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Quiz 4: Applications of Derivatives

AP Calculus AB

Name
Date Per

1. On which interval is f(x) = x³ − 6x² + 9x decreasing?
A. (−∞, 1)
B. (1, 3)
C. (3, ∞)
D. (0, 9)
2. If f′(x) > 0 and f″(x) < 0 on (2, 5), then on that interval f is
A. increasing, concave up
B. increasing, concave down
C. decreasing, concave up
D. decreasing, concave down
3. A particle has position s(t) = t³ − 6t². The particle is at rest when
A. t = 0 only
B. t = 4 only
C. t = 0 and t = 4
D. t = 2 and t = 6
4. Which function fails the hypotheses of the Mean Value Theorem on [0, 4]?
A. f(x) = x²
B. f(x) = |x − 2|
C. f(x) = sin x
D. f(x) = eˣ
5. The absolute maximum of f(x) = 4x − x² on [0, 3] occurs at
A. x = 0
B. x = 2
C. x = 3
D. x = 4
6. If g′(x) changes from negative to positive at x = c, then g has
A. a local maximum at c
B. a local minimum at c
C. an inflection point at c
D. no extremum at c
7. A ladder slides down a wall. This is best modeled as a problem in
A. related rates
B. optimization
C. linear approximation
D. implicit differentiation only
8. The linearization of f(x) = √x at x = 9 is
A. L(x) = 3 + (x − 9)/6
B. L(x) = 3 + (x − 9)/3
C. L(x) = 9 + (x − 3)/6
D. L(x) = 3 + 6(x − 9)

Unit 5 Reading Quiz

Civil War and Reconstruction

Name Per

1. Which best explains why the Compromise of 1850 failed to settle sectional conflict?
A. It ended the slave trade in every state
B. The Fugitive Slave Act forced northern enforcement
C. It admitted Texas as a free state
D. It repealed the Missouri Compromise line
2. The Thirteenth, Fourteenth, and Fifteenth Amendments are best understood as
A. a limit on federal authority
B. an expansion of federal authority over the states
C. a restoration of prewar state powers
D. a compromise with former Confederate leaders
3. True or false: Radical Reconstruction retained strong northern political support through 1876.
A. True
B. False
4. The Compromise of 1877 most directly resulted in
A. the passage of the Civil Rights Act
B. the withdrawal of federal troops from the South
C. the impeachment of Andrew Johnson
D. the readmission of Virginia to the Union
5. Briefly explain one reason Reconstruction ended when it did.

Unit 7 Quiz: Memory

AP PSYCHOLOGY

October 14

Answer every question. Starred questions match what your professor emphasized in lecture.

1.Which memory store holds a sound for only a few seconds?2 pts

a. Iconic memory

b. Echoic memory

c. Semantic memory

d. Procedural memory

2.Recalling the first items in a list best is the effect.2 pts

3.Name the three stages of memory in order.3 pts

4.Sketch the forgetting curve. Where does spaced review flatten it?★★★4 pts

5.True or False: rehearsal alone moves facts into long-term memory.2 pts

6.Define a retrieval cue and give one example from this week.★3 pts

7.Explain why deep processing beats rereading the chapter.4 pts

Unit 7 Quiz: MemoryAP PSYCHOLOGY

October 14

Question 4 of 7

4 points

Which study schedule flattens the forgetting curve the most?

aRereading the chapter the night before

bSpacing short reviews across several days

cHighlighting the key terms once

dOne long session right before class

Exit quizCheck answer

“Wednesday, I’m not asking you to define the forgetting curve. I’m asking which study schedule flattens it.”

AP Psychology · Lecture 12 · Oct 9

It all starts with the input.

Serona listens to your lectures and reads your screenshots, notes, and documents.

Transcript

Biology · Lecture 08 · 52 min

12:29

Last week we finished cellular respiration. Keep that in your head, because today is basically the same reaction running backwards.

12:54

Okay, today we're on photosynthesis, the reaction that turns carbon dioxide and water into glucose and oxygen using light. Make sure you can write the full equation, because it is going to be on the quiz.

13:16

So the light reactions happen in the thylakoid, and the Calvin cycle happens in the stroma. If you remember one thing from today, remember where each stage happens.

Saved to Biology

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Photosynthesis

Light reactions happen in the thylakoid
Calvin cycle runs in the stroma

Equation: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂

Oxygen comes from splitting water, not CO₂
Ask about ATP synthase in office hours Friday

Calvin cycle

Uses the ATP and NADPH from the light reactions
3 turns make 1 G3P, which becomes glucose
Slows down within minutes in the dark

Exam prep

Quiz Friday: write the full equation from memory
Know which stage happens where (thylakoid vs stroma)
Practice: draw the chloroplast and label the grana
Compare to cellular respiration, it runs the other way

Questions for next class

Why does the cycle need three turns for one G3P?
What limits photosynthesis on a cloudy day?
How do C4 plants avoid wasting energy?

