in the subtrahend, and place in the remainder a decimal point under those of the numbers subtracted.
Multiplication47 of decimals differs somewhat from the previous operations mentioned for the reason that we do not necessarily place the decimal points directly under each other. The right-hand figure of the multiplier usually goes under the right-hand figure of the multiplicand and the problem is then worked out as in multiplying whole numbers. When the product is obtained we point off as many decimal places in it as there are in both the multiplier and the multiplicand.
Let us take as an example: Multiply 2.648 by 2.35
[59]
Multiplicand 2.648
Multiplier 2.35
———–
13240
7944
5296
———–
Product 6.22280
It will be seen that there are three decimals in the multiplicand and 2 decimals in the multiplier, hence we point off five decimals in the product.
In the operation of division of decimals the decimal point is not considered until the result is obtained. If the number of decimal places in the dividend48 is less than the number of decimal places in the divisor ciphers must be annexed49 or added to make up the deficiency, and the decimal point is then suppressed, thus reducing the operation to the division of two whole numbers. If there is no remainder, the quotient is a whole number, if there is a remainder, add a cipher44 to the right of it and place a decimal point to the right of the quotient obtained, then continue the division as far as desirable by adding ciphers to the right of the successive remainders, for each of which a new decimal will be obtained in the quotient.
Divide 460 by .5.
[60]
.5) 460 (92
45
—
10
10
—
0
Fractions are reduced to decimals by annexing50 ciphers to the numerator and then dividing by the denominator.
For instance—5/8 equals what decimal?
8) 5.000 (.625 = 5/8
4?8
—
.20
?16
?—
.40
?40
Lessons by Prof. Jean P. Genthon, C.E., Member Society of Municipal Engineers and Author of “The Assistant Engineer,” “The Chief’s” Text Book on Civil Engineering.
In solving problems the process should be not merely indicated, but all the figures necessary in solving each[61] problem should be given in full. The answers to each problem should be indicated by writing “Ans.” after it.
Arithmetic is the science of numbers.
A Number is the result of the comparison (also called measurement) of a magnitude or quantity with another magnitude or quantity of the same kind supposed to be known.
A Concrete Number is one the nature of the unit of which is known.
Denominate Number.—A concrete number the standard of which is fixed51 by law or established by long usage.
An Abstract Number is one of which the nature of the unit is unknown.
How to Read Numbers.—The right way to read 101,274, etc., is one hundred one, two hundred seventy-four, etc.
The Decimal Point.—A period, called decimal point, is placed in a mixed number between the integral part and the decimal portion which follows. It should never be omitted.
Roman Numbers.—I stands for 1, V for 5, X for 10, L for 50, C for 100, D for 500 and M for 1,000.
Abbreviations.—A smaller unit, written to the left of a greater one, is subtracted from the latter, as: IV = 4[62] (IV is marked IIII on clock and watch dials); IX = 9; XC = 90; CD = 400, etc. Sometimes a Roman number is surmounted52 by a dash or vinculum; it then expresses thousands, as IX = 9,000.
Addition.
Addition.—Operation which consists in taking in any order all the units and portions of units of several numbers and forming with them a single number called their Sum or Total.
Addition of Long Columns of Numbers.—When long columns of numbers are to be added, the student should endeavor to add more than one figure at a time. He may pick those which aggregate53 10, 15, 20, etc., and add the intermediate figures when convenient.
Sign of Addition.—The sign of addition is the horizontal-vertical or Roman cross + placed between all the numbers to be added; it is read Plus.
To Prove an Addition.—The shortest way to prove an addition is to do it over again from bottom to top.
Sign of Equality.—The sign of equality is two short equal horizontal parallels =; it reads Equal.
Subtraction.
Subtraction.—An operation which consists in taking from a number called minuend (m) all the units and parts of units contained in another number called subtrahend (s).[63] The result is called the difference (d) of the two numbers or the remainder of their subtraction.
Sign of Subtraction.—The sign of subtraction is a horizontal dash - placed between the minuend, written first, and the subtrahend. Thus: 84 - 38 = d; 84 - 38 = 46. Generally m - s = d.
