Everyday Activities

get up		take a shower		brush my teeth
floss my teeth		shave		get dressed

wash my face		put on makeup		brush my hair
comb my hair		make the bed		get undressed

take a bath		go to bed		sleep
make breakfast		make lunch		cook/make dinner

eat/have breakfast		eat/have lunch		eat/have dinner

Measurements, Geometric shapes, Area and Volume Formulas

MEASUREMENTS AND GEOMETRIC SHAPES

A. Measurements

1. height
2. width
3. depth

4. length
5. inch
6. foot-feet
7. yard
8. centimeter
9. meter

10. distance
11. mile
12. kilometer

B. Lines

13. straight line
14. parallel lines
15. perpendicular lines

C. Geometric Shapes

16. square a. side
17. rectangle
a. length
b. width
c. diagonal
18. right triangle
a. apex
b. right angle
c. base
d. hypotenuse
19. isosceles triangle
a. acute angle
b. obtuse angle
20. circle
a. center
b. radius
c. diameter
d. circumference
21. ellipse/oval

D. Solid Figures

22. cube
23. cylinder
24. sphere
25. cone
26. pyramid
1 inch(1") = 2.54 centimeters (cm)
1 foot (1') = 0.305 meters (m)
1 yard (1yd.) = 0.914 meters (m)
1 mile (mi.) = 1.6 kilometers (km)

Rectangle

Area   A = l *w

Perimeter   P=   2l + 2w

Square

Area A= s*s

Perimeter P= 4s

Triangle

Area A= b*h* 1/2

Parallelogram

Area A= b*h

Trapezoid

A= (b1+b2)*h * 1/2

Circle

Area A= ∏*r*r

Circumference C= ∏*d = 2*∏*r

Prism

Surface Area S = 2*B + P*h

Volume V = B*h

Cylinder

Surface Area S = 2*B + C*h = 2*∏*r*r + 2*∏*r*h

Volume V = B*h = ∏ *r*r*h

Pyramid

Surface Area

S= B + P*l*1/2

Volume V = B*h*1/3

Cone

Surface Area

S= B + ∏*r*l = ∏*r*r + ∏*r*l

Volume V = B*h*1/3 = ∏*r*r*h

Table of Measures

TIME

60 seconds (sec) = 1 minute (min)

60 minutes = 1 hour (hr)

24 hours = 1 day

7 days = 1 week

4 weeks (approx.) = 1 month

365 days = 52 weeks (approx.) = 12 months = 1 year

10 years = 1 decade

100 years = 1 century

Length

10 millimeters (mm) = 1 centimeter (cm)

100 cm = 1000 mm = 1 meter (m)

1000 m = 1 kilometer (km)

Area

100 square millimeters (mm2) = 1 square centimeter (cm2)

10,000 cm2 = 1 square meter (m2)

10,000 m2 = 1 hectare (ha)

Volume

1000 cubic millimeters (mm3) = 1 cubic centimeter (cm3)

1,000,000 cm3 = 1 cubic meter (m3)

Liquid Capacity

1000 milliliters (mL) = 1 liter (L)

1000 L = 1 kiloliter (kL)

Mass

1000 milligrams (mg) = 1 gram (g)

1000 g = 1 kilogram (kg)

1000 kg = 1 metric ton (t)

Temperature

Degrees Celsius (°C)

0°C = freezing point of water

37°C = normal body temperature

100°C = boiling point of water

next and nearest

1. Nearest is used for place - it means 'most near in space'

• Excuse me. Where's the nearest tube station?
  (not... the next tube station?)


• If you want to find Alan, just look in the nearest in the pub.

Next is usually used for time - it means 'nearest in the future'

• We get off at the next station (=the station that we will reach first)


• I'm looking forward to her next visit.

2. We use next in a few expressions to mean 'nearest in space'.
The most common are next door and next to.

• My girl-friend lives next door.


• Come and sit next to me.

neither, nor and not... either

1. We use neither and not to mean 'also not' . They mean the same.
Neither and nor come at the beginning of a clause, and are followed by auxiliary verb + subject.

neither/ nor + auxiliary verb + subject

• I can't swim. Neither can I ( NOT I also can't)


• I don't like opera. Nor do I (NOT I don't too)

2. We can use not...either with the same meaning

• I can't  swim. I can't either


• I don't like opera. I don't either.

look (at), watch and see

1. See is the ordinary word to say something 'comes to our eyes'

• Suddenly I saw something strange. Can you see me?


• Did you see the article about the strike in today's paper?

See in not used in progressive tenses with this meaning.
When we want to say that we see something at the moment of speaking, we often use can see.

• I can see an plane. (NOT I am seeing....)

2. We use look (at) to talk about concentrating, paying attention, trying to see as well as possible.

Compare

• I looked at the photo, but I didn't see anybody I knew.


• Do you see the man in the raincoat? Yes .
  Look again. Good heaves! It's Moriaty!

We use look when there is no object, and look at before an object.

Compare

• Look! (NOT look at)


• Look at me! (NOT look me)

long and for a long time

Long is most common in questions and negative sentences, and after too and so.

• How long did you wait? I didn't play for long.


• The concert was too long.

In affirmative sentences, we usually use a long time.

• I waited (for) a long time. ( I waited long is possible, but not usual.)


• It takes a long time to get to her house.

last and the last

Last week, last month etc is the week or month just before this one.
If I am speaking in July, last month was June.
If I speaking in 1985, last year was 1984.
(Note that prepositions are not used before these time-expressions)

• I had a cold last week. Were you at the meeting last Tuesday?


• We bought this house last year.

The last week, the last month etc is the period of seven days, thirty days etc up to the moment of speaking.
On July 15th, 1985, the last month is the period from June 15th to July 15th.

• I've had a cold for the last week
  (=for the seven days up to today)


• We've lived here for the last year
  (= since twelve months ago)

prepositions: in and into

1. To talk about the position of something (with no movement), we use in.

• Where's Susie? In the bedroom.


• My mother's the woman in the chair by the window.

2. When we talk about a movement, we usually use into.

• She came into my room holding a paper.


• I walked out into the garden to think.

After some words, both are possible. (For example throw, jump, cut, push).
We prefer into when we think of the movement, and in when we think of the end of the movement-
the place where something will be.