Typed notes

Get caught right up with your old notes

Chapter 8 Reading.pdf

CHAPTER 8142

8.1 Overview of Photosynthesis

Plants, algae, and some bacteria capture the energy of sunlight and store it in the chemical bonds of sugar. The overall reaction can be written as a single balanced equation.

6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂

Although the equation looks simple, it summarises dozens of steps carried out by enzymes in two connected stages, the light reactions and the Calvin cycle.

Both stages take place inside the chloroplast, an organelle found mainly in the cells of the leaf mesophyll.

CHAPTER 8143

8.2 The Light Reactions

Photosynthesis takes place in two linked stages. In the light reactions, pigments in the thylakoid membranes absorb light.

The light reactions produce ATP and NADPH, which power the Calvin cycle in the stroma.

CHAPTER 8144

8.3 The Calvin Cycle

The Calvin cycle uses ATP and NADPH from the light reactions to turn carbon dioxide into sugar. It runs in the stroma and does not need light directly.

Stage	Location	Output
Light reactions	Thylakoid	ATP, NADPH, O₂
Calvin cycle	Stroma	G3P, glucose

For every three molecules of CO₂ fixed, the cycle releases one molecule of G3P that the plant can use to build glucose.

8.2The Light Reactions

Photosynthesis takes place in two linked stages. In the light reactions, pigments embedded in the thylakoid membranes absorb light and use its energy to split water, releasing oxygen.

The light reactions produce ATP and NADPH, which power the Calvin cycle in the stroma. Without this supply, carbon fixation slows and soon stops.

Each granum is a stack of thylakoids joined to its neighbours by lamellae, giving the membrane a very large surface for capturing light.

Figure 8.4 Structure of a chloroplast. Light reactions occur in the thylakoid membranes; the Calvin cycle runs in the stroma.

The pigments that capture light are grouped into two photosystems. Photosystem II absorbs light first and passes excited electrons down an electron transport chain, pumping protons into the thylakoid space as it goes.

The protons flow back out through ATP synthase, and the energy of that flow is used to make ATP. Photosystem I then re-energises the electrons so they can reduce NADP⁺ to NADPH.

Check your understanding. Where does the oxygen released by photosynthesis come from, and which photosystem splits water to produce it?

Plants that grow in bright, dry places often close their stomata to save water, which limits how much carbon dioxide reaches the leaf. Section 8.4 explains how some of these plants keep photosynthesis going anyway.

Light intensity, temperature, and carbon dioxide level each set an upper limit on the rate of photosynthesis. Whichever factor is in shortest supply is called the limiting factor.

8.3The Calvin Cycle

The Calvin cycle uses the ATP and NADPH made in the light reactions to build sugar from carbon dioxide. It runs in the stroma and does not need light directly.

Each turn fixes one CO₂ onto RuBP; three turns release one G3P that the plant can use to make glucose.

Because the cycle depends on a steady supply of ATP and NADPH, it slows within minutes when a plant is moved into darkness.

Figure 8.6 The three phases of the Calvin cycle: fixation, reduction, and regeneration of RuBP.

Rubisco, the enzyme that attaches CO₂ to RuBP, is probably the most abundant protein on Earth. It works slowly, so a leaf needs a great deal of it to fix carbon at a useful rate.

In hot weather Rubisco sometimes grabs oxygen instead of carbon dioxide, a wasteful process called photorespiration. C4 and CAM plants reduce this loss by concentrating CO₂ around the enzyme.

Check your understanding. Why does the Calvin cycle stop soon after the lights are switched off, even though it does not use light directly?

The G3P made by the cycle is the starting point for glucose, sucrose, starch, and cellulose, which is why the Calvin cycle sits at the base of almost every food chain.

Together, the light reactions and the Calvin cycle turn sunlight, water, and carbon dioxide into the sugars that nearly every living thing depends on.

Documents

PDFs, slideshows, readings, and review sheets

Your math notes should not look like your history notes.

Every class gets its own style of note, and you decide what that is. Pick what fits you and the subject.

Blueprint works every problem through to the answer

Recap boils a whole session down to what matters

Roundtable writes down who said what in a discussion

A review that knows what matters.

The same class becomes a focused review with priorities, formulas, and the concepts that still need attention.

High-priority concepts rise to the top

Formulas and definitions receive their own space

Open questions show exactly what to revisit

The class you cannot take notes in.

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Every question becomes a thread with its own arc

Quotes are verbatim and attributed, never guessed

Every thread closes with a "Where we landed" line

Serona note

Unit 3: Linear Equations

Blueprint

Overview

Point-slope form is the equation of a line built from one known point and the slope. Plug both facts in, simplify, and the full line falls out as y = mx + b.