To Prove a Subtraction.—Add from bottom to top the difference and the subtrahend; the sum must equal the minuend.
Multiplication.
Multiplication.—An operation which consists in repeating a number called multiplicand (M) as many times as there are units in another column called multiplier (m); the result is called the product (p) of the numbers, and the numbers themselves are called factors of the product. This definition may be extended to the case where the factors are not whole numbers.
Sign of Multiplication.—The sign of multiplication is the oblique54 or St. Andrew’s cross ×, called multiplied by, and placed between the factors written one after the other.
Thus: 35 × 7 = p; 35 × 7 = 245. Generally M × m = p.
To Prove a Multiplication.—Multiplication may be proved by a second multiplication in which the factors are inverted55.
[64]
This is the surest but the longest method.
Another Proof of the Multiplication.—Find the residue56 of the multiplicand and multiplier. Multiply them and find the residue of their product; this is equal to the residue of the product of the multiplication.
64327 4 Residue of the multiplicand.
781 7 Residue of the multiplier.
———— —
64327
514616
450289
————
50239387 1 Residue of the product of multiplication.
Proof Not Absolute.—Practically a proof is not absolute, because an error may be committed in its use, and also it may not work well in all cases.
Power of a Number.—When the factors of a product are equal, the product is called a power of the factor.
Square of a Number.—A power is a square when it is the product of two (2) equal factors, as 7 × 7 = 49, in which 49 is the square of 7. The term square is derived58 from the fact that the area of a square is obtained by multiplying the length of its side by itself, or taking it twice as a factor.
Cube of a Number.—A power is a cube when it is[65] the product of three (3) equal factors, as 5 × 5 × 5 = 125, in which 125 is the cube of 5.
The term cube is derived from the fact that the volume of a cube is obtained by multiplying the length of its side by itself and again by itself, or by taking it three times as a factor.
A product, for instance, of 4, 9, etc., equal factors would be called the 4th or the 9th, etc., power of that number.
Division.
Division.—An operation by means of which we find one of two factors of a product when that product and the other factor are given. The given product is called Dividend (D) of the division; the known factor is called the Divisor (d), and the unknown factor which is sought is called Quotient (q). We know that a quotient is seldom exact and that there is generally a Remainder (r) or Residue.
Sign of Division.—The sign of division is a small dash with a point above and one below ÷; it is read divided by, is placed after the dividend, and is followed by the divisor. For instance, to indicate the division of 72 by 8, which we know gives the quotient 9, we write 72 ÷ 8 = 9; generally D ÷ d = q.
Other Sign of Division.—In the study of fractions[66] it is shown that a fraction expresses the quotient of its numerator by its denominator, so that the preceding identity may be written
72
8
= 9, or more generally
D
d
= q, and another sign of division is a horizontal line separating the dividend written above it from the divisor written below it.
Proof of the Division.—We prove a division by multiplying the divisor by the quotient and adding the remainder, if there is any; the result thus obtained must equal the dividend. When there is a remainder, the formula of division is D = dq + r.
By 2.—A number is divisible by 2 when it is an even number, that is to say when it ends with 0, 2, 4, 6 or 8, as 70,836.
By 3.—A number is divisible by 3 when its residue is zero or is divisible by 3.
By 4.—A number is divisible by 4 when the number formed by the last two figures to the right is divisible by 4; 7528 is divisible by 4 because 28 is divisible by 4.
By 5.—A number is divisible by 5 when it ends with 0 or 5, as 75,270.
By 6.—A number is divisible by 6 when it is divisible by 2 and 3, as 474, because when a number is divisible by several others it is divisible by their product.
By 8.—A number is divisible by 8 when the number formed by the last three figures to the right is divisible[67] by 8; 37104 is divisible by 8 because 104 is divisible by 8.
By 9.—A number is divisible by 9 when its residue is 9 or 0.
By 10.—A number is divisible by 10 when the last figure to the right is 0.
By 100.—A number is divisible by 100 when the last two figures to the right are 00.
