2003 AIME II problem 5 minor correction | Math for fun and glory | Khan Academy
A1 A2 B1 B2 C1 C2
anyway
US / ˈeniweɪ /
•UK / ˈɛniˌwe /
- adverb
- A word used to change the topic of a conversation
shade
US / ʃeɪd /
•UK / ʃed /
- noun
- Area of darkness when something blocks the light
- Something that blocks or reduces light
- Color that is a little darker or brighter than
- verb
- To shelter something from direct light
- To change the truth to deceive or influence
- To make one part of a picture darker or lighter
just
US / dʒʌst /
•UK / dʒʌst /
- adjecitve
- Proper or appropriate; as is deserved
- Doing or being what is right or fair
- Legally correct; having enough evidence
- adverb
- Almost; nearly
- Exactly at the time of
- Exactly (the same as, like)
perpendicular
US / ˌpɜ:pənˈdɪkjələ(r) /
•UK / ˌpə:pənˈdɪkjəlɚ /
- adjecitve
- Being at right angles to a given line or plane
clarify
US / 'klærəfaɪ /
•UK / ˈklærəˌfaɪ /
- verb
- To make a liquid become clear or pure
- To state again so that a point is clearer
for
US / fə(r) /
•UK / fɔr,fə /
- preposition
- Used to show the purpose, or need of something
height
US / haɪt /
•UK / haɪt /
- noun
- Distance of something from the bottom to the top
trick
US / trɪk /
•UK / trɪk /
- adjecitve
- Not reliable; likely to deceive you
- noun
- Act of trying to fool someone
- Quick or skillful way of doing something
- Something done to make someone laugh
- verb
- To fool someone in order to obtain a result
- To playfully tease or fool to make someone laugh
where
US / hwɛə /
•UK / hwɛr, wɛr /
- conjunction
- At or in the place which
- In whatever place
- pronoun
- Word you use to ask the location of something
theta
US / ˈθi:tə /
•UK / ˈθetə, ˈθi- /
- noun
- 8th letter of the Greek alphabet
call
US / kɔ:l /
•UK / kɔl /
- noun
- A order or request for action
- The sound an animal makes, often when in danger
- A correct prediction, e.g. a decision in a game
- A short visit to a place or person
- A decision by a referee or umpire in a game
- verb
- To make a request or order for action
- (Animal) to make sounds to warn of danger
- To announce the date of an election
- To make a judgment about something
- To give someone or something a name
- To guess in advance the result or outcome
- To visit a place or person for a short time
- To phone someone
- To speak, announce or shout in a loud voice
version
US / ˈvə:ʃən /
•UK / ˈvɚʒən, -ʃən /
- noun
- Different way that someone interprets something
- New or different form of something
- An updated form of some software
stack
US / stæk /
•UK / stæk /
- noun
- A large number or amount of something
- Large tube through which smoke exits a building
- verb
- To arrange cards in a certain order, to cheat
- To put one thing on top of another, e.g. boxes
incorrect
US / ˌɪnkəˈrekt /
•UK / ˌɪnkəˈrɛkt /
- adjecitve
- Being wrong or inaccurate
hopefully
US / ˈhəʊpfəli /
•UK / ˈhopfəli /
- adverb
- In a manner wishing something to happen
and
US / ənd /
•UK / ənd, ən,ænd /
- conjunction
- Used to refer to two or more things
- Plus; in addition; on top of that
- Used to introduce an action that follows another
hey
US / heɪ /
•UK / he /
- exclamation
- What you say when you want someone's attention
another
US / əˈnʌðə(r) /
•UK / əˈnʌðɚ /
- adjecitve
- One more, but not this
- determiner
- One more added
- pronoun
- One more (thing)
over
US / 'əʊvə(r) /
•UK / ˈovɚ /
- adverb
- Finished; no longer happening
- Towards the ground/away from a standing position
- noun
- A set of six consecutive balls bowled in cricket
- other
- Finished
- preposition
- Showing the relation when a thing is above another
- On or covering something
- Above or across something
- More than you need
- From one side to the other
- In the direction of; toward
out
US / aʊt /
•UK / aʊt /
- adverb
- No longer stylish (e.g. fashion)
- Away from home, business, or the usual place
- In a direction/movement away from inside or center
- noun
- Act when a batter cannot continue playing
- verb
- To tell people a secret
minus
US / ˈmaɪnəs /
•UK / ˈmaɪnəs /
- adjecitve
- Being close to the bottom of a letter grade
- noun
- Negative quality; disadvantage
- Sign that indicates subtraction
- preposition
- Being less than zero in number
- Used when subtracting one number from another
- verb
- To take one number away from another; subtract
along
US / əˈlɒŋ /
•UK / əˈlɔ:ŋ /
- adverb
- As a companion; taken with someone
- preposition
- At a point on a line
anything
US / ˈeniθɪŋ /