Compare

• She threw her ring into the air.


• She threw her ring in(to) the river.

We use in after sit down, and very after put.

• He sat down in his favourite armchair (NOT He sat down into...)


• I put my hand in my pocket.

if so and if not

We can use these expressions instead of repeating a verb that has already been mentioned.

• Are you free this evening? If so, let's go out for a meal.
  (=... If you are...)


• I might see you tomorrow. If not, then I'll be Saturday.
  (=... if I don't...)

how and what...like?

1. We use how to ask about things that change - for example people's mood and health.
We use what... like to ask about things that do not change - for example, people's appearance and character. Compare:

• How's Ron? He's very well.


• What's Ron like. He's tall and dark, and a bit shy.


• How does he look?. Surprised.


• What does he look like. Nice

2. We often use how to ask about people's reactions to their experiences

• How was the film? Great.


• How's your steak?


• How's the new job?

3. Don't confuse the preposition like (in What... like?) with the verb like.

Compare:

• What is she like? Lovely


• What does she like? Dancing and fast cars

hear and listen (to)

1. Hear is the ordinary word to say that something ‘comes to our ears’

• Suddenly I heard a strange noise


• Can you hear me?


• Did you hear the Queen’s speech yesterday?

Hear is not used in progressive tenses. When we want to say that we hear something at the moment of speaking, we often use can hear.

• I can hear somebody coming. (not I am hearing)

2. We use listen (to) to talk about concentrating, paying attention, trying to hear as well as possible.

Compare:

• I heard them talking in the next room, but I didn’t really listen to what they were saying.


• ‘Listen carefully please’ ‘Could you speak a bit louder? I can’t hear you very well’

We use listen when there is no object, and listen to before an object.

Compare.

• Listen! (Not Listen to)


• Listen to me! (Not Listen me)

hard and hardly

1. Hard can be an adjective or an adverb

• It's a hard job (adjective)


• This is very hard bread (adjective)


• You have to word hard. (adverb)
  (not You have to work hardly)


• Hit it hard. (adverb)

2. Hardly in an adverb. It means 'almost no' or 'almost not'

• He hardly works at all (= He does very little work)


• I've got hardly any money.


• He knows hardly anything about geography.

Note that hardly, hardly any, hardly ever etc are much more common than almost not, almost no, almost never etc

for, since, from , ago and before

1. For, since and from 'point forwards' in time
Ago and before 'point backwards' in time.

2. We use for to say how long something lasts

for + period of time

• I once studied the guitar for three years


• That house has been empty for six weeks


• We go away for three weeks every summer.


• My boss will be in Italy for the next ten days.

When we talk about a period of time up to the present, we use for with the present perfect tense (have+ past participle)

• I've known her for a long time (NOT I know her...)

A present progressive with for often refers to the future.

• How long are you staying for? (=Until when)

We can leave out for with How long....?

• How long are you staying?


• How long have you been waiting?

3. From and since give the starting point of an action or state: they say when something begins or began.

from/ since + starting point

• I'll be here from three o'clock onwards.


• I word  from nine to five.


• From now on. I'm going to go running every day.


• From his earliest childhood he loved music


• I've been waiting since ten o'clock.


• I've known her since January.

Since gives the starting point of actions and states that continue up to the present; from gives the starting point of other actions and states

4. For and since can both be used with the present perfect (have + past participle). They are not the same

for+ period

• I've known her for three days.


• I've been here for a month.


• I've had my car for ages.

since + starting point

• I've known her since Tuesday.


• I've been here since July.


• I've had my car since 1980

fewer and less

Fewer is the comparative of few (used before plural nouns)
Less is the comparative of little (used before uncountable nouns which are singular)

• few problems/ fewer problems


• little money/ less money


• I've got fewer problems than I used to have


• I earn less money than a postman.

In informal English, some people use less with plural words

• I've got less problems than I used to have.

(a) few and (a) little

1. We use few with plural nouns, and little with singular (uncountable) nouns.
Compare:

• Few politicians are really honest.


• I have little interest in politics

2. There is a difference between a few and few, and between a little and little.
Few and little are rather negative: they mean 'not much/many'.
A few and a little are more positive, their meaning is more like 'some'.
Compare:

• His ideas are very difficult, and few people understand them.
  (=not many people,  hardly any people)


• His ideas are difficult, but a few people understand them.
  (=some people- better than nothing)


• I need little water


• Give the roses a little water every day.

3. Few and little (without a) are rather formal. In conversation, we prefer not many, not much, only a few or only a little.

• Only a few people speak a foreign language perfectly.


• Come on! We haven't got much time!

farther and further

1. We use both farther and further to talk about distance.
There is no difference of meaning.

• Edinburgh is farther/further away than York.

2. We  can use further (but not farther) to mean 'extra', 'more advanced', 'additional'

• For further information, see here


• College of Further Education

Far and a long way

Far is most common in questions and negative sentences, and after too and so.

• How far did you walk?


• I don’t live far from here.


• You’ve gone too far.


• ‘Any problems?’’ Not so far’ (=not up to now.)

In affirmative sentences, we usually use a long way.

• We walked a long way. (We walked far is possible, but not usual.)


• She lives a long way from here.

fairly, quite, rather and pretty

1. Fairly modifies adjectives and adverbs. It is not very strong:
if you say that somebody is "fairly nice" or "fairly clever", she will not be very pleased.

• "How was the film?" "Fairly good. Not the best one I've seen this year"


• I speak Greek fairly well - enough for most everyday purposes.

2. Quite is a little stronger than fairly

• " How was the film?" "Quite good. You ought to go"


• He's been in Greece for two years , so he speaks Greek quite well.

Quite can modify verbs

• It was a good party. I quite enjoyed myself.

3. Rather is stronger than quite. It can mean "more than is usual" , "more than was expected" or  "more than is wanted

• "How was the film?" "Rather good- I was surprised"


• Maurice speaks Greek rather well. People often think he's Greek


• I think I'll put the heating on. It's rather cold.

Rather can modify verbs

• I rather like gardening.

4. Pretty is similar to rather. It is only used in informal English

• "How are you feeling?" "Pretty tired. I'm going to bed"

5. Note

1. The exact meaning of these words may depend on the intonation used


2. Quite is not used very much in this way in American English


3. We put quite and rather before a/an

• It was quite a nice day.


