When we "take the derivative" of a function what are we finding?

The rate at which our struggles in Calculus are increasing.

Find the derivative of f ( x ) = x e x f\left(x\right)=xe^x f ( x ) = x e x

f ′ ( x ) = e x + x e x f'\left(x\right)=e^x+xe^x f ′ ( x ) = e x + x e x

f ′ ( x ) = e x f'\left(x\right)=e^x f ′ ( x ) = e x

f ′ ( x ) = 2 x e x f'\left(x\right)=2xe^x f ′ ( x ) = 2 x e x

f ′ ( x ) = e x − x e x f'\left(x\right)=e^x-xe^x f ′ ( x ) = e x − x e x

AP Calculus AB - Unit 2 Review

Authored by Anthony Record

Mathematics

9th - 12th Grade

CCSS covered

Used 545+ times

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About

This quiz covers derivatives and differentiation, the fundamental Unit 2 topics in AP Calculus AB at the 12th grade level. Students must demonstrate mastery of multiple derivative concepts including the definition of a derivative as a limit, basic differentiation rules (power, product, quotient, and chain rules), derivatives of trigonometric functions, exponential and logarithmic functions, and applications such as finding tangent lines and rates of change. The problems require students to compute limits in difference quotient form, apply differentiation formulas systematically, evaluate derivatives at specific points, and interpret geometric meanings of derivatives. Students need solid algebraic manipulation skills, thorough knowledge of derivative formulas, and the ability to connect the analytical concept of instantaneous rate of change with geometric interpretations like slopes of tangent lines and continuity versus differentiability. Created by Anthony Record, a Mathematics teacher in US who teaches grade 9-12. This comprehensive review quiz serves as an excellent tool for reinforcing derivative concepts before assessments or as homework to solidify understanding of differentiation techniques. Teachers can use this as a formative assessment to identify areas where students need additional practice, particularly with more complex applications like quotient rule problems and product rule scenarios involving transcendental functions. The quiz effectively prepares students for AP Calculus AB Unit 2 assessments by covering essential skills aligned with standards CCSS.MATH.CONTENT.HSF.IF.B.6 (rate of change and behavior of functions) and AP Calculus learning objectives related to derivatives as functions, basic differentiation rules, and interpreting derivatives in context. The variety of question types makes it suitable for warm-up activities, review sessions, or comprehensive practice before unit exams.

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36 questions

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MULTIPLE CHOICE QUESTION

45 sec • 1 pt

$\lim_{h\rightarrow0}\left(\frac{5\left(x+h\right)^2-5x^2}{h}\right)$

$5x^2$

$10x$

DNE

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the derivative.

sinx

-sinx

tanx

-tanx

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Given $y=\frac{u}{v}$ , what is $y'$ ?

(vu' - uv')/v²

(uv' - vu')/v²

(vu' - uv')/u²

(uv' - vu')/u²

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.APR.D.6

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What is the average rate of change of f(x) = x² on the interval [1,3]?

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What is the instantaneous rate of change of f(x) = x²at x = 3?

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

The derivative of which function is itself?

e^x

sinx

tanx

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Write the slope of the line tangent to the graph of the function below at the point x = 8.
$y=x^2-2$

-4

-8

MULTIPLE CHOICE QUESTION

1 min • 1 pt

This is the equation of the line tangent to the graph of the function below at the point (-1, 4).
$y=x^2+3$

y = -2x + 2

y = 2x + 2

-(1/2)x + (7/2)

y = (1/2)x + (7/2)

Tags

CCSS.HSA.REI.C.7

CCSS.HSA.REI.D.11

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AP Calculus AB - Unit 2 Review

$\lim_{h\rightarrow0}\left(\frac{5\left(x+h\right)^2-5x^2}{h}\right)$

Find the derivative.

Given $y=\frac{u}{v}$ , what is $y'$ ?

What is the average rate of change of f(x) = x² on the interval [1,3]?

What is the instantaneous rate of change of f(x) = x²at x = 3?

The derivative of which function is itself?

Write the slope of the line tangent to the graph of the function below at the point x = 8.
$y=x^2-2$

This is the equation of the line tangent to the graph of the function below at the point (-1, 4).
$y=x^2+3$

Which option is using correctly the quotient rule?

Find the value of the derivative at the indicated x-value.

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AP Calculus AB - Unit 2 Review

lim⁡h→0(5(x+h)2−5x2h)\lim_{h\rightarrow0}\left(\frac{5\left(x+h\right)^2-5x^2}{h}\right)h→0lim​(h5(x+h)2−5x2​)

Find the derivative.

Given y=uvy=\frac{u}{v}y=vu​ , what is y′y'y′ ?

What is the average rate of change of f(x) = x2 on the interval [1,3]?

What is the instantaneous rate of change of f(x) = x2 at x = 3?

The derivative of which function is itself?

Write the slope of the line tangent to the graph of the function below at the point x = 8. y=x2−2y=x^2-2y=x2−2

This is the equation of the line tangent to the graph of the function below at the point (-1, 4). y=x2+3y=x^2+3y=x2+3

Which option is using correctly the quotient rule?

Find the value of the derivative at the indicated x-value.

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Discover more resources for Mathematics

$\lim_{h\rightarrow0}\left(\frac{5\left(x+h\right)^2-5x^2}{h}\right)$

Given $y=\frac{u}{v}$ , what is $y'$ ?

What is the average rate of change of f(x) = x² on the interval [1,3]?

What is the instantaneous rate of change of f(x) = x²at x = 3?

Write the slope of the line tangent to the graph of the function below at the point x = 8.
$y=x^2-2$

This is the equation of the line tangent to the graph of the function below at the point (-1, 4).
$y=x^2+3$