By 11.—A number is divisible by 11 when the sum of the figures of even rank subtracted from the sum of the figures of uneven59 rank (increased by 11 if necessary) is 0 or divisible by 11, as 95832, 3304081.
By 12.—A number is divisible by 12 when it is divisible by 3 and 4, as 756.
By 15.—A number is divisible by 15 when it is divisible by 3 and 5, as 255.
[68]
[69]
Suggestions for the Study of
Arithmetic
By ERNEST L. CRANDALL
Former Civil Service Examiner
There are certain “standard errors,” so to speak, that the unsuccessful candidate makes nine times out of ten, and if these are eliminated every one, with a little practice, may put himself in line for 100 per cent.
While the examples may take the form of “problems,” the only processes involved will be simple addition, subtraction, multiplication and division—no fractions or decimals.
[70]
In addition there is but one thing to be observed. If your numbers are not all of equal length arrange them so that the last figures are all in the same column. Suppose you have to add 357,856, 7,596, 452 and 29,360. Following are the right and wrong ways to arrange them:
Right way. Wrong way.
357,856 357856
7,596 7596
452 452
29,360 29360
——— ———
This arrangement is necessary because of the inherent properties of numbers as expressed in figures, under what we call our decimal system, which means simply the practice we have adopted of expressing our numbers in multiples of ten. This arose from the fact that we happen to be born with ten fingers, and our ancestors, like our children, learned to count by means of those very useful “markers.”
In the system of counting every place, or column, counting from the right, has a value ten times greater than the one in the place or column nearest on the right. Thus in the number 36,542 the first figure on[71] the right represents “ones,” the next ten times as much or “tens,” the next ten times as much again or “hundreds,” and so on. We really read this number backward when we name it, for in handling it in any way we have to start with the last figure, representing the “ones.” The number really means two ones, four tens, five hundreds, six thousands and three ten thousands. It is built up this way, really by addition:
2
40
500
6000
30000
———
36,542
Now, this principle underlies60 the processes called “carrying” and “borrowing.” You wish to add 26 and 37. Adding the 6 ones to the 7 you get 13 ones, or 3 ones and 1 ten. So you “carry” that 1 ten to the column where it belongs, leaving the 3 ones in their proper column. Thus, in your tens column you have 2 tens plus 3 tens plus the 1 ten “carried,” which makes 6 tens; and your result is 63, or 6 tens and 3 ones.
Again, you want to subtract 19 from 38. As you cannot take 9 from 8, you “borrow” one of the 3 tens,[72] making your 8 into 18 and subtract 9 from that, leaving 9. By so doing you have left but 2 tens in your tens column, and so there your subtraction is now from 2, leaving 1. Hence your result is 9 ones and 1 ten, or 19.
Here is an example in subtraction which was once used, and which is as likely to trip one up as any that could be set. Subtract 199,999 from 320,012. The result is as follows:
320,012
199,999
———
120,013
Now, you cannot take 9 from 2, so you “borrow” one from the left and make your two 12. Then 9 from 12 leaves 3. In borrowing from the left you reduce the 1 in the tens column to 0. As you cannot take 9 from 0, you must again borrow from the left. But what are you to borrow from? In the third, or hundreds column there is only a 0. Hence, before you can borrow from this column you must make this 0 a 10 by borrowing from the fourth, or thousands column (counting your columns always from the right).
[73]
But again here you find only a 0, and so before you can make even this “borrow” you must borrow one from the 2 in the ten thousands column. Now see what happens. With the one which you have finally borrowed you have made the 0 left in the second or tens column into a 10, and you take 9 from 10, which leaves 1.
Now, here is where you forget something. When you started out to “borrow” you had to go away over to the 2 in the fifth column; that made your 0 in the fourth column a 10, but you immediately passed this one on to the third column, which left only 9; again you passed it on from the third to the second column, which left only a 9 in the third column. Hence you have now a 9 in the third and in the fourth columns, and your results there will be in each case 9 from 9 leaves 0.
Coming to the fifth you have a 1 instead of a 2, having borrowed 1; and you have to borrow again from the 3 to make your 1 into an 11, obtaining 9 from 11 leaves 2; and your sixth and last figure, being reduced from 3 to 2, your last result is 1 from 2 leaves 1.