• I'm reading rather an interesting book

excuse me, pardon and sorry

1. We usually say excuse me before we interrupt or disturb somebody;
we say sorry after we disturb or trouble somebody.

Compare:

• Excuse me, could I get past?... Oh, sorry, did I step on your foot?


• Excuse me, could you tell me the way to the station?

I beg your pardon is a more formal way of saying sorry.

• I beg your pardon. I'm afraid I didn't realize this was your

2. If we do not hear or understand what people say, we usually say Sorry? What? (informal) or (I beg your) pardon?
Americans also say Pardon me?

• "Mike's on the phone." " Sorry?" I said "Mike's on the phone"


• "See you tomorrow". "What?" I said "See you tomorrow".


• "You're going deaf"." I beg your pardon?"

every and every one

1. We use every before a singular noun

every + singular noun

• I see her every day (NOT... every days)


• Every room is being used

2. We use every one of before a pronoun or determiner (for example the, my, these). The pronoun or noun is plural

every one of us/you/them
every one of + determiner + plural noun

• His books are wonderful. I've read every one of them


• Every one of the plates is broken

3. We can use every one without a noun

• Every one is broken


• I've read every one

4. Every is used with a plural noun in expressions like every three days, every six weeks

• I go to Italy every six weeks

5. Everybody, everyone and everything are used with singular verbs, like every.

• Everybody has gone home (NOT Everybody have...)


• Everything is ready.

each other and one another

1. Each other and one another mean the same.

• Mary and I write to each other/ one another every day


• They sat without looking at each other/one another.

2. There is a possessive each other's/ one another's

• We often borrow each other's clothes.


• They stood looking into one another's eyes

Each other/ one another are not used as subjects

• We must each listen carefully to what the other says
  (NOT we must listen carefully to what each other say.)

3. Note the difference between each other/ one another and
ourselves/yourselves/themselves.

Compare:

• They were looking at each other
  (= Each person was looking at the other)


• They ware looking at themselves
  (= Each person was looking at him or herself)

each and every

1. We use each to talk about two or more people or things.
We use every to talk about three or more (instead of "every two" we say both)

2. We say each when we are thinking of people or things separately, one at a time.
We say every when we are thinking of people or things together, in a group (Every is closer to all)

Compere:

• We want each child to develop in his or her own way


• We want every child to be happy


• Each person in turn went to see the doctor


• He gave every patient the same medicine.

The difference is not always very great, and often both words are possible.

• You look more beautiful each/every time I see you.

during and in

1. We use both during and in to say that something happens inside a particular period of time

• We'll be on holiday during/in August


• I woke up during/in the night

2. We prefer during when we stress that we are talking about the whole of the period

• The shop's closed during the whole of August
  (not in the whole of August)

3. We use during, not in, when we say that something happens between the beginning and end of an activity
(not a period of time)

• He had some  strange experiences during his military service.
  (not in his military service)


• I'll try to phone you during the meeting (not in the meeting)

during and for

During says when something happens
For says how long it takes

Compare

• My father was in hospital during the summer


• My father was in hospital for six weeks (not during six weeks)


• It's rained during the night for two or three hours


• I'll call in and see you for a few minutes during the afternoon

do and make

These words are very similar but there are some differneces

1. We use do when we do not say exactly what activity we are talking about-
for example with something, nothing, anything, everything,what.

• Do something! I like doing nothing


• What shall we do? Then he did a very strange thing

2. We use do when we talk about work and in the structure do -ing

• I'm not going to do any work today. I'm going to do some reading.


• I dislike doing housework. I hate doing the cooking and shopping.


• Would you like to do my job.

3. We often use make to talk about constructing building, building, creating etc

• I've just made a cake. Let's make a plan.


• My father and I once made a boat.

4, Learn these expressions

• do good/ harm/ business/ one's best/ a favour


• make an offer/ arrangements/ suggestion/ a decision/
  an attempt/ an effort/ an excuse/ an exception/ a mistake/
  a noise/ a journey/ a phone call/ money/ a profit/ love/ peace/
  war/ a bed


• .......

EXPONENTS AND RADICALS

1. Multiplying and Dividing Powers

To multiply powers with the same base, add the exponents and keep the same base:

3                 4          3+4               7

b     X     b =    b         =   b

To divide powers with the same base, subtract the exponents and keep the same base:

12          8             12-8               4

b   /     b   =     b        =     b

2. Raising Powers to Powers

To raise a power to a power, multiply the exponents:

3    5         3x5              15

(x   )  =   x      =     x

3. Negative Powers

A number raised to a negative exponent is simply the reciprocal of that number raised to the corresponding positive exponent.

-3

2   = 1 =  1

3       8

2

4. Simplifying Square Roots ________

V

To simplify a square root, factor out the perfect squares under the radical, unsquare them and put the result in front:

__       ____     __         __           ___

V12 = V 4X3 = V 4   X  V 3    = 2 V 3

5. Adding and Subtracting Roots

You can add or subtract radical expressions when the part under the radicals is the same:

__        __       ___

2 V7 + 3 V7 = 5 V7

Don't try to add or subtract when the radicals are different.  You cannot simplify expressions like:          ___             __

2  V 3     +  3  V 5

6. Multiplying and Dividing Roots

The product of square roots is equal to the square root of the product:

__          __       ______       ___

V 2    x  V 3  =  V 2 X  3  =  V 6

The quotient of square roots is equal to the square root of the quotient:

__            ___         ____        ___

V 8    /     V  2     =  V 8/4   =  V 2

AVERAGE, MEDIAN, AND MODE

1. Average or Arithmetic Mean

To find the average of a set of numbers, add them up and divide by the number of numbers.

Sum of the terms

Average                        =         Number of terms

To find the average of the five numbers 12, 15, 23, 40, and 40, first add them:

12 + 15 + 23 + 40 + 40 = 130. Then divide the sum by 5: 130 / 5 = 26.

2. Using the Average to Find the Sum

Sum = (Average) X (Number of terms)

If the average of ten numbers is 60, then they add up to 10 X 60, or 600.

