Escape from Pixel Castle
Start
Introduction
While you are traveling through unexplored areas of China, you have been captured by the soldiers of the Pixel King's Castle. You will need to gather courage and overcome the trials that the King will put you through in order to try to obtain the pixel coins, pay for your release with them, and continue your journey.
Let's go!
select mission
PIXEl rolls
Fake doors
MATHS JUMP
coins
Dancing stones
Fake doors
You must correctly answer the various questions to find the only true door and advance in your mission.
Start
A function is not continuous at a point if:
The graph is smooth
The limit does not exist
The limit exists and equals the function value
1/3
Great!
You chose the correct door
Next
1/3
The derivative of a function represents:
The slope of the tangent line
The area under the curve
The y-intercept
2/3
Take it!
You chose the correct door
Next
2/3
What is the derivative of a constant such as f(x) = 9?
3/3
Well done!
You have a pixel coin! Three more will be enough to buy your freedom
Continues
3/3
ERROR!
Ouch! What a headache.Try again.
Return
ERROR!
Ouch! What a headache.Try again.
Return
Error!
Ouch! What a headache.Try again.
Return
MISSION MAPS
PIXEL rolls
Fake doors
MATHS JUMP
coins
Dancing stones
Maths jump
Solve math calculation problems to advance in this mission. Jump on the correct answer and demonstrate your skills.
Start
The slope of a tangent line is equivalent to what concept in calculus?
A. Secant Line
B. Area under the Curve
C. Derivative
D. No Right Answer
1/4
Well done!
You have jumped to the correct answer
Next
1/4
Find the slope of the tangent line of the function f(x) = x^2 at point P = 2.
A. 0
B. 4
C. 3
D. 5
2/4
Yeah!
You have jumped on the correct answer
Next
2/4
Which rule is used when finding the derivative of f(x) = 6x⁷ ?
A. Power Rule
B. Product Rule
C. Chain Rule
D. Quotient Rule
3/4
Got it!
You have jumped to the correct answer
Next
3/4
Differentiate the rational function y = x²/x+5.
A. 2x
B. x²-10x/x+5
C. 3x²+5x/(x+5)²
D. x²+10x/(x+5)²
4/4
WELL DONE!
You have earned one more pixel coin. You have two left to pay the King of the castle.
Continúa
4/4
Error
Wow! It seems like the answer is incorrect.
Return
ERROR
Wow! It looks like the answer is incorrect.
Return
ERROR
Wow! It seems like the answer is incorrect.
Return
ERROR
Wow! It looks like the answer is incorrect.
Go back
MISSION MAP
PIXEL rolls
Fake doors
MATHS JUMP
COINS
Dancing stones
PIXELrolls
You must maintain balance and jump from one roller to another by answering the questions correctly in order to progress.
Start
For what value of a is the function f(x) continuous at x = 3?
1/5
Which of the following functions is continuous everywhere in the interval
f(x) = √x
f(x) = x/x²-1
f(x)= x/x²+1
2/5
What is the limit of
as
and is the function continuous at x = 0
Limit is 0, Continuous
Limit is 1, Not Continuous
Limit is 1, Continuous
3/5
Given
how can we redefine f( - 3)
to make the function continuous at x = - 3?
f(-3) = 0
f(-3) = 3
f(-3) = -6
4/5
Find the derivative of f(x) 2x³+ 4x
6x²+ 4
6x + 4
6x² + 2
5/5
WELL DONE!
You have earned one more pixel coin. You need one more to pay the King of the castle.
Continue
5/5
ERROR
Oh! It seems you got soaked
Return
MISSION MAP
PIXEL rolls
Fake doors
MATHS JUMP
coins
Dancing stones
Dancing stones
Choose the right stones and stand on them while answering the questions correctly to move forward without falling into the water.
Start
Let's go!
Choose a rock to jump on
1/5
The chain rule is used when:
Differentiating a composite function
Differentiating a constant
Differentiating a product
1/5
Let's go!