This last part is easy, but one out of practice is almost certain to forget that his 0’s in the third and[74] fourth columns became 9’s. If you have any difficulty with subtraction, study out the processes in this example until you understand them and you will never make a mistake again.
Now, as to the shape in which the examples will be given: The plain problems in addition will be unmistakable. You will be told that a concern sold 27,356 barrels of flour in one month, 38,452 the next, etc., and you cannot well run off the track. But you may find both processes involved in one “problem,” and you must then be careful to understand just what is meant by the question, so that you will know what you are expected to do with the figures.
Take this, for example: “A had $3,465 and B $4,895. A gained $1,146 and B lost $602. Which then had the more, and how much?”
Here you must add A’s gain to his principal—that is, the sum he had to start with—and subtract B’s loss from his principal; then subtract the smaller result from the larger, stating which is the “winner.” Thus:
$3,465 $4,895 $4,611
1,146 602 4,293
——— ——— ———
$4,611 $4,293 $318
Answer.—A has $318 more.
When it comes to multiplication and division, there is just one “catch,” so it might appear to the untrained[75] mind of some poor candidate, which is made to play a part in nearly every problem. It is safe to say that 90 per cent. of the failures on these two processes turn on this one point. It is a very simple one and really the same in both processes. It arises in the handling of the “naught61” or “cipher,” as we used to call it, the “zero”—call it what you like, it is nothing, anyhow. And that’s the point to be remembered.
Here is an example: Multiply 3,125 by 208. Now it seems almost incredible, but I have seen literally62 hundreds of papers, it seems to me, where this very simple problem was worked out this way:
The Wrong Way.
3,125
208
———
25000
3125
6250
———
681250
Or else this:
[76]
Another Wrong Way.
3125
208
———
25000
6250
———
87500
The trouble is that when the poor fellow came to multiply by the “naught” he forgot in the first instance that it was nothing, and that the biggest number in the world multiplied by nothing will produce nothing. He knew that something ought to go down there, and so in sheer desperation he wrote down the number he was multiplying.
In the second instance, while he recognized that nothing is nothing, he forgot that all our figuring is done by columns, as we saw in our last lesson; so that when we are multiplying by tens we must put our first figure down in the hundreds column, and so on. By forgetting this he multiplied his number by two hundreds, but put his first figure down in the tens columns, and thus he really multiplied by only 28 instead of 208.
Now, the very simplest way to avoid this sort of[77] mistake is to “go through the motions” of multiplying by the “naught” or “zero.” Thus:
The Right Way. 3,125
208
———
25000
0000
6250
———
650,000
This looks a little clumsy, perhaps, but it is the logical way—to go through the process of saying naught times 5 is naught, naught times 2 is naught, etc., putting down the results in the proper columns. It is the safest way, if you are the least bit weak on the principles of numbers, to do even the process of multiplying by whole hundreds. Thus:
3,125
200
———
0000
0000
6250
———
625,000
[78]
By writing his example in the “short cut” style I have seen many a man make this mistake:
Wrong. 3,125
200
———
62500
That is, after setting down his two surplus ciphers, when he obtained another in multiplying 5 by 2, he forgot that it was a new one and went right on to the next process. If you are in that position that you must really learn your arithmetic all over again, stick to the logical method of showing every process and learn the “short cuts” afterward63.
Now, when the reverse situation arises in division, a similar error is of frequent occurrence. Suppose we are to divide 650,000 by 3,125. This sometimes results:
The Wrong Way. 3,125) 650,000 (28
625 0
———
25,000
25,000
That is, the figurer, when he came to try to divide 2,500 by 3,125, realizing that it would not “go,” simply[79] “brought down” another figure. He forgot that the real mental process was 3,125 goes into 2,500 no times, or produces “naught,” and that “naught,” or “cipher,” must be set down in the proper tens column. The only safe way, again, is to indicate every process; to “bring down” but one figure at a time and to set down every result, even the “nothings,” in its proper place. That will make our example look like this:
The Right Way. 3,125) 650,000 (208
625 0
25 00
00 00
———
25 000
25 000
Very simple, but let me “whisper,” if you really master and understand the mysteries of “long division,” you have crossed the Rubicon of education. There is no door in all human learning that need remain forever sealed to a persistent64 mind that has truly found its way clearly and understandingly through this first great stumbling block. Ask any old-fashioned school teacher to dispute that proposition. And, “whisper” again, there are men counting coupons66 who[80] can do long division, to be sure, but who could not tell you why it is done as it is, if the price of stocks depended on it.