•UK / ˈɛniˌθɪŋ /
- pronoun
- A thing of any kind
aim
US / eɪm /
•UK / em /
- noun
- Act of pointing something at a target
- Purpose or goal
- verb
- To point something at a target
- To intend to get a thing or for a thing to happen
obviously
US / ˈɒbviəsli /
•UK / ˈɑːbviəsli /
- adverb
- In a way that is obvious/easy to see or understand
matter
US / 'mætə(r) /
•UK / ˈmætɚ /
- noun
- Material all things are made of that fills space
- Problem or reason for concern
- verb
- To be of great importance; to count
ourselves
US / ɑ:ˈselvz /
•UK / aʊrˈsɛlvz, ɑr- /
- pronoun
- (Showing speaker is affected by their own action)
actually
US / ˈæktʃuəli /
•UK / ˈæktʃuəli /
- adverb
- Used to add new (often different) information
quick
US / kwɪk /
•UK / kwɪk /
- adjecitve
- Using very little time; moving far in little time
- Learning and understanding rapidly and easily
here
US / hɪə(r) /
•UK / hɪr /
- adverb
- In this place; at this location, position or time
axis
US / ˈæksɪs /
•UK / ˈæksɪs /
- noun
- A line about which a rotating body turns
side
US / saɪd /
•UK / saɪd /
- adjecitve
- In addition to the central or most important thing
- Next to, or very close to, the right or left of
- noun
- Position or opinion that is opposite to another
- Right or left part of a person's body
- Feature of someone's personality
- Straight edge of an object
- One of two or more groups fighting each other
- verb
- To decide to agree with one point, not the other
plus
US / plʌs /
•UK / plʌs /
- noun
- A benefit or advantage
- preposition
- In addition; add
- In addition to; Indicates a number above
- Having a value greater than zero
take
US / teɪk /
•UK / tek /
- noun
- Filming of a single scene for TV or the movies
- verb
- To accept something that is offered
- To use a method of traveling, e.g. a bus or train
- To use a camera to make (a photo)
- To pick up something and go away with it
- To study a subject in school
- To attempt to pass (an exam)
- To require a certain amount of time, money, space
add
US / æd /
•UK / æd /
- verb
- To include as well
- To put two things or numbers together, e.g. 2+2
log
US / lɒg /
•UK / lɔ:g /
- noun
- Detailed account of events and progress on journey
- Piece of a tree that has fallen or been cut
- verb
- To move a certain distance or speed, as recorded
- To leave a website or computer account
- To record something in an official account
- To cut trees down and take the wood to use it
clearly
US / ˈklɪəlɪ /
•UK / ˈklɪrlɪ /
- adverb
- In a way that is easy to understand; obviously
look
US / lʊk /
•UK / lʊk /
- noun
- Person's beauty or physical attractiveness
- Particular style of dress, clothes, or appearance
- The way someone, something appears to be
- Act of searching for or examining something
- verb
- To appear to be; seem
show
US / ʃəʊ /
•UK / ʃo /
- noun
- False display of love, emotion or action
- An event for displaying or promoting goods
- Play, opera or theater production
- Presentation that is broadcast on TV or radio
- verb
- To be easily seen or displayed
- To display your emotions or feelings
- To let someone see something; display
- To explain or teach how something is done
- To lead someone somewhere; point them to something
- To prove something to be true, correct
- To reveal or allow something to be seen
way
US / weɪ /
•UK / we /
- adverb
- Used to emphasize the amount of something
- noun
- Particular aspect of something being thought about
- One of various choices that could be made
- Particular existing condition or state
- (Often long) distance or length of time
- How something is done
- Route to go to a place
- Small street
- Usual behavior, emotions or habits of someone
figure
US / ˈfiɡə /
•UK / ˈfɪɡjɚ /
- noun
- Your body shape
- Numbers in a calculation
- Doll-like thing meant to represent a person
- Picture or diagram giving information in a text
- Person who is very important or famous
- Shape of a person seen indistinctly or in outline
- Amount that is expressed in numbers
- verb
- To appear in a game, play or event
- To calculate how much something will cost
- To understand after thinking; work out
work
US / wɜ:k /
•UK / wɚk /
- adjecitve
- Activity completed in order to make money
- noun
- The product of some artistic or literary endeavor
- Everything created by an author, artist, musician
- Activity you do in order to make money
- Place of employment
- Final product or result of a some labor or effort
- verb
- To bring into a specific state of success