Choose a rock to jump on
2/5
Differentiate x²+y²= 25
2x + 2y = 0
2x+2y dy/dx = 0
x + y = 0
2/5
Let's go!
Choose a rock to jump on
3/5
Find the derivative of f(x) = (2x³+5)⁴
4(2x³+5)3
24x³(2x³+5)³
24x²(2x³+5)³
3/5
Let's go!
Choose a rock to jump on
4/5
Find the derivative of f(x)=(x²+3x)⁵
5(x²+3x)⁴
10x+15(x²+3x)⁴
(2x+3)⁵
4/5
Let's go!
Choose a rock to jump on
5/5
Find the derivative of f(x)= (x²+1)³
3x(x²+1)²
6x(x²+1)²
3(x²+1)³
5/5
WELL DONE!
It seems you have obtained the 4 pixel coins, talk to the Castle King to be released
Continue
5/5
Error
Oh! It looks like you got soaked
Return
MISSION MAP
PIXEL rolls
Fake doors
MATHS JUMP
coins
Dancing stones
use coins
Good!
King Pixel has finally set you free! You can now see the sunset at the lake.
Let's go!
YOU HAVE ESCAPED AND YOU ARE FREE!
Now you can enjoy the pleasant view of the lake at sunset
Start over
YOU ARE NOT READY YET You must complete the previous missions to continue
YOU ARE NOT READY YET You must complete the previous missions to continue
Be careful!
If you go back to the beginning, you will lose all progress and have to start over.
Continue
Exit
NOT YET READY You must complete the previous missions to continue
Be careful!
If you go back to the beginning, you will lose all progress and have to start over.
Continue
Exit
YOU ARE NOT READY YET You must complete the previous missions to continue
Be careful!
If you go back to the beginning, you will lose all progress and have to start over.
Continue
Exit
YOU ARE NOT READY YET You must complete the previous missions to continue
Be careful!
If you go back to the beginning, you will lose all progress and have to start over.
Continue
Exit
YOU ARE NOT READY YET You must complete the previous missions to continue
Escape from Pixel Castle
John Kylle Enclano
Created on March 14, 2026
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Transcript
Escape from Pixel Castle
Start
Introduction
While you are traveling through unexplored areas of China, you have been captured by the soldiers of the Pixel King's Castle. You will need to gather courage and overcome the trials that the King will put you through in order to try to obtain the pixel coins, pay for your release with them, and continue your journey.
Let's go!
select mission
PIXEl rolls
Fake doors
MATHS JUMP
coins
Dancing stones
Fake doors
You must correctly answer the various questions to find the only true door and advance in your mission.
Start
A function is not continuous at a point if:
The graph is smooth
The limit does not exist
The limit exists and equals the function value
1/3
Great!
You chose the correct door
Next
1/3
The derivative of a function represents:
The slope of the tangent line
The area under the curve
The y-intercept
2/3
Take it!
You chose the correct door
Next
2/3
What is the derivative of a constant such as f(x) = 9?
3/3
Well done!
You have a pixel coin! Three more will be enough to buy your freedom
Continues
3/3
ERROR!
Ouch! What a headache.Try again.
Return
ERROR!
Ouch! What a headache.Try again.
Return
Error!
Ouch! What a headache.Try again.
Return
MISSION MAPS
PIXEL rolls
Fake doors
MATHS JUMP
coins
Dancing stones
Maths jump
Solve math calculation problems to advance in this mission. Jump on the correct answer and demonstrate your skills.
Start
The slope of a tangent line is equivalent to what concept in calculus?
A. Secant Line
B. Area under the Curve
C. Derivative
D. No Right Answer
1/4
Well done!
You have jumped to the correct answer
Next
1/4
Find the slope of the tangent line of the function f(x) = x^2 at point P = 2.
A. 0
B. 4
C. 3
D. 5
2/4
Yeah!
You have jumped on the correct answer
Next
2/4
Which rule is used when finding the derivative of f(x) = 6x⁷ ?
A. Power Rule
B. Product Rule
C. Chain Rule
D. Quotient Rule
3/4
Got it!
