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PHYSICS I · UNIT 1 · CALCULUSSCENEOn the parabola f(x)=x2f(x)=x^2 over [1,3][1,3] the secant is drawn. Find the point cc where the tangent runs parallel to it.f(x)=x2 on [1,3]f(x)=x^2 \text{ on } [1,3]c = 2.14the tangent draws when you send
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PHYSICS I · UNIT 1 · CALCULUS1 of 6Functions, Domains, and RepresentationsA function assigns exactly one output to every input in its domain.f:D⊆R⟶Rf : D \subseteq \mathbb{R} \longrightarrow \mathbb{R}For f(x)=1x−2f(x)=\tfrac{1}{x-2} we need x≠2x \neq 2, so D=R∖{2}D = \mathbb{R}\setminus\{2\}. The number sets nest: N⊂Z⊂Q⊂R\mathbb{N}\subset\mathbb{Z}\subset\mathbb{Q}\subset\mathbb{R}.FormExampleExplicity=3x+2y = 3x + 2Implicitx2+y2=9x^{2}+y^{2}=9Parametric(cos⁡t,  sin⁡t)(\cos t,\; \sin t)
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BUSINESS I · UNIT 6 · MATRICESMULTIPLE CHOICEA 2×2 matrix has eigenvalues λ1=3\lambda_1 = 3 and λ2=5\lambda_2 = 5. What is det⁡(A)\det(A)?A15B8C2D−15NEXT
Correct!NEXT
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# AP Biology Study
142 members · 18 online
Pinned: Unit 4 Quiz is live. Try it now →
Alex M.
Alex M.2:01 PM
Has anyone finished the photosynthesis unit yet?
Elena K.
Elena K.2:02 PM
Just did! The AI quiz at the end was really good
Message #AP Biology Study...
Study Call
0:02 · 4 participants
LIVE
Alex M.
Alex M.
Elena K.
Wait, doesn't NADPH come from the light reactions?
Elena K.
Jordan L.
Jordan L.
You
You
Organic reaction maps for the whole unitAP Chemistry 128
Mini-courseKinematics in 6 questions
Physics I 77
Anyone else find the Krebs cycle easier as a loop diagram than a list?
AP Biology 23
Organic reaction maps for the whole unitAP Chemistry 128
Mini-courseKinematics in 6 questions
Physics I 77
Anyone else find the Krebs cycle easier as a loop diagram than a list?
AP Biology 23
Organic reaction maps for the whole unitAP Chemistry 128
Mini-courseKinematics in 6 questions
Physics I 77
Anyone else find the Krebs cycle easier as a loop diagram than a list?
AP Biology 23
Organic reaction maps for the whole unitAP Chemistry 128
Mini-courseKinematics in 6 questions
Physics I 77
Anyone else find the Krebs cycle easier as a loop diagram than a list?
AP Biology 23
Finally understood integration by parts. The trick is picking u so it gets simpler when you differentiate.
Maths Society 41
Timeline: the road to 1939History Club 96
Finally understood integration by parts. The trick is picking u so it gets simpler when you differentiate.
Maths Society 41
Timeline: the road to 1939History Club 96
Finally understood integration by parts. The trick is picking u so it gets simpler when you differentiate.
Maths Society 41
Timeline: the road to 1939History Club 96
Finally understood integration by parts. The trick is picking u so it gets simpler when you differentiate.
Maths Society 41
Timeline: the road to 1939History Club 96
My revision wall for finals weekStudy Together 302
Recursion, drawn outCS Basics 54
My revision wall for finals weekStudy Together 302
Recursion, drawn outCS Basics 54
My revision wall for finals weekStudy Together 302
Recursion, drawn outCS Basics 54
My revision wall for finals weekStudy Together 302
Recursion, drawn outCS Basics 54
Elena K.3h agoMade a 3-question warm-up on equilibrium — try it before the test.Adding more product shifts the equilibrium toward the …reactantsreactantsproductscatalyst✓ Correct! 34 6Sarah K. Q3 finally made Q vs K click. Thank you!
Alex M.5h agoAnnotated my whole titration write-up. 12 2
Jordan L.1d agoUnit 4 summary, 12 pages.
NewestTopUnanswered
▲24▼Why is chlorophyll green rather than black?✓ 3 answers412 viewsResolvedElena K. · 2h ago
▲11▼Is the second derivative test ever inconclusive?2 answers96 viewsOpenAlex M. · 5h ago
▲7▼Best way to memorise the Krebs cycle?0 answers58 viewsOpenJordan L. · 1d ago
▲2▼Does anyone have last year’s mock paper?4 answers231 viewsClosedSam R. · 2d ago
Maths Society · RoomsOpen▲11▼Is the second derivative test ever inconclusive?I know it fails when f″(c) = 0, but is that the only case?Alex M. · 5h ago · 97 views2 ANSWERS▲9▼Yes — f″(c) = 0 is the only inconclusive case. Then it can be a max, a min or neither, so you fall back to the sign of f′ either side.Priya N. · 4h✓ ACCEPTED▲3▼Worth remembering x⁴ and x³ at 0: both have f″ = 0 there, and one is a minimum while the other is not an extremum at all.Tomás R. · 2h✓ ACCEPTED▲0▼So for x³ the sign of f′ never changes across 0 — that is the "neither" case, and the first-derivative test settles it.You · just nowAdd an answer…↑
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Why is momentum conserved in a collision?
✳