- To be functioning properly, e.g. a car
- To do your job in your company or workplace
- To make an effort to do something
- To operate a machine or device
top
US / tɒp /
•UK / tɑp /
- adjecitve
- Being good or great; excellent
- Being the most in degree or quality
- noun
- Item of clothing covering shoulders to waist, hips
- A cover or lid
- Part (e.g. road) that is the furthest away
- Highest or upper part or point of something
- Best or highest status or position
- Flat upper surface or edge of an object
- Child's toy that spins on its point
- Upper section or leaves of fruits and vegetables
- Winning in a sport or contest
- verb
- To be higher or larger than a specific value
- To arrive at the highest point of something
- To put a cover or layer or over something
- To kill; murder
- To hold the highest position on a list
- To be more important, successful or better than
- To beat someone or win at a game
apologize
US / ə'pɒlədʒaɪz /
•UK / əˈpɑləˌdʒaɪz /
- verb
- To say sorry because of a mistake or injury
very
US / 'verɪ /
•UK / ˈvɛri /
- adjecitve
- Concerning a large degree or amount
- adverb
- A lot; much; many
- Used to stress or emphasize a noun
volume
US / ˈvɒlju:m /
•UK / ˈvɑljum, -jəm /
- noun
- Number or amount of something e.g. sales
- Amount of space that something takes up
- One book that is part of a set of books
- Level of sound produced by radio or television
they
US / ðeɪ /
•UK / ðe /
- pronoun
- Two or more people, animals, or things
incorrectly
US / ˌɪnkə'rektlɪ /
•UK / ˌɪnkə'rektlɪ /
- adverb
- In a way that is incorrect or wrong
cylinder
US / ˈsɪlɪndə(r) /
•UK / ˈsɪləndɚ /
- noun
- Tube shape with flat ends
solve
US / sɒlv /
•UK / sɑ:lv /
- verb
- To figure out a way to handle a difficult problem
right
US / raɪt /
•UK / raɪt /
- adjecitve
- Correct or true
- The south side of you looking at the rising sun
- adverb
- Exactly in a place or time
- Being appropriate for a particular event
- In a straight or direct manner
- noun
- Something you are legally or morally allowed to do
- Ideal of what is just and good
- Political view based on conservatism
- verb
- To fix something previously wrong or unjust
- To make upright, as a boat that has turned over
then
US / ðen /
•UK / ðɛn /
- adverb
- A time that is not now
- Following another thing in time or arrangement
- Following on reasonably from what was just stated
- At that time, not now
remind
US / rɪ'maɪnd /
•UK / rɪˈmaɪnd /
- verb
- To cause someone to remember what they forgot
what
US / wɒt /
•UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /
- pronoun
- Thing or things that; the same kind as
- Used to emphasize something you are about to say
- adjecitve
- Used to refer to a particular amount, or number
- Used to place emphasis on a particular quality
- adverb
- To a certain degree
- determiner
- Question words used for asking for information
- exclamation
- Used to express excitement, shock, or surprise
- Used to ask people to repeat something they said
that
US / ðæt /
•UK / ðæt, ðət /
- adjecitve
- The person or thing being talked about
- Used to identify something both the speakers know
- adverb
- Used to reinforce adjectives and adverbs
- To such a degree
- conjunction
- Used to connect a noun clause
- Used to introduce an adverbial clause
- Used to introduce a noun clause
- determiner
- Used as a noun to refer to something
- pronoun
- Referring an object far away
- Used to refer to the relative pronoun ‘which’
like
US / laɪk /
•UK / laɪk /
- adjecitve
- Being equal in status or kind to something else
- Similar; the same
- adverb
- For example
- preposition
- Used as a filler; used to ad emphasis
- In a way similar to the way something is done
- Such as; for example
- verb
- To want to
- To find something pleasing; to prefer something
end
US / end /
•UK / ɛnd /
- noun
- The point where a process or activity stops
- A point that marks the limit of something; finish
- Goal or desired result
- The tip, edge or limit of something
- verb
- To be the last part of something
see
US / si: /
•UK / si /
- verb
- To go on a date with someone
- To predict whether something is, or will be true
- To understand what someone says
- To use your eyes to look at something
- To visit a place often for sightseeing or pleasure
- To visit or meet with someone
- To find out by waiting or looking
- To watch (a game, movie or TV show)
misspeak
US / ˌmɪs'spi:k /
•UK / mɪs'spi:k /
- intransitive verb
- Express oneself insufficiently clearly or accurately.
