Calculus Deriver’s License Quizzes

In order to ensure that my students memorize and master their derivative rules, I have students work through a series of 25 derivative quizzes in order to earn a “Deriver’s License.”

Inspiration for this Activity

The concept of a “deriver’s license” is not an original one. It’s a classic calculus teaching pun, and you can find variations on the deriver’s license idea on TPT. But, this process of completing 25 quizzes in order to earn it is my own spin on the idea.

Several years ago, I was working on AP review questions with my calculus students, and I repeatedly heard students saying things like “What’s the quotient rule, again?!?” This made me want to cry, and I have to admit that my overall AP scores that year left much to be desired.

Last year, I implemented this Deriver’s License process on a whim to emphasize the importance of memorizing the derivative rules and being able to fluently apply them to my calculus students. The results were truly beautiful. When we got to AP review, we were able to focus on working through FRQs instead of reviewing all of the derivative rules yet again.

Activity Set-Up

Decorating the Cars

I introduce the concept of earning a deriver’s license to students by giving them a car to color. I took a piece of basic car clipart and printed it 8 to a page.

Each student colored their car, and I ran them through my personal laminator. Students cut out the laminated car and placed a ceramic disc magnet on the back to make it magnetic.

Display and Posters

Why do the cars need to be magnetic? So they can move along the road towards the end goal of earning a deriver’s license.

I used a dry erase marker to draw a road-like path from a laminated poster that reads “Road to Your Deriver’s License” to another laminated poster featuring a “Deriver’s License” for Albert Einstein.

Along the path, I placed 25 orange yield signs that I printed on orange paper and laminated. These represent the 25 derivative quizzes that students must pass in order to earn their deriver’s license.

The Quizzes and Logistics

I chose to have my students work through 25 derivative quizzes that go through power rule, basic derivatives, product rule, quotient rule, trig derivatives, chain rule, multiple derivatives, implicit differentiation, and inverse derivatives.

You can modify the number of quizzes and the extent of the quizzes to match what fits with the structure of your class.

I administer all of the 25 quizzes in Delta Math. Students are required to earn a 100% on each quiz before moving on to the next quiz. As students ace each quiz, they move their car down the road on the dry erase board to symbolize their progress towards their deriver’s license.

If a student misses a question, they must retake the entire quiz. Because the questions are on Delta Math, they are randomly generated each time with new numbers/equations.

Each quiz is 2-6 questions that are administered with a time limit of usually 6-8 minutes depending on the difficulty level. Students are not shown their score until all of the questions are submitted or the time limit elapses. I do this because I don’t want students to ask to restart a quiz just because they know they missed the first question.

I teach AP Calculus third period, and this is the same period where my school has morning announcements and the pledge of allegiance during the last ten minutes of class. I always aim to finish my lecture/notes/activities in the first 40 minutes of class so that students have all of the time left after the pledge of allegiance to work on their deriver’s license quizzes during the last ten minutes of class. Yes, we are multi-tasking while listening to the lunch menu and announcements…

Important note: my calculus classes are relatively small. Last year, I had 12 AP Calculus students and this year I have 15 AP Calculus students. If you are dealing with much larger class sizes and/or more than one period a day of AP Calculus, you might have to drastically alter how you carry out this activity.

I start these deriver’s license quizzes in mid-September when we learn the power rule. Students must complete them before Christmas break in December.

Breakdown of 25 Derivative Quizzes

Each quiz is administered in Delta Math. (Contact me via email (sarah (at) mathequalslove (dot) net) for my Delta Math teacher code if you would like to copy the assessments that way.)

Quiz 1 – Power Rule (No Radicals)

• Power Rule Single Term (Non-Constant)
• (2) Derivatives of Polynomials
• (2) Power Rule Level 2 (X in Denominator)
• Power Rule Single Term (Constant)

Quiz 2 – Power Rule (Radicals)

• (3) Power Rule level 2 (Radical in Numerator)
• (3) Power Rule Level 2 (Radical in Denominator)

Quiz 3 – Power Rule (Mixed)

• Power Rule Level 2 (Radical in Numerator)
• Power Rule Single Term (Non-Constant)
• Derivatives of Polynomials
• Power Rule Single Term (Constant)
• Power Rule Level 2 (Radical in Denominator)
• Power Rule Level 2 (X in Denominator)