3. Finding a Missing Number

To find a missing number when you're given the average, use the sum.   If the average of four numbers is 7, then the sum of those four numbers is 4  X  7, or 28.   Suppose that three of the numbers are 3, 5, and 8. These three numbers add up to 16 of that 28, which leaves 12 for the fourth number.

4. Median

The median of a set of numbers is the value that falls in the middle of the set. If you have five test scores, and they are 88, 86, 57, 94, and 73, you must first list the scores in increasing or  decreasing order: 57,73, 86, 88, 94.

The median is the middle number, or 86. If there is an even number of values in a set (six test scores, for instance), simply take the average of the two middle numbers.

5. Mode

The mode of a set of numbers is the value that appears most often.   If your test scores were 88, 57, 68, 85,99, 93, 93, 84, and 81, the mode of the scores would be 93 because it appears more often than any other score.  If there is a tie for the most common value in a set, the set has more than one mode.

6. Standard Deviation

Standard Deviation is a complex statistical measure, but for the test you mainly need to know that the it is the measure of how spread out a group of numbers are.  For example, the numbers {0, 10, 20} have a Standard Deviation of about 8.17 while the numbers {9, 10, 11} have a Standard Deviation of about 0.82.   Both have an average of 10, but because the first group was more "spread out" it had a higher Standard Deviation.

RATIOS, PROPORTIONS, AND RATES

1. Setting up a Ratio

To find a ratio, put the number associated with the word of in the nominator and the quantity associated with the word to in the denominator. Then reduce.   The ratio of  15 cakes to 12 candys is 15/12,  which reduces to 5/4.

2. Part-to-Part Ratios and Part-to-Whole Ratios

If the parts add up to the whole, a part-to-part ratio can be turned into two part-to-whole ratios by putting each number in the original ratio over the sum of the numbers.

Example:  If the ratio of cats to dogs is 1 to 5, then the cat-to-whole ratio is 1 / (1 + 5) = 1/6

and the dog-to-whole ratio is 5 / (1 + 5) = 5/6.  In other words, 5/6 of the animals are dogs.

3. Using Ratios to Solve Rate Problems

Example: If snow is falling at the rate of one foot every four hours, how many inches of snow will fall in seven hours?

Setup:

1 foot =       x inches

4 hours                         7 hours

Make the units the same:

12 inches =    x inches

4 hours             7 hours

Solve:

4x= 12 X 7

x= 21

4. Average Rate

Average rate is NOT simply the average of the rates.

Total A

Average A per B =         Total B

Total distance

Average Speed =          Total time

To find the average speed for 120 miles at 40 mph and 120 miles at 60 mph, don't just average the two speeds.   First figure out the total distance and the total time. The total distance is 120 + 120 = 240 miles. The times are two hours for the first leg and three hours for the second leg, or five hours total. The average speed, then, is 240/5 = 48 miles per hour.

5)   Common Formulas for Word Problems:

a)  Distance = Rate x Time

Example:  Two cars leave Miami at the same time traveling in opposite directions.  One car travels at 60 mph and the other travels at 50 mph.  In how many hours will they be 880 miles apart?

Let R1 be the rate of the first car;  let R2 be the rate of the second car

Let T1 be the time of the first car;  let T2 be the time of the second car

The distance the first car travels is R1 x T1 and the distance the second car travels is R2 x T2

R1 T1 + R2 T2 = 880.  We also know that T1 = T2.  Our new equation is:

60T + 50T = 880

T = 8

It will take 8 hours for the cars to be 880 miles apart.

b)  Work = Rate x Time

Example:  If Jasmine can sew a dress alone in 6 days and Amy can sew the same dress in 8 days, how long will it take them to sew the dress if they both work on it?

Let x be the number of hours if they work together.

Jasmine                        Amy                 Together

Hours to sew                             6                                  8                      x

Part done in one day                 1                                  1                      1

1/6  +  1/8  =  1/x

Solving for x, we get 3  3/7 days

c)  Interest = Principal Amount x Rate x Time

Example:  If Michelle has $6,700 in a bank that pays 4% simple interest for three years, how much interest will she earn in three years?  (Assume no compounding).

Interest = Principal Amount x Rate x Time

Interest = (6700)(0.04)(3) = $804

PERCENTS

1. Percent Formula

Part = Percent X Whole

Example: What is 32% of 25?                            Setup: Part = .32  X  25

Example: 15 is 12% of what number?                  Setup: 15 = .12  X  Whole

Example: 25 is what percent of 7?                      Setup: 25 = Percent  X   7

2. Percent Increase and Decrease

To increase a number by a percent, add the percent to 100 percent, convert to a decimal, and

multiply.   To increase 60 by 25 percent, add 25 percent to 100 percent, convert 125 percent to 1.25, and multiply by 60.      1.25 X 60 = 75.

3. Finding the Original Whole

To find the original whole before a percent increase or decrease, set up an equation. Think of

the result of a 17 percent increase over x as 1.17x.

Example: After a 75 percent increase, the population was 5,879. What was the population before the increase.  Setup: 1.07x = 5,879

4. Combined Percent Increase and Decrease

To determine the combined effect of multiple percent increases and/or decreases, start with 100 and then combine.

Example: A price went up 12 percent one year, and the new price went up 24 percent the next year. What was the combined percent increase?

Setup: First year: 100 + (12 percent of 100) =112.

Second year:   112 + (24 percent of 112) = 139.

That's a combined 39 percent increase.

NUMBER PROPERTIES

1. Integers

Integers are whole numbers.. .-4,-3,-2,-1,0, 1,2,3,4,5.......

Positive integers are the numbers 1,2,3,4,5....

Zero is neither positive nor negative.

Negative integers are the numbers -1,-2,-3,-4,-5,-6,-7

Consecutive integers are writeen as x, x+1, x+2,....

Consecutive even or odd integers are written as x, x+2, x+4, x+6,.....

2. Nonintegers

Nonintegers are numbers which have a fractional part.

Examples of nonintegers are t, 3.75, -1/2, 5/6 and pi.

3. Adding/Subtracting Signed Numbers

To add a positive and a negative, first ignore the signs and find the positive difference between the number parts. Then attach the sign of the original number with the larger number part.

For example, to add 41 and -28, first we ignore the minus sign and find the positive difference between 41 and 28,which is 13. Then we attach the sign of the number with the larger number part.  In this case it's the plus sign from the 41.   So, 41 + (-28) = 13.

