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Unit 3 Review

Summary

Students are doing well with implicit differentiation and the chain rule on their own, but many slip up when applying them to trig functions, including Timothy R., Megan G. and Luke J. Worth a quick review of trig derivatives.

Submitted

42/52

Accuracy

85%

of submitted work

Accuracy by class

Period 115/17 · 92%

Period 316/19 · 84%

Period 611/16 · 77%

Questions

Correct

Q7
If $\ln x + \sin y = 1$ , what is $\frac{dy}{dx}$ in terms of $x$ and $y$ ?
Implicit Differentiation · Trig Functions
64%
Q5
If $f(x) = \sin\left(x^2 + \frac{2\pi}{3}\right)$ , what is $f'\left(\sqrt{\frac{\pi}{3}}\right)$ ?
Chain Rule · Trig Functions
68%
Q3
If $xy^2 + x^2 - y = 3$ , then at the point $(1, 2)$ , what is $\frac{dy}{dx}$ ?
Implicit Differentiation
88%
Q6
A particle's velocity is $v(t) = 3\ln(2t + 1) - t^2$ . What is its acceleration at $t = 2$ ?
Chain Rule · Straight-Line Motion
90%

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3/4

FRQ 1(a) · Methods & Control

You scored 3 out of 4

✓
Calls getNumberOfDigits and getDigit
+1
✓
Calculates one partial sum
+1
✓
Calculates all partial sums in a loop
+1
✗
Returns the last digit of the sum
Returns sum / 10 instead of sum % 10
+0

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Unit 3 Review · 6 questions

1The Chain RuleMCQ
2Inverse FunctionsMCQ
3Inverse Trig FunctionsFRQ
4Higher-Order DerivativesMCQ

✦ 2 new · Implicit Differentiation

5Implicit DifferentiationMCQ
6Implicit DifferentiationFRQ

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Add two more questions on implicit differentiation.

Passionfruit AIDone! I added an MCQ and an FRQ on implicit differentiation as questions 5 and 6.

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Mastery by student

Unit 1Unit 2Unit 3Unit 4

Maya T.

Jordan K.

Priya S.

Leo M.

Sofia P.

MasteredProficientWeakNot started

Who's falling behind on Unit 3?

Inverse functions are the weakest topic in your class. These students are struggling the most:

Jordan K.Priya S.Leo M.

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FRQ · Related Rates

A 10-foot ladder leans against a wall. The bottom slides away at 2 ft/s. How fast is the top sliding down when the bottom is 6 ft from the wall?

Idk how to do this

PassionfruitDo you remember the first step to solving this kind of problem?

I think I need to write out the equation first?

PassionfruitYep, that's right! Let's give it a try. What equation connects x and y?

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Computer Science Dept. Chair
California High School

+35%

average improvement on multiple-choice

+20%

average improvement on free-response

+25%

improvement on timed practice exams

Average score gain from first 25% to last 25% of attempts, for students using Passionfruit 2+ weeks.

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