You have jumped to the correct answer
Next
3/4
Differentiate the rational function y = x²/x+5.
A. 2x
B. x²-10x/x+5
C. 3x²+5x/(x+5)²
D. x²+10x/(x+5)²
4/4
WELL DONE!
You have earned one more pixel coin. You have two left to pay the King of the castle.
Continúa
4/4
Error
Wow! It seems like the answer is incorrect.
Return
ERROR
Wow! It looks like the answer is incorrect.
Return
ERROR
Wow! It seems like the answer is incorrect.
Return
ERROR
Wow! It looks like the answer is incorrect.
Go back
MISSION MAP
PIXEL rolls
Fake doors
MATHS JUMP
COINS
Dancing stones
PIXELrolls
You must maintain balance and jump from one roller to another by answering the questions correctly in order to progress.
Start
For what value of a is the function f(x) continuous at x = 3?
1/5
Which of the following functions is continuous everywhere in the interval
f(x) = √x
f(x) = x/x²-1
f(x)= x/x²+1
2/5
What is the limit of
as
and is the function continuous at x = 0
Limit is 0, Continuous
Limit is 1, Not Continuous
Limit is 1, Continuous
3/5
Given
how can we redefine f( - 3)
to make the function continuous at x = - 3?
f(-3) = 0
f(-3) = 3
f(-3) = -6
4/5
Find the derivative of f(x) 2x³+ 4x
6x²+ 4
6x + 4
6x² + 2
5/5
WELL DONE!
You have earned one more pixel coin. You need one more to pay the King of the castle.
Continue
5/5
ERROR
Oh! It seems you got soaked
Return
MISSION MAP
PIXEL rolls
Fake doors
MATHS JUMP
coins
Dancing stones
Dancing stones
Choose the right stones and stand on them while answering the questions correctly to move forward without falling into the water.
Start
Let's go!
Choose a rock to jump on
1/5
The chain rule is used when:
Differentiating a composite function
Differentiating a constant
Differentiating a product
1/5
Let's go!
Choose a rock to jump on
2/5
Differentiate x²+y²= 25
2x + 2y = 0
2x+2y dy/dx = 0
x + y = 0
2/5
Let's go!
Choose a rock to jump on
3/5
Find the derivative of f(x) = (2x³+5)⁴
4(2x³+5)3
24x³(2x³+5)³
24x²(2x³+5)³
3/5
Let's go!
Choose a rock to jump on
4/5
Find the derivative of f(x)=(x²+3x)⁵
5(x²+3x)⁴
10x+15(x²+3x)⁴
(2x+3)⁵
4/5
Let's go!
Choose a rock to jump on
5/5
Find the derivative of f(x)= (x²+1)³
3x(x²+1)²
6x(x²+1)²
3(x²+1)³
5/5
WELL DONE!
It seems you have obtained the 4 pixel coins, talk to the Castle King to be released
Continue
5/5
Error
Oh! It looks like you got soaked
Return
MISSION MAP
PIXEL rolls
Fake doors
MATHS JUMP
coins
Dancing stones
use coins
Good!
King Pixel has finally set you free! You can now see the sunset at the lake.
Let's go!
YOU HAVE ESCAPED AND YOU ARE FREE!
Now you can enjoy the pleasant view of the lake at sunset
Start over
YOU ARE NOT READY YET You must complete the previous missions to continue
YOU ARE NOT READY YET You must complete the previous missions to continue
Be careful!
If you go back to the beginning, you will lose all progress and have to start over.
Continue
Exit
NOT YET READY You must complete the previous missions to continue
Be careful!
If you go back to the beginning, you will lose all progress and have to start over.
Continue
Exit
YOU ARE NOT READY YET You must complete the previous missions to continue
Be careful!
If you go back to the beginning, you will lose all progress and have to start over.
Continue
Exit
YOU ARE NOT READY YET You must complete the previous missions to continue
Be careful!
If you go back to the beginning, you will lose all progress and have to start over.
Continue
Exit
YOU ARE NOT READY YET You must complete the previous missions to continue