Make subtractions simpler by turning them into addition. For example, think of

-18 -(-26) as -18 + (+26).

To add or subtract a string of positives and negatives, first turn everything into addition. Then

combine the positives and negatives so that the string is reduced to the sum of a single positive

number and a single negative number.

4. Multiplying/Dividing Signed Numbers

To multiply and/or divide positives and negatives, treat the numbes as usual and attach a minus sign if there were originally an odd number of negatives.

For example, to multiply -2, -4, and -6, first multiply the number parts:

2 X 4 X 6 = 30.   Then go back and note that there were three negatives (an odd number), so the

product is negative: (-2) X (-4) X (-6) = -48.

5. Order of Operations

Perform multiple operations in the following order:

a)  Parentheses

b)  Exponents

c)  Multiplication and Division (left to right)

d)  Addition and Subtraction (left to right)

In the expression 9 -3 X (6 -3) + 6/3 , begin with the parentheses: (6 -3) = 3. Then do the exponent: (3)(3) = 9.   Now the expression is: 9 -3 X 9 + 6/3.   Next do the multiplication and division to get: 9 - 21 + 2, which equals -10.

6. Counting Consecutive Integers

To count consecutive integers, subtract the smallest from the largest and add 1. To count the

integers from 18 through 56, subtract: 56 -18 = 38.   Then add 1: 38 + 1 = 39.

7. Absolute Value

The absolute value of any number is its distance from zero on the number line. The absolute value of a positive number is simply that number. To find the absolute value of a negative number, just drop the negative sign. Absolute value is represented by putting two vertical lines around the number. So the absolute value of 8 = /8/ = 8. The absolute value of -43 = /-43/ = 43. The absolute value of any nonzero number is always positive. The absolute value of 0 is 0.

Basic Mathematic United States Customary Vocabulary

Length

12 inches (in.) = 1 foot (ft)

36 in. = 3 ft= 1 yard (yd)

5280 ft = 1760 yd = 1 mile (mi)

Area

144 square inches (in.2) = 1 square foot (ft2)

9 ft2 = 1 square yard (yd2)= 43,560 ft2

4840 yd2 = 1 acre (A)

Volume

1728 cubic inches (in.3) = 1 cubic foot (ft3)

27 ft3 = 1 cubic yard (yd3)

Liquid Capacity

8 fluid ounces (fl oz) = 1 cup (c)

2 c = 1 pint (pt)

2 pt = 1 quart (qt)

4 qt = 1 gallon (gal)

Weight

16 ounces (oz) = 1 pound (lb)

2000 lb = 1 ton (t)

Temperature

Degrees Fahrenheit (°F)

32°F = freezing point of water

98.6°F = normal body temperature

212°F = boiling point of water

MORE:

1 foot = 12 inches

1 yard = 3 feet

1 quart = 2 pints

1 gallon = 4 quarts

1 pound = 16 ounces

1 inch = 2.54 centimeters

1 liter = 1.06 quarts

1 kilogram = 2.2 pounds

Fluid Ounces	29.57	grams
Ounces (dry)	28.35	grams
Grams	0.0353	ounces
Grams	0.0022	pounds
Kilograms	2.21	pounds
Pounds	453.6	grams
Pounds	0.4536	kilograms
Quarts	0.946	liters
Quarts (dry)	67.2	cubic inches
Quarts (liquid)	57.7	cubic inches
Liters	1.0567	quarts
Gallons	3,785	cubic centimeters
Gallons	3.785	liters

Measuring Liquids

1 dash	6 drops
24 drops	1/4 tsp
3 tsp	1 tbsp
1 tbsp	1/2 fluid ounce
2 tbsp	1 fluid ounce
2 cups	16 fluid ounces (1 pint)
3 tbsp	1.5 fluid ounces (1 jigger)
1/2 cup	4 fluid ounces
16 tbsp	1 cup
1 cup	8 fluid ounces (1/2 pint)
2 pints	1 quart
4 quarts	1 gallon

/ae/ and /a/

cats/cots


ran/Ron

hat/hot

stacking/stocking

Dan/Don

sack/sock

cap/cop

impassable/impossible

Verb Phrase Z

zero in on +	discover, pinpoint	I think I have zeroed in on what has been causing the problem.
zip around +	move quickly from place to place	I zipped around town after work today.
zone out	stop paying attention	He zoned out during class.
zonk out	fall asleep	Jill was so exhausted after taking the TOEFL test that she zonked out before dinner.
zoom in	focus	You need a telephoto lens to zoom in.
zoom in on +	focus on something, pinpoint	She zoomed in on his face while taking the picture.

Verb Phrase Y

yak on	to continue talking in an annoying way ("on" can be repeated for emphasis)	He just yakked on and on and on.
yak on about +	to continue talking in an annoying way about something ("on" can be repeated for emphasis)	She just yakked on and on about her husband's new job.
yammer on	to talk in an annoying way or complain ("on" can be repeated for emphasis)	They yammered on and on and on.
yammer on about +	to talk in an annoying way about something or complain about ("on" can be repeated for emphasis)	He just yammered on and on about how horrible the waiter was.

Verb Phrase V

veer away from +

stay away from, avoid

I veer away from the same old summer blockbuster films.

Verb Phrase U

use * up

use all of something

I used up all of the soap, so we need to buy some more.

Verb Phrase W

wait on +	serve, service (a table)	Each waitress waits on three different tables in the restaurant.
wait up	not sleep because you are waiting for something or someone	Don't wait up.
wait up for +	not sleep because you are waiting for someone or something	Let's wait up for Mary to see how her date went.
wake * up +	awaken someone	The car alarm woke me up at 6:00 in the morning.
wake up	awaken	Wake up. It's time to get ready for work.
wash up	clean oneself	Make sure you wash up before dinner.
wash * up +	clean	If we work together, we can wash the kitchen up in a few minutes.
watch out	be careful	Watch out - there's a rattlesnake!
watch out for +	be careful of	Watch out for snakes while you are hiking in the desert.
wear off	disappear after a period of time	The affects of the medicine will wear off after a few hours.
wear * out	use until something is not useable anymore	If you wear the same shoes everyday, you'll wear them out.
wear * out	cause to be very tired	Her three kids wore me out.
wind up +	finish (inf.)	If he doesn't get his act together, he is going to wind up in jail.
wind * up +	tighten the spring of a watch or similar machine	He wound up the toy dog and set it on the floor.
wind * up +	cause an animal or a child to behave wildly	The kids always get wound up when Uncle Henry comes over.
wipe * out +	massacre or destroy	The tidal wave wiped out the small fishing village.
wipe * out	cause to be very tired	After surfing all day, I was completely wiped out.
work * out +	solve	I hope you two can work out your problems.
work out	exercise	I work out three times a week at the fitness center.
work out	be successful	I am glad your new catering business is working out.
write * down +	record	Write down the directions so you don't forget them.
write * out +	write down every word or letter	He wrote out the lyrics so I could understand what the singer was saying.
write * up +	prepare a report	He wrote up a business proposal in order to get a loan.

