a bit longer
US
UK
- Phrase
- For a slightly longer period of time.
- Slightly more extended in length.
A1Moreanti
US /ˈæntaɪ, -ti/
UK /'æntɪ/
- Adjective
- A prefix meaning 'against' or 'opposed'
B2Moreassume
US /əˈsum/
UK /ə'sju:m/
- Transitive Verb
- To act in a false manner to mislead others
- To believe, based on the evidence; suppose
A2TOEICMoreat least
US /æt list/
UK /æt li:st/
- Adverb
- As a minimum
- Not less than
- Phrase
- No less than; at the minimum
- Used to indicate that something is positive in a bad situation.
C2Moreat some point
US /æt sʌm pɔɪnt/
UK /æt sʌm pɔint/
- Phrase
- At an unspecified time, usually in the future.
A1Moreaverage
US /ˈævərɪdʒ, ˈævrɪdʒ/
UK /'ævərɪdʒ/
- Noun (Countable/Uncountable)
- Total of numbers divided by the number of items
- Transitive Verb
- To add numbers then divide by the number of items
A2TOEICMoreaxis
US /ˈæksɪs/
UK /ˈæksɪs/
- Noun
- A line about which a rotating body turns
B1Morebased on
US
UK
- Phrasal Verb
- To use something as the foundation or starting point for something else.
- Preposition
- Using something as the main idea or foundation.
- Relying on something as evidence or justification.
A1Morebow to
US /bo tu/
UK /bəu tu:/
- Phrasal Verb
- To bend the head or body as a sign of respect or greeting.
- To give in or submit to something, often unwillingly.
B2Morebuild on
US /bɪld ɑn/
UK /bild ɔn/
- Phrasal Verb
- To develop or expand something; to use something as a foundation for further progress.
- To use something as a base or foundation for further development or success.
A2Morecalculate
US /ˈkælkjəˌlet/
UK /'kælkjʊleɪt/
- Transitive Verb
- To find an answer using mathematics
- To make an educated guess about something
B2Morecalculus
US /ˈkælkjələs/
UK /ˈkælkjələs/
- Uncountable Noun
- Branch of math dealing with rates of change, etc.
C1Morechop
US /tʃɑp/
UK /tʃɒp/
- Verb (Transitive/Intransitive)
- To cut into pieces with an up and down motion
- To hit someone with your hand
- Noun (Countable/Uncountable)
- A hit with the hand in a sideways motion
- Thick slice of meat still attached to a bone
B1Morechop up
US
UK
- Phrasal Verb
- To cut something into small pieces.
- To sample and rearrange a piece of music.
B2Moreclaim
US /klem/
UK /kleɪm/
- Noun (Countable/Uncountable)
- To say that something is true, often without proof.
- A statement that something is true.
- Transitive Verb
- To demand or ask for something that you believe is rightfully yours.
- To take or cause the loss of (e.g., a life, property).
A2Morecompound
US /kɑmˈpaUnd/
UK /'kɒmpaʊnd/
- Noun (Countable/Uncountable)
- Series of buildings that are walled or fenced off
- Chemical made up of several others
- Transitive Verb
- To pay interest on a loan including the interest
- To make something from various parts or components
B1Moreconception
US /kənˈsɛpʃən/
UK /kənˈsepʃn/
- Noun
- Moment when a woman's pregnancy begins
- Idea about something, or how it should be
B1Moreconstant
US /ˈkɑnstənt/
UK /'kɒnstənt/
- Adjective
- Happening frequently or without pause
- Remaining the same over time or not changing.
- Noun
- Thing that happens always or at a regular rate
- A physical quantity that is believed to have a fixed value and is used in calculations.
A2TOEICMorecourt
US /kɔrt, kort/
UK /kɔ:t/
- Transitive Verb
- To act in a way to shows you wish to marry someone
- To encourage dangerous behavior
- Noun
- Place king or queen meet people, makes laws etc.
- Place where legal cases are decided
A2TOEICMoredatum
US /ˈdetəm, ˈdætəm, ˈdɑtəm/
UK /ˈdeɪtəm/
- Noun
- Item of factual information
B1Moredefender
US /dɪˈfɛndɚ/
UK /dɪˈfendə(r)/
- Countable Noun
- Fighter who fights against attack
B1Moredifferential
US /ˌdɪfəˈrɛnʃəl/
UK /ˌdɪfəˈrenʃl/
- Adjective
- Different, as in treatment; discriminatory
- Relating to or based on a difference; involving derivatives.