Point-Slope Form

y − y₁ = m(x − x₁)

You have a point on the line but not the intercept.

Working one through

Find the line through (1, 4) and (3, 10)

m = (10 − 4)/(3 − 1)| rise over run

m = 6/2 = 3| the slope

y − 4 = 3(x − 1)| plug in (1, 4)

y − 4 = 3x − 3| distribute

y = 3x + 1| add 4 to both sides

Answer: y = 3x + 1, the equation of the line

Serona note

Conditioning and Learning

Recap

Overview

This session covered how reward timing shapes behavior: the four schedules, their patterns, and the one fact exams love.

Schedules of reinforcement

Ratio schedules count behaviors, and interval schedules count time. The unpredictable ones hold up best when rewards stop.

Schedule	Pattern
Fixed ratio	high rate, pause after each reward
Variable ratio	highest and steadiest, hardest to break
Fixed interval	ramps up as the deadline nears
Variable interval	slow and steady

Fixed interval: cramming right before each quiz

Common mistake: Negative reinforcement is not punishment.

Exam watch: “There will be a gambling question on Friday’s quiz. When you see it, the answer is variable ratio.”

Serona note

The Great Gatsby Seminar

Roundtable

Session Overview

Most of the hour went to one question: does Gatsby love Daisy, or the life she represents? The room split early and never fully came back together.

Does Gatsby love Daisy, or what she represents?

Most of the class read the obsession as ambition: Daisy is shorthand for the life Gatsby was locked out of. A smaller group held out for real love, pointing to the five years of letters.

Classmate: “He isn’t in love with Daisy. He’s in love with 1917.”

Professor: “Then ask what happens to the dream the moment she says yes.”

View: The green light only matters while it is out of reach.

Counter: Chapter 5 shows him happiest with Daisy actually in the room.

Where we landed: No consensus. The ambition reading held the room, but the letters kept it an open question.

Your math notes should not look like your history notes.

Every class gets its own style of note, and you decide what that is. Pick what fits you and the subject.

Blueprint works every problem through to the answer

Recap boils a whole session down to what matters

Roundtable writes down who said what in a discussion

Serona note

Unit 3: Linear Equations

Blueprint

Overview

Point-slope form is the equation of a line built from one known point and the slope. Plug both facts in, simplify, and the full line falls out as y = mx + b.

Point-Slope Form

y − y₁ = m(x − x₁)

You have a point on the line but not the intercept.

Working one through

Find the line through (1, 4) and (3, 10)

m = (10 − 4)/(3 − 1)| rise over run

m = 6/2 = 3| the slope

y − 4 = 3(x − 1)| plug in (1, 4)

y − 4 = 3x − 3| distribute

y = 3x + 1| add 4 to both sides

Answer: y = 3x + 1, the equation of the line

Serona note

Conditioning and Learning

Recap

Overview

This session covered how reward timing shapes behavior: the four schedules, their patterns, and the one fact exams love.

Schedules of reinforcement

Ratio schedules count behaviors, and interval schedules count time. The unpredictable ones hold up best when rewards stop.

Schedule	Pattern
Fixed ratio	high rate, pause after each reward
Variable ratio	highest and steadiest, hardest to break
Fixed interval	ramps up as the deadline nears
Variable interval	slow and steady

Fixed interval: cramming right before each quiz

Common mistake: Negative reinforcement is not punishment.

Exam watch: “There will be a gambling question on Friday’s quiz. When you see it, the answer is variable ratio.”

Serona note

The Great Gatsby Seminar

Roundtable

Session Overview

Most of the hour went to one question: does Gatsby love Daisy, or the life she represents? The room split early and never fully came back together.

Does Gatsby love Daisy, or what she represents?

Most of the class read the obsession as ambition: Daisy is shorthand for the life Gatsby was locked out of. A smaller group held out for real love, pointing to the five years of letters.

Classmate: “He isn’t in love with Daisy. He’s in love with 1917.”

Professor: “Then ask what happens to the dream the moment she says yes.”

View: The green light only matters while it is out of reach.

Counter: Chapter 5 shows him happiest with Daisy actually in the room.

Where we landed: No consensus. The ambition reading held the room, but the letters kept it an open question.

Every line of your study guide, backed by receipts.

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Cell respiration★★★

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Transcript

Typed notes

Documents

Your math notes should not look like your history notes.

A review that knows what matters.

The class you cannot take notes in.

Overview

Point-Slope Form

Your math notes should not look like your history notes.

Overview

Point-Slope Form

Overview

Schedules of reinforcement

Session Overview

Every line of your study guide, backed by receipts.

Syllabus tracking

Exam prediction

Flashcards

Frequently asked questions

How does Serona know what's likely on the test?

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