Verb Phrase T

take after +	resemble a parent or relative	I take after my father. Who do you take after?
take * away +	remove, seize or capture	The soldiers took the captives away.
take * back +	retract something you said	I demand that you take back what you said.
take * back +	return an item to a store	The dress my grandmother bought for me didn't fit, so I took it back and exchanged it for a pair of pants.
take * down +	write down what is said	Would you mind taking down my messages while I am on vacation?
take * down +	remove (from a high place)	The city government made the shop take down their bright, neon sign.
take * for	consider, view as	Do you take me for an idiot?
take * in +	learning	Are you taking in all of these phrasal verbs?
take * in +	deceive a person	He was taken in by the con artist.
take * in +	make smaller when sewing	I lost weight, so I need to take some of my skirts to the tailor to have them taken in.
take * off	when a plane or rocket leaves the ground	My stomach felt funny when the plane took off.
take * off +	remove	In many cultures, it is appropriate to take off your shoes when entering a house.
take * off +	leave work or school for a period of time	I was sick last week, so I took a few days off of work.
take off	leave	We took off after dinner.
take on +	accept (responsibilities, work)	She has taken on too much responsibility in this project.
take * over +	take control of	Who is going to take over the family business when Aretha's father dies?
take over	take control of	If the President is assassinated, the Vice-president will take over.
take * out +	accompany a person on a date (for dinner, the movies)	I can't meet you tonight because I am taking Fernanda out to dinner.
take * up +	begin a new hobby	Have you taken up any new hobbies since you moved here?
take * up +	discuss (at a later date)	We should take this issue up in the meeting tomorrow.
take * up +	shorten a garment when sewing	This dress is too long, I am going to take it up.
take up +	occupy space	This couch takes up too much space in the living room.
talk back	respond in an impolite way to an adult	Don't talk back!
talk back to +	respond in an impolite way to an adult	Children should not talk back to their parents.
talk * over +	discuss	I hope my parents talk their relationship problems over before they get divorced.
tear * down +	destroy	The county decided to tear down the dilapidated school and build a new one.
tear * up +	tear or rip into small pieces	I always tear up my personal papers before I throw them out.
tell * off +	criticize a person severely, reprimand (inf.)	Carolina told me off when she found out I was gossiping about her date with Martin.
tell on +	report a crime to the police or bad behavior to a parent	Every time I did something wrong when I was a child, my sister would tell on me.
think * over +	consider	Think over the offer before you sign the contract.
think * through +	consider carefully	You need to think this through carefully before you make a decision.
think * up +	create or invent a false story	I need to think up an excuse for not going to her party.
throw * away +	discard	Don't throw away those bottles; we can recycle them.
throw * out +	discard	I asked him not to throw out the Sunday newspaper because I wanted to save an article.
throw * out +	remove by force from (a room, school, a house, etc.)	Mary threw out her roommate because she stopped paying rent.
throw up	vomit	If you drink too much alcohol, you might throw up.
tie * up +	tie securely	When we dock, make sure you tie the boat up.
tire * out	cause someone to be very tired	Speaking English all day tires me out.
touch on +	talk about for a short time	The presidential candidates touched on the subject of health care during the debates.
touch * up	make the final improvements	We didn't paint the whole kitchen, we just touched up the cabinets.
try * on +	put on to make sure a piece of clothing fits	Try on the pants before you buy them.
try * out	test	Try out this massage chair - it feels great!
turn * away	refuse to deal with or give service	They turned us away at the border because we didn't have visas.
turn * around	change or reverse direction	Turn the car around and go back home.
turn * down +	refuse an offer; reject an application	She turned down the new job in New York, because she didn't want to move.
turn * down +	lower the volume or intensity of a TV, radio, or other machine	I'm studying! Please turn down the TV.
turn * in	submit	You need to turn your essays in next week.
turn in	go to bed (inf.)	It's getting late. I think it is about time to turn in.
turn into +	become something different, transform	When she kissed the frog, it turned into a handsome prince.
turn * off +	stop the function of (a stove, a water faucet, a car, etc.)	Don't forget to turn off the iron before you leave the house.
turn on +	attack unexpectedly	The pit bull suddenly turned on the small child.
turn * on	cause to be excited sexually	Scientists have discovered that the smell of cinnamon turns many people on.
turn * on +	start the function of a TV, a radio, a machine	Turn on the TV. The baseball game starts in a few minutes.
turn * out	produce	The weavers can turn out two or three rugs a month.
turn * out	switch off a light	Turn out the light before you go to bed.
turn out	audience members to a function	Over 100,000 people turned out for the concert.
turn out	end up being	She turned out to be the murderer after all.
turn * over	give to authorities (said of evidence or stolen / lost property)	They turned the wallet over to the police.
turn * up +	increase the volume or intensity of a TV, radio, or other machine	Turn up the TV. I can't hear what they're saying.
turn up	find unexpectedly	My keys turned up in the bedroom.