- Noun
- A gear to let back wheels spin at different speeds
- An infinitesimal change in a variable; a derivative.
B2Moredifferentiation
US /ˌdɪfəˌrɛnʃiˈeʃən/
UK /ˌdɪfəˌrenʃɪ'eɪʃn/
- Noun (Countable/Uncountable)
- Difference between things different and distinct
- The process by which cells or tissues undergo change toward more specialized forms or functions.
B1Moreeach end
US
UK
- Phrase
- At both extremities or sides of something.
A1Moreemphasize
US /ˈɛmfəˌsaɪz/
UK /'emfəsaɪz/
- Transitive Verb
- To stress the items that are important
B2TOEICMoreend up with
US
UK
- Phrasal Verb
- To have something as a result.
A1Moreestimate
US /ˈɛstəˌmet/
UK /'estɪmət/
- Noun (Countable/Uncountable)
- Guess or calculation of cost, size or value
- A judgment or opinion.
- Transitive Verb
- To guess or calculate the cost, size or value of
- To form an approximate idea or judgment of.
A2TOEICMoreexact
US /ɪɡˈzækt/
UK /ɪɡ'zækt/
- Adjective
- Completely correct; accurate; specific
- Transitive Verb
- To get something, sometimes using force
A2TOEICMorefor example
US
UK
- Phrase
- As an illustration or instance.
force in
US /fɔrs ɪn/
UK /fɔ:rs ɪn/
- other
- To enter a place by applying physical force.
B2Morefunction
US /ˈfʌŋkʃən/
UK /'fʌŋkʃn/
- Noun
- Social event, or party such as a wedding
- Mathematical operation used in calculations
- Intransitive Verb
- To serve a certain purpose or role
- To be operating, working or achieving its purpose
A2TOEICMorefundamental
US /ˌfʌndəˈmɛntl/
UK /ˌfʌndəˈmentl/
- Adjective
- Forming a necessary part, base, or core
- Of central importance.
- Noun (Countable/Uncountable)
- A basic part of something
- (Music) the lowest note in a harmony
A2TOEICMoreget back to
US /ɡɛt bæk tu/
UK /ɡet bæk tu:/
- Phrasal Verb
- To get in contact with someone again
- To return to someone or something; to respond at a later time.
A1Morein order to
US /ɪn ˈɔrdɚ tu/
UK /in ˈɔ:də tu:/
- Preposition
- For the purpose of; with the aim of.
- Phrase
- In a specific sequence or arrangement.
- With the aim of; for the purpose of.
C1Morein reality
US /ɪn riˈælɪti/
UK /in riˈæliti/
- Phrase
- Actually; in fact; truly.
B2Morein the first place
US
UK
- Phrase
- To begin with; as the first point or consideration.
- From the beginning; initially.
A1Morein the future
US /ɪn ði ˈfjutʃɚ/
UK /in ðə ˈfju:tʃə/
- Phrase
- At a later time; in times to come.
A1Morein time
US /ɪn taɪm/
UK /in taim/
- Adverb
- Eventually; after a period of time.
- Not late; with enough time to spare.
- Phrase
- Eventually; before it is too late.
- According to the scheduled time; punctual.
A1Moreinstead of
US /ɪnˈstɛd ʌv/
UK /inˈsted ɔv/
- Preposition
- When one thing is replaced by another
- Adverb
- As a substitute or alternative.
A1Moreintegral
US /ˈɪntɪɡrəl, ɪnˈtɛɡrəl/
UK /ˈɪntɪgrəl/
- Adjective
- Being an essential part of something; necessary
- Being an essential part of something.
- Noun
- A function whose derivative is a given function.
B1Moreintegration
US /ˌɪntɪˈɡreʃən/
UK /ˌɪntɪ'ɡreɪʃn/
- Uncountable Noun
- Act of bringing things together into a whole
- The finding of an integral.
