Alice in Wonderland Escape Room

Stuck In

Wonderland

By Brielle, Tia, & Tanisha

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Backstory...

While following a strange white rabbit, you fell down a rabbit hole! Upon awaking, you realize you are in Wonderland and mysteriously have awoken with the Red Heart Ruby that belongs to the Queen! Now you must escape in order to be free from the Queen's wrath! Go through the map starting at the Rabbit Hole and ending at the Trial Tower to collect the cards to solve the coded message and see if you can escape your fate!

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Start

Room 1: Question 1

Use the graph to determine the value of the limits:

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Room 1: Question 2

Determine the value of k from the function.

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Room 1: Question 3

Use the definition of a derivative to evaluate the limit. Plug in x=0 to get your final answer.

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Room 1: Question 4

Evaluate the limit using L'Hospital's Rule.

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Room 1: Question 5

Evaluate the limit using L'Hospital's Rule.

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Congrats! You have successfully escaped the Rabbit HOle!

As you leave, you hear strange noises drawing you to the dark forest. Sounds of a tea party lure you into the gloom of the forest. Who knows what horrors await...

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Start

ROOM 2: QUESTION 1

Evaluate to find the derivative at x=0 using the product rule.

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ROOM 2: QUESTION 2

Evaluate to find the derivative at x=1/2 using the quotient rule.

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ROOM 2: QUESTION 3

Evaluate to find the derivative at x=6 using chain rule.

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ROOM 2: QUESTION 4

Use implicit differentiation to solve for the second derivative at the point (3,3).

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ROOM 2: QUESTION 5

Evaluate to find the derivative at x=1 using chain rule.

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Congrats! You have successfully escaped the Tea party!

While you leave the tea party, a strange feeling arises within you as you draw closer to the infamous Queen of Heart's castle. She cannot know you have her Red Heart Ruby!

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Start

Room 3: Question 1a

The speed of Alice is modeled in the given table during the first 30 seconds of her journey to the Queen's Castle. Use RRAM to estimate Alice's displacement after 20 seconds. Include units in your answer.

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Room 3: Question 1b

The speed of Alice is modeled in the given table during the first 30 seconds of her journey to the Queen's Castle. Use trapezoidal approximation to estimate Alice's displacement after 20 seconds. Include units in your answer.

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Room 3: Question 2

Evaluate the following integral. Use u-substitution if necessary.

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Room 3: Question 3

Evaluate the following integral. Use u-substitution if necessary.

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Room 3: Question 4

Evaluate the following integral. Use u-substitution if necessary.

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Room 3: Question 5

Use the rules for definite integrals to determine the values of the integrals, given the following information.

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Congrats! You have successfully escaped the Queen's Castle!

The Queen has found the Ruby on you! Now, you are being led to the Trial Tower where you will go to trial for attempted theft and treason! Good luck!

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Start

Room 4: Question 1

The White Rabbit, who is 3 feet tall, is walking toward the tower at a rate of 2 ft/sec. A card soldier at the tower is on the lookout and is holding a flashlight at 8 feet above the ground, thus casting a shadow. How fast is the length of the rabbit's shadow changing when the rabbit is 12 feet from the card soldier?

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Room 4: Question 2

Alice is standing at the edge of a river that she needs to cross to reach the Trial Tower. The river is7 miles wide. She can swim at 3 mph and walk at 5 mph. She must first swim across the river to any point on the opposite bank. From there, Alice can walk to the tower, which is 10 miles from the point directly across the river from where she began her swim. How far should she swim to take the least amount of time?

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Room 4: Question 3

The Mad Hatter has a container of tea. The number of ounces of tea in the container after it started to leak is C(t)=16t^2 + 4(-t+2)^3, with t being in minutes. How fast is the tea leaking at the end of 7 minutes? What is the average rate at which the tea flows out in the time interval [0,7]?

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Room 4: Question 4

The caterpillar’s position can be modeled by the function S(t) = -2cos(2t) + 2t. It is known that S(0) = 8. For 0<t<π, determine when the caterpillar is moving left, right, and is stopped. Assume the caterpillar's velocity is measured in m/s.

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Room 4: Question 5

Determine the volume of the solid obtained by rotating the region bounded by the two functions given about the line y=-5.

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Congrats! You have successfully escaped the Trial Tower!

But the adventure isn't over yet! Hope you kept those playing cards you mysteriously found, because you will need to unscramble them to unlock the door to truly escape!

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You successfully escaped!

Thanks for Playing!

Hope you enjoyed the adventure...or was it just a dream?