Verb Phrase S

save * up +	accumulate (money)	I hope I will be able to save up enough money to go to school.
see about +	arrange or consider something	My dad said he was going to see about buying me a car.
see * off	say good-bye to someone at the beginning of their trip (at the airport, train station)	Did you see your sister off at the train station?
see to +	make sure something happens, arrange	I'll see to it that Mr. Ramirez gets your message.
see * through	finish something despite difficulties	Are you going to be able to see your studies through now that you have a baby?
sell * out	tell on someone	My partner in crime sold me out for a reduced jail sentence.
set * up	arrange a relationship	My mom set me up with her friend's son.
set * up	falsely incriminate a person	I don't think he killed those men. Somebody set him up.
set up +	arrange (an appointment, a meeting,etc.)	I set up an appointment with my doctor at 3:30 this afternoon.
settle on +	make a decision after a period of time	I settled on the job at the oil company.
settle up	pay one's debts	We need to settle up before you move.
show * off +	show to everybody with a lot of pride	He always shows off his new things.
show off	boast, draw attention to oneself	Young boys show off in order to impress girls.
show * up	make someone seem inferior	He's always trying to show up his co-workers in order to get ahead.
show up	arrive without previous notice	I hadn't seen my cousin for years, and all of a sudden, he showed up at my workplace yesterday!
shut * off	stop from functioning	If you don't pay your electric bill, your power is going to get shut off.
shut * up	make quiet	Would someone shut him up! He's talking so loudly that we're going to get in trouble.
slow * down +	make move more slowly	Because Mary's level in English is lower than the rest of the students, she slows the class down.
slow * up +	make move more slowly	Because Mary's level in English is lower than the rest of the students, she slows the class up.
spell * out +	to explain something in a detailed way so that the meaning is clearly understood	He's so stupid that you have to spell everything our for him.
stand by	wait	I need you to stand by and answer the phone when my broker calls.
stand for +	represent	SCUBA stands for "self contained underwater breathing apparatus."
stand for +	tolerate	I won't stand for people criticizing me.
stand out	be very noticeable	Soledad is so beautiful! She really stands out in a crowd.
stand * up	not arrive to a date or an appointment (inf.)	I arranged to meet Joe at the library at 8:00, but he stood me up. I hope he has a good excuse.
stand up for +	defend (something one believes in)	Every individual must stand up for what they believe in.
stand up to +	defend oneself against someone or something	I think you should stand up to your older brother and tell him to stop pushing you around.
stay over	spend the night at a person's house	It takes you so long to take the bus home, so why don't you just stay over?
stick it to +	severely criticize a person (inf.)	My boss really stuck it to me when I arrived late to work for the third time this week.
stick to +	persevere, keep trying	Even though English is a hard language to master, you must stick to it!
stick up for +	defend oneself or opinions	Joseph joined the army because he believes he must stick up for his country.

Verb Phrase R

read up on +	research a topic for a reason	I need to read up on the company before I go on the job interview.
ring * up	telephone	Jack rung me up last night at 3:00 in the morning.
rule * out +	eliminate	I wouldn't rule out the possibility of moving to another country if I get a good job offer.
run across +	find or meet unexpectedly	I ran across some old photos while I was cleaning my house.
run against +	compete in an election	Gore ran against Bush in the 2000 elections in the U.S.A.
run away	leave home permanently before you are a legal adult	The child ran away because her parents beat her.
run away from +	escape from	The child ran away from its parents.
run * down	trace	Have you run down those phone numbers I asked for last week?
run * down	criticize	My boss runs everyone down.
run * down	hit with a car	My dog was run down by a bus.
run down	loose power, be very tired	You need to wind your watch so it doesn't run down.
run for +	campaign for a government position	Gore is running for president of the U.S.A.
run into +	meet unexpectedly	I ran into my English teacher at the movies last night. She's so nice!
run * off +	make leave	The new government is trying to run the drug traffickers off.
run * off	reproduce (photocopies)	Would you mind running off 10 copies of this document for me?
run off	leave quickly	Why did you run off after the party?
run off	waste water	You shouldn't swim where the sewage runs off into the ocean.
run out of +	not have any more of something	We ran out of milk this morning, so we need to go to the store.

Verb Phrase Q

quiet * down +

be quiet, or cause to be quiet

The neighbors told us to quiet down last night or they would call the police.

Verb Phrase P

pan out	be successful, turn out well	The trip to Vegas didn't pan out.
pass away	die	After battling cancer for several years, he finally passed away at the age of 87.
pass * off +	try to convince someone that something is real	He tried to pass the fake watch off as a real Rolex.
pass * on +	transmit	Please pass this message on to your co-workers.
pass on +	not accept (an invitation to eat or do something)	Jennifer passed on the invitation to join us for dinner.
pass on	die	I am afraid Professor Johnson has passed on.
pass * out +	distribute	We need to pass out these flyers for the concert tomorrow.
pass out	become unconscious	He passed out because the room was too hot.
pass * up +	not take advantage (of an opportunity)	I can't believe she passed up the opportunity to study in Rome.
pay * back +	repay	If I loan you money, will you pay me back.
pay * off +	complete payment on a debt	It took me ten years to pay off my credit card debt.
pay * off +	to bribe	Don't try to pay the police officer off if you get pulled over for speeding.
pick on +	to tease, bully	She keeps picking on me! Make her stop.
pick * out +	choose	Diane picked out a lovely dress for the dance.
pick * up +	to lift an object with the hands	Keep your back straight when you lift the TV up.
pick * up +	come and get someone in a car	What time are you going to pick me up.
pick * up +	learn something without effort	It's possible to pick up enough English in two weeks to get by on your trip to Los Angeles.
pick * up +	try to initiate a relationship with someone (often in a bar)	Some weird guy tried to pick Patricia up at the bar.
pick up	grow, increase (inf.)	Business is really picking up this quarter.
play * down +	make less important (inf.)	The President played down his affair with the intern.
play * up	highlight something (inf.)	She played up her part in the new movie, but it was actually a very small role.
play up to +	flatter someone for your personal advantage	She has been playing up to the boss because she wants a promotion.
point * out +	indicate	I'd like to point out that figures in column two might be outdated.
pull down	earn	He pulls down about $300,000 a year.
pull in	park (a vehicle)	Mark pulled in too quickly and crashed into the wall.
pull out	depart (a vehicle)	Our train pulls out at 8:00, so don't be late.
pull through	barely survive	I didn't think she was going to make it, but she pulled through in the end.
put * across +	communicate (an idea or suggestion) clearly so that it is understood	I thought Ms. Smith put her ideas across rather clearly in the meeting.
put * away +	return to the proper place of storage	I told you kids to put your toys away.
put * down +	insult, say bad things about	She always puts down people who don't share her opinions.
put in +	officially submit a request (in the armed forces or public services)	He put in for a transfer to the division in Los Angeles.
put * off +	postpone	Don't put off your work - do it now!
put * on +	wear	Make sure you put on a sweater before you go outside.
put * on +	deceive	I didn't believe a thing he said. I think he was putting me on.
put * out +	extinguish (a fire)	Don't use water to put out a grease fire.
put * out +	inconvenience someone	I don't want to put you out, but could you pick me up at the airport.
put out +	spend (usually used with unreasonably large sums of money)	I can't put out that much money each month.
put * up	have a guest stay in your house for a short time	Can you put me up while I'm in town.
put up with +	tolerate	Sandy will not put up with smoking in her house.