B1Moreinterval
US /ˈɪntəvəl/
UK /ˈintəvəl/
- Noun (Countable/Uncountable)
- Distance in pitch between two notes
- Distance between two points, numbers or times
B1Moremultiplication
US /ˌmʌltəplɪˈkeʃən/
UK /ˌmʌltɪplɪˈkeɪʃn/
- Uncountable Noun
- Increase in the number of something
- Process of multiplying one number by another
B1Moremultiply
US /ˈmʌltəˌplaɪ/
UK /ˈmʌltɪplaɪ/
- Verb (Transitive/Intransitive)
- To increase in number by reproducing/having babies
- To increase something by a large quantity
B1Morenotation
US /noˈteʃən/
UK /nəʊ'teɪʃn/
- Noun
- Set of written signs are used in music or math
C2Morenumerical
US /nu:ˈmerɪkl/
UK /nju:ˈmerɪkl/
- Adjective
- Concerning or involving numbers
B2Moreof course
US /ʌv kɔː(r)s/
UK /ɔv kɔː(r)s/
- Adverb
- Sure ; Certainly
- Phrase
- For sure; certainly
A2Morepole
US /pol/
UK /pəʊl/
- Noun
- One of two opposite ideas, qualities or positions
- Most northern or most southern point on a planet
- Transitive Verb
- To move a boat with a stick or pole
B1Moreprocess
US /ˈprɑsˌɛs, ˈproˌsɛs/
UK /prə'ses/
- Transitive Verb
- To organize and use data in a computer
- To deal with official forms in the way required
- Noun (Countable/Uncountable)
- Dealing with official forms in the way required
- Set of changes that occur slowly and naturally
A2TOEICMorepull back
US /pʊl bæk/
UK /pul bæk/
- Phrasal Verb
- To move to a safer area; retreat
A1Morerather than
US
UK
- Adverb
- More exactly; more correctly
- Preferably; instead
- Preposition
- Instead of
A1Moreratio
US /ˈreɪʃioʊ/
UK /ˈreɪʃiəʊ/
- Noun (Countable/Uncountable)
- The relationship in relative size, etc.
- The quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
C2Morereality
US /riˈælɪti/
UK /rɪ'ælətɪ/
- Noun (Countable/Uncountable)
- What is true, as opposed to what is imagined
- The state of things as they actually exist, rather than as they may appear or might be imagined.
A2Morerecognize
US /ˈrek.əɡ.naɪz/
UK /ˈrek.əɡ.naɪz/
- Transitive Verb
- To accept the truth or reality of something
- To consider something as important or special
A2TOEICMorescale
US /skel/
UK /skeɪl/
- Noun (Countable/Uncountable)
- Size, level, or amount when compared
- Small hard plates that cover the body of fish
- Verb (Transitive/Intransitive)
- To change the size of but keep the proportions
- To climb something large (e.g. a mountain)
A2TOEICMoreset up
US /sɛt ʌp/
UK /set ʌp/
- Phrasal Verb
- To make arrangements for something; establish
- Verb (Transitive/Intransitive)
- To arrange or prepare something for use.
- To start a business, organization, etc.
A1Moreshoot an arrow
US /ʃut ən ˈæroʊ/
UK /ʃu:t æn ˈærəu/
- Transitive Verb
- To propel an arrow from a bow.
A1Moresolar
US /ˈsolɚ/
UK /'səʊlə(r)/
- Adjective
- Concerning the sun, or its heat
B1Morestraight
US /stret/
UK /streɪt/
- Adjective
- Not having curves, bends, or angles
- Not gay; heterosexual
- Adverb
- in a line; immediately; honestly and directly
- In a straight line; directly.
A2TOEICMoresummation
US /səˈmeʃən/
UK /sʌˈmeɪʃn/
- Noun
- Concluding summary
C2Moretheorem
US /ˈθiərəm, ˈθɪrəm/
UK /ˈθɪərəm/
- Noun
- A statement that can be proved
B2Morethink about
US /θɪŋk əˈbaʊt/
UK /θiŋk əˈbaut/
- Phrasal Verb
- To consider something carefully.
- To remember or call to mind.
A1Morethink of
US /θɪŋk ʌv/
UK /θiŋk ɔv/
- Phrasal Verb
- To look on as (being something specific); consider
- To consider or remember something.
- Verb (Transitive/Intransitive)
- To imagine or call something to mind
A1Moretiny
US /ˈtaɪni/
UK /'taɪnɪ/
- Adjective
- Very, very small
A2Morewrite down
US /raɪt daʊn/
UK /rait daun/
- Phrasal Verb
- To record in writing
A1More
Vocabulary
- set up
- pull back: To move to a safer area; retreat
- chop up: To cut something into small pieces.