Punctuation.
Punctuation is a system of marks the purpose of which is to indicate to the eye the relation of words to one another in meaning, and so the relative importance of the component67 parts of a written composition.
The marks of Punctuation, corresponding, for the most part, to pauses in spoken language, are the comma (,), the period (.), the note of interrogation (?), the note of exclamation69 (!), the colon70 (:), the semi-colon (;), the dash (—), parentheses71 ( ), brackets [ ], quotation72 marks (“ ”), and the hyphen (-).
Purpose of Punctuation.—To make a written composition clear and intelligent, and to facilitate the task of reading.
Avoid All Unnecessary Remarks.—In modern writings punctuation marks are less frequently used than they were among writers in the early part of the last century. A sentence consisting of a simple subject, a simple predicate, and a simple object, or the relation of whose parts is clearly intelligible73 without marks, should not be encumbered74 with any. Take, for instance, the following two sentences:
[81]
“On the very morning of the massacre76 they were in the houses and at the tables of those whose deaths they were plotting.”
Comma.—Three or more words of the same part of speech not connected by conjunctions should be separated from one another by commas.
“He was strong, alert, active.”
“New York City is grand, immense, beautiful.”
Two words contrasted with one another are separated by a comma.
“He is slow, but sure.”
Words in a series of pairs should be separated by a comma. “Young and old, strong and weak, fair and dark, good and bad.”
Explanatory and parenthetical words or phrases (such as “therefore,” “moreover,” “indeed,” “however,” “in fact,” “to some extent,” etc.), inserted into the body of a sentence are usually marked off by commas.
A comma is inserted after the name of a person or thing addressed.
“John, you were mistaken.”
“My country, I am proud of thee.”
Period.—The period (.) is put at the end of every complete sentence that is not exclamatory or interrogative. It is also used as a part of every abbreviation, and after every initial letter standing65 in place of the[82] full word in a name. “A. M.” (for Master of Arts), “Mr.” (for Mister), “Esq.” (for Esquire), “R. W. Emerson” (for Ralph Waldo Emerson), “Dr.” (for doctor).
Note of Interrogation.—The note of interrogation (?) should follow every direct question: “Are you coming?” “Shall I buy it?” An interrogation point does not, however, follow an indirect question, such as “Let me know what he says.”
Note of Exclamation.—The note of exclamation (!) follows an exclamation, or any series of words denoting an outburst of feeling. “Alas!” “Three cheers!” “Hurrah!”
Colon.—The colon (:) is used to divide from one another the several co-ordinate members of a compound sentence, when they might each of them form an independent sentence, but are ranged side by side in a compound sentence for the sake of better showing how they illustrate one another.
“New York is a wonderful city: The wealthiest in America.”
A quotation or enumeration77 of details is often preceded by a colon.
Semi-Colon.—The semi-colon (;) separates co-ordinate[83] sentences more dependent on one another than are those parted by the colon.
“Where it is prescribed that an act is to be done; or that the adverse78 party has a specified79 time to do an act; if service required is doubly the time allowed; except that,” etc.
In sentences containing two sets of subjects and predicates where either clause is very long or contains a subordinate clause, it is well to use a semi-colon.
Parentheses.—Parentheses (?) are used to enclose words or phrases in a sentence, inserted by way of explanation or comment, but lying outside of the construction of the sentence:
“You see (as I predicted would be the case) I have had a long journey for nothing.”
Dash.—The dash (—) denotes, in most cases, a sudden digression from the general run of the sentence: “I want to tell you—but first let us go into the house.”