properly
US / ˈprɔpəlɪ /
•UK / ˈprɑːpərli /
- adverb
- In an appropriate or correct manner
know
US / nəʊ /
•UK / noʊ /
- verb
- To be familiar with a person or place, thing
- To feel sure or be convinced about something
- To discover or be aware of something
- To be able to distinguish
- To have knowledge of things
could
US / kəd /
•UK / kʊd /
- other
- Past form of 'can' to mean have ability
- Used to ask for something politely, or to offer
last
US / lɑ:st /
•UK / læst /
- adjecitve
- Most recent; the latest
- The one before
- adverb
- Final; with nothing following; after all others
- Most recent; the latest
- determiner
- The one at the end
- verb
- To remain or continue for a certain period of time
have
US / həv /
•UK / hæv /
- verb
- To drink, smoke, eat or use something
- To experience the effects of something
- To organize an event, or join in an activity
- To own, possess, or hold something
- To cause to happen or produce a particular effect
draw
US / drɔ: /
•UK / drɔ /
- noun
- Something that attracts people to visit a place
- A lottery or prize
- Result of a game, contest where the score is equal
- verb
- To attract attention to someone or something
- To get closer to or approach something or someone
- To influence a person's involvement in something
- To move an object by pulling
- To create an image using pen or pencil and paper
- To take one thing out of a container, etc.
- (Of 2 teams) to finish a game with the same score
problem
US / ˈprɒbləm /
•UK / ˈprɑbləm /
- adjecitve
- Causing trouble
- noun
- Something difficult to deal with or causes trouble
- Question to show understanding of a math concept
cut
US / kʌt /
•UK / kʌt /
- noun
- Act/instance of reducing the size or amount of
- Small opening made using a sharp object, knife
- A wound on someone's skin caused by a sharp object
- verb
- To reduce the size or amount of something
- To use knife or scissors to divide, open surfaces
but
US / bət /
•UK / bʌt,bət /
- conjunction
- Used before you say something different, opposite
video
US / 'vɪdɪəʊ /
•UK / ˈvɪdiˌo /
- adjecitve
- Of a moving film, with sound
- noun
- Recording capturing action with sound
- verb
- To make a moving film of, with sound
want
US / wɔnt /
•UK / wɑnt, wɔnt /
- noun
- Something you desire or wish for
- State or condition of poverty
- verb
- To desire or wish for something; hope for a thing
would
US / wʊd /
•UK / wʊd /
- other
- Used to indicate something imagined
- Used to ask or request something politely
- Verb used to indicate possibility, request etc.