Quiz 4 – Important Derivatives

• (2) Basic Trig Derivatives with/without Chain Rule (No Chain Rule Required)
• (2) Derivative of e (No Chain Rule) (Sum and Difference)
• (2) Derivative of ln (No Chain Rule) (Sum and Difference)

Quiz 5 – Product Rule (Polynomials and Trig Functions)

• Product Rule (Level 1) (No Negative Exponents are Present)
• Product Rule (Level 1) (Negative Exponents are Present)
• Product Rule (Level 2) (Form (polynomial) * trig))
• Product Rule (Level 2) (Form ax^n * trig))
• Product Rule (Level 2) (Form (radical) * trig))
• Product Rule (Level 2) (Form (term) + (tern) * trig))

Quiz 6 – Product Rule (e^x and ln(x))

• (3) Derivative of e (No Chain Rule) (product)
• (3) Derivative of ln (No Chain Rule) (product)

Quiz 7 – Quotient Rule

• Quotient Rule
• Derivative of e (No Chain Rule) (quotient)
• Derivative of ln (No Chain Rule) (quotient)

Quiz 8 – Trig Derivatives

• (6) All Trig Derivatives with/without Chain Rule (Chain Rule Not Required)

Quiz 9 – Chain Rule Level 1

• (5) Chain Rule Level 1

Quiz 10 – Chain Rule Level 2

• (1) Chain Rule Level 2 (Outer power in numerator)
• (1) Chain Rule Level 2 (Outer power in denominator)
• (1) Chain Rule Level 2 (Outer radical in numerator)
• (1) Chain Rule Level 2 (Outer radical in denominator)

Quiz 11 – Chain Rule Level 3

• (1) All Trig Derivatives with/without Chain Rule (Chain Rule Not Required)
• (2) All Trig Derivatives with/without Chain Rule (Multiple of x)
• (2) All Trig Derivatives with/without Chain Rule (Chain Rule: Trig Function to Power)

Quiz 12 – Chain Rule Level 4

• (1) Chain Rule Level 3 (Form a*sqrt(trig(x))
• (1) Chain Rule Level 3 (Form a*trig&n(x))
• (1) Chain Rule Level 3 (Form a*trig(polynomial))
• (1) Chain Rule Level 3 (Form atrig(bsqrt(x)))

Quiz 13 – Chain Rule Level 5

• (3) Derivative of e
• (3) Derivative of ln

Quiz 14 – Chain Rule Level 6

• (2) Derivative of base not e
• (2) Derivative of log

Quiz 15 – Chain Rule Level 7

• (1) Chain Rule Level 4 (Form a*trig^n(polynomial))
• (1) Chain Rule Level 4 (Form a*trig((polynomial)^n)
• (1) Chain Rule Level 4 (Form atrig((polynomial)^n) OR (Form atrig^n(polynomial))

Quiz 16 – Chain Rule Level 8

• (1) Chain Rule Level 4 (Form a*sqrt(trig(polynomial))
• (1) Chain Rule Level 4 (Form a*trig(sqrt(polynomial))
• (1) Chain Rule Level 4 (Form asqrt(trig(polynomial)) OR (Form atrig(sqrt(polynomial))

Quiz 17 – Multiple Derivatives A

• (1) Multiple Derivative Rules (Product and Chain Rules No Trig)
• (1) Multiple Derivative Rules (Quotient and Chain Rules No Trig)

Quiz 18 – Multiple Derivatives B

• (1) Multiple Derivative Rules (Product and Chain Rules With Trig)
• (1) Multiple Derivative Rules (Quotient and Chain Rules With Trig)

Quiz 19 – Derivatives from Limit Notation

• (4) Find Derivative from Limit Definition

Quiz 20 – Implicit Differentiation A

• (2) Derivative Notation (Level 1)
• (2) Derivative Notation (Level 2)

Quiz 21 – Implicit Differentiation B

• (2) Implicit Differentiation (Level 1)

Quiz 22 – Implicit Differentiation C

• (2) Implicit Differentiation (Level 2)

Quiz 23 – Implicit Differentiation D

• (1) Implicit Differentiation (Level 3)
• (1) Implicit Differentiation (Level 1)

Quiz 24 – Derivatives of Inverse Functions

• (2) Derivatives of Inverse Functions (Table)
• (2) Derivatives of Inverse Functions (Equation)

Quiz 25 – Inverse Trig Functions

• (2) Derivatives of Inverse Trig Functions (Function notation, evaluate f’(a))
• (2) Derivatives of Inverse Trig Functions (Function Notation, f’(x) using chain rule)

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