Momentum is conserved because the forces the two carts exert on each other are equal and opposite, so the total change cancels. Try it: if the 2 kg cart slows by 3 m/s, what happens to the 3

+Explain it in your own words…↑
DocumentsFlashcardsQuiz
AllScienceMathematicsLanguagesHistory
PDFThermodynamicsMaría G. 142
PDFLinear AlgebraAlex P. 89
IMGAP BiologySarah K. 234
DOCFrench VerbsJules M. 67
IMGWorld HistoryChen W. 178
PDFOrganic ChemLiam R. 95
DOCCognitive ScienceDr. Reyes 311
IMGRecursion NotesPriya N. 58
PDFStatisticsTomás R. 120
DOCSpanish IdiomsMarta L. 74
PDFThe Cold WarWei C. 163
DOCCell RespirationSam R. 91
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Chemistry I — draftUnsavedPreview
STRUCTURE
Unit 1 · Equilibrium
Le ChatelierWhat shifts a systemAdding productRaising temperature+ Question
Reaction quotientQ against KPredicting direction
Unit 2 · Kinetics
Unit 3 · Thermochemistry
+ Unit
Multiple choiceWhich way does the equilibrium shift when you add more product?Towards the reactantsCORRECTTowards the productsIt does not shift+ OptionWhich way does the equilibrium shift when you add more product?Towards the reactantsTowards the productsIt does not shiftPublish
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What is Tryals?
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Tryals is an interactive learning platform. It has twenty free courses in seven languages, a Gymnasium that builds courses and flashcards from your own PDFs and documents, an AI tutor, a speaking partner for language practice, and study groups where people share notes and courses. It runs on Android and in the browser.

Is Tryals free to use?
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Yes. Every course, the community and the study notes are free, and the Gymnasium runs on rubies you earn by learning. If you want more of those than you earn, there are two optional plans you can buy on the web — nothing is locked behind them.

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The Gymnasium has four rooms. Tutor: ask anything and work through it step by step. Courses: turn a PDF or one of your documents into an interactive course with more than 30 question types. Flashcards: make a deck from the same material. Speaking: practise a language out loud with an AI partner.

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Pick a language and talk. The AI partner answers out loud, and when you finish you get a review of the conversation: what you said, a better way to say it and why, what went well, and what to practise next. It works from what you say, not from how you pronounce it. A session costs rubies.

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Rubies are the in-app currency: you earn them by finishing lessons, keeping streaks and inviting friends, and you spend them in the Gymnasium. Hearts are your lives inside a lesson: a wrong answer costs one. Streaks count the days in a row you have learned.