Verb Phrase O

occur to +	pop into one's mind, come to one's mind	It didn't occur to us that we had left the iron on.
open up	share feelings	I'm  glad that John feels comfortable enough around me to open up.
out to + verb	try to	She is out to get revenge now that her husband left her for another woman.

Verb Phrase N

name * after +	name a child using another family member's name	I was named after my grandfather.
nod off	fall asleep	The movie was so boring that I nodded off before it was finished.
nose around +	sneak around	I hate it when my mother noses around my room.

Verb Phrase M

make * out	decipher	I can't make out your handwriting. What does this say?
make * out +	write a check or other document	Who should I make this check out to?
make out	succeed	He really made out in the stock market last year.
make out	progress	How is your son making out in his new job?
make out	kiss passionately	I saw Benno and Isabelle making out in the movie theater last night!
make out with +	kiss someone passionately	Did you make out with Sally?
make * over	do again	The teacher made me do my homework over.
make * up +	invent ( a story)	Don't believe anything she says. She always makes things up.
make * up +	complete what was missed	Fortunately, my professor let me make up the exam I missed yesterday.
make * up +	put on cosmetics	I takes me 10 minutes to make my face up.
make up	reconcile	You two have been friends for so long that I think you should make up.
make up for +	compensate for	Allen made up for being late by getting me flowers.
mix * up +	confuse	I sometimes mix the verb tenses up.
mix * up +	blend	We need to mix up these different kinds of nuts before we put them in a bowl.
mix * up +	make lively (a party)	Let's mix up this party with a little disco music.

Verb Phrase L

lay  away +	save for the future	Why don't you lay away your wedding outfit?
lay down +	establish (laws, rules)	Lori lays down the law in her class. English only!
lay in on +	scold or criticize severely	My mom really laid in on me when I got home at 4:00 in the morning last night.
lay into +	scold or criticize severely	I saw Reto's mom lay into him when he came home late last night.
lay * off +	suspend someone from a job (during a slow period)	The company was losing money, so they had to lay off 100 workers.
lay * out +	arrange	Why don't we lay the pieces of the table out before we put it together.
leave * out +	not include, omit	Why did your parents leave you out of their vacation plans?
let * down	disappoint	I felt let down when I didn't receive a birthday card from my sister.
let * down	lengthen (pants in sewing)	My uncle is a tailor, so he can let your pants down.
let * out	release	I am happy my brother was let out of prison early.
let * out	make bigger (in sewing)	I need to let out this skirt because I have gained weight.
let up	weaken in intensity	I told her NO a thousand times, but she won't let up.
lie down	rest, recline	I need to lie down before we go out tonight.
lie down on +	rest, recline ( on a couch, bed)	I'm going to lie down on the sofa for a while.
lie with +	be decided by	Whether or not you can go to the party lies with your father.
light * up +	illuminate	Let's get some candles to light this room up.
light up +	to smoke	Do you have to light up another cigarette? I thought you were trying to cut down.
live * down +	live in a way that a shameful or embarrassing event is forgotten	Jose will never live down singing that song at the karaoke bar.
live on +	survive from	I could live on bread and cheese.
live up to +	keep a standard	It would be hard to live up to her parent's expectations.  They are so demanding.
look after +	take care of (a child, a house, a pet)	When my sister goes on vacation, I look after her dog.
look back on +	to remember nostalgically	When I look back on my childhood, I often feel angry.
look down on +	see as inferior	She's so conceited. She looks down on everybody else.
look for +	to seek or search for	I'm looking for my keys. Have you seen them?
look forward to +	anticipate with pleasure	I am looking forward to traveling to New York next year.
look into +	investigate	The police are looking into the murder.
look on	observe as a spectator	Everybody just looked on as the two men fought.
look out	be careful, pay attention, heed a certain danger	Look out, there's a black widow spider on the wall.
look * over +	examine, review	When I'm camping, I look my shoes over before I put them on.
look * up +	search for (in a dictionary)	I takes time to look up new vocabulary words.
look * up +	locate and visit	If you ever travel to California, you should look me up.
look up to +	respect, admire someone	He looks up to his father.

Verb Phrase K

keep * around	have handy, have accessible	I always keep a dictionary around to translate new words.
keep at +	not give up (an activity), to persevere	You should keep at your studies.
keep * away	prevent access to, hold back	Keep the kids away from the cookies.
keep * back	maintain a safe distance, cause to maintain a safe distance	Keep back! The burning building is about to collapse.
keep * down	not vomit, not throw up, keep in one's stomach	If I ate that, I down know if I could keep it down.
keep * in	keep in a particular place, have something in a specific location	When I am not using it, I keep my passport in this drawer.
keep * off	prevent from stepping or climbing on to something	Keep the cat off the couch.
keep on	continue	He kept on talking after everybody asked him to stop.
keep * out	prevent from entering	Keep the dog out of the garden; he keeps digging up the flowers.
keep * over	cover something with, put something above	I keep a tarp over my bicycle at night to prevent it from getting wet.
keep to +	continue, persist in (an activity)	Everybody said she would never finish the puzzle, but she kept to it until it was done.
keep up	stay on the required schedule	You have to keep up if you want to work here.
keep * up +	continue	You are doing a great job! Keep it up.
keep up with +	stay on schedule with (a person, the workload, homework)	I have so much reading that I can't keep up with the writing exercises.
kick back	sit or lie back (to relax)	After work, I like to kick back in front of the TV and relax.
kick in	begin taking effect	The medicine takes one hour to kick in.