- based on: To use something as the foundation or starting point for something else.
- think about: To consider something carefully.
- think of: To look on as (being something specific); consider
- bow to: To bend the head or body as a sign of respect or greeting.
- in reality: Actually; in fact; truly.
- force in: To enter a place by applying physical force.
- a bit longer: For a slightly longer period of time.
- shoot an arrow: To propel an arrow from a bow.
- instead of: When one thing is replaced by another
- rather than: More exactly; more correctly
- build on: To develop or expand something; to use something as a foundation for further progress.
- in time: Eventually; after a period of time.
- each end: At both extremities or sides of something.
- end up with: To have something as a result.
- write down: To record in writing
- at some point: At an unspecified time, usually in the future.
- for example: As an illustration or instance.
- of course: Sure ; Certainly
- get back to: To get in contact with someone again
- in order to: For the purpose of; with the aim of.
- in the future: At a later time; in times to come.
- in the first place: To begin with; as the first point or consideration.
- at least: As a minimum
- assume: To act in a false manner to mislead others
- process: To organize and use data in a computer
- recognize: To accept the truth or reality of something
- situation: Place, position or area that something is in
- constant: Happening frequently or without pause
- straight: Not having curves, bends, or angles
- scale: Size, level, or amount when compared
- average: Total of numbers divided by the number of items
- force: Group of persons trained for military action; army
- sense: Certain mental feeling or emotion
- develop: To explain something in steps and in detail
- exact: Completely correct; accurate; specific
- claim: To say that something is true, often without proof.
- amount: Quantity of something
- fundamental: Forming a necessary part, base, or core
- reality: What is true, as opposed to what is imagined
- compound: Series of buildings that are walled or fenced off
- estimate: Guess or calculation of cost, size or value
- function: Social event, or party such as a wedding
- court: To act in a way to shows you wish to marry someone
- tiny: Very, very small
- emphasize: To stress the items that are important
- integral: Being an essential part of something; necessary
- reason: To think and make conclusions in a logical manner
- break: To create a new record e.g. running the 100m dash
- ratio: The relationship in relative size, etc.
- lot: What happens to a person in life from chance; fate
- sign: Indication that something exists or will happen
- chop: To cut into pieces with an up and down motion
- integration: Act of bringing things together into a whole
- learn: To get knowledge or skills by study or experience
- multiply: To increase in number by reproducing/having babies
- piece: A counter in a board game
- pole: One of two opposite ideas, qualities or positions
- point: An item to be discussed
- solar: Concerning the sun, or its heat
- wrong: Action that is harmful, unjust or illegal
- pull: Act of breathing in smoke, as from a pipe
- change: To exchange one set of clothes for another
- axis: A line about which a rotating body turns
- interval: Distance in pitch between two notes
- anti: A prefix meaning 'against' or 'opposed'
- calculate: To find an answer using mathematics
- datum: Item of factual information
- conception: Moment when a woman's pregnancy begins
- multiplication: Increase in the number of something
- notation: Set of written signs are used in music or math
- calculus: Branch of math dealing with rates of change, etc.
- numerical: Concerning or involving numbers
- defender: Fighter who fights against attack
- differentiation: Difference between things different and distinct
- summation: Concluding summary
- differential: Different, as in treatment; discriminatory
- theorem: A statement that can be proved
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01:03
She took a brave step forward, leaving behind her comfort zone to chase her dreams.
Vocabulary
- brave
adj. Having courage
- comfort zone
phr. A familiar situation where one feels safe
Explanation
a brave step is a noun phrase, where brave is an adjective modifying the noun step, meaning "a courageous step".
forward is an adverb modifying step, meaning "ahead".
The whole phrase serves as the object, answering the "what" of took (verb) — she took a brave step forward.
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brave
US/brev/
UK/breɪv/
adj.Brave
v.t.To bravely face
A2 Elementary
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80
What is Integration? 3 Ways to Interpret Integrals
0
Jasmine Chen cc posted on 2026/07/06Think you learned integration the 'right' way in calculus? This video challenges that idea, revealing how a common understanding of "finding areas under curves" can actually hinder real-world problem-solving! You'll discover a more powerful perspective on integration as "adding up tiny bits of a quantity" and see it applied to fascinating scenarios like archery and basketball.
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