Calculus I · 2B · exam

Unit 2B Practice Exam A

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

Notice

A complete response includes setup, calculus, candidates or rates, units, interpretation, and a reasonableness check.

Decide

Choose the governing relationship before calculating, then use the attempt-gated answer as feedback rather than as a shortcut.

Avoid

Reading an answer before modeling the problem or treating every miss as algebra when the first error was conceptual.

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: 120 minutes. Show the model, calculus, and interpretation.

Exercise

A particle has $s(t)=t^3-6t^2+5t$ . Find rest times, direction intervals, acceleration, and speeding-up intervals on $[0,6]$ .

Exercise

Use linearization at $a=25$ to estimate $\sqrt{25.4}$ and discuss whether the estimate is high or low.

Exercise

A measured sphere radius is $12.0\pm0.05$ cm. Estimate maximum volume error and percentage error.

Exercise

Use two Newton iterations to approximate the positive root of $x^3+x-4=0$ , starting from a sensible integer.

Exercise

A $10$ -foot ladder slides away from a wall at $1$ ft/s. Find the rate of the top when the bottom is $6$ feet from the wall.

Exercise

A radar station is $3$ km from the point below a rising balloon. The balloon rises at $0.2$ km/min. Find the angle rate when the balloon is $4$ km high.

Exercise

Verify the Mean Value Theorem for $f(x)=1/x$ on $[1,4]$ and find $c$ .

Exercise

Find intervals of increase, decrease, concavity, and all extrema and inflection points for $f(x)=x^3-3x^2$ .

Exercise

A rectangle is inscribed under $y=16-x^2$ , symmetric about the $y$ -axis. Find maximum area.

Exercise

A manufacturer's average cost is $A(q)=1500/q+12+0.01q$ . Find the output minimizing average cost and interpret $A'(100)$ .

Exercise

Evaluate $\lim_{x\to0}(e^{2x}-1-2x)/x^2$ .

Exercise

Evaluate $\lim_{x\to\infty}(\sqrt{x^2+8x}-x)$ .

Exercise

A concentration model is $C(t)=30te^{-0.4t}$ . Find peak time, peak concentration, and the interval of increase.

Exercise

Explain using a theorem why a differentiable function with $|f'|\le3$ on $[1,5]$ cannot satisfy $|f(5)-f(1)|>12$ .

Structured concept quiz

Unit 2B 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

A particle has $s(t)=t^3-6t^2+5t$ . Find rest times, direction intervals, acceleration, and speeding-up intervals on $[0,6]$ .

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

Use linearization at $a=25$ to estimate $\sqrt{25.4}$ and discuss whether the estimate is high or low.

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

A measured sphere radius is $12.0\pm0.05$ cm. Estimate maximum volume error and percentage error.

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

Use two Newton iterations to approximate the positive root of $x^3+x-4=0$ , starting from a sensible integer.

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

A $10$ -foot ladder slides away from a wall at $1$ ft/s. Find the rate of the top when the bottom is $6$ feet from the wall.

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

A radar station is $3$ km from the point below a rising balloon. The balloon rises at $0.2$ km/min. Find the angle rate when the balloon is $4$ km high.

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

Verify the Mean Value Theorem for $f(x)=1/x$ on $[1,4]$ and find $c$ .

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 intervals of increase, decrease, concavity, and all extrema and inflection points for $f(x)=x^3-3x^2$ .

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-09

A rectangle is inscribed under $y=16-x^2$ , symmetric about the $y$ -axis. Find maximum area.

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

A manufacturer's average cost is $A(q)=1500/q+12+0.01q$ . Find the output minimizing average cost and interpret $A'(100)$ .

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

Evaluate $\lim_{x\to0}(e^{2x}-1-2x)/x^2$ .

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-12

Evaluate $\lim_{x\to\infty}(\sqrt{x^2+8x}-x)$ .

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-13

A concentration model is $C(t)=30te^{-0.4t}$ . Find peak time, peak concentration, and the interval of increase.