- Used to indicate a preference
- Used to indicate a reaction
- Indicates something that occurred repeatedly
- Used to indicate willingness or ability to do
can
US / kæn /
•UK / kən,kæn /
- noun
- A metal container for storing food
- other
- Able to; have the skill to; have the time to
- verb
- To have permission to
- To be possible to do
- To preserve food by sealing it in a metal container
now
US / naʊ /
•UK / naʊ /
- adverb
- At the present time or moment
- Right away or in the next possible moment
- Used to refer to something that just happened
- Time between the present and a moment in the past
- conjunction
- Resulting from or because of something
angle
US / ˈæŋgl /
•UK / ˈæŋɡəl /
- noun
- Place where two lines or surfaces meet
reasonable
US / ˈri:znəbl /
•UK / ˈrizənəbəl /
- adjecitve
- Being somewhat good, but not great
- Fair and sensible; appropriate
not
US / nɒt /
•UK / nɑt /
- adverb
- Word indicating the negative
- (Used to form the negative of verbs)
visualize
US / ˈvɪʒuəlaɪz /
•UK / ˈvɪʒuəˌlaɪz /
- verb
- To create a picture in your mind of something
round
US / raʊnd /
•UK / raʊnd /
- adjecitve
- Being in the shape of a circle or ball
- Consisting of curved and not straight lines
- Somewhat fat or curved in physical appearance
- Being a whole number, not a fraction, decimal
- adverb
- From beginning to end (e.g. of the year)
- noun
- One of the three-minute periods in boxing
- Drinks bought by one person for a group
- Series regular visits, routes, or stops at places
- Single shot or bullet fired from a gun
- An object with a circular shape
- One stage in a series of games, e.g. football
- One's turn in a game such as cards
- preposition
- Going around
- verb
- To cause or make a circular or curved shape
- To go or pass around the bend or corner
- To change from a fraction to nearest whole number
same
US / seɪm /
•UK / sem /
- adjecitve
- Being equal in quality and amount
- Identical; not different
- Not changing; constant
make
US / meɪk /
•UK / mek /
- noun
- Product made by a particular company; brand
- verb
- To arrange or prepare something e.g. dinner
- To get to (a place) on time
- To gain the status of (teacher, lawyer, etc.)
- To create something by putting things together
- To earn a certain amount of money at a job
- To cause or force a person to do something
- To cause something to happen or be formed
than
US / ðən /
•UK / ðən /
- conjunction
- Used to compare two things that are not equal
one
US / wʌn /
•UK / wʌn /
- pronoun
- You; we; people in general; someone
- The thing or person previously referred to
- adjecitve
- Used to refer to people generally
- Being a strong example of (something mentioned)
- number
- Number 1
lucky
US / 'lʌkɪ /
•UK / ˈlʌki /
- adjecitve
- Fortunate; having good things happen by chance
you
US / jʊ /
•UK / ju /
- pronoun
- Person someone is speaking or writing to
- Person or people in general
kind
US / kaɪnd /
•UK / kaɪnd /
- adjecitve
- In a caring and helpful manner
- friendly and considerate
- noun
- One type of thing
also
US / 'ɔ:lsəʊ /
•UK / ˈɔlso /
- adverb
- In addition; too; in a similar way
this
US / ðɪs /
•UK / ðɪs /
- adjecitve
- Used to indicate something already been discussed
- Used to indicate something happening around now
- adverb
- An indication by a physical motion or gesture
- A specific amount of
- determiner
- Person, thing, or idea near you
- pronoun
- Person, thing that has already been discussed
flip
US / flɪp /
•UK / flɪp /
- noun
- Act of turning your body in the air; somersault
- Movement of something from one position to another
- verb
- To turn your body in the air, as in gymnastics
- To move into a different position quickly
- To move a button or switch to turn on or off
visualization
US / ˌvɪʒʊəlaɪ'zeɪʃn /
•UK / ˌvɪʒʊəlɪˈzeʃən /
- noun
- Act of creating an image in your mind
the
US / ðə /
•UK / ðə /
- article
- Used to refer to something already mentioned
- Used to show there is only one of something
- determiner
- Used to describe all of a family
let
US / let /
•UK / lɛt /
- verb
- To allow someone to do something
- Introducing a suggestion to do something together
- To rent a house, etc. to others
big
US / bɪɡ /
•UK / bɪɡ /
- adjecitve
- Popular
- Serious
- Large
solution
US / səˈlu:ʃn /
•UK / səˈluʃən /
- noun
- Mix of a liquid and a solid or a gas
- Way to solve or deal with a problem
less
US / les /
•UK / lɛs /
- adjecitve
- Smaller in amount or degree
- adverb
- To a smaller degree
- noun
- A smaller amount
- preposition
- With the subtraction of