Calculus I · 2A · exam

Unit 2A Practice Exam A

Complete Unit 2A Practice Exam A as a cumulative Calculus I assessment, then use the separately published answer key for review.

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Section overview

Review, practice, exams, and reference

What this section is building

Complete Unit 2A Practice Exam A as a cumulative Calculus I assessment, then use the separately published answer key for review.

Notice

A dependable solution separates interpretation, rule selection, calculation, and verification.

Decide

Classify first, calculate second, and use answer reveals to diagnose the first incorrect decision.

Avoid

Reading the solution before making a complete attempt or treating every miss as mere algebra.

Answer key published

Finish first. Then check every answer.

The complete numbered key is online as its own easy-to-find route.

View the complete answer key →

Practice Exam A

Suggested time: 100 minutes. Show structure and algebra.

Exercise

Use the limit definition to find the derivative of $f(x)=x^2+3x$ at $x=1$ .

Exercise

Find the tangent and normal lines to $y=1/x$ at $x=2$ .

Exercise

Differentiate $4x^{7/3}-5x^{-2}$ .

Exercise

Differentiate $(x^2+1)^4e^x$ .

Exercise

Differentiate $\ln(1+\sin^2x)$ .

Exercise

Differentiate $[\tan(1+x^2)]^5/(x^3+1)$ .

Exercise

Find $dy/dx$ for $x^2+xy+2y^2=10$ .

Exercise

Find the tangent line to $y=\arcsin(x/2)$ at $x=1$ .

Exercise

If $g=f^{-1}$ , $f(2)=5$ , and $f'(2)=-3$ , find $g'(5)$ .

Exercise

Use logarithmic differentiation to differentiate $(x^2+1)^{e^x}$ .

Exercise

Find the first four derivatives of $x^4-3x^3+2x$ .

Exercise

Explain why differentiability at $a$ implies continuity at $a$ , but continuity does not imply differentiability.

Exercise

A response model is $R(d)=100d/(d+12)$ . Find $R'(d)$ and interpret $R'(12)$ .

Exercise

Write a rule-selection explanation, without computing, for $y=e^{\sin(x^2)}(x+1)^3$ .

Structured concept quiz

Unit 2A Practice Exam A

Write a response before revealing the model. These conceptual items use an honest attempt-and-reveal rubric rather than pretending an open response has one machine-provable wording.

Interactive checkexam-a-01

Use the limit definition to find the derivative of $f(x)=x^2+3x$ at $x=1$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-02

Find the tangent and normal lines to $y=1/x$ at $x=2$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-03

Differentiate $4x^{7/3}-5x^{-2}$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-04

Differentiate $(x^2+1)^4e^x$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-05

Differentiate $\ln(1+\sin^2x)$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-06

Differentiate $[\tan(1+x^2)]^5/(x^3+1)$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-07

Find $dy/dx$ for $x^2+xy+2y^2=10$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-08

Find the tangent line to $y=\arcsin(x/2)$ at $x=1$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-09

If $g=f^{-1}$ , $f(2)=5$ , and $f'(2)=-3$ , find $g'(5)$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-10

Use logarithmic differentiation to differentiate $(x^2+1)^{e^x}$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-11

Find the first four derivatives of $x^4-3x^3+2x$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-12

Explain why differentiability at $a$ implies continuity at $a$ , but continuity does not imply differentiability.

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-13

A response model is $R(d)=100d/(d+12)$ . Find $R'(d)$ and interpret $R'(12)$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-14

Write a rule-selection explanation, without computing, for $y=e^{\sin(x^2)}(x+1)^3$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Source & rights

Original instruction with traceable references.

BetterGrades-original composition declared by source handoff; owner provenance review required before public release

Reference textbooks remain rights-separated and are not published as application assets. Any direct adaptation requires separate identification and attribution.

Practice Exam A

Suggested time: 100 minutes. Show structure and algebra.

Exercise

Use the limit definition to find the derivative of $f(x)=x^2+3x$ at $x=1$ .

Exercise

Find the tangent and normal lines to $y=1/x$ at $x=2$ .

Exercise

Differentiate $4x^{7/3}-5x^{-2}$ .

Exercise

Differentiate $(x^2+1)^4e^x$ .

Exercise

Differentiate $\ln(1+\sin^2x)$ .

Exercise

Differentiate $[\tan(1+x^2)]^5/(x^3+1)$ .

Exercise

Find $dy/dx$ for $x^2+xy+2y^2=10$ .

Exercise

Find the tangent line to $y=\arcsin(x/2)$ at $x=1$ .

Exercise

If $g=f^{-1}$ , $f(2)=5$ , and $f'(2)=-3$ , find $g'(5)$ .

Exercise

Use logarithmic differentiation to differentiate $(x^2+1)^{e^x}$ .

Exercise

Find the first four derivatives of $x^4-3x^3+2x$ .

Exercise

Explain why differentiability at $a$ implies continuity at $a$ , but continuity does not imply differentiability.

Exercise

A response model is $R(d)=100d/(d+12)$ . Find $R'(d)$ and interpret $R'(12)$ .

Exercise

Write a rule-selection explanation, without computing, for $y=e^{\sin(x^2)}(x+1)^3$ .

Structured concept quiz

Unit 2A Practice Exam A

Write a response before revealing the model. These conceptual items use an honest attempt-and-reveal rubric rather than pretending an open response has one machine-provable wording.

Interactive checkexam-a-01

Use the limit definition to find the derivative of $f(x)=x^2+3x$ at $x=1$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-02

Find the tangent and normal lines to $y=1/x$ at $x=2$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-03

Differentiate $4x^{7/3}-5x^{-2}$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-04

Differentiate $(x^2+1)^4e^x$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-05

Differentiate $\ln(1+\sin^2x)$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-06

Differentiate $[\tan(1+x^2)]^5/(x^3+1)$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-07

Find $dy/dx$ for $x^2+xy+2y^2=10$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-08

Find the tangent line to $y=\arcsin(x/2)$ at $x=1$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-09

If $g=f^{-1}$ , $f(2)=5$ , and $f'(2)=-3$ , find $g'(5)$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-10

Use logarithmic differentiation to differentiate $(x^2+1)^{e^x}$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-11

Find the first four derivatives of $x^4-3x^3+2x$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-12

Explain why differentiability at $a$ implies continuity at $a$ , but continuity does not imply differentiability.

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-13

A response model is $R(d)=100d/(d+12)$ . Find $R'(d)$ and interpret $R'(12)$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkexam-a-14

Write a rule-selection explanation, without computing, for $y=e^{\sin(x^2)}(x+1)^3$ .

Your work stays on this device. No account or AI grader is used.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Source & rights

Original instruction with traceable references.

BetterGrades-original composition declared by source handoff; owner provenance review required before public release

Reference textbooks remain rights-separated and are not published as application assets. Any direct adaptation requires separate identification and attribution.

Finish first. Then check every answer.

Practice Exam A

Related resources

Original instruction with traceable references.

Finish first. Then check every answer.

Practice Exam A

Related resources

Original instruction with traceable references.