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

Explain using a theorem why a differentiable function with $|f'|\le3$ on $[1,5]$ cannot satisfy $|f(5)-f(1)|>12$ .

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.

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: 120 minutes. Show the model, calculus, and interpretation.

Exercise

A particle has $s(t)=t^3-6t^2+5t$ . Find rest times, direction intervals, acceleration, and speeding-up intervals on $[0,6]$ .

Exercise

Use linearization at $a=25$ to estimate $\sqrt{25.4}$ and discuss whether the estimate is high or low.

Exercise

A measured sphere radius is $12.0\pm0.05$ cm. Estimate maximum volume error and percentage error.

Exercise

Use two Newton iterations to approximate the positive root of $x^3+x-4=0$ , starting from a sensible integer.

Exercise

A $10$ -foot ladder slides away from a wall at $1$ ft/s. Find the rate of the top when the bottom is $6$ feet from the wall.

Exercise

A radar station is $3$ km from the point below a rising balloon. The balloon rises at $0.2$ km/min. Find the angle rate when the balloon is $4$ km high.

Exercise

Verify the Mean Value Theorem for $f(x)=1/x$ on $[1,4]$ and find $c$ .

Exercise

Find intervals of increase, decrease, concavity, and all extrema and inflection points for $f(x)=x^3-3x^2$ .

Exercise

A rectangle is inscribed under $y=16-x^2$ , symmetric about the $y$ -axis. Find maximum area.

Exercise

A manufacturer's average cost is $A(q)=1500/q+12+0.01q$ . Find the output minimizing average cost and interpret $A'(100)$ .

Exercise

Evaluate $\lim_{x\to0}(e^{2x}-1-2x)/x^2$ .

Exercise

Evaluate $\lim_{x\to\infty}(\sqrt{x^2+8x}-x)$ .

Exercise

A concentration model is $C(t)=30te^{-0.4t}$ . Find peak time, peak concentration, and the interval of increase.

Exercise

Explain using a theorem why a differentiable function with $|f'|\le3$ on $[1,5]$ cannot satisfy $|f(5)-f(1)|>12$ .

Structured concept quiz

Unit 2B 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

A particle has $s(t)=t^3-6t^2+5t$ . Find rest times, direction intervals, acceleration, and speeding-up intervals on $[0,6]$ .

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

Use linearization at $a=25$ to estimate $\sqrt{25.4}$ and discuss whether the estimate is high or low.

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

A measured sphere radius is $12.0\pm0.05$ cm. Estimate maximum volume error and percentage error.

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

Use two Newton iterations to approximate the positive root of $x^3+x-4=0$ , starting from a sensible integer.

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

A $10$ -foot ladder slides away from a wall at $1$ ft/s. Find the rate of the top when the bottom is $6$ feet from the wall.

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

A radar station is $3$ km from the point below a rising balloon. The balloon rises at $0.2$ km/min. Find the angle rate when the balloon is $4$ km high.

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

Verify the Mean Value Theorem for $f(x)=1/x$ on $[1,4]$ and find $c$ .

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 intervals of increase, decrease, concavity, and all extrema and inflection points for $f(x)=x^3-3x^2$ .

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-09

A rectangle is inscribed under $y=16-x^2$ , symmetric about the $y$ -axis. Find maximum area.

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

A manufacturer's average cost is $A(q)=1500/q+12+0.01q$ . Find the output minimizing average cost and interpret $A'(100)$ .

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

Evaluate $\lim_{x\to0}(e^{2x}-1-2x)/x^2$ .

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-12

Evaluate $\lim_{x\to\infty}(\sqrt{x^2+8x}-x)$ .

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-13

A concentration model is $C(t)=30te^{-0.4t}$ . Find peak time, peak concentration, and the interval of increase.

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

Explain using a theorem why a differentiable function with $|f'|\le3$ on $[1,5]$ cannot satisfy $|f(5)-f(1)|>12$ .

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.

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.