Sometimes the dash takes the place of the parentheses, when the clause, though digressive80, bears some relation to the context.
Brackets.—Brackets [?] are used to isolate81 interpolated words from the passage in which they are used:
“The examiner said that if they [the candidates] were discovered talking with each other he [the examiner][84] would have them [the candidates] expelled from the room.”
Hyphen.—A hyphen (-) is used, first to connect the part of a word at the end of a line with the remaining letters or syllables82 of the word beginning the next line; second, to conjoin two or more words into a compound word; as, “a never-to-be-forgotten day;” “long-winded,” etc.
The part of a word to which the hyphen is attached should be an integral part; that is, an entire syllable33, and not merely certain letters composing only a part of a syllable.
Quotation Marks.—Quotation marks (“?”) are used to distinguish a word, phrase, clause, sentence, or passage taken word for word, from any source outside that of the writing into which it is inserted.
A quotation within a quotation is marked off only by a single inverted comma before and after it. But a quotation within the second quotation requires double marks.
A passage quoted, not word for word, but only in substance, is often distinguished83 by but one quotation mark before and after it.
Capital Letters.—In examinations containing papers the rating of which is determined84 in part by correctness in the use of capital letters the average candidate is usually at a disadvantage. The following rules, if[85] committed to memory, will enable the candidate to avoid errors which, if made, might cause him to fail in the examination.
The first word of every sentence should begin with a capital letter.
The days of the week, the months of the year, and holidays.
The names of places and countries; as, England, Yonkers, Belmont Park, etc.
The names of States, Mountains, Rivers and Lakes.
All words used to signify the Deity; as, He, Him, His, Thou, Thee, Thine, etc.
The names of persons, the titles of persons, and the titles of books; as, John Brown, Lord Salisbury, Senator Mitchell, “The Marble Faun.”
The first word in every line of poetry.
The pronoun I, and the exclamation O, or Oh.
The first word of a direct quotation should also begin with a capital; as, “To thine own self be true.”
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contingency
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Vogue
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deity
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| n.神，神性；被奉若神明的人(或物) | |
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worthy
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yoke
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| n.轭；支配；v.给...上轭，连接，使成配偶 | |
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paltry
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| adj.无价值的，微不足道的 | |
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aspirant
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| n.热望者；adj.渴望的 | |
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anvil
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| n.铁钻 | |
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rumor
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| n.谣言，谣传，传说 | |
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brutal
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| adj.残忍的，野蛮的，不讲理的 | |
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cholera
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| n.霍乱 | |
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glimmer
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| v.发出闪烁的微光；n.微光，微弱的闪光 | |
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chirp
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| v.(尤指鸟)唧唧喳喳的叫 | |
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delightful
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| adj.令人高兴的，使人快乐的 | |
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niche
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| n.壁龛；合适的职务(环境、位置等) | |
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autocrat
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| n.独裁者；专横的人 | |
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usury
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| n.高利贷 | |
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delicacy
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| n.精致，细微，微妙，精良；美味，佳肴 | |
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equitable
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| adj.公平的；公正的 | |
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credulous
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| adj.轻信的，易信的 | |
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21
asthma
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| n.气喘病，哮喘病 | |
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maniac
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| n.精神癫狂的人；疯子 | |
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irritable
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| adj.急躁的；过敏的；易怒的 | |
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conservatory
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| n.温室，音乐学院；adj.保存性的，有保存力的 | |
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anomalous
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| adj.反常的；不规则的 | |
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melodious
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| adj.旋律美妙的，调子优美的，音乐性的 | |
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convertible
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| adj.可改变的，可交换，同意义的；n.有活动摺篷的汽车 | |
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adversary
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| adj.敌手，对手 | |
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mammoth
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| n.长毛象；adj.长毛象似的，巨大的 | |
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illuminate
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| vt.照亮，照明；用灯光装饰；说明，阐释 | |
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presumption
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| n.推测，可能性，冒昧，放肆，[法律]推定 | |
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stencil
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| v.用模版印刷；n.模版；复写纸，蜡纸 | |
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syllable
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| n.音节；vt.分音节 | |
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degradation
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| n.降级；低落；退化；陵削；降解；衰变 | |
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apprentice
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| n.学徒，徒弟 | |
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saucy
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| adj.无礼的；俊俏的；活泼的 | |
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recollect
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| v.回忆，想起，记起，忆起，记得 | |
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longitude
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| n.经线，经度 | |
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previously
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| adv.以前，先前（地） | |
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denomination
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| n.命名，取名，(度量衡、货币等的)单位 | |
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subtraction
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| n.减法，减去 | |
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illustrate
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| v.举例说明，阐明；图解，加插图 | |
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punctuation
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| n.标点符号，标点法 | |
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cipher
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| n.零；无影响力的人；密码 | |
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ciphers
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| n.密码( cipher的名词复数 )；零；不重要的人；无价值的东西 | |
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annex
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| vt.兼并，吞并；n.附属建筑物 | |
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multiplication
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| n.增加，增多，倍增；增殖，繁殖；乘法 | |
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dividend
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| n.红利，股息；回报，效益 | |
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annexed
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| [法] 附加的，附属的 | |
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annexing
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| 并吞( annex的现在分词 )； 兼并； 强占； 并吞（国家、地区等） | |
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fixed
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| adj.固定的，不变的，准备好的；(计算机)固定的 | |
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surmounted
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| 战胜( surmount的过去式和过去分词 )； 克服（困难）； 居于…之上； 在…顶上 | |
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aggregate
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| adj.总计的，集合的；n.总数；v.合计；集合 | |
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oblique
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| adj.斜的，倾斜的，无诚意的，不坦率的 | |
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inverted
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| adj.反向的，倒转的v.使倒置，使反转( invert的过去式和过去分词 ) | |
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residue
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| n.残余，剩余，残渣 | |
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residues
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| n.剩余，余渣( residue的名词复数 )；剩余财产；剩数 | |
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derived
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| vi.起源；由来；衍生；导出v.得到( derive的过去式和过去分词 )；（从…中）得到获得；源于；（从…中）提取 | |
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uneven
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| adj.不平坦的，不规则的，不均匀的 | |
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underlies
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| v.位于或存在于（某物）之下( underlie的第三人称单数 )；构成…的基础（或起因），引起 | |
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naught
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| n.无，零 [=nought] | |
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literally
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| adv.照字面意义，逐字地；确实 | |
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afterward
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| adv.后来；以后 | |
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persistent
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| adj.坚持不懈的，执意的；持续的 | |
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standing
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| n.持续，地位；adj.永久的，不动的，直立的，不流动的 | |
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coupons
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| n.礼券( coupon的名词复数 )；优惠券；订货单；参赛表 | |
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component
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| n.组成部分，成分，元件；adj.组成的，合成的 | |
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68
spoke
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| n.（车轮的）辐条；轮辐；破坏某人的计划；阻挠某人的行动 v.讲，谈（speak的过去式）；说；演说；从某种观点来说 | |
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69
exclamation
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| n.感叹号，惊呼，惊叹词 | |
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colon
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| n.冒号，结肠，直肠 | |
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71
parentheses
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| n.圆括号，插入语，插曲（ parenthesis的名词复数 ） | |
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quotation
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| n.引文，引语，语录；报价，牌价，行情 | |
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intelligible
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| adj.可理解的，明白易懂的，清楚的 | |
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encumbered
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| v.妨碍，阻碍，拖累( encumber的过去式和过去分词 ) | |
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75
secrecy
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| n.秘密，保密，隐蔽 | |
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76
massacre
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| n.残杀，大屠杀；v.残杀，集体屠杀 | |
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77
enumeration
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| n.计数，列举；细目；详表；点查 | |
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78
adverse
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| adj.不利的；有害的；敌对的，不友好的 | |
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specified
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| adj.特定的 | |
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digressive
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| adj.枝节的，离题的 | |
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81
isolate
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| vt.使孤立，隔离 | |
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82
syllables
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| n.音节( syllable的名词复数 ) | |
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83
distinguished
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| adj.卓越的，杰出的，著名的 | |
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determined
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| adj.坚定的；有决心的 | |
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